a search for new physics in high-mass ditau events in the atlas detector Ryan Reece a dissertation in Physics and Astronomy Presented to the Faculties of The University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2013 H.H. Williams, Professor, Physics Supervisor of Dissertation Randall Kamien, Professor, Physics Graduate Group Chairperson Dissertation Committee Randall Kamien, Professor, Physics I. Joseph Kroll, Professor, Physics Burt Ovrut, Professor, Physics Evelyn Thomson, Associate Professor, Physics H.H. Williams, Professor, Physics a search for new physics in high-mass ditau events in the atlas detector Copyright (CC-BY 4.0) 2013 Ryan Reece This work is licensed under a Creative Commons Attribution 4.0 International (CC-BY 4.0) license. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ Acknowledgements Graduate school has been an incredible time and a period growth for me. Several people have been a guide, inspired my interests, taught me a concept or skill, and/or been an exceptional collaborator. First, I would like to thank my advisor Brig Williams who is an amazing leader of a strong research group at Penn. Brig has enabled me in so many ways, often been a source of council, and had a caretaker-sense of what is important. Thanks also to Brig for all his help reviewing this thesis and helping improve the text in many ways. I am indebted to all of the Penn faculty in the ATLAS group in some way. Thanks go to Joe Kroll for being so welcoming and often having a constructive, critical eye. Thanks to Evelyn Thomson for sharing her office at Penn and her advice, and for introducing me at the BNL Jamboree that guided me through my first steps in ATLAS software. I am grateful to Elliot Lipeles for helping me with a place to live when I first moved to CERN, and for demonstrating such an example of breadth and depth of knowledge. Burt Ovrut's lectures on quantum field theory and our discussions have been hugely influential on how I view physics, for which I will always be grateful. Thanks to Jean O'Boyle for helping keep us all organized. Thanks to the Project Leader of the TRT during the start-up of the LHC, Christoph Rembser, for his direction and support. Many thanks go to the instrumentation group at Penn, in particular Rick Van Berg, Mitch Newcomer, and Paul Keener, who together with Ole Røhne, Franck Martin, Mike Hance, and Ben LeGeyt, pushed me up the ramp of understanding the basics of electronics and DAQ during the commissioning of the TRT. I was always playing catch-up and grateful to learn so much from the from the rest of the TRT DAQ on-call team: Mike Hance, Dominick Olivito, Jamie Saxon, Jon Stahlman, Peter Wagner, and Sarah Heim. A large part of the day-by-day success of the TRT should be accredited to the TRT Run Coordinators: Anatoli Romaniouk, Jim Degenhardt, and Andrey Loginov. I would like to thank my collaborators that helped with the TRT straw hit efficiency study: Saša Fratina, Jared Adelman, Esben Klinkby, and Dan Guest, and the tracking experts: Andreas iii iv Salzburger and Markus Elsing, who helped me to learn how to use track-extrapolation tools for the study. I thank the conveners of the ATLAS tau working group that have helped us to deliver robust and performant tau identification: Elzbieta Richter-Was, Wolfgang Mader, Soshi Tsuno, Yann Coadou, Stan Lai, Stefania Xella, and Martin Flechl. Thank you to all the other collaborators that have debated the subtleties and strategies behind the ATLAS tau reconstruction and identification with me, especially Will Davey, Dugan O'Neil, Michel Trottier-McDonald, Noel Dawe, Mogens Dam, Marcus Morgenstern, Saminder Dhaliwal, Almut Pingel, and Alex Tuna. Many thanks to the team with which I worked to observe and measure the cross section of Z → ττ , including: Donatella Cavalli, Elias Coniavitis, Sofia Consonni, Sinead Farrington, Felix Friedrich, Aimee Larner, Caterina Pizio, Serban Protopopescu, Trevor Vickey, Sahal Yacoob, but especially thanks for the dedication of Justin Griffiths, Anna Kaczmarska, and Susanne Kuehn. Thanks also go to the editorial board for our Z → ττ result, including Attilio Andreazza, Massimiliano Bellomo, Eric Torrence, and Susana Cabrera Urban. Thanks to those with whom I worked closely on the search for Z ′, including: Alex Tuna, Will Davey, Andres Florez, Gabriel Palacino, and Peter Wagner. Very special thanks goes to Alex Tuna and Will Davey, whose contributions to the fake factor methods for background estimation and the development of high-pT tau systematics, respectively, have made my thesis something it would not have been otherwise. Thanks also for the attention and support of our editorial board, including: Yann Coadou, Gideon Bella, Jean-Baptiste De Vivie De Regie, and Ashutosh Kotwal. Thanks go to collaborators Koji Nakamura and Keita Hanawa from the H → ττ analysis, for comparing and discussing many issues concerning the use of fake factor methods in tau analyses. Kyle Cranmer, Amir Farbin, and Akira Shibata helped me to first appreciate the software requirements of an analysis of ATLAS data. Attila Krasznahorkay is a careful custodian of the SFrame framework, for which I am grateful, and was so useful to me during the measurement of Z → ττ . Thanks to Scott Snyder organizing the ATLAS D3PDMaker to make it easy to flatten our data, and for helping Dugan, Michel, and I design a D3PDMaker for the tau working group. A huge thanks to Paul Keener, for being an observant watchman of the computing resources at Penn that enable so much of our analysis. Thanks to Tae Min Hong for often taking the time to look out for my interests and to help to bounce and refine my ideas. Thanks to Zach Marshall for often being so generous with his time and his expertise, particularly for pointing out many of the distinctions between quark and gluon jets. Thanks to Devin Harper for working so many late nights with me, and for helping me work through the CLs method, among other adventures. Thanks to Josh Kunkle for being such an v outstanding roommate, and examining with me whatever minutiae that came up concerning ATLAS or its software. I learned so much in that apartment. I am grateful to CERN and all the countries that fund it for being such an amazing example international scientific collaboration. I am grateful for the LHC and all the R&D efforts that bring the highest energies in reach in a laboratory. Thanks to all the members of the ATLAS Collaboration that make the functioning of the experiment possible. In the US, I would also like to acknowledge the support of the American taxpayers and the DOE and NSF agencies through which American research in particle physics is funded. I would especially like to thank John Alison and Dominick Olivito of my incoming class, for being partners in taking apart so many problems (physics or not) in our study sessions in the Zoo and our work at CERN. More than most, you have helped shape my skills in critical thinking. Thanks also to everyone in the community of Penn dinners and all the young students at CERN that gave me a tribe to belong to. Thanks to everyone who traveled a European city or went climbing with me. You helped keep me sane and its been an incredible ride. Thanks to Charlie Sell for helping me get serious about writing that day in January in the library in Geneva. Thanks to Jim Halverson and Austin Purves for reviewing my review of the SM in the appendix. Many, many thanks to Susan Fowler for reading and editing so many versions. I would still like to thank Shaleena and the McGee and Rao families for their love and support throughout much of the start of this journey. My love and thanks go to the Reece and Moss families, especially my parents David and Linda, for all of your love and support throughout my life. You share in this honor too. My final thanks and love go to Susan who has been the most patient, loving, and encouraging during my months of writing. abstract a search for new physics in high-mass ditau events in the atlas detector Ryan Reece H.H. Williams This thesis presents a review of work on the performance of the reconstruction and identification of hadronic tau decays and studies of events reconstructed with a `τh final state with the ATLAS detector at the Large Hadron Collider. The first cut-based tau identification used with ATLAS data and the first observations of W → τν and Z → ττ at ATLAS are described, as well as many of the issues concerning the calibration and systematic uncertainties of reconstructed taus. The first measurement of the Z → ττ cross section at ATLAS with 2010 dataset is reviewed. Last, results are presented from the first search for high-mass resonances decaying to τ+τ− at ATLAS with the 2011 dataset. A preprint can be found at CDS: CERN-THESIS-2013-075. vi Contents Acknowledgements iii Abstract vi Contents vii Preface xiii Timeline of my experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii About the text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1 Introduction 1 1.1 Exploring at the high-energy frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 The theoretical situation 3 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The search for the Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Before the start-up of the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.2 Observations of a Higgs-like excess at the LHC . . . . . . . . . . . . . . . . . 7 2.4 Limitations of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.1 Neutrino masses and mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.2 Ad hoc features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.3 The hierarchy problem(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.4 Matter-antimatter asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.5 Dark matter and dark energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 Scenarios beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . 14 vii viii contents 2.5.1 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5.2 Running of the couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5.3 Grand unified theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 The LHC and ATLAS 17 3.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 The ATLAS experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 Magnet systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.3 Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.4 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.5 Muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.2 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.3 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3.4 Electrons and photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.5 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.6 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.7 Hadronic tau decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.8 Missing transverse momentum . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4 Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.1 Level 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.2 Level 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4.3 Event filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.5 Running conditions and dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.5.2 Pile-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.6.1 Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.6.2 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.6.3 Corrections and scale factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.7 Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.7.1 Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.7.2 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 contents ix 4 Tau reconstruction and identification 51 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2 Tau reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.2 Seeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.3 Four-momentum definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.2.4 Track counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2.5 Vertex selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3 Tau identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.1 Identification variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.2 Cut-based jet-tau discrimination . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3.3 pT-parametrized cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3.4 Multivariate techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3.5 Electron-tau discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.4 Performance and systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 72 4.4.1 First data-MC comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.4.2 Observation of W → τν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.4.3 Jet discrimination performance . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.4.4 Electron discrimination performance . . . . . . . . . . . . . . . . . . . . . . . 78 4.4.5 Energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4.6 Tau identification efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.4.7 Performance at high-pT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.4.8 Variation of jet fake rates with composition . . . . . . . . . . . . . . . . . . . 89 4.4.9 Pile-up robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5 Measurement of the Z → ττ cross section 105 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.1.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.2 MC studies of `τh event kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2.1 Multijet background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2.2 W+jets background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2.3 Preliminary event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.3 Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 x contents 5.3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.4 Z → ττ → `τh selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.4.1 Event preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.4.2 Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.4.3 Object preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.4.4 Object selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.4.5 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.5 Observation of Z → ττ → `τh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.6 Kinematics of selected Z → ττ → `τh events . . . . . . . . . . . . . . . . . . . . . . . 134 5.7 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.7.2 W Monte Carlo scale factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.7.3 Multijet background estimation from the same-sign sample . . . . . . . . . . 139 5.7.4 Multijet background estimation from non-isolated leptons . . . . . . . . . . . 142 5.7.5 Summary of backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.8 Method for calculating the cross section . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.9 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.9.1 Cross sections and integrated luminosity . . . . . . . . . . . . . . . . . . . . . 149 5.9.2 Tau energy scale and efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5.9.3 Multijet background estimation from the same-sign sample . . . . . . . . . . 150 5.10 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6 Search for high-mass resonances decaying to τ+τ− 153 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 6.2 Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.2.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.3 Object preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.3.1 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.3.2 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.3.3 Hadronic tau decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.3.4 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.3.5 Missing transverse energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6.4 Search in the `τh channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6.4.1 Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 contents xi 6.4.2 Object selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.4.3 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 6.4.4 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.5 Search in the τhτh channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.5.1 Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.5.2 Object selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.5.3 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.5.4 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.6 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 6.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.7.1 Observed events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.7.2 Likelihood model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.7.3 Limit-setting procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6.7.4 Model dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 7 Conclusion 191 A A review of the Standard Model 194 A.1 Quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 A.1.1 A brief history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 A.1.2 The measurement problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 A.1.3 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 A.1.4 The importance of symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 A.1.5 Scattering theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 A.1.6 Gauge invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 A.2 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 A.2.1 Quarks, leptons, and gauge bosons . . . . . . . . . . . . . . . . . . . . . . . . 212 A.2.2 The Standard Model Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . 214 A.2.3 The Higgs mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 A.2.4 Electroweak theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 A.2.5 Strong interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 A.2.6 Quark flavor mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A.2.7 Neutrino flavor mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 B Tau identification variables 233 xii contents List of Tables 237 List of Figures 238 Bibliography 239 Preface Timeline of my experience During my time as a graduate student at the University of Pennsylvania, working with the ATLAS experiment at the Large Hadron Collider (LHC), I have witnessed one of the world's most complex scientific undertakings during its final construction, commissioning, operation, and announcement of the discovery of a Higgs-like new particle. It has been an exciting time. Penn helped design, assemble, and install the front-end electronics that read out, control, and power the Transition Radiation Tracker (TRT), the outermost sub-detector of the ATLAS tracker. I spent my first summers as a student with Penn (2006–08) at CERN, participating in the integration and commissioning of the TRT. I helped with diagnostic checks of the TRT front-end before the TRT was installed in ATLAS, and developed software for normalizing the analog-to-digital thresholds in the front-end electronics of the TRT. In January of 2009, I moved to the Geneva area to work at CERN full-time with the ATLAS Collaboration, and stayed there for the next four years. ATLAS began taking data from collisions at the LHC in November of 2009. Throughout most of the running of the LHC from 2010–2012, I rotated with others the on-call responsibility for the TRT DAQ. My timing with the commissioning of the TRT and the arrival of the first collision data allowed me to contribute to a broad range of research efforts. The focus of my research with the data from ATLAS has been on the reconstruction of hadronic decays of tau leptons and their use in searches for new physics. I helped with the commissioning and validation of the ATLAS offline tau reconstruction with the first data, and the development of the cut-based identification. I contributed to the observation Z → ττ and the measurement of its cross section, which lead to searching for new physics in high-mass ditau events. xiii xiv preface About the text The organization of the text is outlined in Section 1.2 of the introduction. There are some places where I have adapted large portions of text from other references, sometimes nearly verbatim, but only from references and sections therein, for which I was a primary author or editor, and had often drafted the original text. These include: • Chapter 4 which follows ATLAS-CONF-2011-077, ATLAS-CONF-2011-152, and ATL-COM-PHYS-2012-394 in many places; • Chapter 5 which follows a combination of ATL-PHYS-INT-2009-044, ATL-COM-PHYS-2011-416, and arxiv:1108.2016 [hep-ex]; • Chapter 6 which follows a combination of ATL-COM-PHYS-2012-394 and arxiv:1210.6604 [hep-ex]. Ryan Reece Philadelphia, July 2013 Chapter 1 Introduction 1.1 Exploring at the high-energy frontier The reductionist program and scientific method have been hugely successful in describing nature with progressively better precision. At the most fundamental level explored experimentally, we know the nuclei of atoms are bound systems of sub-atomic particles called "quarks". The quarks together with another class of particles called "leptons", to which the electron belongs, are all the known fermions which make-up stable matter. The Standard Model (SM) of particle physics is a quantum field theory where fermions interact by exchanging gauge bosons which are the quanta of the fundamental forces. Experimental research efforts world-wide in the last 100 years have probed interactions at successively higher energies, discovering the ingredients that would be pieced together into the SM in the 1960s. The Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) laboratory, located on the French-Swiss border outside Geneva, is currently the world's highest energy particle collider. For three years from 2010–2012, the LHC was operational and delivered proton-proton collisions at a center-of-momentum energy of 7–8 TeV. It is currently shutdown for maintenance and upgrades, but is expected to run again in 2015 and for much of this decade. The consistency of the SM depends on nature having certain gauge symmetries, but that the electroweak symmetry is broken via the Higgs mechanism as a way to allow gauge bosons to have masses that would otherwise ruin gauge invariance. The last few years, with the start-up of the LHC have brought the frontier of high-energy physics to a critical level of sensitivity to the Higgs boson and to many scenarios of new physics beyond the SM. The discovery of a new particle at the LHC in 2012, so far consistent with the Higgs boson, completes the cast as the last missing particle in the SM to be found. There are many ways the SM has been tested to fantastic precision, such as the g-factor of the electron, but there are others such as the Higgs-coupling and neutrino-mixing 1 2 1. introduction parameters that have only recently been measured to ∼ 10% or have not yet been measured. Being a gauge theory with 12 fermions, the SM is amazingly simple for a theory that describes the fundamental interactions underlying all observable phenomena apart from gravity. However, the SM is also very ad hoc in its structure and the values of its 19 or more parameters. It is also at risk of needing to be oddly fine-tuned to be consistent without extending the model in some way with additional structure at higher energies. These and other compelling theoretical arguments give reasons to expect there to be new physics to be discovered at the TeV scale. Many theories of physics beyond the SM have revolutionary implications for the concepts of symmetry and space-time, and for our understanding of the early universe. The ATLAS experiment is a massive multi-purpose detector, built in the Point 1 cavern of the LHC tunnel, one of four points where experiments are situated at beam crossings. The physics program of ATLAS and its 3000 collaborators includes the successful search for the Higgs boson as well as searches for other new exotic particles and evidence for physics beyond the SM. 1.2 Outline This thesis presents a summary of much of my graduate work during the start-up of the LHC and the collection of the first years of data with ATLAS. The central topics of my research have been the reconstruction and identification of hadronic decays of tau leptons, and their use in searching for new physics. In particular, I discuss: the first cut-based tau identification used with ATLAS data, the first observations and systematic uncertainties derived for taus at ATLAS, the first measurement of the Z → ττ cross section, and the first limit on high-mass resonances decaying to τ+τ− with ATLAS data. Tau leptons play an important role in the physics program of ATLAS because they can have preferred couplings to new physics such as searches for the Higgs boson (H → ττ) and new resonances (Z ′ → ττ). First in Chapter 2, I briefly describe the SM and introduce many of the reasons to be interested in searches for physics beyond the SM at the LHC. That chapter is suppported by Appendix A, where I give a brief review of some of the founding literature in quantum mechanics and the formation of the SM. Chapter 3 briefly describes the LHC, the ATLAS detector, and its computing and reconstruction. Chapter 4 outlines how tau reconstruction and identification work at ATLAS and reviews many of its advancements in the years 2010–2012. Chapter 5 summarizes the first ATLAS Z → ττ cross section measurement, and Chapter 6 summarizes the first ATLAS search for high-mass resonances decaying to τ+τ−. Chapter 2 The theoretical situation This chapter introduces the Standard Model of particle physics, including a brief review of the discovery of a Higgs-like particle at the LHC in the summer of 2012. Then it discusses how our understanding of particle physics is incomplete and that there are several scenarios for physics beyond the Standard Model. 2.1 Introduction The Standard Model (SM) of particle physics is our best model of fundamental physics, describing the quantum behavior of three of the fundamental forces: electromagnetic, weak, and strong, but not the weakest force: gravity. It is at the same time very simple, very rich phenomenologically, very deep, and very ad hoc. The discovery of a new particle at the LHC in 2012, so far consistent with the SM Higgs boson, brings the initial signs of a warranted confirmation of the ideas behind electroweak symmetry breaking in the SM. However, this still leaves several questions unanswered as to why the SM is the way it is. Finding answers to, or a better understanding of, these questions that concern the fundamental nature of our universe is the motivation of high-energy physics research programs world-wide. 2.2 The Standard Model The SM is the culmination of several incremental discoveries, many of which are reviewed briefly in Appendix A; the structure of the SM is summarized here. The fundamental ingredients of the SM are a set of Dirac fermion fields in certain multiplet representations of a particular gauge group: SU(3)C × SU(2)L ×U(1)Y . 3 4 2. the theoretical situation Being based on a type of quantum field theory (QFT) called a "Yang-Mills theory" [1], the interactions between the fermions are described by gauge bosons, and the structure of those interactions is determined by gauge invariance described by Lie groups of the type SU(n). For a QFT to have a local gauge invariance requires the existence of gauge boson fields to form a gauge-covariant derivative. In the case of the SM, gauge invariance implies the existence of following gauge boson fields: SU(3)C × SU(2)L × U(1)Y ⇓ ⇓ ⇓ Gαμ W a μ Bμ α ∈ { 1, 2, . . . , 8 } a ∈ { 1, 2, 3 } There are 8 gluon fields, Gαμ , that describe the strong interactions, while the W a μ and Bμ fields together describe the electroweak interactions. The Higgs mechanism demonstrates that a QFT with local gauge invariance can have massive gauge bosons if the gauge symmetry is spontaneously broken by the non-zero value of a scalar Higgs field in the ground state, and was developed independently by three groups: Robert Brout and Francois Englert [2]; Peter Higgs [3, 4]; and Gerald Guralnik, Carl R. Hagen, and Tom Kibble [5]. This explains how masses can be generated for gauge bosons and also for chiral fermions, while maintaining the gauge invariance that is fundamental to the theory but would otherwise exclude such masses. The gauge structure of the electroweak model was proposed by Sheldon Glashow [6], Steven Weinberg [7], and Abdus Salam [8, 9, 10] in the 1960s. The SU(2)L ×U(1)Y part of the gauge group describing the electroweak interactions is spontaneously broken by the Higgs mechanism with the following breaking pattern: SU(2)L ×U(1)Y → U(1)EM . In the low-energy vacuum, the W aμ and Bμ fields mix to form the W ± and Z fields of the massive gauge bosons mediating the weak force. The remaining U(1)EM gauge invariance corresponds to an orthogonal mixing that gives a massless gauge boson, Aμ, which is the photon mediating the electromagnetic force. In the 1970s, the SU(3) theory of quantum chromodynamics (QCD) was developed, describing the strong interactions that bind quarks into hadrons and bind the nuclei of atoms. Soon after, the demonstration of asymptotic freedom in the strong interactions by Politzer, Gross, and Wilczek [11, 12, 13, 14] showed that QCD has a perturbative regime because the strong interactions get weaker at higher energies. The combination of the GWS electroweak theory and QCD [15] has become known as the "Standard Model" of particle physics. 2.3 the search for the higgs boson 5 u up u up u up (1964) u up (1964) u up (1964) u up (1964) u up (1964) u up (1964) u up (1964) d down (1964) c charm (1974) s strange (1964) t top (1995) b bottom (1977) e electron (1897) μ muon (1936) τ tau (1975) νe electron neutrino (1953) νμ muon neutrino (1962) ντ tau neutrino (2000) g gluon (1979) W± (1983) Z (1983)  photon (1900) H Higgs (2012?) Quarks Leptons Gauge bosons Higgs boson } } Fermions Bosons Figure 2.1: An illustration of the field content of the Standard Model. The numbers in parentheses denote the year the particle for that field was discovered. Note that the fermions are only grouped into doublets for their left-chiral parts. The right-chiral parts are SU(2)L singlets. The structure of the gauge group representations is shown in more detail in Figure A.3 in Appendix A. The SM fermions come in two categories: quarks, which participate in the strong interactions as SU(3) color triplets, and the leptons, which, being color singlets, do not participate in the strong interactions. The fermion fields form chiral representations of the SU(2)L symmetry. The left-chiral parts of the fermions form doublet representations, and the right-chiral parts of the fermions are SU(2) singlets. The field content of the Standard Model is summarized in Figure 2.1. 2.3 The search for the Higgs boson 2.3.1 Before the start-up of the LHC Several generations of colliders and fixed-target experiments have contributed to the experimental support for the SM and for searching for new physics, each successively climbing in energy to gain sensitivity to physics at higher energy scales. Figure 2.2 shows a plot the effective energy of collisions probed if it were a fixed-target experiment as a function of the time the experiment began taking data. By the year 2000, LEP had reached its highest energy of √ s = 209 GeV, and combined searches of the LEP experiments excluded a SM Higgs with a mass less than 114 GeV in 2003 [17]. Figure 2.3 (left) shows the upper limit on the ratio of the coupling for Higgs decays through H → ZZ∗ compared to the SM as a function of the Higgs mass. Then the Tevatron took the lead in searching for the Higgs boson. In 2009, before the the start6 2. the theoretical situation 1,000TeV 10,000TeV 100,000TeV 1,000,000TeV 100TeV 10TeV 1TeV 100GeV 10GeV 1GeV 100MeV 10MeV 1MeV 1930 1950 1970 YearofCommissioning 1990 2010 P ar ti cl e E n er g y ProtonStorageRings Colliders Proton Synchrotrons ElectronLinacs Synchrocyclotrons ProtonLinacs Cyclotrons Electron Synchrotrons Sector-Focused Cyclotrons Electrostatic Generators Rectifier Generators Betatrons ElectronPositron StorageRingColliders ElectronProton Colliders Linear Colliders A "Livingston plot" showing the evolution of accelerator laboratory energy from 1930 until 2005. Energy of colliders is plotted in terms of the laboratory energy of particles colliding with a proton at rest to reach the samecenterofmass energy. HERA LHC Tevatron SppS _ ISR LEP II Figure 2.2: The "Livingston plot", showing the effective energy of collisions probed for various collider and fixed-target particle experiments as if they were each fixed-target experiments, as a function of the time the experiment began taking data [16]. 2.3 the search for the higgs boson 7 10 -2 10 -1 1 20 40 60 80 100 120 mH(GeV/c 2) 95 % C L lim it on ξ 2 LEP √s = 91-210 GeV Observed Expected for background (a) 10 -2 10 -1 1 20 40 60 80 100 120 mH(GeV/c 2) 95 % C L lim it on ξ 2 B (H → bb– ) LEP √s = 91-210 GeV H→bb – (b) 10 -2 10 -1 1 20 40 60 80 100 120 mH(GeV/c 2) 95 % C L lim it on ξ 2 B (H → τ+ τ- ) LEP √s = 91-210 GeV H→τ+τ- (c) Figure 10: The 95% confidence level upper bound on the ratio !2 = (gHZZ/gSMHZZ) 2 (see text). The dark and light shaded bands around the median expected line correspond to the 68% and 95% probability bands. The horizontal lines correspond to the Standard Model coupling. (a): For Higgs boson decays predicted by the Standard Model; (b): for the Higgs boson decaying exclusively into bb and (c): into "+"! pairs. 22 21 is less than or equal to one would indicate that that particular Higgs boson mass is excluded at the 95% C.L. The combinations of results of each single experiment, as used in this Tevatron combination, yield the following ratios of 95% C.L. observed (expected) limits to the SM cross section: 3.6 (3.2) for CDF and 3.7 (3.9) for DØ at mH = 115 GeV/c 2, and 1.5 (1.6) for CDF and 1.3 (1.8) for DØ at mH = 165 GeV/c 2. The ratios of the 95% C.L. expected and observed limit to the SM cross section are shown in Figure 4 for the combined CDF and DØ analyses. The observed and median expected ratios are listed for the tested Higgs boson masses in Table XVIII for mH ! 150 GeV/c2, and in Table XIX for mH " 155 GeV/c2, as obtained by the Bayesian and the CLS methods. In the following summary we quote only the limits obtained with the Bayesian method since they are slightly more conservative (based on the expected limits) for the quoted values, but all the equivalent numbers for the CLS method can be retrieved from the tables. We obtain the observed (expected) values of 2.5 (2.4) at mH = 115 GeV/c 2, 0.99 (1.1) at mH = 160 GeV/c 2, 0.86 (1.1) at mH = 165 GeV/c 2, and 0.99 (1.4) at mH = 170 GeV/c 2. We exclude at the 95% C.L. the production of a standard model Higgs boson with mass between 160 and 170 GeV/c2. This result is obtained with both Bayesian and CLS calculations. 1 10 100 110 120 130 140 150 160 170 180 190 200 mH(GeV/c 2) 95 % C L Li m it/ SM Tevatron Run II Preliminary, L=0.9-4.2 fb-1 Expected Observed ±1σ Expected ±2σ Expected LEP Exclusion Tevatron Exclusion SM March 5, 2009 FIG. 4: Observed and expected (median, for the background-only hypothesis) 95% C.L. upper limits on the ratios to the SM cross section, as functions of the Higgs boson mass for the combined CDF and DØ analyses. The limits are expressed as a multiple of the SM prediction for test masses (every 5 GeV/c2) for which both experiments have performed dedicated searches in di!erent channels. The points are joined by straight lines for better readability. The bands indicate the 68% and 95% probability regions where the limits can fluctuate, in the absence of signal. The limits displayed in this figure are obtained with the Bayesian calculation. Figure 2.3: (left) The 95% CL upper limit on the coupling for Higgs production at LEP, ξ2 = (gHZZ/g SM HZZ) 2, as a function of the Higgs mass [17]. (right) The 95% CL upper li it on the signal strength for the SM Higgs boson as a function of t mass [19]. up of the LHC, the CDF and DØ experiments at the Tevatron had collected 4 fb−1 and excluded a SM Higgs boson in the mass range of 160–170 GeV at 95% CL. Figure 2.3 (right) shows the excluded signal strength (the ratio of the rate of Higgs production to that expected in the SM) as a function of the Higgs mass, also showing the LEP limit at low mass1. Indirect constraints on the Higgs mass were also made, in addition to the theoretical constraints discussed in Section 2.4.3. Assuming the SM Higgs boson exists, it contributes to virtual corrections to several EW observables, most notably through loop diagrams that contribute to the Higgs and W boson propagators that are sensitivite to the W and top quark masses. Precision measurements of the W and top quark masses, among other observables measured at LEP and the Tevatron, were combin d by the LEP EW Working Group to test which Higgs mass is most preferred by the data. Figure 2.4 shows the result of the combined fit to the Tevatron and LEP results in 2009, resulting in a best fit of mH = 87 +35 −26 GeV, equivalent to an upper limit of mH < 157 GeV at 95% CL. Interestingly, this shows a preferrence for a low-mass Higgs with a best fit mass below that excluded by LEP, but still consistent with mH ≈ 115–160 GeV. 2.3.2 Observations of a Higgs-like excess at the LHC With the 4.8 fb−1 of integrated luminosity at √ s = 7 TeV collected in 2011, both ATLAS [21] and CMS [22] reported excesses which were compatible with SM Higgs boson production and decay in 1 Later in 2010, the Tevatron extended its analysis with the entire Tevatron dataset of 10 fb−1, extending the mass range excluded to 147–180 GeV, and reporting a compeling excess in the unexcluded lower-mass region at mH ≈ 120–130 GeV, corresponding to a local significance of 3.0 standard deviations (σ) for the background only hypothesis [18]. 8 2. the theoretical situation 0 1 2 3 4 5 6 10030 300 mH [GeV] ∆χ 2 Excluded Preliminary ∆αhad = (5) 0.02758±0.00035 0.02749±0.00012 incl. low Q2 data Theory uncertainty August 2009 mLimit = 157 GeV Figure 2.4: The distribution of the ∆χ2 = χ2−χ2min as a function of the SM Higgs mass, mH , for the combined LEP-Tevatron EW fit. The blue band illustrates the theoretical uncertainty due to missing higher order corrections. The yellow vertical bands show the mH regions excluded by LEP-II (up 114 GeV) and the Tevatron (160–170 GeV), as of August 2009. The best-fit result is mH = 87 +35 −26 GeV, equivalent to an upper limit of mH < 157 GeV at 95% CL [20]. the mass range 124–126 GeV, with significances of 2.9 and 3.1 standard deviations (σ), respectively. By the summer of 2012, the LHC had delivered about 5.8 fb−1 of integrated luminosity at √ s = 8 TeV. Combining results from searches for the Higgs boson with both the 2011 and 2012 datasets, on July 4, 2012, the ATLAS [23] and CMS [24] experiments independently announced discovery of a new particle consistent with a SM Higgs boson with mH ≈ 125 GeV, with significances of 5.9 and 5.8 σ, respectively. Through the Yukawa couplings and the EW interactions, the SM Higgs has many ways it can decay, especially within the preferred Higgs mass range mH ≈ 115–160 GeV. Figure 2.5 (left) shows a plot of the Higgs branching fractions as a function of the Higgs mass. Both the ATLAS and CMS experiments search for the Higgs boson in H → γγ, ZZ∗, WW ∗, ττ , and bb decays. Table 2.1 highlights the approximate branching fractions for a SM Higgs with mH = 125 GeV. Table 2.1: The approximate branching ratios for the decays of the SM Higgs boson with mH = 125 GeV [27]. channel: bb WW ∗ ττ ZZ∗ γγ branching ratio [%]: 58 22 6.3 2.6 0.23 2.3 the search for the higgs boson 9 6 [GeV]HM 100 120 140 160 180 200 H ig gs B R + T ot al U nc er t -310 -210 -110 1 LH C H IG G S XS W G 2 01 1 bb ττ cc gg γγ γZ WW ZZ FIG. 1: Higgs branching ratios and their uncertainties for the low mass range. V. RESULTS In this Section the results of the SM Higgs branching ratios, calculated according to the procedure described above, are shown and discussed. Figure 1 shows the SM Higgs branching ratios in the low mass range, 100 GeV ! MH ! 200 GeV as solid lines. The (coloured) bands around the lines show the respective uncertainties, estimated considering both the theoretical and the parametric uncertainty sources (as discussed in Section IV). The same results, but now for the "full" mass range, 100 GeV ! MH ! 1000 GeV, are shown in Figure 2. More detailed results on the decays H " WW and H " ZZ with the subsequent decay to 4f are presented in Figures 3 and 4. The largest "visible" uncertainties can are found for the channels H " !+!!, H " gg, H " cc and H " tt, see below. Tables VI–XV, which can be found at the end of the paper, show the branching ratios for the Higgs two-body fermionic and bosonic final states, together with their total uncertainties, estimated as discussed in Section IV.4 represents Tables XI–XV also contain the total Higgs width !H in the last column. More detailed results for four representative Higgs-boson masses are given in Table IV. Here we show the BR, the PU separately for the four parameters as given in Table II, the total PU, the theoretical uncertainty TU as well as the total uncertainty on the Higgs branching ratios. The TU are most relevant for the H " gg, H " Z" and H " tt branching ratios, reaching O(10%). For the H " bb, H " cc and H " !+!! branching ratios they remain below a few percent. PU are relevant mostly for the H " cc and H " gg branching ratios, reaching up to O(10%) and O(5%), respectively. They are mainly induced by the parametric uncertainties in #s and mc. The PU resulting from mb a"ect the BR(H " bb) at the level of 3%, and the PU from mt influences in particular the BR(H " tt) near the tt threshold. For the H " "" channel the total uncertainty can reach up to about 5% in the relevant mass range. Both TU and PU on the important channels H " ZZ and H " WW remain at the level of 1% over the full mass range, giving rise to a total uncertainty below 3% for MH > 135 GeV. Finally, Tables XVI–XX and Tables XXI–XXV, to be found at the end of the paper, list the branching ratios for the most relevant Higgs decays into four-fermion final states. The right column in these Tables shows the total relative uncertainties on these branching ratios in percentage. These are practically equal for all the H " 4f branching ratios 4 The value 0.0% means that the uncertainty is below 0.05%. 14 ATLAS Collaboration / Physics Letters B 716 (2012) 1–29 Table 7 Characterisation of the excess in the H ! Z Z (") ! 4!, H ! " " and H ! W W (") ! !#!# channels and the combination of all channels listed in Table 6. The mass value mmax for which the local significance is maximum, the maximum observed local significance Zl and the expected local significance E(Zl) in the presence of a SM Higgs boson signal at mmax are given. The best fit value of the signal strength parameter μ at mH = 126 GeV is shown with the total uncertainty. The expected and observed mass ranges excluded at 95% CL (99% CL, indicated by a *) are also given, for the combined # s = 7 TeV and #s = 8 TeV data. Search channel Dataset mmax [GeV] Zl [$ ] E(Zl) [$ ] μ(mH = 126 GeV) Expected exclusion [GeV] Observed exclusion [GeV] H ! Z Z (") ! 4! 7 TeV 125.0 2.5 1.6 1.4 ± 1.1 8 TeV 125.5 2.6 2.1 1.1 ± 0.8 7 & 8 TeV 125.0 3.6 2.7 1.2 ± 0.6 124–164, 176–500 131–162, 170–460 H ! " " 7 TeV 126.0 3.4 1.6 2.2 ± 0.7 8 TeV 127.0 3.2 1.9 1.5 ± 0.6 7 & 8 TeV 126.5 4.5 2.5 1.8 ± 0.5 110–140 112–123, 132–143 H ! W W (") ! !#!# 7 TeV 135.0 1.1 3.4 0.5 ± 0.6 8 TeV 120.0 3.3 1.0 1.9 ± 0.7 7 & 8 TeV 125.0 2.8 2.3 1.3 ± 0.5 124–233 137–261 Combined 7 TeV 126.5 3.6 3.2 1.2 ± 0.4 8 TeV 126.5 4.9 3.8 1.5 ± 0.4 7 & 8 TeV 126.5 6.0 4.9 1.4 ± 0.3 110–582 111–122, 131–559 113–532 (*) 113–114, 117–121, 132–527 (*) uncertainties, evaluated as described in Ref. [138], reduces the local significance to 5.9$ . The global significance of a local 5.9$ excess anywhere in the mass range 110–600 GeV is estimated to be approximately 5.1$ , increasing to 5.3 $ in the range 110–150 GeV, which is approximately the mass range not excluded at the 99% CL by the LHC combined SM Higgs boson search [139] and the indirect constraints from the global fit to precision electroweak measurements [12]. 9.3. Characterising the excess The mass of the observed new particle is estimated using the profile likelihood ratio %(mH ) for H ! Z Z (") ! 4! and H ! " " , the two channels with the highest mass resolution. The signal strength is allowed to vary independently in the two channels, although the result is essentially unchanged when restricted to the SM hypothesis μ = 1. The leading sources of systematic uncertainty come from the electron and photon energy scales and resolutions. The resulting estimate for the mass of the observed particle is 126.0 ± 0.4 (stat) ± 0.4 (sys) GeV. The best-fit signal strength μ is shown in Fig. 7(c) as a function of mH . The observ d excess corresponds to μ = 1.4 ± 0.3 for mH = 126 GeV, which is co sistent wi th SM Higgs boson hypoth sis μ = 1. A summary of the individual and combined best-fit values of the strength parameter for a SM Higgs boson mass hypothesis of 126 GeV is shown in Fig. 10, while more information about the three main channels is pr vid d in Tabl 7. In order to test which values of the strengt and mass of a signal hypothesis are simultaneously consistent with the data, the profile likelihood ratio %(μ,mH ) is used. In the presence of a strong signal, it will produce closed contours around the best-fit point (μ,mH ), while in th absence of a signal the contours will be upper limits on μ for all values of mH . Asymptotically, the test statistic $2 ln %(μ,mH ) is distributed as a &2 distribution with two degrees of freedom. The resulting 68% and 95% CL contours for the H ! " " and H ! W W (") ! !#!# channels are shown in Fig. 11, where the asymptotic approximations have been validated with ensembles of pseudo-experiments. Similar contours for the H ! Z Z (") ! 4! channel are also shown in Fig. 11, although they are only approximate confidence intervals due to the smaller number of candidates in this channel. These contours in the (μ,mH ) plane take into account uncertainties in the energy scale and resolution. The probability for a single Higgs boson-like particle to produce resonant mass peaks in the H ! Z Z (") ! 4! and H ! " " Fig. 10. Measurements of the signal strength parameter μ for mH = 126 GeV for the individual channels and their combination. Fig. 11. Confidence intervals in the (μ,mH ) plane for the H ! Z Z (") ! 4!, H ! " " , and H ! W W (") ! !#!# channels, including all systematic uncertainties. The markers indicate the maximum likelihood estimates (μ,mH ) in the corresponding channels (the maximum likelihood estimates for H ! Z Z (") ! 4! and H ! W W (") ! !#!# coincide). channels separated by more than the observed mass difference, allowing the signal strengths to vary independently, is about 8%. The contributions from the different production modes in the H ! " " channel have been studied in order to assess any tension between the data and the ratios of the production cross Figure 2.5: (left) The branching ratios the SM Higgs decays with estimated theoretically uncertainties shown by the bands [25, 26]. (right) Measurements of the signal strength parameter μ for mH = 126 GeV for the individual channel and their combinatio [23]. 100 110 120 130 140 150 160 E ve n ts / G e V 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 Data 2011 and 2012 = 126.5 GeV) H Sig + Bkg inclusive fit (m 4th order polynomial Selected diphoton sample -1 Ldt = 4.8 fb! = 7 TeV, s -1 Ldt = 5.9 fb! = 8 TeV, s ATLAS Preliminary [GeV]""m 100 110 120 130 140 150 160 D a ta B kg -100 0 100 Figure 15: Invariant mass distribution for the combined ! s = 7 TeV and ! s = 8 TeV data samples. Superimposed is the result of a fit including a signal component fixed to a hypothesized mass of 126.5 GeV and a background component described by a fourth-order Bernstein polynomial. The bottom inset displays the residual of the data with respect to the fitted background. 28 ATLAS Collaboration / Physics Letters B 716 (2012) 1–29 5 Fig. 2. The distribution of the four-lepton invariant mass, m4! , for the selected candidates, compared to the background expectation in the 80–250 GeV mass range, for the combination of the ! s = 7 TeV and !s = 8 TeV data. The signal expectation for a SM Higgs with mH = 125 GeV is also shown. Table 3 The numbers of expected signal (mH = 125 GeV) and background events, together with the numbers of observed events in the data, in a window of size ±5 GeV around 125 GeV, for the combined ! s = 7 TeV and !s = 8 TeV data. Signal Z Z (") Z + jets, tt Observed 4μ 2.09 ± 0.30 1.12 ± 0.05 0.13 ± 0.04 6 2e2μ/2μ2e 2.29 ± 0.33 0.80 ± 0.05 1.27 ± 0.19 5 4e 0.90 ± 0.14 0.44 ± 0.04 1.09 ± 0.20 2 (±2.3%/±7.6%) for m4! = 115 GeV. The uncertainty on the electron energy scale results in an uncertainty of ±0.7% (±0.5%/±0.2%) on the mass scale of the m4! distribution for the 4e (2e2μ/2μ2e) channel. The impact of the uncertainties on the electron energy resolution and on the muon momentum resolution and scale are found to be negligible. The theoretical uncertainties associated with the signal are described in detail in Section 8. For the SM Z Z (") background, which is estimated from MC simulation, the uncertainty on the total yield due to the QCD scale uncertainty is ±5%, while the effect of the PDF and "s uncertainties is ±4% (±8%) for processes initiated by quarks (gluons) [53]. In addition, the dependence of these uncertainties on the four-lepton invariant mass spectrum has been taken into account as discussed in Ref. [53]. Though a small excess of events is observed for m4l > 160 GeV, the measured Z Z (") # 4! cross section [93] is consistent with the SM theoretical prediction. The impact of not using the theoretical constraints on the Z Z (") yield on the search for a Higgs boson with mH < 2mZ has been studied in Ref. [87] and has been found to be negligible. The impact of the interference between a Higgs signal and the nonresonant gg # Z Z (") background is small and becomes negligible for mH < 2mZ [94]. 4.4. Results The expected distributions of m4! for the background and for a Higgs boson signal with mH = 125 GeV are compared to the data in Fig. 2. The numbers of observed and expected events in a window of ±5 GeV around mH = 125 GeV are presented for the combined 7 TeV and 8 TeV data in Table 3. The distribution of the m34 versus m12 invariant mass is shown in Fig. 3. The statistical interpretation of the excess of events near m4! = 125 GeV in Fig. 2 is presented in Section 9. Fig. 3. Distribution of the m34 versus the m12 invariant mass, before the application of the Z -mass constrained kinematic fit, for the selected candidates in the m4! range 120–130 GeV. The expected distributions for a SM Higgs with mH = 125 GeV (the sizes of the boxes indicate the relative density) and for the total background (the intensity of the shading indicates the relative density) are also shown. 5. H ! ! ! channel The search for the SM Higgs boson through the decay H # # # is performed in the mass range between 110 GeV and 150 GeV. The dominant background is SM diphoton production (# # ); contributions also come from # + jet and jet + jet production with one or two jets mis-identified as photons (# j and j j) and from the Drell–Yan process. The 7 TeV data have been re-analysed and the results combined with those from the 8 TeV data. Among other changes to the analysis, a new category of events with two jets is introduced, which enhances the sensitivity to the VBF process. Higgs boson events produced by the VBF process have two forward jets, originating from the two scattered quarks, and tend to be devoid of jets in the central region. Overall, the sensitivity of the analysis has been improved by about 20% with respect to that described in Ref. [95]. 5.1. Event selection The data used in this channel are selected using a diphoton trigger [96], which requires two clusters formed from energy depositions in the electromagnetic calorimeter. An ET threshold of 20 GeV is applied to each cluster for the 7 TeV data, while for the 8 TeV data the thresholds are increased to 35 GeV on the leading (the highest ET) cluster and to 25 GeV on the sub-leading (the next-highest ET) cluster. In addition, loose criteria are applied to the shapes of the clusters to match the expectations for electromagnetic showers initiated by photons. The e!ciency of the trigger is greater than 99% for events passing the final event selection. Events are required to contain at least one reconstructed vertex with at least two associated tracks with pT > 0.4 GeV, as well as two photon candidates. Photon candidates are reconstructed in the fiducial region |$| < 2.37, excluding the calorimeter barrel/endcap transition region 1.37 ! |$| < 1.52. Photons that convert to electron–positron pairs in the ID material can have one or two reconstructed tracks matched to the clusters in the calorimeter. The photon reconstruction e!ciency is about 97% for ET > 30 GeV. In order to account for energy losses upstream of the calorimeter and energy leakage outside of the cluster, MC simulation results are used to calibrate the energies of the photon candidates; there are separate calibrations for unconverted and converted Figure 2.6: The distributions of the reconstructed mH invariant mass of H → γγ [28] (left) and H → ZZ∗ → 4` [23] (right) candidates aft r all selections for the combined 7 TeV (2011) and 8 TeV (2012) data sample. 10 2. the theoretical situation ATLAS Collaboration / Physics Letters B 716 (2012) 1–29 11 Table 5 The expected numbers of signal (mH = 125 GeV) and background events after all selections, including a cut on the transverse mass of 0.75mH < mT < mH for mH = 125 GeV. The observed numbers of events in data are also displayed. The eμ and μe channels are combined. The uncertainties shown are the combination of the statistical and all systematic uncertainties, taking into account the constraints from control samples. For the 2-jet analysis, backgrounds with fewer than 0.01 expected events are marked with '–'. 0-jet 1-jet 2-jet Signal 20 ± 4 5 ± 2 0.34 ± 0.07 W W 101 ± 13 12 ± 5 0.10 ± 0.14 W Z (!)/Z Z/W ! (!) 12 ± 3 1.9 ± 1.1 0.10 ± 0.10 tt 8 ± 2 6 ± 2 0.15 ± 0.10 tW /tb/tqb 3.4 ± 1.5 3.7 ± 1.6 – Z/! ! + jets 1.9 ± 1.3 0.10 ± 0.10 – W + jets 15 ± 7 2 ± 1 – Total background 142 ± 16 26 ± 6 0.35 ± 0.18 Observed 185 38 0 generators. The potential impact of interference between resonant (Higgs-mediated) and non-resonant gg " W W diagrams [116] for mT > mH was investigated and found to be negligible. The effect of the W W normalisation, modelling, and shape systematics on the total background yield is 9% for the 0-jet channel and 19% for the 1-jet channel. The uncertainty on the shape of the total background is dominated by the uncertainties on the normalisations of the individual backgrounds. The main uncertainties on the top background in the 0-jet analysis include those associated with interference effects between tt and single top, initial state an final state radiation, b-tagging, and JER. The impact on the total background yield in the 0-jet bin is 3%. For the 1-jet analysis, the impact of the top background on the total yield is 14%. Theoretical uncertainties on the W ! background normalisation are evaluated for each jet bin using the procedure described in Ref. [117]. They are ±11% for the 0-jet bin and ±50% for the 1-jet bin. For W ! ! with m"" < 7 GeV, a k-factor of 1.3 ± 0.3 is applied to the MadGraph LO prediction based on the comparison with the MCFM NLO calculation. The k-factor for W ! !/W Z (!) with m"" > 7 GeV is 1.5±0.5. These uncertainties affect mostly the 1-jet channel, where their impact on the total background yield is approximately 4%. 6.4. Results Table 5 shows the numbers of events expected from a SM Higgs boson with mH = 125 GeV and from the backgrounds, as well as the numbers of candidates observed in data, after application of all selection criteria plus an additional cut on mT of 0.75mH < mT < mH . The uncertainties shown in Table 5 include the systematic uncertainties discussed in Section 6.3, constrained by the use of the control regions discussed in Section 6.2. An excess of events relative to the background expectation is observed in the data. Fig. 6 shows the distribution of the transverse mass after all selection criteria in the 0-jet and 1-jet channels combined, and for both lepton channels together. The statistical analysis of the data employs a binned likelihood function constructed as the product of Poisson probability terms for the eμ channel and the μe channel. The mass-dependent cuts on mT described above are not used. Instead, the 0-jet (1-jet) signal regions are subdivided into five (three) mT bins. For the 2-jet signal region, only the results integrated over mT are used, due to the small number of events in the final sample. The statistical interpretation of the observed excess of events is presented in Section 9. Fig. 6. Distribution of the transverse mass, mT, in the 0-jet and 1-jet analyses with both eμ and μe channels combined, for events satisfying all selection criteria. The expected signal for mH = 125 GeV is shown stacked on top of the background prediction. The W + jets background is estimated from data, and W W and top background MC predictions are normalised to the data using control regions. The hashed area indicates the total uncertainty on the background prediction. 7. Statistical procedure The statistical procedure used to interpret the data is described in Refs. [17,118–121]. The parameter of interest is the global signal strength factor μ, which acts as a scale factor on the total number of events predicted by the Standard Model for the Higgs boson signal. This factor is defined such that μ = 0 corresponds to the background-only hypothesis and μ = 1 corresponds to the SM Higgs boson signal in addition to the background. Hypothesised values of μ are tested with a statistic #(μ) based on the profile likelihood ratio [122]. This test statistic extracts the information on the signal strength from a full likelihood fit to the data. The likelihood function includes all the parameters that describe the systematic uncertainties and their correlations. Exclusion limits are based on the C Ls prescription [123]; a value of μ is regarded as excluded at 95% CL when C Ls is less than 5%. A SM Higgs boson with mass mH is considered excluded at 95% confidence level (CL) when μ = 1 is excluded at that mass. The significance of an excess in the data is first quantified with the local p0, the probability that the background can produce a fluctuation greater than or equal to the excess observed in data. The equivalent formulation in terms of number of standard deviations, Zl , is referred to as the local significance. The global probability for the most significant excess to be observed anywhere in a given search region is estimated with the method described in Ref. [124]. The ratio of the global to the local probabilities, the trials factor used to correct for the "look elsewhere" effect, increases with the range of Higgs boson mass hypotheses considered, the mass resolutions of the channels involved in the combination, and the significance of the excess. The statistical tests are performed in steps of values of the hypothesised Higgs boson mass mH . The asymptotic approximation [122] upon which the results are based has been validated with the method described in Ref. [17]. The combination of individual search sub-channels for a specific Higgs boson decay, and the full combination of all search channels, are based on the global signal strength factor μ and on the identification of the nuisance parameters that correspond to the correlated sources of systematic uncertainty described in Section 8. 8. Correlated systematic uncertainties The individual search channels that enter the combination are summarised in Table 6. 14 ATLAS Collaboration / Physics Letters B 716 (2012) 1–29 Table 7 Characterisation of the excess in the H ! Z Z (") ! 4!, H ! " " and H ! W W (") ! !#!# channels and the combination of all channels listed in Table 6. The mass value mmax for which the local significance is maximum, the maximum observed local significance Zl and the expected local significance E(Zl) in the presence of a SM Higgs boson signal at mmax are given. The best fit value of the signal strength parameter μ at mH = 126 GeV is shown with the total uncertainty. The expected and observed mass ranges excluded at 95% CL (99% CL, indicated by a *) are also given, for the combined # s = 7 TeV and #s = 8 TeV data. Search channel Dataset mmax [GeV] Zl [$ ] E(Zl) [$ ] μ(mH = 126 GeV) Expected exclusion [GeV] Observed exclusion [GeV] H ! Z Z (") ! 4! 7 TeV 125.0 2.5 1.6 1.4 ± 1.1 8 TeV 125.5 2.6 2.1 1.1 ± 0.8 7 & 8 TeV 125.0 3.6 2.7 1.2 ± 0.6 124–164, 176–500 131–162, 170–460 H ! " " 7 TeV 126.0 3.4 1.6 2.2 ± 0.7 8 TeV 127.0 3.2 1.9 1.5 ± 0.6 7 & 8 TeV 126.5 4.5 2.5 1.8 ± 0.5 110–140 112–123, 132–143 H ! W W (") ! !#!# 7 TeV 135.0 1.1 3.4 0.5 ± 0.6 8 TeV 120.0 3.3 1.0 1.9 ± 0.7 7 & 8 TeV 125.0 2.8 2.3 1.3 ± 0.5 124–233 137–261 Combined 7 TeV 126.5 3.6 3.2 1.2 ± 0.4 8 TeV 126.5 4.9 3.8 1.5 ± 0.4 7 & 8 TeV 126.5 6.0 4.9 1.4 ± 0.3 110–582 111–122, 131–559 113–532 (*) 113–114, 117–121, 132–527 (*) uncertainties, evaluated as described in Ref. [138], reduces the local significance to 5.9$ . The global significance of a local 5.9$ excess anywhere in the mass range 110–600 GeV is estimated to be approximately 5.1$ , increasing to 5.3 $ in the range 110–150 GeV, which is approximately the mass range not excluded at the 99% CL by the LHC combined SM Higgs boson search [139] and the indirect constraints from the global fit to precision electroweak measurements [12]. 9.3. Characterising the excess The mass of the observed new particle is estimated using the profile likelihood ratio %(mH ) for H ! Z Z (") ! 4! and H ! " " , the two channels with the highest mass resolution. The signal strength is allowed to vary independently in the two channels, although the result is essentially unchanged when restricted to the SM hypothesis μ = 1. The leading sources of systematic uncertainty come from the electron and photon energy scales and resolut s. The resulting estimate for the mass of the observed particle is 126.0 ± 0.4 (stat) ± 0.4 (sys) GeV. The best-fit signal strength μ is shown in Fig. 7(c) as a function of mH . The observed excess corresponds to μ = 1.4 ± 0.3 for mH = 126 GeV, which is consistent with the SM Higgs boson hypothesis μ = 1. A summary of the individual and combined best-fit values of the strength parameter for a SM Higgs boson mass hypothesis of 126 GeV is shown in Fig. 10, while more information about the three main channels is provided in Table 7. In order to test which values of the strength and mass of a signal hypothesis are simultaneously consistent with the data, the profile likelihood ratio %(μ,mH ) is used. In the presence of a strong signal, it will produce closed contours around the best-fit point (μ,mH ), while in the absence of a signal the contours will be upper limits on μ for all values of mH . Asymptotically, the test statistic $2 ln %(μ,mH ) is distributed as a &2 distribution with two degrees of freedom. The resulting 68% and 95% CL contours for the H ! " " and H ! W W (") ! !#!# channels are shown in Fi . 11, where the asymptotic appr ximations have been validated with ensembles of p eudoxperiments. Similar contours for the H ! Z Z (") ! 4! channel are also shown in Fig. 11, although they are only approximate confidence intervals due to the smaller number of candidates in this channel. These contours in the (μ,mH ) plane take into account uncertainties in the energy scale and resolution. The probability for a single Higgs boson-like particle to produce resonant mass peaks in the H ! Z Z (") ! 4! and H ! " " Fig. 10. Measurements of the signal strength parameter μ for mH = 126 GeV for the individual channels and their combination. Fig. 11. Confidence intervals in the (μ,mH ) plane for the H ! Z Z (") ! 4!, H ! " " , and H ! W W (") ! !#!# channels, including all systematic uncertainties. The markers indicate the maximum likelihood estimates (μ,mH ) in the corresponding channels (the maximum likelihood estimates for H ! Z Z (") ! 4! and H ! W W (") ! !#!# coincide). channels separated by more than the observed mass difference, allowing the signal strengths to vary independently, is about 8%. The contributions from the different production modes in the H ! " " channel have been studied in order to assess any tension between the data and the ratios of the production cross Figure 2.7: (left) The distribution of the tr nsverse mass of the dilepton system and the missing transverse omentum, mT, in the 0-jet and 1-jet channels of the H → WW ∗ → eμ search f r ev n s satisfying all selectio criteria [23]. (right) Confi nce inte vals in the (μ, mH) pla for the H → γγ, → ZZ∗ → 4`, and H → WW ∗ → `ν`ν channels, including all syst matic uncertainties. The markers indicate the maximum likelihood estimates. The significance of the excesses reported in the July 2012 observation is dominated by the H → γγ, H → ZZ∗ → 4`, and H → WW ∗ → `ν`ν searches. The H → γγ and H → ZZ∗ → 4` channels fully reconstruct the decay products of the Higgs boson and have mass resolutions better than a percent. Figure 2.6 shows the reconstructed Higgs mass distributions for the H → γγ and H → ZZ∗ → 4` searches. The H →WW ∗ → `ν`ν channel has good sensitivity to the SM Higgs but a poor mass resolution because of th production of neutrinos. The distribution of the transverse mass of the dilepton system and the missing transverse momentum of the selected events in the H → WW ∗ → eνμν channel with the 2012 data is shown in Figure 2.7 (left). Using only the 2012 data and only the H → γγ, H → ZZ∗ → 4`, and H →WW ∗ → eνμν channels, the combined local signific nce is 4.9 σ at mH = 126.5 GeV [23]. The ATLAS H → γγ and H → ZZ∗ → 4` channels, having precise mass resolution, are combined to measure the mass of the excess, giving a best-fit mass of mH = 126.0± 0.4 (stat)± 0.4 (sys) GeV. The best-fit signal strength for a SM Higgs with mH = 126, combining all channels (γγ, ZZ ∗, WW ∗, ττ , and bb) is μ = 1.4 ± 0.3 [23]. Figur 2.5 (right) shows the estimated μ in each channel and the combination. Likelihood contours for 68% and 95% CL in the μ vs mH plane are shown in Figure 2.7 (right). The searches for H → ττ [29] nd H → bb [30] at ATLAS are approaching sensitivity to the SM Higgs, having urrently reported observed (expected) 95% CL upper limits on the signal strength2, μ, of 1.9 (1.2) and 1.8 (1.9) , respectively, for mH = 125 GeV. Both analyses are being updated 2 The signal strength is the ratio of the rate of Higgs production to that expected in the SM. 2.4 limitations of the standard model 11 with the total 21 fb−1 collected in 2012. 2.4 Limitations of the Standard Model 2.4.1 Neutrino masses and mixing In the SM, neutrinos are massless since there are no right-chiral parts for neutrino fields (or left-chiral parts for anti-neutrinos). Incorporating neutrino masses within the SM is theoretically possible in at least a few ways, but not currently resolved. In 1998, the Super Kamiokande experiment published the first3 evidence of neutrino oscillations in atmospheric neutrinos [31]. In 2001, the Sudbury Neutrino Observatory provided conclusive evidence of oscillation in solar neutrinos [32]. Neutrino oscillation requires that the weak eigenstates of neutrinos be a mix of mass eigenstates with different masses. Therefore, it is now well-accepted that the neutrino mass eigenstates have small (. 1 eV) but non-zero masses. Recently, there has been significant progress in measuring the mass differences and mixing parameters of the neutrino sector. Its structure, however, is not completely determined, including the issue of whether neutrinos are Dirac fermions like the rest of the fermions of the SM, or whether they are Majorana fermions, which are identical to their anti-particles. 2.4.2 Ad hoc features The SM has many features that are arguably ad hoc, and a more fundamental theory or mechanism that could explain or motivate these features would be preferred. First, the particular direct product of gauge groups, SU(3)C × SU(2)L ×U(1)Y, and the corresponding structure of the fermion representations are arbitrary. Why is the SU(2) part chiral but the SU(3) part non-chiral? How are the hypercharges of quarks and leptons related, resulting in the seemingly exact balance of EM charges among hadrons and leptons? Why are there three generations of fermions for both the leptons and quarks? The SM requires the values of 19 independent parameters4 be given, with an additional 7–9 parameters depending on the type of neutrino sector. It is also worth noting that the implementation of the Higgs mechanism in the SM is done minimally, but there could be more than one type of Higgs field in more complicated representations than the simple SM Higgs doublet [33]. 3 Neutrino oscillation has been considered since the 1950s. The first evidence of solar neutrino oscillation dates back to the experiments of Ray Davis Jr. in the 1960s, sparking the Solar Neutrino Problem, but was not seen to be conclusive until the experiments of SNO and others around the beginning of the 21st century. See the discussion of neutrino oscillation in Appendix A.2.7. 4 The 19 SM parameters are: 6 quark masses, 3 charged lepton masses, 3 gauge couplings (g1, g2, g3), 2 Higgs parameters (μ2, λ), 4 CKM parameters, and θQCD. 12 2. the theoretical situation Figure 2: Summary of the uncertainties connected to the bounds on MH . The upper solid area indicates the sum of theoretical uncertainties in the MH upper bound for mt = 175 GeV [12]. The upper edge corresponds to Higgs masses for which the SM Higgs sector ceases to be meaningful at scale ! (see text), and the lower edge indicates a value of MH for which perturbation theory is certainly expected to be reliable at scale !. The lower solid area represents the theoretical uncertaintites in the MH lower bounds derived from stability requirements [9, 10, 11] using mt = 175 GeV and !s = 0.118. Looking at Fig. 2 we conclude that a SM Higgs mass in the range of 160 to 170 GeV results in a SM renormalisation-group behavior which is perturbative and well-behaved up to the Planck scale !P l ! 1019 GeV. The remaining experimental uncertainty due to the top quark mass is not represented here and can be found in [9, 10, 11] and [12] for lower and upper bound, respectively. In particular, the result mt = 175 ± 6 GeV leads to an upper bound MH < 180 ± 4 ± 5 GeV if ! = 1019 GeV, (4) the first error indicating the theoretical uncertainty, the second error reflecting the residual mt dependence [12]. 5 Figure 2.8: The triviality upper bound and vacuum stability lower bound on the SM Higgs boson mass vs the cut-off scale, Λ, where new physics is required to keep the theory consistent [34]. 2.4.3 The hierarchy problem(s) Within the SM, there a e several instances of vas ly differing scales for the values of parameters in the theory that re seen as problematic or unnatural. This is often referred to as the "hierarchy problem". First, as the only fundamental scalar in the SM, the m ss of the Higgs boson has exceptionally large quantum corrections fr m loop diagrams that tend to drive it much higher than the electroweak scale. For theoretical reasons, the mass of the Higgs boson cannot be too large (. 1 TeV) due to the unitarity bound to keep longitudinal WW and ZZ scattering processes from diverging at high energies, and the triviality bound that requires that the Higgs self-coupling, λ, not diverge when it is renormalized at higher energies. Similarly, the Higgs mass is also bounded from below by requiring that λ > 0 for the Higgs potential to have a stable minimum for vacuum stability [34]. Figure 2.8 summarizes these theoretical bounds on the Higgs mass as a function of the scale where new physics would be required to keep the theory consistent. Even within the region of Higgs masses theoretically allowed, there must be a delicate cancellation of the quantum corrections to keep the Higgs mass from being driven much higher, unless one introduces new physics at higher mass scales [35, 33]. Another way of phrasing the hierarchy problem is: why is the electroweak scale (set by the Higgs) so much smaller than the Planck mass, mP ≈ 1× 1019 GeV, the scale where gravity becomes important to quantum effects? Or, why is gravity so much weaker than the other forces? Other forms of hierarchy problems exist in the SM, including the issue of why do the fermion 2.4 limitations of the standard model 13 masses (or equivalently the Yukawa couplings) range over so many orders of magnitude? The quark masses range over 5 orders of magnitude, while the lepton masses range over at least 9 due to the exceptionally small masses of the neutrinos5. 2.4.4 Matter-antimatter asymmetry One of the mysteries in particle physics concerns explaining the abundance of matter in the universe when the laws of physics seem virtually symmetric for matter and anti-matter. The Sakharov conditions [36] enumerate the requirements for an excess of matter to survive annihilation in the development of the very early universe. They require that baryon number, C-symmetry, and CPsymmetry be violated in interactions out of thermal equilibrium such that baryons are generated at a higher rate than anti-baryons during a process called baryogenesis. The known sources of CP violation in the SM are currently thought to be too small to account for the excess of matter, but many extensions to the SM have the potential to bring new sources of CP violation that could help explain it. 2.4.5 Dark matter and dark energy Several astronomical observations including the rotational speeds of galaxies, instances of gravitational lensing, and detailed measurements of the Cosmic Microwave Background (CMB), suggest that there is much more matter in the universe than can be explained by the normal baryonic matter of the SM. Dark matter refers to this unexplained part of matter that must not interact electromagnetically or strongly, but still gathers together gravitationally with the normal matter in galaxies. The latest measurements of the CMB by the Planck satellite estimate the total energy content of the visible universe to be about 5% ordinary matter, 27% dark matter, and 68% dark energy. Therefore, dark matter is estimated to constitute about 85% of the total matter in the universe [37]. Dark energy is another unexplained component of the universe that hypothetically permeates empty space and drives the current accelerated expansion of the universe. It is hoped that some of this mystery could be resolved if particle experiments discover new weakly interacting stable particles that could be candidates for what constitutes the dark matter. 5 The range of fermion masses is illustrated in Figure A.4 of Appendix A.2.5. 14 2. the theoretical situation Figure 6.8: Two-loop renormalization group evolution of the inverse gauge couplings !!1a (Q) in the Standard Model (dashed lines) and the MSSM (solid lines). In the MSSM case, the sparticle masses are treated as a common threshold varied between 500 GeV and 1.5 TeV, and !3(mZ) is varied between 0.117 and 0.121. 2 4 6 8 10 12 14 16 18 Log10(Q/GeV) 0 10 20 30 40 50 60 α -1 U(1) SU(2) SU(3) This unification is of course not perfect; !3 tends to be slightly smaller than the common value of !1(MU ) = !2(MU ) at the point where they meet, which is often taken to be the definition of MU . However, this small di!erence can easily be ascribed to threshold corrections due to whatever new particles exist near MU . Note that MU decreases slightly as the superpartner masses are raised. While the apparent approximate unification of gauge couplings at MU might be just an accident, it may also be taken as a strong hint in favor of a grand unified theory (GUT) or superstring models, both of which can naturally accommodate gauge coupling unification below MP. Furthermore, if this hint is taken seriously, then we can reasonably expect to be able to apply a similar RG analysis to the other MSSM couplings and soft masses as well. The next section discusses the form of the necessary RG equations. 6.5 Renormalization Group equations for the MSSM In order to translate a set of predictions at an input scale into physically meaningful quantities that describe physics near the electroweak scale, it is necessary to evolve the gauge couplings, superpotential parameters, and soft terms using their renormalization group (RG) equations. This ensures that the loop expansions for calculations of observables will not su!er from very large logarithms. As a technical aside, some care is required in choosing regularization and renormalization procedures in supersymmetry. The most popular regularization method for computations of radiative corrections within the Standard Model is dimensional regularization (DREG), in which the number of spacetime dimensions is continued to d = 4 ! 2". Unfortunately, DREG introduces a spurious violation of supersymmetry, because it has a mismatch between the numbers of gauge boson degrees of freedom and the gaugino degrees of freedom o!-shell. This mismatch is only 2", but can be multiplied by factors up to 1/"n in an n-loop calculation. In DREG, supersymmetric relations between dimensionless coupling constants ("supersymmetric Ward identities") are therefore not explicitly respected by radiative corrections involving the finite parts of one-loop graphs and by the divergent parts of two-loop graphs. Instead, one may use the slightly di!erent scheme known as regularization by dimensional reduction, or DRED, which does respect supersymmetry [109]. In the DRED method, all momentum integrals are still performed in d = 4 ! 2" dimensions, but the vector index μ on the gauge boson fields Aaμ now runs over all 4 dimensions to maintain the match with the gaugino degrees of freedom. Running couplings are then renormalized using DRED with modified minimal subtraction (DR) rather than 61 Figure 2.9: Two-loop renormalization group evolution of the inverse gauge couplings α−1(Q) in the Standard Model (dashed lines) and the Minimal Supersymmetric Standard Model (MSSM, solid lines). In the MSSM case, the sparticle masses are treated as a common threshold varied between 500 GeV (blue) and 1.5 TeV (red) [39]. 2.5 Scenarios beyond the Standard Model 2.5.1 Supersymmetry Supersymmetry (SUSY) is a natural extension of the Standard Model that introduces a symmetry r l ting fermions a d bosons. Under reasonable assumptio s, it is the un que extension to the usual Poincaré and internal symmetries of a relativistic quantum field theory, as demonstrated by the H ag-Lopuszanski-Sohniu 6 theorem [38]. In some SUSY model , there is a Lightest Supersymmetric Particle (LSP) that must be stable to conserve the R-parity quantum number. The LSP is presumably only weakly inte acting. It therefore would go undetected directly, but may result in events with significant missing energy in addition to the jets and/or leptons produced in the cascade of a SUSY decay. If such stable weakly interacting SUSY particl s exist, hey could explain the prevalence of dark matter. 2.5.2 Running of the couplings Renormalization is a process by which the bare couplings of a QFT accumulate higher-order quantum corrections, from which relationships can be derived that describe how the ffective physical couplings of the theory scale with the energy of an interaction, called the "renormalization group equations". 6 See the discussion in Appendix A.1.4. 2.5 scenarios beyond the standard model 15 By 1991, the experiments at the Large Electron Positron Collider (LEP) at CERN had measured the three gauge couplings of the SM with sufficient precision such that one could calculate how the couplings hypothetically scale at higher energies [40, 41] as shown in Figure 2.9. The horizontal axis shows the energy scale, Q, of an interaction and is plotted on a logarithmic scale because the couplings run slowly as logarithms of the energy. The renormalization group equations that determine the slopes of the running of the couplings depend on the particle content of the theory. The dotted lines show the strength of the couplings extrapolated to higher energies assuming only the particle content of the SM. The converging of the couplings at high energies is thought by many to possibly indicate a unification of the forces of the SM in scenarios called "grand unified theories". With the precision of the measurements of the couplings from LEP, gauge coupling unification is actually ruled out in the SM since the dotted lines do not converge to a single coupling strength. Remarkably, if one extends the of the Standard Model with SUSY, then the renormalization group equations have to be modified to account for these additional particles, and a unification seems possible at a very high mass scale, MGUT ∼ 1016 GeV, as indicated by the extrapolation of the solid lines. Moreover, the unification prefers the masses of the SUSY partners to be near the TeV scale, and possibly within the reach of the experiments at the LHC [42, 43, 44, 45]. It should be noted though, that this extrapolation to the scale of MGUT is many orders of magnitude above the energies that can currently be probed at collider experiments. New experimental clues are necessary to know the spectrum of particles at higher energies (with or without SUSY), which is one of the primary motivations to search for new physics at the energy frontier. 2.5.3 Grand unified theories Grand unified theories (GUTs) refer to gauge field theories that unify the strong, weak, and electromagnetic interactions of the SM by describing them with a single simple gauge group. They combine both the quarks and leptons into larger multiplet representations of the complete symmetry group, and assume that the gauge group of the SM is the result of a larger symmetry breaking process than just electroweak symmetry breaking. Grand unified theories have the potential to explain many of the ad hoc features of the SM, including the structure of the representations and relations among the hypercharges of quarks and leptons. The first grand unified theories developed in the 1970s are the Pati-Salam model [46] based on SU(4)C × SU(2)L × SU(2)R, and the SU(5) model of Georgi and Glashow [47, 48]. Both of these models can be spontaneously broken to give the gauge group of the SM, along with direct products of additional SU(2) and/or U(1) symmetries that imply the existence of new heavy gauge bosons, often denoted W ′ and Z ′, respectively [33]. Both the Pati-Salam and Georgi-Glashow models can 16 2. the theoretical situation be further embedded in larger groups, such as Spin(10), the breaking patterns of which have been studied in detail [49, 50]. These larger gauge groups can also result from string theories and predict the existence of heavy Z ′ bosons [51, 52, 53]. A search for Z ′ bosons decaying to tau leptons at ATLAS is the topic of Chapter 6. Clearly this is an exciting time for particle physics. The discovery of a new particle, so far consistent with the Higgs boson, is a fantastic confirmation for the Standard Model. However, ATLAS and CMS are only just beginning to constrain its parameters and measuring the properties of the Higgs will continue to be a driving topic in the future runs of the LHC. There are also many interesting reasons to look for new physics at the TeV scale, to try to resolve the issues of whether nature has more (broken) gauge-symmetries, whether nature is supersymmetric, and what constitutes the dark matter, among others. Chapter 3 The LHC and ATLAS This chapter introduces the the Large Hadron Collider and the ATLAS experiment, including brief discussions of the ATLAS reconstruction, triggering, running conditions, simulation, and computing infrastructure. 3.1 The Large Hadron Collider The Large Hadron Collider (LHC) is currently the highest-energy particle collider in the world. The LHC is a discovery machine. Its purpose is to push the frontier of experimental high-energy particle collisions in both energy and luminosity. It enables experiments observing the collision products to test the agreement of the SM at higher energies than previous probed and to search for new physics, including hypothetical particles too massive or too weakly interacting to have been produced at previous generations of colliders. Analyses of data from the LHC have unprecedented potential to measure the properties of the Higgs boson and possibly to discover evidence for physics beyond the Standard Model, such as supersymmetry or evidence for grand unified theories. To probe the physics of the electroweak scale and beyond requires high-energy collisions. Figure 3.1 shows the production cross section for several processes of interest at hadron colliders. Note that the rate for electroweak physics processes including W , Z, and Higgs boson production, grows significantly with the center-of-momentum energy, √ s. From 2010–2012 the LHC collided protons with protons at a center-of-momentum energy7 of 7–8 TeV and with a peak luminosity of the order of 1032–1033 cm−2 s−1. The LHC is located near and operated by the European Organization for Nuclear Research (CERN) laboratory, outside Geneva, Switzerland. It is situated inside a ring-shaped tunnel, ap7 The Superconducting Super Collider (SSC) that was to be built near Dallas, TX in the 1990s would have created even more energetic proton-proton collisions, designed with √ s = 40 TeV, but it was cancelled by the US Congress in 1993 because its budget was not supported [56, 57]. 17 18 3. the lhc and atlas 0.1 1 10 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 ! ZZ ! WW ! WH ! VBF M H =125 GeV WJS2012 ! jet (E T jet > 100 GeV) ! jet (E T jet > "s/20) ! ggH LHCTevatron e v e n ts / s e c f o r L = 1 0 3 3 c m -2 s -1 ! b ! tot proton - (anti)proton cross sections ! W ! Z ! t ! ! ! ! (( ((n b )) )) "s (TeV) { Figure 3.1: Production cross sections from proton-(anti)proton collisions for several processes of interest as a function of center-of-momentum energy, √ s. The discontinuity at ≈ 4 TeV is from the difference in pp cross sections on the left for the Tevatron, and pp cross sections on the right for the LHC. The vertical lines indicate the center-of-momentum energy for the Tevatron at 1.96 TeV (2001-2011), for the LHC at 7 TeV (2010-2011) and 8 TeV (2012) and 13 TeV (target for future 2015 run) [54, 55]. 3.1 the large hadron collider 19 Figure 3.2: An illustration of the location of the LHC, facing south between the Alps and Jura mountain chains on the left and right respectively. The vertical dimension is exaggerated since the LHC is about 100 m underground and 27 km in circumference or 9 km in diameter [58]. proximately 100 m underground and 27 km (17 miles) in circumference, crossing the French-Swiss border four times. The same tunnel was used by the Large Electron-Positron Collider (LEP) from the years 1989 to 2000 (see Figure 3.2). The LHC and its experiments are technologically exceptional, pushing the boundaries of engineering complexity and scale in many ways. For example, approximately 100 metric tons of liquid helium are needed to cool the superconducting magnets in LHC to 1.9 K (-271.3◦C), making the LHC the largest cryogenic facility in the world at liquid helium temperature [59]. To process the data produced from the experiments at the LHC requires one of the largest world-wide distributed computing grids8 ever assembled, storing over 100 petabytes (1 PB = 1015 bytes = 106 GB). Finally, the experiments at the LHC are each massive technological undertakings, some with collaborations of scientists and engineers numbering in the thousands. There are four primary experiments at the LHC, each at a different point around the ring where 8 The LHC computing grid is discussed more in Section 3.7.1. The same pressures to organize and share information previously led CERN to develop the World Wide Web in the early 1990s [60, 61]. 20 3. the lhc and atlas Figure 3.3: The CERN accelerator complex for the LHC [62, 63]. the proton beams collide: ATLAS, CMS, ALICE, and LHCb. All four are designed to explore highenergy phenomena in the SM and to look for new physics. ATLAS and CMS are general purpose high-energy physics experiments. ALICE specializes in heavy-ion collision runs that happen for about a month per year of LHC operation. LHCb is optimized to study the physics of B meson decays. Each of these experiments have predecessors from previous generations of colliders, like the Tevatron, but they are now the flagship experiments in their sub-fields. The LHC is supported by the CERN accelerator complex to supply it with high-energy proton beams (see Figure 3.3). First, proton beams with an energy of 50 MeV per proton are provided by a linear accelerator, LINAC2, and passed through the Proton Synchrotron Booster (PSB) which raises the energy to 1.4 GeV. The beams are collected in the Proton Synchrotron (PS) where they are split into bunches of ∼ 1011 protons and accelerated to 25 GeV per proton. Then, the PS feeds the bunches to the Super Proton Synchrotron (SPS), in 3–4 batches of 72 bunches each. The SPS accelerates the beam to 450 GeV per proton and injects the beam into the LHC. The entire process can be repeated to fill the total number of bunches in the two independent, oppositely circulating, proton beams in the LHC. There were over a thousand bunches per beam in typical runs9 in the years 2011 and 2012. 9 The running conditions of the LHC will be discussed in more detail in Section 3.5. 3.1 the large hadron collider 21 Figure 3.4: An illustration of the relative sizes of the region enveloping the beam at the interaction point in ATLAS [64]. At the point of collisions the beams are squeezed in the transverse plane to be confined in an area of about 0.1 mm× 0.1 mm. After a complete fill, which usually takes less than 20 minutes, the LHC ramps the beam energy to its maximum of 3.5–4 TeV per proton in the timespan of about another 20 minutes. Then the beams are focused and brought into collision with √ s = 7–8 TeV. A run can last 12 hours or more before the beams have dissipated significantly and are safely dumped so that a new fill can be initiated. In the luminous region where the protons collide, or beamspot, the beams are squeezed in the transverse plane to be confined in an area of about 0.1 mm× 0.1 mm (see Figure 3.4). The primary vertices from collisions are distributed10 in z within about 10 cm, reflecting the approximate length of a bunch along the beamline. Most of the circumference of the LHC consists of the 1232 dipole magnets, each 15 m long with a 8.3 T magnetic field that provides the bending power to keep the beams in the ring. Unlike LEP, which produced e+e− collisions with a maximum energy of √ s = 209 GeV limited by the loss of beam energy due to synchrotron radiation, the LHC is limited by the bending power of the magnets. Table 3.1 summarizes some notable facts about the design of the LHC [62, 66]. 10 During the 2011 run, the typical beamspot where primary vertices were distributed had a width in the transverse plane of about 0.1 mm (2 σx = 2 σy) and about 10 cm long in ẑ (2 σz) [65]. Table 3.1: Some notable facts about the LHC. The LHC beam parameters are shown in more detail in Table 3.4. 27 km circumference ≈ 1000 bunches per beam 1232 dipoles: 15 m, 8.3 T ≈ 1011 protons per bunch 100 metric tons liquid He (1.9 K) bunch spacing: 50 ns pp collisions at √ s = 7–8 TeV bunch-crossing rate: 20 MHz instantaneous luminosity: 1032–1034 mean interactions per crossing: 1–40 revolution rate: 11.2 kHz ∼ 0.5× 109 interactions/second 22 3. the lhc and atlas Figure 3.5: An illustration giving an overview of the ATLAS experiment [68]. 3.2 The ATLAS experiment 3.2.1 Overview ATLAS [67, 68, 69] is a multi-purpose experiment inside the Point 1 cavern of the LHC tunnel designed to study a wide range of high-energy physics processes. ATLAS consists of several layers of sub-detectors. Starting from the interaction point and moving outwards11, there is the inner detector, the electromagnetic and hadronic calorimeters, and finally the muon spectrometer (see Figure 3.5). The collaboration supporting ATLAS has over 2900 members, coming from 177 different universities and laboratories in 38 different countries [70]. 3.2.2 Magnet systems Three types of superconducting magnet systems in ATLAS provide Tesla-level magnetic fields to bend the path of tracks inversely proportional to their momentum to enable tracking reconstruction 11 The ATLAS coordinate system [68] is a right-handed system with the x-axis pointing to the center of the LHC ring, the y-axis pointing upwards, and the z-axis following the beam line. The spherical coordinates φ and θ are defined in the usual way, with the azimuthal angle, φ, measuring the angle in the xy-plane from the positive x-axis, increasing towards positive y. The polar angle, θ, measures the angle from the positive z-axis, but this coordinate is often specified by the pseudorapidity, η, defined as η = − ln(tan θ 2 ). The transverse momentum pT, the transverse energy ET, and the missing transverse momentum E miss T ; are defined in the x-y plane. The distance ∆R in the η-φ space is defined as ∆R = √ ∆η2 + ∆φ2. 3.2 the atlas experiment 23 ATLAS Fact Sheet Central Solenoid Magnet ORQJPGLDPHWHUFPWKLFN WRQQHZHLJKW WHVOD7PDJQHWLFILHOGZLWKDVWRUHG HQHUJ\RIPHJDMRXOHV0- NPRIVXSHUFRQGXFWLQJZLUH 1RPLQDOFXUUHQWNLORDPSHUHN$  Barrel Toroid parameters P OHQJWK P RXWHUGLDPHWHU   VHSDUDWHFRLOV *- VWRUHGHQHUJ\ WRQQHV FROGPDVV WRQQHV ZHLJKW 7  PDJQHWLFILHOGRQ VXSHUFRQGXFWRU NP $O1E7L&XFRQGXFWRU N$ QRPLQDOFXUUHQW . ZRUNLQJSRLQWWHPSHUDWXUH NP VXSHUFRQGXFWLQJZLUH  ATLAS Magnet System Parameters for each End-cap Toroid  P D[LDOOHQJWK P RXWHUGLDPHWHU FRLOV FRLOVLQDFRPPRQFU\RVWDWHDFK *- VWRUHGHQHUJ\LQHDFK WRQQHV FROGPDVVHDFK WRQQHV ZHLJKWHDFK 7  PDJQHWLFILHOGRQVXSHUFRQGXFWRU NP $O1E7L&XFRQGXFWRUHDFK N$ QRPLQDOFXUUHQW . ZRUNLQJSRLQWWHPSHUDWXUH )RUFRPSDULVRQDQRUGLQDU\05,PDJQHWLQD KRVSLWDOKDVDPDJQHWLFILHOGRIWHVOD7 7KHWRURLGVDUHUDUHDQGYHU\LPSUHVVLYHWRVHH DQGWKHODUJHPDJQHWLFILHOGYROXPHLVTXLWH XQLTXH 4 Central Solenoid Barrel Toroid Endcap Toroid Bends charged particles for momentum measurement Figure 3.6: An illustration of the ATLAS magn t systems [70] to resolve the momentum of charged particles (see Figure 3.6). The multi-part magnet system is one of the most notable differences in the designs of ATLAS and CMS [71], which has a single 3.8 T solenoid surrounding its entire inner detector and calorimetry sub-systems. A summary of some of the key differences between the designs of the ATLAS and CMS experiments is given in Table 3.2. A central solenoid, 5.8 m long and 2.5 m in diameter, surrounds the ATLAS inner detector, and immerses it in a 2 T magnetic field along the beam axis (ẑ). The design of the central solenoid has been optimized to provide a high magnetic field while minimizing the material thickness to approximately 0.66 radiation lengths, since the central solenoid is inside the calorimeters. The flux is returned by the steel of the ATLAS hadronic calorimeter and its girder structure. Outside the calorimeters, a barrel toroid consisting of 8 independent coils, each 25.3 m long, provides a peak magnetic field of 4 T for bending tracks in the muon spectrometer. Two end-cap toroids provide a peak magnetic field of 4 T for bending tracks in the forward muon detectors. Both toroids produce magnetic fields circling along φ, bending muons in η [68]. 3.2.3 Inner detector The inner detector is designed to provide high precision tracking information for measuring the momentum and track parameters of charged particles. It consists of three sub-systems: the Pixel Table 3.2: Some of the key differences in the designs of the ATLAS and CMS experiments [68, 71]. ATLAS CMS length × diameter: 44 m × 25 m 25 m × 15 m magnet systems: 2 T solenoid (inside the calo.) 3.8 T solenoid (outside the calo.) 4 T air-core toroid EM calorimeter: 3-layer Pb-LAr sampling PbWO4 crystal 24 3. the lhc and atlas 43 Transition Radiation Tracker Pixel DetectorSCT Detector Inner Detector Barrel straws parallel z-axis Endcap straws radial Barrel modules overlap in z and q Endcap modules overlap im qEndcap discs differently sized Barrel modules overlap in z and q Dimensions radius 1150 mm full length 5600 mm coverage |d| < 2.5 Magnetic field solenidal, 2 T (central) Readout Channels (approx.) Pixels 80 mio SCT 6 mio TRT 400 000 Figure 4.5: The components of the ATLAS Inner Detector. The insets show details of the components of the three sub-detectors: the pixel detector, the SCT and the TRT[108]. Figure 3.7: An illustration of the ATLAS inner detector and its sub-systems [68, 72]. 3.2 the atlas experiment 25 detector, the Semi-Conductor Tracker (SCT) and the Transition Radiation Tracker (TRT). The Pixel detector consists of three finely-granulated layers of silicon detectors with approximately 80 M channels (about 90% of the total readout channels in ATLAS, see Table 3.3) to provide precise measurements of the tracking parameters near the interaction point. The first layer, the so-called B-layer, is essential for good secondary vertexing. The intrinsic accuracies in the barrel of the Pixels are 10 μm in R-φ and 115 μm in z. The Pixel detector has a very high hit efficiency of about 99%. The SCT surrounds the Pixel detector and is in turn enveloped by the TRT. Similar to the Pixel detector, the SCT uses silicon detector elements in small strips with intrinsic accuracies of 17μm in R-φ and 580 μm in z, and with a very high hit efficiency of about 99% [68]. The TRT is a gaseous straw-tube tracker with straws of 4 mm diameter that serve as the active elements. Each conducting straw body is held at a high negative voltage of typically -1.4 kV with an anode wire held at ground potential running down the center of the straw. A charged particle passing through a straw ionizes some of the Xe-CO2-O2 gas mixture in the straws, forming an avalanche onto the wire with a gain of a few times 104. The front-end electronics of the TRT amplify and digitize the ionization current read from the wire with two thresholds for discrimination. The low threshold12 provides the discriminant for tracking hits, and the high-threshold is sensitive to transition radiation [76, 77, 78, 79]. The width of the pulse in time, a result of the drift time of the avalanche, is sensitive to the distance from the wire to the track of a charged particle. Precise reading of the timing allows for a hit resolution of approximately 130μm. The measurement from a 12 The author designed the algorithm for calibrating the the low thresholds channel-by-channel to give a uniform noise occupancy, as described in Ref. [73]. He also contributed to studies of the TRT straw hit efficiency, as described in Refs. [74, 75]. Table 3.3: Number of readout channels per sub-detector in ATLAS for the primary sub-detectors (ignoring the minbias trigger system, luminosity monitors, and DCS sensors) [68]. inner detector Pixels 80 M SCT 6.3 M TRT 350 k EM calorimeter LAr barrel 110 k LAr end-cap 64 k hadronic calorimeter tile barrel 9.8 k LAr end-cap 5.6 k LAr forward calo. 3.5 k muon spectrometer MDTs 350 k CSCs 31 k RPCs 370 k TGCs 320 k total 88 M 26 3. the lhc and atlas Distance to wire [mm] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Ef fic ie nc y 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 ATLAS = 0.9 TeVs TRT barrel Data 2009 Monte Carlo (a) function of the relativistic ! factor is shown in Fig. 15 for particles in the forward region. This region is displayed because there are more conversion candidates and they have higher momenta than in the barrel. factor γ 10 210 310 410 H ig hth re sh ol d pr ob ab ilit y 0 0.05 0.1 0.15 0.2 0.25 0.3 ATLAS = 0.9 TeVs TRT end-caps Data 2009 Monte Carlo Pion momentum [GeV] 1 10 Electron momentum [GeV] 1 10 Figure 15: The fraction of high-threshold transition radiation hits on tracks as a function of the relativistic ! factor (see text for details). The high-! part of the distribution is constructed using electrons from photon conversions while the low-! component is made using charged particle tracks with a hit in the B-layer and treating them as pions. All tracks are required to have at least 20 hits in the TRT. The photon conversions are found similarly to those in Section 6.7 with at least one silicon hit, but the transition radiation electron identification was not applied to the electron that was being plotted. To ensure high purity (about 98%), the conversion candidates are also required to have a vertex more than 40 mm away from the beam axis. The pion sample excludes any photon conversion candidate tracks. 5.6 Tracking E!ciency for Level-2 Trigger The L2 track trigger is one component of the HLT whose performance can be tested with current data. The trigger runs custom track reconstruction algorithms at L2, designed to produce fast and e!cient tracking using all tracking subdetectors. Tracking information forms an integral part of many ATLAS triggers including electron, muon and tau signatures [16]. These use L1 information to specify a region of interest to examine. In the 2009 data there were few high-pT objects, so the results here are taken from a mode which searches for tracks across the entire tracking detector and is intended for B-physics and beam-position determination at L2. O"ine tracks with |d0| < 1.5 mm and |z0| < 200 mm are matched to L2 tracks if they are within #R = ! #"2 + ##2 < 0.1. The e!ciency is defined as the fraction of o"ine tracks which are matched and is shown in Fig. 16 as a function of the track pT. 16 Figure 3.8: (left) A plot of the TRT hit efficiency as a function of the distance of the track from the wire in the centre of the straw, for straws in the barrel of the TRT [75]. (right) A plot of the probability for a hit on a track to trigger the TRT high-threshold as a function of γ factor, for samples of pions and electrons in the TRT end-caps [68]. B th of hese plots use the first collision data taken in 2009 at √ s = 0.9 TeV and compare the corresponding distributions from Monte Carlo simulation. straw hit and its associated error are referred to as a "drift circle", being a measured distance from a track to a wire. The TRT straw hit efficiency is approximately 94% for tracks that are within the plateau of the efficiency, within about 1.3 mm of the wire (see Figure 3.8 (left)) [74, 75]. The Pixel detector and SCT cover a region of |η| < 2.5 in pseudo-rapidity, while the TRT reaches up to |η| = 2.0. A track typically crosses three layers of the Pixel detector. For the SCT barrel region the typical number of hits per track are eight, and the TRT typically provides about 36 hits per track. The TRT provides electron identification information through the detection of transition radiation in the xenon-based gas mixture of its straw tubes. Transition radiation photons are emitted when charged particles cross a boundary between media with different dielectric constants. In the TRT barrel, radiator mats of fine polypropylene/polyethylene fibers are situated perpendicular to the barrel straws, with punched holes that the straws pass through. Thin polypropylene foils are layered between wheels of radial straws in the TRT end-caps. When a charged particle with energy E and mass m crosses a transition of two materials with different dielectric constants, it has a probability proportional to γ = E/m to emit photons in the keV range (soft X-rays). These high-energy photons convert in the Xenon gas via the photoelectric effect and cause a large avalanche that triggers the high-threshold for a straw. This effect is more pronounced for electrons than pions because the small electron mass gives it a high γ-factor and correspondingly higher probability to fire the high threshold, as shown in Figure 3.8 (right). This provides electron identification13 [80] information that is completely uncorrelated with the shower-shape information used from the calorimeters. 13 Electron reconstruction and identification are introduced in Section 3.3.4. 3.2 the atlas experiment 27 Figure 3.9: An illustration of the ATLAS calorimeter and its sub-systems [68]. The transverse momentum resolution of the inner detector was measured with Z → μμ events in the 2010 collision data, and parametrized [81] as approximately σpT pT = 1.6–3.4% ⊕ 50–140% ( pT TeV ) , with better pT-resolution in the barrel than in the end-caps. 3.2.4 Calorimeters The ATLAS electromagnetic and hadronic calorimeters are designed to absorb and measure the energy of high-energy electrons, photons, and hadrons up to |η| < 4.9, and consist of the subsystems shown in Figure 3.9. Each sub-system is a type of sampling calorimeter, with alternating layers of a dense absorber material to help initiate an electromagnetic or hadronic shower, and layers of an active material for detecting the shower. The EM calorimeter consists of a barrel part (|η| < 1.475), two end-caps (1.375 < |η| < 3.2), and a presampler (|η| < 1.8) used to correct for the energy that electrons and photons lose upstream of the calorimeters. It is constructed with lead absorber plates layered between electrodes bathed in liquid argon (LAr), in an accordion-like geometry to maximize coverage. The EM calorimeter is finely segmented, with nearly 170k total readout channels. The region with |η| < 2.5 has significantly finer granularity, since it is within the acceptance of the ATLAS tracking system and needed for precise measurements of electrons and photons. Figure 3.10 shows the granularity of the readout 28 3. the lhc and atlas 2008 JINST 3 S08003 Δφ = 0.0245 Δη = 0.025 37.5mm/8 = 4.69 mm Δη = 0.0031 Δφ=0.0245x4 36.8mmx4 =147.3mm Trigger Tower TriggerTowerΔφ = 0.0982 Δη = 0.1 16X0 4.3X0 2X0 15 00 m m 47 0 m m η φ η = 0 Strip cells in Layer 1 Square cells in Layer 2 1.7X0 Cells in Layer 3 Δφ× Δη = 0.0245× 0.05 Figure 5.4: Sketch of a barrel module where the different layers are clearly visible with the ganging of electrodes in f . The granularity in h and f of the cells of each of the three layers and of the trigger towers is also shown. 5.2.2 Barrel geometry The barrel electromagnetic calorimeter [107] is made of two half-barrels, centred around the zaxis. One half-barrel covers the region with z > 0 (0 < h < 1.475) and the other one the region with z < 0 ( 1.475 < h < 0). The length of each half-barrel is 3.2 m, their inner and outer diameters are 2.8 m and 4 m respectively, and each half-barrel weighs 57 tonnes. As mentioned above, the barrel calorimeter is complemented with a liquid-argon presampler detector, placed in front of its inner surface, over the full h-range. A half-barrel is made of 1024 accordion-shaped absorbers, interleaved with readout electrodes. The electrodes are positioned in the middle of the gap by honeycomb spacers. The size of the drift gap on each side of the electrode is 2.1 mm, which corresponds to a total drift time of about 450 ns for an operating voltage of 2000 V. Once assembled, a half-barrel presents no – 114 – Figure 3.10: An illustration of th ATLAS barrel EM calorimet r and the granularity of its readout cells [68]. cells in the various layers of the barrel EM calorimeter. The first layer of the barrel EM calorimeter is a presampler layer (not shown), divided into readout cells with ∆η×∆φ = 0.025× 0.1. The next layer, Layer 1, is even more finely segmented in η. It has thin strip-shaped cells with ∆η ×∆φ = 0.025/8×0.1 to provide a good position measurement for the shower and good separation of prompt photons from the double-peaks of π0 → γγ decays. Layer 2 is the thickest layer, having about 16 radiation lengths and cells in a grid with ∆η ×∆φ = 0.025 × 0.025. Layer 3 is doubly coarse in η, with ∆η ×∆φ = 0.0 × 0.025, and measures the tail of an electromagnetic show r. The hadronic tile calorimeter is a sampling calorimeter covering |η| < 1.7, using steel as the absorber and scintillating tiles as the active material. There are three layers of readout cells, with the finest layer having a granularity of ∆η × ∆φ = 0.1 × 0.1. The region with 1.7 < |η| < 3.2 is covered by the Hadronic End-cap Calorimeter (HEC), placed directly behind the end-cap EM calorimeter. It uses copper as the absorber and LAr as the active material, with the granularity of finest layer of readout cells being ∆η × ∆φ = 0.1 × 0.1. Finally, the Forward Calorimeter (FCal) covers the most forward region up to approximately 3.1 < |η| < 4.9 and consists of three modules 3.2 the atlas experiment 29 Figure 3.11: An illustration of the ATLAS muon spectrometer and its sub-systems [68]. in each end-cap, the first made of copper and the other two of tungsten, with LAr as the active material. The energy resolutions of sub-sections of the ATLAS calorimeter were measured in studies using π± and electron test-beams in an independent setup at CERN before the start-up of the LHC, and were parametrized [68] as approximately σE E = 10%√ E/GeV EM calorimeter, σE E = 56%√ E/GeV ⊕ 6% hadronic barrel, σE E = 70%√ E/GeV ⊕ 6% hadronic end-cap, σE E = 94%√ E/GeV ⊕ 8% forward calorimeter. 3.2.5 Muon spectrometer Muons with pT & 4 GeV have enough energy to not curl back before reaching the ATLAS muon spectrometer, which provides measurements of muon track parameters. In the central barrel part of the muon spectrometer, the large barrel toroid provides the magnetic field for muons with |η| < 1.4. 30 3. the lhc and atlas For 1.6 < |η| < 2.7, the magnetic field is provided by two end-cap toroid magnets, while for the transition region 1.4 < |η| < 1.6 it is provided by a combination of the barrel and end-cap fields. Three layers of Monitored Drift Tubes (MDTs) are used over most of the η-range for the precision measurement of muon tracks in the bending direction of the magnetic field in η. Cathode Strip Chambers (CSCs) are used in the innermost plane for 2 < |η| < 2.7. Finally, to obtain the muon φ-coordinate in the direction orthogonal to the precision-tracking chambers, as well as for triggering, Resistive Plate Chambers (RPCs) are used in the barrel and Thin Gap Chambers (TGCs) in the end-caps. Combined, there are approximately 1.2 M readout channels in the muon spectrometer (see Figure 3.11). The transverse momentum resolution of the muon spectrometer was measured with Z → μμ events in the 2010 collision data, and parametrized [81] as approximately σpT pT = 0–6% ( 4 GeV pT ) ⊕ 4–9% ⊕ 23–30% ( pT TeV ) , with better performance in the barrel and end-caps than in the transition region. The inner detector provides the best measurement at low to intermediate momenta, whereas the muon spectrometer takes over above ≈ 30 GeV. 3.3 Reconstruction 3.3.1 Introduction Offline reconstruction software processes the raw data from ATLAS to find the signatures of high-pT particles streaking through the detector. The primary reconstructed objects are tracks in the inner detector and muon spectrometer, and clustered energy deposits in the calorimeter. Dedicated reconstruction algorithms search for electrons, photons, muons, jets, b-jets, hadronic tau decays, and reconstruct the missing transverse momentum. ATLAS developed the Athena framework [82], which divides the reconstruction problem into several algorithms, tools, and detailed representations of the detector geometry and conditions. The output of reconstruction14 is generally a set of collections of candidates for electrons, muons, etc. Athena reconstruction produces two types of output files: ESDs and AODs (see Figure 3.12). Event Summary Data (ESD) files contain the outputs of basic calibration and pattern recognition algorithms, including hits and drift circles in the tracking systems and detailed cell-based information from the calorimeters, as well as the full derived objects from object-level reconstruction like electrons, muons, jets, etc. The ESD includes sufficient information to re-run basic-level reconstruction, including tracking and clustering. Analyses Object Data (AOD) files contain a smaller subset 14 The ATLAS computing infrastructure for reconstruction, analysis, production of MC is discussed in Section 3.7. 3.3 reconstruction 31 ESD AOD RDO Reconstruction Analysis Object Data (AOD) 1-2 MB/event 100-200 kB/event 1-2 MB/event Figure 3.12: An illustration of the inputs and outputs of ATLAS reconstruction. Raw Data Object (RDO) files are typically the input to reconstruction (event size: 1–2 MB/event). Event Summary Data (ESD) files are produced, containing the hitand cell-level information as well as the reconstructed objects (1–2 MB/event). The reconstruction also produced Analysis Object Data (AOD) files, containing a sub-set of the information in the ESD intended for use in analyses (100–200 kB/event). of the data in an ESD, giving the derived objects intended for use by analyses, including tracks, vertices, and all derived objects, but not the full hitand cell-based information. An analysis will typically define a preselection of objects with a loose selection and basic quality requirements. Pre-selected electrons and muons are then used to remove overlapping candidates for hadronic tau decays or jets in a selection process called overlap removal. Then, an analysis typically defines an object selection, resulting in the accepted objects later used in the event selection15. 3.3.2 Tracking Tracks are reconstructed from the hits produced by charged particles passing through the inner detector. First, the primary track-finding forms space-points in the Pixel and SCT detectors and builds track-segments that later seed inside-out track-finding that extrapolates a track outward and associates hits in the TRT. The track parameters on the surface of each active detector element (pixel, strip, or straw) are determined from a combined fit of the hits on a track using track extrapolation 15 Since reconstructed candidates for electrons, jets, taus, etc. can all arise from the same track or clustered energy deposit, the reconstruction is not unique and has overlapping candidates. Typically analyses select objects in the order: muons, electrons, taus, and then jets, as needed, removing overlapping candidates if they are selected. More details about overlap-removal and the object selection used in analyses is discussed in Sections 5.4.3 and 6.3. 32 3. the lhc and atlas Trk::Extrapolator The ATLAS Track Extrapolation Package, ATL-SOFT-PUB-2007-005 Extrapolates track parameters from one surface to another. Stochastically models material e!ects. Errors get worse with the distance propagated. I constrain the extrapolation to TRT hits, only extrapolating between them. Holes are any TRT straws crossed by the extrapolator between hits.Ryan Reece | Penn | ryan.reece@cern.ch | TRT Straw E!ciency 3 / 15 5 p track d0 ex ey ez p T x-y plane z0 φ θ Figure 3: The perigee representation expressed in the ATLAS track parameterisation. The local expression of the point of closest approach is given by the signed transverse impact parameter d0 and the longitudinal impact parameter z0. The momentum direction is expressed in global coordinates using the azimuthal angle   that is defined in the projected x   y plane and the polar angle ✓, which is measured with respect to the global z axis. Neutral Parameters Recently, the ATLAS tracking EDM has been extended to deploy a dedicated schema for neutral particle representations [8]. The fifth parameter of the representation as given in Eq. (1) is hereby modified to represent 1/q, omitting the charge definition. Charged and neutral trajectory representations are realised through the same templated class objects to avoid code duplication, while keeping the type diversity to prevent misinterpretations to happen during the reconstruction flow. The extrapolation package and propagation tools have been adapted to cope with both charged and neutral types, but the ATLAS Track class remains restricted to charged trajectories2. Neutral parameters are only transported along a straight line to the provided target surface. Material e↵ects are not taken into account and thus the navigation process is not necessary in this context. This documents concentrates therefore on the extrapolation process of charged track representations and will only briefly mention the particularities for neutral parameterisation in the various di↵erent modules. 2 Propagation The mathematical propagation of track parameters to a destination surface is - when omitting energy loss and multiple scattering e↵ects - determined by the starting parameters and the traversed magnetic field. A homogenous magnetic field setup (no field or constant field value and direction) allows to use an underlying parametric track model for the propagation. Many propagation processes can then be solved purely analytically to find the intersection of the track with the destination surface and even for the transported covariances. However, the highly inhomogeneous magnetic field of the ATLAS detector setup requires tracking of particles by numerical methods. Figure 4 shows the magnetic field of the ATLAS detector in an r   z projection for both, the Inner Detector in detail, and the Muon Spectrometer. The variety of the di↵erent propagation techniques is enhanced by di↵erent implementations of a common abstract AlgTool interface, the IPropagator. The interface for propagator AlgTool classes is kept very simple; it reflects the pure principle of the task: an input TrackParameters object, a destination surface, magnetic field properties and a boolean for the surface bound handling is passed through the method signature, while on the other hand the propagated parameters are returned as the method value. Returning a pointer to a new object puts the responsibility of memory cleanup onto the client algorithm, but complies fully with the factory pattern design described in Sec. 1.2. The following main interface methods are defined for the IPropagator interface: • The propagate() method shall be used in cases when the track parameters to be transported are likely to carry a covariance matrix and the client algorithm relies on the transported error description as well. If the input parameters do not have associated errors, only the parameters are transported to the destination surface. • To save CPU time, the propagateParameters() that only performs the transport of the pa2This is because neutral particles are not subject of tracking in the classical terms of track finding and track fitting. Figure 3.13: (left) An illustration of a typical extrapolation process within a Kalman filter step. The track parameters on an active layer of the detector, Module 1, are propagated onto the next measurement surface, resulting in the track prediction on Module 2. The traversing of the material layer betwe n the two modules is accounted for by inflati the uncertainties on the track parameters. The final resulting measurement of the track parameters (shown in red) is improved by co bination of all the hits on track. (right) An illustration of the perigee parameters for a track: the longitudinal coordinate along the beamline, z0, and the impact parameter, d0, being the distance-of-closestapproach of a track to the beamline in the transverse plane [83]. tools and the Kalman filtering method, which takes into account the smearing of a track from multiple scattering when going through material in the detector and a detailed map of the magnetic field (see Figure 3.13 (left)). A second outside-in tracking reconstruction builds track segments from the remaining hits and in the TRT, and extr polates backwards t combine hits in the silicon detectors [83, 84]. The most important track parameters are reconstructed at the perigee point, the point along the track that is closest to the beamline. Figure 3.13 (right) illustrates the z0 parameter, giving the the longitudinal position of a track along the beamline, and the d0 parameter, giving the distance of the perigee point from the beamline in the transverse plane. The z0 parameter has a resolution of approximately 100μm, and is often used to select tracks near a particular vertex. The d0 parameter has a resolution of approximately 10μm, and is important for selecting or suppressing in-flight decays such as muons from B meson decays, and is used in tagging b-jets and hadronic tau decays [68]. 3.3 reconstruction 33 Figure 3.14: An event display of a eeμμ candidate event from a search for H → ZZ∗ → 4` with the 2011 dataset [85]. The masses of the lepton pairs are 76.8 GeV and 45.7 GeV, and the event has m4l = 124.3 GeV. The tracks from the muon candidates are traced in blue. The electron candidates are absorbed in the calorimeter and traced in red [86]. 3.3.3 Muons Muon candidates are primarily seeded by track segments found in the muon spectrometer as standalone muon candidates and matched to tracks in the inner detector, forming combined muon candidates. More inclusive selections can use segment-tagged muons, which did not successfully form a stand-alone muon candidate, but have a muon segment matching an inner-detector track [69, 68]. As an example of muon candidates in the ATLAS detector, Figure 3.14 shows an event display of a ZZ∗ → eeμμ candidate event. Analyses discussed in this document preselect muon candidates with |η| < 2.5, pT > 10 GeV, and passing various quality cuts discussed in Chapters 5 and 6. These quality requirements correspond to a muon reconstruction and identification efficiency of approximately 95% for combined muons in 34 3. the lhc and atlas Figure 3.15: An event display of an e+ candidate in a W+ → e+ν candidate event in the ATLAS 2010 run. The positron track is traced in yellow and the energy deposit in the EM calorimeter is indicated in yellow as well. High-threshold hits in the TRT are indicated by the red dots. The positron has pT = 23 GeV and η = 0.6. The missing transverse momentum, EmissT , was measured to be 31 GeV and its direction is indicated by the red line from the beam axis. The transverse mass of the combination of the positron and the EmissT is 55 GeV [86]. the majority of the combined acceptance of the muon spectrometer and inner detector (|η| < 2.5), dipping to 80% in the most central (η ∼ 0) and crack regions between the barrel and end-caps [87]. 3.3.4 Electrons and photons Electron candidates are reconstructed by matching clustered energy deposits in the EM calorimeter to tracks found in the inner detector. Electron reconstruction is seeded by clusters found in the EM calorimeter with a sliding-window algorithm [69], independent of the topological clusters used to build jets. Then, tracks are matched with the EM clusters, resulting in electron candidates if they have a track and photon candidates if they are without a track. Special attention is payed to tagging electrons that are actually from converted photons by finding the secondary vertex, since about half of the high-pT photons in ATLAS will have a conversion before reaching the EM calorimeter [68]. Figure 3.15 shows an event display of a selected electron candidate in ATLAS in a W → eν candidate event. Analyses discussed here typically preselect electron candidates if they have pT > 15 GeV, |η| < 2.47, are not in the barrel-end-cap transition region where 1.37 < |η| < 1.52 (also called the "crack" re3.3 reconstruction 35 65 φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 1 10 Presampler φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 1 10 10 2 10 3 ECAL Front φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 1 10 10 2 10 3 10 4 ECAL Middle φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 1 10 10 2 10 3 ECAL Back φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 10 10 2 10 3 10 4 Tile 1 φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 1 10 Scintillator φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 1 10 10 2 10 3 Tile 2 φ 2 2.2 2.4 η -1.2 -1 -0.8 -0.6 1 10 Tile 3 |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 Presampler |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 ECAL Front |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 ECAL Middle |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 ECAL Back |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 HEC1 Front |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 HEC1 Back |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 HEC2 Front |η5-| -2.5 -2 -1.5 -1 -0.5 0 | η 5- | -2.5 -2 -1.5 -1 -0.5 0 HEC2 Back Figure 7.7 A topological cluster in the barrel (top) and end-cap (bottom). Figure 3.16: Plots of the energy in MeV distributed in η × φ cells in each layer of the barrel calorimeter for a single topological cluster from a simulated charged pion. Each pane shows a different layer of the calorimeter but within the same η × φ range [92]. gion), and pass ATLAS cut-based identification [88, 89]. The identification thins the list of electron candidates considered, rejecting fa es from charged and neutral pions by requiring track quality criteria, strict track-cluster matching, cuts on EM calorimeter shower shapes, and by requiring highthreshold hits in the TRT. The cut-based identification has tight, medium, and loose working points. The medium working point is the most commonly used, and has a high-pT electron efficiency of near 90% for a few percent fake rate for charged pions [90]. 3.3.5 Clustering Energy deposits in the calorimeter are grouped into three-dimensional clusters using a topological clustering technique [91], incorporating both the EM and hadronic layers of the calorimeter. The standard topological clustering algorithm in ATLAS uses the 4-2-0 method, where clusters are seeded by cells that are 4 times the noise level for that cell, ranging from approximately 30 MeV to 3 GeV, increasing in |η| [68]. Then, adjacent cells are added to the cluster if they are over 2 times the noise level, and then any cells adjacent to those are added as well. Figure 3.16 shows an illustration of a topological cluster from a simulated charged pion in the ATLAS barrel calorimeter, showing the variety of cell granularities between layers of the calorimeter that are all combined 3.16. Topological clusters are used to assemble reconstructed jets and hadronic tau decays as described in the following sub-sections. 36 3. the lhc and atlas 3.3.6 Jets As a consequence of the strength of the strong interaction and its confining properties discussed briefly in Appendix A.2.5, out-going scattered quarks or gluons produce additional quarks and gluons almost immediately to nullify any free color charge. An out-going quark or gluon, struck out of a proton in the colliding beams, goes through a hadronization process where multiple (meta)stable hadrons are produced, resulting in a spray of nearby energy deposits in the calorimeters called a "jet". An industry of algorithms has grown for finding jets by appropriately associating clustered energy deposits. The process of jet reconstruction uses such a jet-finding algorithm to identify jets, and produces a collection of reconstructed four-momenta for the initial scattered out-going partons. Sophisticated techniques are used to calibrate the energy of jets depending on things such as the geometry of the jet with respect to the detector and the primary vertex, parametrizations for the amount of expected additional energy deposited due to in-time and out-of-time pile-up16, the number reconstructed primary vertices, and the bunch position in time within the trains of adjacent proton bunches in the LHC [93]. For the analyses discussed here, jets are reconstructed with the anti-kt algorithm [94] with distance parameter R = 0.4, taking as input three-dimensional topological clusters [91] of the cells in both the EM and hadronic calorimeters. The clusters are corrected for dead material and outof-cluster energy losses, and the energy scale is calibrated with the local hadron calibration scheme (LC) [95], where the energy is split and corrected for each cluster in a jet [93]. Jets with pT > 25 GeV, |η| < 4.5, and passing some recommended cleaning criteria17, are preselected. Especially for the highest luminosity runs (L ∼ 1033 cm−2 s−1) in the later part of 2011 and throughout 2012, it is not rare for secondary pile-up interactions to produce jets. For jets within the tracking acceptance, one can select jets with energy deposits consistent with coming from the primary reconstructed vertex with a quantity called "jet-vertex fraction" (JVF) [98, 99]. JVF is in general a function of any pairing of a jet and a primary vertex within an event. First, tracks are matched to the jet in question (fundamentally a calorimeter-based object) if the ∆R between the tangent vector of a track extrapolated to the beamline and the jet axis is less the size of the R-parameter used for the jet (typically 0.4 in this work). Then, JVF is defined as the fraction of the scalar sum of the transverse momentum of those matching tracks that are associated with the 16 See the discussion of pile-up in Section 3.5.2. 17 Jet cleaning cuts are described in more detail on JetEtMiss twiki internal documentation pages [96] and in Appendix B of Ref. [97]. 3.3 reconstruction 37 ∑ PV pT(track)∑ all pT(track) Fraction of track p from the prima vertex. !"#$%"&'()"*)+ !#,)-.!'()"*)+ !#,)-.!'()"*)+ beamline Jet-vertex fraction (JVF) 0 0.2 0.4 0.6 0.8 1 F ra c ti o n o f je ts 0 0.1 0.2 0.3 0.4 0.5 0.6 (R=0.4) jets t Anti-k , 450ns pile-up-1s-2 cm 32 10 2.0!| " 20 GeV, |# T p Hard-scatter jets Jets from pile-up Figure 3.17: (left) A diagram illustrating tracks from pile-up vertices (in red) falling on a tau candidate (in blue). Conceptually, JVF is the fraction of the scalar sum of the pT of the tracks pointing to the jet seeding the tau candidate that are associated with the chosen primary vertex (i.e. the fraction of the scalar some of the blue and red tracks that is blue). (right) The distribution of JVF from ATLAS simulation for jets truthmatched to the hard-scatter (in red) and jets from pile-up interactions (in blue) for events with L ≈ 1032 cm−2 s−1, corresponding to 〈Nvertex〉 ≈ 5 [99]. vertex in question. That is, JVF(jeti, vertexj) ≡ ∑ k pT(trackk)|vertexj∑ n ∑ ` pT(track`)|vertexn , k ∈ {tracks matching jeti from vertexj} , ` ∈ {tracks matching jeti from vertexn} , n ∈ {vertices} , where k runs over over all tracks matched to jeti from vertexj , where ` runs over over all tracks matched to jeti from vertexn, and n runs over all the reconstructed primary vertices in the event. Figure 3.17 (left) shows an illustration of a jet with nearby tracks from additional pile-up vertices, in which case JVF would be calculated as the ratio of the sum of the pT of the blue tracks (which are associated to the denoted "primary vertex" in question) to that of the combination of the blue and red tracks (which includes pile-up tracks from other vertices). In the language of the ATLAS Collaboration, the "JVF of a jet" often denotes the JVF of that jet and the primary vertex with the highest ∑ p2T of tracks, which is often the vertex of interest for most selections. JVF gives a natural way to quantify how associated a jet is to the hard-scatter interaction. For jets with a substantial fraction of matching tracks coming from the hard-scatter vertex, JVF will be nearly 1, while for jets consistent with coming from pile-up activity, JVF will be closer to 0 (see 38 3. the lhc and atlas Figure 3.17 (right)). For jets without matching tracks, most likely due to being too forward to be accepted by the tracker, JVF is set to -1. Analyses discussed here require |JVF| > 0.75 for jets within |η| < 2.4. Finally, jet candidates that overlap with preselected electron or selected18 hadronic tau candidates within ∆R < 0.2 are removed from consideration. 3.3.7 Hadronic tau decays Tau leptons are the only known leptons massive enough to have hadronic decays, which makes them somewhat similar to B mesons in that they have hadronic signatures that can be tagged with about a 50% efficiency for a few percent or sub-percent fake rate. They decay hadronically approximately 65% of the time, to predominantly either one or three charged pions, with possibly a few additional neutral pions. The ATLAS reconstruction of hadronic tau candidates is seeded by each reconstructed calorimeter jet with pT > 10 GeV and |η| < 2.5. Tracks are associated to the jets, and variables are calculated from the combined tracking and calorimeter information to discriminate hadronic tau decays from fakes and from other hadrons and electrons [100, 101, 102, 103]. Hadronic tau decays can be distinguished in the large multijet background by the close association of one or three tracks with a narrow clustering of EM and hadronic calorimeter activity that is characteristic of hadronic tau decays. Figure 3.18 is an event display of a μτh event with two jets, typical of the type of events studied in this thesis. It illustrates that a hadronic decay has a low track multiplicity and is much more isolated than the deposits associated with the jets in the event from QCD production. The most sophisticated methods of tau identification also make use of the significance of a reconstructed secondary vertex if there is one for 3-track candidates. Multivariate discriminants based on Boosted Decision Trees (BDTs) have been developed to discriminate hadronic tau decays from fakes. One BDT-based discriminant has been developed to discriminate hadronic tau decays from jets produced in strong interactions, and a separate BDTbased discriminant has been developed to reject electrons. Fakes from muons with tracks that happen to overlap with calorimeter clusters are more easily suppressed by removing candidates overlapping with preselected muons, and with a cut-based muon veto. The reconstruction and identification of hadronic tau decays is discussed in more detail in Chapter 4. For the analyses discussed here, tau candidates are preselected if they have pT > 25 GeV, |η| < 2.47 and not in the crack region where 1.37 < |η| < 1.52, and have 1 or 3 core tracks. Core tracks are the tracks associated to a tau candidate, selected to be consistant with the primary vertex associated with the tau candidate, and within ∆R < 0.2 of the tau axis, defined with respect to the η, φ of the 18 See the discussion of selection and preselection in Section 3.3.1. 3.3 reconstruction 39 Figure 3.18: An event display of a μτh + 2 jet candidate event from a search for tt events with hadronic tau decays in the 2011 dataset [104]. The muon track is shown in red, has positive reconstructed electric charge, and pT = 20 GeV. The 3-track tau candidate is shown at the lower right, has negative charge, and pT = 53 GeV [86]. calorimeter jet that seeded the tau candidate [101]. Tau candidates are removed from consideration if they overlap with preselected electron or muon candidates within ∆R < 0.2. 3.3.8 Missing transverse momentum The production of neutrinos or any hypothetical new weakly-interacting particle with some significant pT will result in a imbalance in the vector sum of transverse momentum of all particles produced in the hard scatter. Conceptually, the missing transverse momentum, EmissT (or MET), is reconstructed from the negative vector sum of the transverse momentum of everything reconstructed in the event: ~EmissT = − ∑ ~pT . ATLAS has a so-called refined method of calculating the EmissT , where the terms in the vector sum are calibrated independently for each type of high-pT object (electons, muons, jets, etc.). Additional terms account for the soft jets and remaining calorimeter cells not associated with an identified object [105]. 40 3. the lhc and atlas Fig. 1. ATLAS TDAQ diagram. Black labels are design values, red labels are 2012 peaks. design rate while continuously increasing the instantaneous94 luminosity. Month in 2010 Month in 2011 Month in 2012 Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Pe ak in te ra ct io ns p er c ro ss in g 0 5 10 15 20 25 30 35 40 45 50 = 7 TeVs = 7 TeVs = 8 TeVs ATLAS Online Luminosity Fig. 2. Evolution of peak number of interactions per bunch crossing(μ). 95 During 2011, L1 is operated at ⇠65 kHz in order to prevent96 excessive dead time. This corresponded to a data transfer rate97 of approximately 80 GB/s from RODs to ROSes. In parallel,98 L2 and EF rates are increased to ⇠5.5 kHz and ⇠600 Hz,99 resulting in ⇠6.5 GB/s event building and ⇠700 MB/s event100 storage rates respectively. Furthermore, disk sizes of the five101 Data Logger nodes are increased to keep the pace with the102 data rate.103 Additionally, HLT computing resources were incremented104 by ⇠50% by introducing new nodes through a rolling replace-105 ment policy though this led to an increased heterogeneity of106 the both network and CPU resources of the HLT farms.107 During 2012 winter shutdown, another sixteen of the XPU108 racks were replaced and an additional BE network core router109 was installed to provide redundancy. Meanwhile, ROS soft-110 ware was modified to collect calorimeter summary information111 from all calorimeter front-end electronics and make it available112 to L2. This provided a possibility to allow trigger selection113 based on missing transverse energy at L2. Substantial effort114 was also dedicated to improve monitoring tools, bottleneck115 prediction and automatic recovery procedures and they are116 described in [5].117 B. Pileup dependency118 The cost of achieving nearly the design luminosity at119 the half the bunch-crossing rate was resulted in higher120 than expected average number of interactions per bunch-121 crossing (hμi). Figure 2 shows the evolution of hμi since the122 start of LHC operation in 2010. In 2012 data taking period123 hμi is more than doubled compared to 2011. Even though124 L1 and HLT output rates are stayed about the same in both125 years, aside from a 1 kHz rise to 6.5 kHz in L2 output rate,126 data rates are increased in 2012 due to increase in event127 sizes. Figure 3 shows the evolution of the average event size128 accepted by different trigger algorithms with respect to number129 of events per bunch crossing (pileup). Event size seems to130 linearly depend on pileup. Extrapolations to hμi = 35 was131 consistent with the average event size which is later observed132 as 1.6 MB. However at higher pileup, event size might change133 observed linear behavior. CPU time also depends on pileup as134 can be seen in figure 4. Newer generation of nodes in HLT135 farms are utilized at about 60%. However, older nodes are136 approaching their processing limit. Yet, it does not pose a137 threat to TDAQ until the long LHC shutdown since it can138 be mitigated by load balancing through changing the numbers139 and types of nodes in L2 and EF. There are approximately140 8000 L2 and 8000 EF processes in TDAQ at the time of this141 writing.142 III. EVOLUTION143 The LHC will undergo maintenance and upgrade in 2013144 and 2014. In 2015 it is expected to start operating at full design145 Figure 3.19: The design of the ATLAS trigger and DAQ architecture, indicating the event rate passing the trigger levels on the left, and showing the flow of the data volume on the right. The numbers in black indicate the design specifications and the numbers in red indicate th peak running conditions in 2012 [106]. 3.4 Triggering ATLAS has a three-level trigger architecture for reducing the dat rate from co lisions. The first level (L1) uses custom hardware based on ASICs and FPGAs, while level 2 (L2) and third level Event Filter (EF) uses software algorithms running on farms of commercial CPUs [68]. Figure 3.19 illustrates the design of the ATLAS trigger and data acquisition system (DAQ). 3.4.1 Level 1 The L1 trigger uses coarse information from calorimeters and muon systems, but no information from the inner detector. It reduces the bunch-crossing rate of 20 MHz by approximately a factor of 300 to about 65 kHz for events accepted by L1. It quickly identifies Regions of Interests (RoIs) in ∆η × ∆φ that are passe to th L2 algorithms for further investigation. Da a streaming from the detector are buffered in custom front-end hardware waiting for a L1 accept within a latency of less than 2.5 μs. Events passing L1 ar s to detector-specific Read Out Drivers (ROD) to be assembled and pushed to the dedicated memories on Read Out System (ROS) PCs. 3.4 triggering 41 Minimum Bias Electrons/photons Jets/taus/missing ET Muons/B-physics ATLAS Trigger Operation 2011 Figure 3.20: The Event Filter (EF) bandwidth used by each trigger stream as function of time in the year 2011 [107]. 3.4.2 Level 2 The L2 trigger receives RoI-based information from L1 and fetches only the data in these regions from respective ROSes, where the full event data is buffering. The L2 trigger applies a set of fast and coarse selection algorithms on RoI data to reduce the event rate by approximately a factor of ten, from 65 kHz to 6.5 kHz with an average latency of 40 ms. A L2 accept initiates the Event Builder (EB) which retrieves all of the event data from the ROSes, together with L2 results. The EB assembles the full event data and assigns it to Event Filter (EF) process. 3.4.3 Event filter The EF has access to full event data and the same functionalities as the offline reconstruction. It applies detailed objectand event-level selection algorithms to reduce the event rates by about a factor of ten, from 6.5 kHz to about 500 Hz. Each EF process uses about four seconds on average to reach a decision. Accepted events are recorded in permanent storage at CERN [106]. The data are accepted in different streams19 depending on the type of trigger that fired, leading to different files. The main physics streams are called Muons, Egamma, and JetTauEtMiss for events triggered by muons, electrons/photons, and jet/tau/EmissT -based signatures, respectively. Figure 3.20 shows the EF bandwidth used by each trigger stream as function of time in the year 2011. 19 The ATLAS trigger streams are inclusive in that an event with both signatures can end up in both the muon and egamma streams. 42 3. the lhc and atlas 3.5 Running conditions and dataset 3.5.1 Overview After many months in 2008 of ATLAS doing commissioning runs triggering on cosmic ray muons, the LHC delivered the first proton-proton collisions in the LHC at √ s = 900 GeV on November 23, 2009. A few μb−1 of integrated luminosity of minbias events were collected in the following weeks that were used for further commissioning studies of the performance of ATLAS [75]. The first substantial dataset for physics analysis came in 2010 with approximately 36 pb−1 of integrated luminosity at the record-breaking energy of √ s = 7 TeV. This dataset allowed ATLAS to make many of its first electroweak SM measurements, including measurements of the W and Z boson production cross sections [108, 109], pT distributions of W and Z bosons [110, 111], and the tt cross section [112]. The measurement of the cross section of Z → ττ at ATLAS [113] is the topic of Chapter 5. Improvements in the number of bunches per beam and the other beam parameters allowed the luminosity of LHC to continue to climb throughout 2009–2012. Figure 3.21 shows distributions of the number of bunches per beam, the peak instantaneous luminosity, and the peak number of interactions per bunch crossing as a function of time. Table 3.4 summarizes typical ranges for some of the important beam parameters of the LHC in different years of running 3.4. The reach of searches for the Higgs boson and new physics at ATLAS were significantly extended with the higher-luminosity runs (∼ 1033cm−2 s−1) in 2011, with approximately 5 fb−1 of integrated luminosity at √ s = 7 TeV, and in 2012, with 21 fb−1 of integrated luminosity at √ s = 8 TeV. Figure 3.22 (left) shows the integrated luminosity vs time for the years 2010, 2011, and 2012. 3.5.2 Pile-up The increase in luminosity of the LHC has led to an increase of pile-up, the overlapping of the detector response from multiple proton-proton interactions within the same event. Pile-up can be in-time, due to the presence of additional proton-proton interactions in the same bunch crossing as Table 3.4: Milestones of some of important beam parameters of the LHC for 2009 to 2012 [66, 115]. design 2009 2010 2011 2012 center-of-momentum energy, √ s [TeV] 14 0.9–2.4 0.9–7 7 8 peak luminosity [cm−2 s−1] 1034 1026 1027–1033 1022–1033 1033 max bunches per beam 2808 9 348 1331 1380 protons per bunch 1011 1010 1011 1011 1011 mean interactions per crossing 23 0 0–2.2 2–20 10–35 3.5 running conditions and dataset 43 Month in 2010 Month in 2011 Month in 2012 Jan Ap r Jul Oct Jan Ap r Jul Oct Jan Ap r Jul Oct C o lli d in g B u n c h e s 0 200 400 600 800 1000 1200 1400 1600 1800 2000 = 7 TeVs = 7 TeVs = 8 TeVs ATLAS Online Luminosity Month in 2010 Month in 2011 Month in 2012 Jan Ap r Jul Oct Jan Ap r Jul Oct Jan Ap r Jul Oct ] -1 s -2 c m 3 3 P e a k L u m in o s it y [ 1 0 0 2 4 6 8 10 = 7 TeVs = 7 TeVs = 8 TeVs ATLAS Online Luminosity Month in 2010 Month in 2011 Month in 2012 Jan Ap r Jul Oct Jan Ap r Jul Oct Jan Ap r Jul Oct P e a k i n te ra c ti o n s p e r c ro s s in g 0 5 10 15 20 25 30 35 40 45 50 = 7 TeVs = 7 TeVs = 8 TeVs ATLAS Online Luminosity Figure 3.21: Distributions of the number of colliding bunches per beam, the peak instantaneous luminosity, and the peak mean number of interactions per bunch crossing, as a function of time for the years 2010–2012 [114]. 44 3. the lhc and atlas Month in Year Jan Ap r Jul Oct ] -1 D e liv e re d L u m in o s it y [ fb 0 5 10 15 20 25 30 35 = 7 TeVs2010 pp = 7 TeVs2011 pp = 8 TeVs2012 pp ATLAS Online Luminosity Mean Number of Interactions per Crossing 0 5 10 15 20 25 30 35 40 45 /0 .1 ] -1 R e c o rd e d L u m in o s it y [ p b 0 20 40 60 80 100 120 140 160 180 Online LuminosityATLAS > = 20.7μ, <-1Ldt = 20.8 fb∫ = 8 TeV, s > = 9.1μ, <-1Ldt = 5.2 fb∫ = 7 TeV, s Figure 3.22: (left) The integrated luminosity delivered by the LHC as a function of time for the years 2010–2012. (right) The distribution of the mean number of interactions per bunch crossing, μ, for the √ s = 7 TeV run in 2011 and the √ s = 8 TeV run in 2012 [114]. Figure 3.23: A close-up event display of the reconstructed primary vertices in a Z → μμ event in the 2012 dataset with 25 vertices. The tracks from the muons are highlighted with thick yellow lines [86]. the primary interaction, or out-of-time, due to the remaining detector response from previous bunch crossings. In the year 2010 (the dataset used for the Z → ττ cross section measurement discussed in Chapter 5), the instantaneous luminosity of the LHC climbed from 1× 1027 to 1033 cm−2 s−1, with the average number of interactions per bunch crossing (μ) typically ranging from 0 to 2.2. In the year 2011 (the dataset used for the Z ′ search discussed in Chapter 6), the instantaneous luminosity was typically 1–4× 1033 cm−2 s−1, with μ = 2–20. In 2012, the luminosity stayed of the order of 1033 cm−2 s−1 with the mean number of interactions per bunch crossing ranging up to 40. Figure 3.22 (right) compares distributions of the mean number of interactions per bunch crossing for the 2011 and 2012 datasets. Tracking-related quantities can often be defined in a pile-up robust way by only considering tracks associated with a chosen vertex [102, 116]. Figure 3.23 shows a close-up event display of reconstructed primary vertices in a Z → μμ event in the 2012 dataset with 25 reconstructed vertices. The precision 3.6 simulation 45 tracking capabilities of the inner detector allow the vertices to be reliably distinguished, and for one to usually associate muon candidates to the correct primary vertex. The proper timing of the detector, fast restoration of the readout electronics, noise suppression, clustering, etc. are expected to sufficiently suppress the effects of out-of-time pile-up such that intime pile-up is the leading contributor of additional clusters in the calorimeter [117]. The effects of pile-up on the reconstruction of hadronic decays of tau leptons will be discussed in some detail in Section 4.4.9. 3.6 Simulation As a very important comparison for understanding the composition of the events and distributions in the data, ATLAS generates fully simulated Monte Carlo samples that behave like the raw data from the detector. Monte Carlo samples used in this analysis were produced as part of the ATLAS mc08, mc09, mc10, mc11c, and mc12a production campaigns. 3.6.1 Generation In the ATLAS simulation infrastructure [118], first Monte Carlo matrix element generators produce the primary kinematics from simulated proton-proton scattering events. Final-state quarks and gluons go through a simulated hadronization step producing the out-going hadrons. Unless otherwise noted, background processes from W and Z + jets events were generated with Alpgen [119]. Samples of tt, Wt, and diboson events (WW , WZ, and ZZ) were generated with MC@NLO [120]. For all of these Monte Carlo samples, the simulated parton shower and hadronization was done with Herwig [121] interfaced with Jimmy [122], specially tuned for the underlying event at ATLAS [123]. Samples of s-channel and t-channel single top events were generated with AcerMC [124], with the parton shower and hadronization done with PYTHIA [125]. Signal samples representing hypothetical Z ′ decays consistent with the SSM were generated with PYTHIA. The effects of QED radiation were generated with PHOTOS [126], and hadronic tau decays were generated with TAUOLA [127]. 3.6.2 Detector simulation After generation, the detector response for each Monte Carlo sample was fully simulated with a GEANT4 [128] model of the ATLAS detector, with a detailed description of the geometry and amount of material. Activity from multiple pile-up interactions per bunch crossing was modeled by overlaying simulated minimum bias events, generated with PYTHIA and specially tuned for 46 3. the lhc and atlas ATLAS Computing Technical Design Report 20 June 2005 54 3 Offline Software The stages in the simulation data-flow pipeline are described in more detail in the following sections. In addition to the full simulation framework, ATLAS has implemented a fast simulation framework that reduces substantially the processing requirements in order to allow larger samples of events to be processed rapidly, albeit with reduced precision. Both these frameworks are described below. 3.8.2 Generators Event generators are indispensable as tools for the modelling of the complex physics processes that lead to the production of hundreds of particles per event at LHC energies. Generators are used to set detector requirements, to formulate analysis strategies, or to calculate acceptance corrections. They also illustrate uncertainties in the physics modelling. Generators model the physics of hard processes, initialand final-state radiation, multiple interactions and beam remnants, hadronization and decays, and how these pieces come together. The individual generators are run from inside Athena and their output is converted into a common format by mapping into HepMC. A container of these is placed into the transient event store under StoreGate and can be made persistent. The event is presented for downstream use by simulation, for example by G4ATLAS simulation (using Geant4) or the Atlfast simulation. These downstream clients are shielded thereby from the inner details of the various event generators. Each available generator has separate documentation describing its use. Simple Filtering Algorithms are provided, as well as an example of how to access the events and histogram the data. Figure 3-5 The simulation data flow. Rectangles represent processing stages and rounded rectangles represent objects within the event data model. Pile-up and ROD emulation are optional processing stages. Generator HepMC Particle Filter MCTruth(Gen) Simulation MCTruth (Sim) Pile-Up HitsDigitizationROD Input Digits MCTruth (Pile-up)Merged Hits ByteStream ConversionSvc ROD Emulation Algorithm ROD Emulation (passthrough) Raw Data Objects ByteStream ATLAS Reco Figure 3.24: The flow of the ATLAS sim lation software, from event generators (top-left) through to the reconstruction (bottom-left). Additional minimum bias pile-up events are generated and overlaid. Monte Carlo truth is saved in addition to energy depositions in the detector (hits). Digitiz tion si ulates the read-out el ctronics and RODs to give simulated raw data that is processed with the Athena reconstruction like the data from ATLAS [82]. minimum-bias interactions at the LHC [129], over the original hard-scattering event. Then the Monte Carlo was processed by sub-detector-specific digitization algorithms, which translate the particle signatures in the detectors into raw byte-stream data of the form that comes from the ATLAS detector. Finally, the fully simulated RDOs are reconstructed with an appro riate release of the ATLAS Athena reconstruction software just like the processing of the real data. Figure 3.24 illustrat s the process of produ ing ATLAS Monte C rlo simul tion, beginni g at the generator in the top-left, going through the GEANT4 simulation, generating and merging pile-up events, through digitization, an pushed through the ATLAS reconstruction. 3.6.3 Corrections and scale factors The accuracy in modeling several effects by the ATLAS simulation is corrected and validated in control samples of th data, including effects like trigger and identification effic encies and the distribution of the number of primary vertices20. Generally, scale factors are used as parametrized corrections, derived i c ntrol samples to bring the Monte Carlo into agreement with the data. This can significantly improve the accuracy of the yields predicted by the simulation. The systematic 20 See the discussion of primary vertex re-weighting in Section 5.3.2. 3.7 computing 47The ATLAS Collaboration: Electron performance measurements with the ATLAS detector 19 [GeV]eem 40 50 60 70 80 90 100 110 120 130 Ev en ts / G eV 10 210 Data Fit Signal (BWCB) Background ATLAS <25 GeVTE20 GeV< =7 TeV,sData 2010, ∫ -140 pb≈tdL [GeV]eem 40 50 60 70 80 90 100 110 120 130 140 Ev en ts / G eV 1 10 210 310 Data Fit Signal (template) Background ATLAS <40 GeVTE35 GeV< =7 TeV,sData 2010, ∫ -140 pb≈tdL Fig. 12. The distributions of the dielectron invariant mass of Z ! ee candidate events, before applying electron identification cuts on the probe electron, in the ET-range (left) 20 " 25 GeV and (right) 35 " 40 GeV. The data distribution (full circles with statistical error bars) is fitted with the sum (full line) of a signal component (dashed line) modelled by a Breit-Wigner convolved with a Crystal Ball function (BWCB) on the left or by a MC template on the right, and a background component (dotted line) chosen here as an exponential decay function convolved with a Gaussian. [GeV]eem 2 2.5 3 3.5 4 Ev en ts / 0. 1 G eV 0 500 1000 1500 2000 2500 3000 Data Fit Signal Background SS data ATLAS <7 GeVTE4 GeV< =7 TeV,sData 2010, ∫ -140 pb≈tdL [GeV]eem 2 2.5 3 3.5 4 Ev en ts / 0. 1 G eV 0 50 100 150 200 250 300 350 400 450 Data Fit Signal Background SS data ATLAS <15 GeVTE10 GeV< =7 TeV,sData 2010, ∫ -140 pb≈tdL Fig. 13. The distributions of the dielectron invariant mass of J/! ! ee candidate events, before applying electron identification cuts on the probe electron, in the ET-range (left) 4 " 7 GeV and (right) 10 " 15 GeV. The data distribution (full circles with statistical error bars) is fitted with the sum (full line) of a signal component (dashed line) described by a Crystal Ball function and two background components, one taken from same-sign pairs in the data (dash-dotted line) and the remaining background modelled by an exponential function (dotted line). chosen isolation threshold, to the number of selected electron probes. Figure 14 shows the I!R=0.4 distribution for the data in two regions of phase space: a low-ET bin, 20 < ET < 25 GeV, where the background contribution is high, and the ET bin, 35 < ET < 40 GeV, which has the largest fraction of the signal statistics and a very high signal-tobackground ratio. Samples obtained after background subtraction Once the background subtraction procedure has been well defined, the next step in the process of measuring the e!ciencies of the electron identification criteria (relative to electron reconstruction with additional track silicon hit requirements, as described above) is to define the total numbers of signal probes before and after applying the identification cuts, together with their statistical and systematic uncertainties. The ratios of these two numbers in each ET-bin or !-bin are the e!ciencies measured in data. Table 5 shows several examples of the numbers of signal and background probes and of the corresponding signal-to-background ratios (S/B) for the three channels and for selected ET-bins. The S/B ratios were found to be fairly uniform as a function of ! for a given channel and ET-bin. In contrast, as expected, the S/B ratios imFigure 3.25: The distributions of the dielectron invariant mass of Z → ee candidate events, efore applying electron identification cuts on the probe electron, in the ET-range 20–25 GeV (left) and 35–40 GeV (right) [90]. uncertainties on the scale factors estimated in thes performance studies are primary sources of systematic uncertainties for analyses of ATLAS data. A common method for deriving a sc le factor is the tag-and-probe method. Essentially it i volves selecting a control sample for which the purity can be estimated, without requiring the identification requirement in question. As an example21, consider the Z → ee tag-and-probe study of the electron identification efficiency. Z → ee events are tagged by selecting events with a single tight electron and another "probe" candidate, without the full identification requirements. Then the efficiency of requiring that identification is compared with data and Monte Carlo simulation. The ratio of data to Monte Carlo is parametrized (as a function of pT, η, . . . ) to be used as a scale factor to weight Monte Carlo events. It is important that the fake electron background is estimated and subtracted in the calculation of the efficiency. Figure 3.25 shows distributions of the dielectron invariant mass in the Z → ee tag-and-probe sample, before requiring electron identification on the probe electron. 3.7 Computing 3.7.1 Infrastructure The demands of the ATLAS computing infrastructure include the real-time processing and reconstruction of the data accepted by the Event Filter at 500 MB/s, large-scale production of Monte Carlo simulation, large-scale re-reconstruction and derived-data production for both ATLAS data and simulation, and analysis jobs from ATLAS collaborators world-wide. 21 Also see the discussion of the tau identification efficiency measurement using a Z → ττ tag-and-probe sample in Section 4.4.6. 48 3. the lhc and atlasThe ATLAS Distributed Computing: the challenges of the future Hiroshi Sakamoto 3 The LHC accelerator delivered 23fb-1 integrated luminosity in 2012 at the collision Fig.4. Progress of the total volume of data files managed by the DQ2 data management system since October 2008. It reached to 140PB at the end of 2012. Fig.5. Progress of the number of files managed by the DQ2 data management system since October 2008. The number of files exceeded 350 million files 0 2E+14 4E+14 6E+14 8E+14 1E+15 1.2E+15 2012/1/1 0:00 2012/2/1 0:00 2012/3/1 0:00 2012/4/1 0:00 2012/5/1 0:00 2012/6/1 0:00 2012/7/1 0:00 2012/8/1 0:00 2012/9/1 0:00 2012/10/1 0:00 2012/11/1 0:00 2012/12/1 0:00 Transfer Volume by Day US UK TW NL ND IT FR ES DE CERN CA 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 2012/1/1 0:00 2012/2/1 0:00 2012/3/1 0:00 2012/4/1 0:00 2012/5/1 0:00 2012/6/1 0:00 2012/7/1 0:00 2012/8/1 0:00 2012/9/1 0:00 2012/10/1 0:00 2012/11/1 0:00 2012/12/1 0:00 Transfer Efficiency by Day Failure Success Fig.6. Transfered volume and success rate of all file transfers of ATLAS per day in 2012.Annual record of transfers and success rates in 2012. The upper graph shows the total volume per day, and the lower graph shows the success rate per day. The average success rate throughout the year 2012 is 92.8%. 100PB 300million 1PB Figure 3.26: (left) Locations of the sites of WLCG computing centers with an orange spot indicating tier-0 at CERN, green spots indicating the 10 tier-1 centers, and blues spots indicating tier-2 centers [130]. (right) The amount of data available to ATLAS users on the WLCG grid, including replicas, as a function of time. By the end of 2012, the data volume exceeded 140 PB = 140 million GB [131]. To satisfy these demands the LHC collaborations have formed the largest existing scientific computing grid, the Worldwide LHC Computing Grid (WLCG). The WLCG utilizes over 100,000 CPUs in more than 170 computing centers located within 36 countries. In the US, this includes the resources of the Open Science Grid (OSG). Figure 3.26 (left) indicates the locations of WLCG sites around the world. Combining data and Monte Carlo production, the four large experiments at the LHC produce about 25 PB of data per year [130]. By the end of 2012, the combined distributed data volume from ATLAS data and Monte Carlo, including replicas, exceeded 140 PB (see Figure 3.26 (right)). The WLCG has a tiered architecture, with tier-0 being a ∼ 1000 CPU computer farm at CERN doing the real-time first-pass reconstruction of the data from ATLAS (see Figure 3.27). The output ESDs and AODs are archived at tier-0. The AODs and a fraction of the ESDs are copied to the 10 tier-1 centers around the world and a few additional replicas are distributed among the tier-2 sites, numbering over a hundred. The data are flattened in large scale productions of ROOT [133] compatible ntuples, denoted "D3PDs", which are als istributed among tier-1 nd tier-2 sites. Users doing analysis often produce more derived ntuples on the grid, and then download them to a private computing cluster or tier-3 where further analysis is done. 3.7 computing 49 NS61CH05-Bird ARI 14 September 2011 12:2 2.3.6. Virtual organization agents. A mechanism is provided to permit experiment-specific services to be run in a standard way at grid sites. The experiment takes responsibility for the management of the service, although the site manages the underlying hardware. 2.3.7. Information service. An information service provides a lookup point for information published by each of the service instances, describing its configuration and details of, for example, the storage and computing resources. 2.3.8. Application software. The experiment application software is regularly updated and must be made available at each site. A suite of standard utilities are also provided. 2.3.9. Interoperability. The WLCG grid infrastructure relies on large national and international grid projects for some of the underlying tools and support services. The major science grid infrastructures are the OpenScience Grid (OSG) in the United States and the European Grid Infrastructure (EGI) in Europe. The latter is the successor to the EGEE and NorduGrid projects, and it coordinates the various national grid initiatives. WLCG works closely with these infrastructures to ensure interoperability, even though they may use different base middleware and tools. 3. DEVELOPMENT AND EVOLUTION OF THE EXPERIMENTS' COMPUTING MODELS All the experiments' computing models were based on the MONARC model discussed above. However, each experiment based its implementation on different key choices, which has resulted in quite distinct models. These models have also evolved after having been tested at scale. Each of the experiments has developed a software layer that integrates its applications with the distributed computing environment. The computing model used by ATLAS (Figure 5) (9) is the closest in concept to the MONARC model. Raw data from the detector are sent to Tier 0 at !320 MB s"1; these data are then archived Tier 2s Monte Carlo production User analysis ATLAS Tier 0 (Re)reconstruction Organized analysis Generation of raw data Reconstruction Calibration and alignment Tier 1 Tier 1 Tier 1 Figure 5 The ATLAS computing model. 108 Bird A nn u. R ev . N uc l. Pa rt. S ci . 2 01 1. 61 :9 911 8. D ow nl oa de d fr om w w w .a nn ua lre vi ew s.o rg by C ER N L ib ra ry o n 07 /0 5/ 12 . F or p er so na l u se o nl y. Figure 3.27: An illustration of the tiered structure of the ATLAS computing infrastructure [132]. Figure 3.28: An illustration of the flow of ATLAS data as it is reconstructed and analyzed on the WLCG computing grid. The process of producing Monte Carlo simulation and pushing it through the same reconstruction and user analysis is also shown [134]. 50 3. the lhc and atlas 3.7.2 Data reduction The data from ATLAS are reduced significantly by reconstruction and selection. Figure 3.28 re-caps the flow of ATLAS data and Monte Carlo. Starting at the top-left, the ATLAS data that pass the 3-level trigger system are recorded and reconstructed, producing the AODs, ESDs, and later D3PDs (collectly denoted "reco" in Figure 3.28). Note that Monte Carlo production involves processing the simulation through the same reconstruction and analysis procedures as the data from the ATLAS detector. In analysis steps, a user may produce and iterate on one or more cycles of derived ntuples, and usually produce several plots to visualize the data. The sequence of progressively reduced data formats used can be summarized as RAW → RDO → AOD/ESD → D3PD ( → skimmed D3PD → personalized ntuple ) . Table 3.5 summarizes the typical sizes per event of the various data formats. Table 3.5: A summary of the size per event for various ATLAS data formats [135]. data format size per event raw data 1–2 MB ESD 1–2 MB AOD 100–200 kB D3PD 100–200 kB personalized ntuple (TNT) 2–3 kB Chapter 4 Tau reconstruction and identification In this chapter, I describe the ATLAS reconstruction of hadronic tau decays and many of the advancements in tau identification and calibration during 2010–2012. In particular, I focus on topics to which I personally contributed including: the first comparisons of ATLAS data and Monte Carlo for tau identification variables in minimum-bias events in 2009, the development of the first cut-based tau identification used with ATLAS data in 2010, the pT-parameterized tau identification, and studies of fake rates and pile-up robustness, but I also try to pedagogically review other major developments, which helps to introduce many of the technical issues and systematic uncertainties involving reconstructed taus, used by the analysis discussed in the following chapters. 4.1 Introduction Having a mean lifetime of 2.9× 10−13 seconds (cτ ≈ 87 μm), tau leptons decay before leaving the ATLAS beam pipe. Tau leptons can decay leptonically, either to eνeντ (branching ratio, BR ≈ 17.9%) or to μνμντ (BR ≈ 17.4%). In the remaining majority of cases (BR ≈ 64.7%), tau leptons decay hadronically, being the only leptons massive enough to do so (mτ ≈ 1.8 GeV). These hadronic final states predominantly consist of one or three charged pions, along with a neutrino, and possibly with a few additional neutral pions. There are also rarer decays involving kaons, with a branching fraction of 2.9%. The hadronic decays of tau leptons are generally categorized by the number of charged decay products, that is, the number of tracks or "prongs" observable in the detector. Hadronic 1-prong decays are the most common (BR ≈ 49.5%), followed by 3-prong decays (BR ≈ 15.2%). Figure 4.1 illustrates the approximate branching ratios of the tau lepton. Throughout this thesis, "1-prong" refers to the hadronic decay modes with a single track, excluding the leptonic decays of the tau lepton. 51 52 4. tau reconstruction and identification Figure 4.1: The approximate branching ratios of the dominate decay modes of the tau lepton. For the decays within the hadronic mode, the branching ratios are shown as the fraction of the total hadronic mode and not the fraction of all decays. A majority of hadronic decays of the tau lepton go through the intermediate mesons: ρ±(770 MeV) IG(JPC) = 1+(1−−) τ → ν ρ± → π± π0 ν 26% of BR(τ) , corresponding to 39% of the hadronic mode, and a±1 (1260 MeV) 1 −(1++) τ → a±1 ν → π± π0 π0 ν 9% of BR(τ) τ → a±1 ν → π± π± π∓ ν 9% of BR(τ) , each corresponding to 14% of the hadronic mode [136]. The challenge when identifying hadronic tau decays at high-energy hadron colliders is that the cross section for QCD production of quark or gluon initiated jets, which can be falsely identified as tau decays, is many orders of magnitude above the cross sections for weak interaction processes involving tau leptons22. Indeed, most of the tracks reconstructed in the ATLAS inner dectector are from charged pions from inclusive QCD processes. Reconstructing and identifying hadronic tau decays involves distinguishing tau-like groupings of pions from other generic pions. The most discriminating features for identifying taus among the multijet background are the characteristic 1or 3-prong signature of a hadronic tau decay, consequently low track multiplicity, relatively narrow 22 For example, the jet production cross section is approximately 4× 103 nb for inclusive jets with pT > 60 GeV and |η| < 2.8 [137], while the cross section for W → τhν production is 6.8 nb at √ s = 7 TeV [138]. 4.2 tau reconstruction 53 clustering of tracks and depositions in the calorimeters, and the existence of a possible displaced secondary vertex. 4.2 Tau reconstruction 4.2.1 Overview The reconstruction of candidates for hadronically decaying tau leptons occurs late in the ATLAS reconstruction chain. Tracks and clusters have already been reconstructed, and clusters have been grouped with jet-finding algorithms (see Section 3.3). Tau reconstruction can be split into the following steps. First, tau reconstruction is seeded by each reconstructed jet. Then, the list of calorimeter clusters associated to each tau candidate23 is refined and calibrated to calculate the four-momentum. Tracks are then associated to the candidate, and a list of identification variables is calculated for each candidate from the combined tracking and calorimeter information. Last, these variables are combined into multivariate discriminants to reject fake candidates from QCD jets and electrons [100, 101, 102, 103]. 4.2.2 Seeding Tau reconstruction is seeded by calorimeter jets, reconstructed with the anti-kt algorithm [94], using distance parameter R = 0.4, from three-dimensional topological clusters [91] of the cells in both the EM and hadronic calorimeters. Each such jet with pT > 10 GeV (at the EM-scale) and within |η| < 2.5, (the η-range of the ATLAS tracking system) is considered as a tau candidate. The reconstruction efficiency for true hadronic tau decays is nearly 100% for tau candidates with pT & 15 GeV and |η| . 2.3, however, this efficiency is only to get a reconstructed candidate in the calorimeter, irrespective of the track association. After associating reconstructed tracks to the candidate, the efficiency to correctly identify 1and 3-prong suffers some track-finding inefficiency24 for each track, degrading the efficiency to correctly reconstruct 3-prong with 3-tracks more than that of 1-prong (see Figure 4.2). 23 There's been perhaps too much debate about notation in ATLAS [139], although I agree that one should be clear. My conventions in this thesis are "1-prong" tau decays are hadronic only. The symbol "τh" denotes the visible sum of a hadronic tau decay, but not the neutrinos. So I would write "Z → ττ → μτh3ν". And "pT(τh)" makes sense, as the visible, reconstructible transverse momentum of a hadronic tau decay, not including the neutrinos. I also often write and say "tau candidate", intending it to be short for a "reconstructed candidate for a tau lepton that decayed hadronically". But I am generally careful to reserve a lone "tau" to refer to the lepton, or to emphasize "tau lepton". 24 Within the ATLAS Tau Performance Group, to incorrectly reconstruct the number of tracks for a hadronic tau decay is often called"track migration", referring to the migration from one bin to another in the distribution of the number of reconstructed tracks (see Figure 4.5). Some effort to mitigate the track association inefficiency with respect to pile-up will be discussed in Section 4.2.5. Issues with tracking inefficiency at high-pT will be discussed in Section 4.4.7. 54 4. tau reconstruction and identification (GeV)visibleTE 0 10 20 30 40 50 60 70 80 90 100 R e c o n s tr u c ti o n e ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 All candidates s!candidates matched with truth s!candidates matched with truth 1 prong s!candidates matched with truth 3 prong ATLAS R e c o n s tr u c ti o n e ff ic ie n c y R e c o n s tr u c ti o n e ff ic ie n c y R e c o n s tr u c ti o n e ff ic ie n c y visible# -3 -2 -1 0 1 2 3 R e c o n s tr u c ti o n e ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 All candidates s!candidates matched with truth s!candidates matched with truth 1 prong s!candidates matched with truth 3 prong ATLAS R e c o n s tr u c ti o n e ff ic ie n c y Figure 4.2: The reconstruction efficiency of true hadronic decays of tau leptons as a function of EvisibleT and η visible from a sample of MC W → τν events (mc08) [140]. of tau candidate (GeV)TE 0 10 20 30 40 50 60 70 80 90 100 F ra c ti o n o f c a n d id a te s -510 -410 -3 10 -210 calo-seeded only both seeds track-seeded only ATLAS econstructed candidates (left) and reconstructed candidates Figure 4.3: The overlap between track and calorimeter seeds as a function of ET in a Monte Carlo sample of true W → τhν decays (mc08) [140]. Historically, ATLAS developed two independent reconstruction algorithms for hadronic tau decays: the calorimeter-seeded tauRec, which used the jet seeding described above, and the trackseeded tau1p3p, which was seeded by inner-detector tracks with pT > 6 GeV. Figure 4.3 shows the overlap between track and calorimeter seeds as a function of ET in a Monte Carlo sample of true W → τhν decays. In 2009, since the track seeds were effectively a subset of the calorimeter seeds, the tauRec algorithm became the preferred reconstruction seed, and the identification variables calculated by the two algorithms were merged [140]. 4.2.3 Four-momentum definition The reconstructed four-momentum of a tau candidate is defined in terms of three degrees of freedom: pT, η, and φ. The η and φ are taken from the seed jet, and are determined by calculating the sum of the four-vectors of the constituent topological clusters, assuming zero mass for each of 4.2 tau reconstruction 55 the constituents [93]. The mass of tau candidates is defined to be identically zero, and therefore transverse momentum, pT, and transverse energy, ET = E sin θ, are identical. Because hadronic tau decays consist of a specific mix of charged and neutral pions, the energy scale of hadronic tau candidates is calibrated independent of the jet energy scale with a Monte Carlo based calibration procedure using the clusters within ∆R < 0.2 of the seed jet barycenter axis. The tau energy calibration is described later, in Section 4.4.5. 4.2.4 Track counting Tracks are associated to each tau candidate if they are within the core cone, defined as the region within ∆R < 0.2 of the axis of the seed jet, and pass the following quality criteria: • pT > 1 GeV, • number of pixel hits ≥ 2, • number of pixel hits + number of SCT hits ≥ 7, • |d0| < 1.0 mm, • |z0 sin θ| < 1.5 mm, where d0 is the distance of closest approach, in the plane transverse to the beamline, of the track to the selected primary vertex (discussed in the next section), while z0 is the distance of closet approach along the beamline. Tau candidates are classified as singleor multi-prong, depending on the number of tracks counted in the core cone. The charge of a tau candidate is reconstructed as the sum of the charges of the associated tracks in the core cone. Tracks within the isolation annulus, defined by 0.2 < ∆R < 0.4 of the axis of the seed jet, are also counted for variable calculations, and are required to satisfy the same track quality criteria. 4.2.5 Vertex selection In order to select the vertex representing the interaction of hardest-scatter in an event, typically analyses select the vertex with the highest ∑ p2T of the tracks associated to it. As discussed in the previous section, it is important to define a vertex with which to calculate z0 and d0 for selecting the tracks to associate to a tau candidate. As the instantaneous luminosity, and consequently the number of reconstructed vertices per event grew at the LHC, the probability also grew for a tau candidate to originate from a vertex without the highest ∑ p2T, and therefore fail to have its track 56 4. tau reconstruction and identification 0.4 0.2 pile-up tau underlying event calculate REM, Rtrack in cone count # tracks in cone ∆R Number of Tracks 0 1 2 3 4 5 6 7 8 9 10 A rb it ra ry U n it s 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 15 GeV<p ATLAS Preliminary Figure 4.4: (left) A sketch illustrating things that can affect tau identification, and that the core tracks are counted in ∆R < 0.2, while many ID variables are calculated in ∆R < 0.4. (right) The Ntrack distribution for simulated hadronic decays of taus in MC W → τν and Z → ττ events, and the distribution for a selection of dijet background events from both the 2010 data and compared with PYTHIA dijet MC (mc09) [100]. selected (see Figure 4.5). While initially the ATLAS tau reconstruction chose the vertex with the highest ∑ p2T, it was improved beginning in 2012 to choose the vertex with the highest JVF 25 for that tau candidate. This method selects the vertex to which a significant fraction of the tracks pointing at that tau candidate are associated, improving the efficiency to select the correct vertex and core tracks, even in the high pile-up scenario with μ ≈ 40 [102]. 4.3 Tau identification 4.3.1 Identification variables As every seed jet forms a tau candidate, the reconstruction of tau candidates provides virtually no rejection against the multijet background to hadronically decaying tau leptons. This rejection is achieved in a separate identification (ID) step, using discriminating variables that are calculated during the reconstruction. In this section, the distributions of some of the most important variables are shown, and the use of those variables in tau identification is discussed. As discussed previously, hadronic tau decays can be distinguished from generic QCD jets because they are generally narrow and well isolated, with one or three tracks. Three of the most important 25 JVF is discussed in some detail in Section 3.3.6. 4.3 tau identification 57 Number of tracks 0 1 2 3 4 1 -p ro n g ! N u m b e r o f s e le c te d 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 =0μ =20μ =20 with TJVAμ Simulation Preliminary ATLAS (a) True .Figure 4.5: (left) The reconstruction efficiency to correctly select the track from a 1-prong hadronic decay as a function of μ in MC Z → ττ events from mc11, using track selection with respect to the "Default" vertex with the highest ∑ p2T, or with respect to the vertex with the highest JVF, called "Tau Jet Vertex Association (TJVA)" in this figure. (right) The Ntrack distribution in ideal MC with no additional pile-up (μ = 0), compared to the distribution with significant pile-up (μ = 20), showing both the Default and TJVA vertex selection (mc11) [102]. tau identification variables used by the cut-based identification quantify the narrowness of a tau candidate in the calorimeter, the close association of the calorimeter activity with one or three tracks, and the momentum fraction carried by the leading track. They are: Electromagnetic radius (REM): the transverse energy weighted shower width in the electromagnetic (EM) calorimeter: REM = ∑∆Ri<0.4 i∈{EM 0−2} ET,i ∆Ri∑∆Ri<0.4 i∈{EM 0−2} ET,i , where i runs over cells in the first three layers of the EM calorimeter (pre-sampler, layer 1, and layer 2), associated to the tau candidate. Track radius (Rtrack): the pT weighted track width: Rtrack = ∑∆Ri<0.4 i pT,i ∆Ri∑∆Ri<0.4 i pT,i , where i runs over all core and isolation tracks of the tau candidate, and pT,i is the track transverse momentum. Note that for candidates with only one track, Rtrack simplifies to the ∆R between the track and the tau candidate axis. 58 4. tau reconstruction and identification Leading track momentum fraction (ftrack): ftrack = ptrackT,1 pτT , where ptrackT,1 is the transverse momentum of the leading pT core track and p τ T is the transverse momentum of the tau candidate, calibrated at the EM energy scale. Note that for candidates with one track, ftrack is the fraction of the candidate's momentum attributed to the track, compared to the total momentum of the candidate, which can have contributions from the calorimeter deposits from π0s and other neutrals. A more complete list of the definitions of the various tau identification variables is given in Appendix B. Distributions of these and other tau identification variables are shown in Figures 4.6 and 4.12-4.14, showing ATLAS simulation of Z → ττ and W → τν for signal, and comparing simulation of dijet events with a sample of dijet events in the 2010 data for background. Table 4.3 shows which identification variables were used by the ATLAS jet-tau discriminants to analyze the 2010 dataset [100]. 4.3.2 Cut-based jet-tau discrimination After the preliminary first collisions at the LHC at √ s = 900 GeV in 2009, efforts in ATLAS began converging to deliver tau discriminants for the first record-energy collisions at √ s = 7 TeV in 2010, the year ATLAS would collect its first significant sample of W and Z boson decays. The simple cutbased identification was optimized with only three of the well-studied variables, and binned in the number of reconstructed core tracks, being one or many. The three variables used are those discussed in the previous section and quantify: the narrowness of the tau candidate in the calorimeter, the close association of the seed jet and the selected tracks, and the fraction of the reconstructed momentum carried by the leading track [141]. The cuts were optimized in three separate working points, called "loose", "medium", and "tight", which are approximately 60%, 50%, and 30% efficient to reconstruct and identify hadronic tau decays with the correct number of tracks. The optimization used a cross-section-weighted sample of fully simulated W → τν and Z → ττ decays to model the signal. A fully simulated sample of dijet events was used to model the background. Figure 4.6 shows distributions of the variables used by the cut-based tau identification, for both signal and background samples, as well as the critical values of the cuts for the identification working points. The working points were optimized by exhaustively constructing each possible combination of cuts on the three variables in reasonably spaced steps, and evaluating their signal and background efficiencies. The combinations that gave efficiencies near the loose/medium/tight targets were then 4.3 tau identification 59 selected and sorted by background efficiency. The final working points were then chosen among the combinations of cuts giving the target signal efficiencies, by selecting those which minimize the background efficiency, under the constraint that the candidates that pass the medium identification are a subset of those that pass loose, and tight a subset of medium. Table 4.1 shows the critical values of the cuts for the working points, as well as their signal and background efficiencies as estimated with simulation [142]. With the 2010 collision data collected by ATLAS, this simple cut-based approach was used for the first data-MC comparisons of tau candidates [144] (discussed in Section 4.4.1), the first observation of W → τν [145] (discussed in Section 4.4.2), and the first observation of Z → ττ [146] (discussed in Section 5.5), 4.3.3 pT-parametrized cuts Following the initial use of the cut-based tau identification in 2010, the cuts were updated to have a more uniform efficiency as a function of the candidate pT. Like the previous version, the method still uses cuts on only three variables: REM, Rtrack, and ftrack, binned in candidates that have one or multiple tracks. The method has been improved by parameterizing the cuts on REM and Rtrack by the pT of the tau candidate, since the optimal cuts are very pT-dependent because of the Lorentz collimation of the decay products in hadronic tau decays. Figure 4.7 shows profile plots26 of the pT-dependence of several of the tau ID variables for both signal and background distributions. Two of the three variables (REM, Rtrack) used by the cut-based identification rely on the narrowness of the width of the hadronic shower in tau decays compared to QCD jets. While the tau can 26 The plots in Figure 4.8 are examples of profile plots which refer to 2-dimensional histograms that has been averaged along one of its dimensions, resulting in a 2-d plot of the mean of some variable 〈y〉 in bins of some other variable x, often also with the standard deviation of y visualzed as a band in the same bins. Table 4.1: The values of the loose/medium/tight cuts for the working points of the 2010 simple cut-based ID [142]. August 12, 2010 – 12 : 32 DRAFT 20 REM < Rtrack < ftrk,1 > sig e! bkg e! 1-prong 0.08 0.09 0.06 0.599 0.137 0.07 0.08 0.12 0.497 0.0825 0.05 0.08 0.12 0.274 0.0262 3-prong 0.15 0.12 0.12 0.57 0.468 0.12 0.08 0.24 0.499 0.161 0.09 0.05 0.32 0.296 0.0282 Table 4: Optimized cut values and e"ciencies. • No pruning applied310 In the following sections, the performance of the BDT for jet rejection and its comparison to data is311 summarized.312 9.1 Systematic Uncertainties313 Currently, the results presented here have statistical uncertainties only. The dominant source of system-314 atic uncertainty on MC rejection is expected to be the choice of Pythia tune. The size of the fluctuation315 due to this choice can easily be evaluated by calculating the final BDT score in other samples generated316 with alternate tunes (which are also compatible with ATLAS data). The combination of this uncertainty317 with minor additional sources, such as JES uncertainty, is a more complicated issue and is under consid-318 eration.319 Figure 17 shows the systematic uncertainty on the BDT score obtained from an alternate choice of320 MC tune. The baseline is Pythia DW, and the uncertainty band comes from calculating the scores in a321 Perugia2010 sample. This figure also shows the a!ect of changing the material model. c a n d id a te s / 0 .0 2 ! N u m b e r o f 0 50 100 150 200 250 300 3 10" c a n d id a te s / 0 .0 2 ! N u m b e r o f -1Integrated Luminosity 244 nb = 7 TeV)sData 2010 ( Perugia2010 PythiaDW Perugia2010/PythiaDW Data/PythiaDW BDT Jet Score 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 BDT Jet Score 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 c a n d id a te s / 0 .0 2 ! N u m b e r o f 0 50 100 150 200 250 3 10" c a n d id a te s / 0 .0 2 ! N u m b e r o f -1Integrated Luminosity 244 nb = 7 TeV)sData 2010 ( Different Material PythiaDW Figure 17: The systematic uncertainty obtained from varying the Pythia tune (left) and the detector material model (right) on the BDT output. 322 60 4. tau reconstruction and identification Simple Cuts: 1-prong EMRadius 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Monte Carlo taus L1Calo data period D trkAvgDist 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Monte Carlo taus L1Calo data period D ptLeadTrkOverEt 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 0.02 0.04 0.06 0.08 0.1 0.12 Monte Carlo taus L1Calo data period D Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 35 / 31 Simple Cuts: 3-prong EMRadius 0 .05 .1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Monte Carlo taus L1Calo data period D trkAvgDist 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.05 0.1 0.15 0.2 0.25 Monte Carlo taus L1Calo data period D ptLeadTrkOverEt 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 0.01 0.02 0.03 0.04 0.05 0.06 Monte Carlo taus L1Calo data period D Ryan Reece | Penn | ry .reece@cern.ch | Cut Based Tau ID: Status and Plans 36 / 31 Simple Cuts: 1-prong EMRadius 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Monte Carlo taus L1Calo data period D trkAvgDist 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Monte Carlo taus L1Calo d ta period D ptLeadTrkOverEt 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 0.02 0.04 0.06 0.08 0.1 0.12 Monte Carlo taus L1Calo data period D Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 35 / 31 Simple Cuts: 3-prong EMRadius 0 0.05 .1 5 0.2 . 5 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Monte Carlo taus L1Calo data period D trkAvgDist 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.05 0.1 0.15 0.2 0.25 Monte Carlo taus L1Calo d ta period D ptLeadTrkOverEt 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 0.01 0.02 0.03 0.04 0.05 0.06 Monte Carlo taus L1Calo data period D Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 36 / 31 Simple Cuts: 1-prong EMRadius 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Monte Carlo taus L1Calo data period D trkAvgDist 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Monte Carlo taus L1Calo data period D ptLeadTrkOverEt 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 0.02 0.04 0.06 0.08 0.1 0.12 Monte Carlo taus L1Calo data period D Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 35 / 31 Simple Cuts: 3-prong EMRadius 0 .05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Monte Carlo t us L1Calo d ta period D trkAvgDist 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40 0.05 0.1 0.15 0.2 0.25 Monte Carlo taus L1Calo data period D ptLeadTrkOverEt 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 0.01 0.02 0.03 0.04 0.05 0.06 Monte Carlo taus L1Calo data period D Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 36 / 31 Figure 4.6: The distributions for the three tau identification variables used by the cut-based ID for 1-prong (left) and 3-prong (right) candidates. The signal sample is MC Z → ττ events (blue) and the background is dijet events from 2010 (red). The cuts for the working poi ts are indicated by the dashe lines. The values of these cuts are shown in Table 4.1 (mc09) [143]. 4.3 tau identification 61 ) [GeV] h τ( T p 20 40 60 80 100 120 〉 E M R〈 0 0.05 0.1 0.15 0.2 ) [GeV] h τ( T p 20 40 60 80 100 120 〉 E M R〈 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 ) [GeV] h τ( T p 20 40 60 80 100 120 〉 tr a c k R〈 0 0.05 0.1 0.15 0.2 0.25 ) [GeV] h τ( T p 20 40 60 80 100 120 〉 tr a c k R〈 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Figure 4.7: The dependence of key tau identification variables as a function of the candidate pT, separately for 1-prong (left) and 3-prong (right) tau candidates. The points indicate the means in each bin. The colored bands indicate the standard deviation. The blue points correspond to tau candidates matched to hadronically decaying taus in simulated W → τν and Z → ττ events. The red points are for the dijet sample from data (mc10) [117]. send its decay products in any direction in the rest frame of the tau lepton, taus are not produced at rest in the ATLAS detector. In the laboratory frame, the decay products will be collimated along the momentum of the tau lepton. The Lorentz boost to the laboratory frame implies that width-like variables, R, should collimate as R(pT) ∝ 1/pT. This can be seen by noting that width-like variables, R, depend linearly on an average among the angles, ∆φ, between axis of the jet seed and the momentum vector of constituent pions in the tau decay. For small angles, this is approximately tan ∆φ, which is the ratio of a constituent's momentum transverse to the jet axis, kT, and the total reconstructed momentum of the tau candidate transverse to the beam line, pT. Therefore, R ∝ ∆φ ≈ tan ∆φ = kT/pT. The collimation of hadronic tau decays makes the optimal cut on variables like REM and Rtrack very pT-dependent. Multiplying R by pT should flatten the pT-dependence, and it largely does (see 62 4. tau reconstruction and identification Figure 4.8). The remaining pT-dependence is parametrized by fitting a second-order polynomial to the means of R× pT, binned in pT, separately for both signal and background distributions. g(pT) = a0 + a1 pT + a2 p 2 T Then, possible cut curves between the signal and background distributions were constructed as Rcut(pT;x) pT = (1− x) gsig(pT) + x gbkg(pT) for different values of the parameter x, where x = 0 is completely along the mean of the signal distribution, and x = 1 is completely along the mean of the background [100]. Figure 4.8 shows that while multiplying R by pT does flatten out the pT-dependence for true hadronic tau decays, QCD jets tend to grow wider with pT at a higher (non-linear) rate, presumably because competing with the effects of Lorentz collimation is the fact that higher-pT jets have more energy to hardonize more particles, producing more tracks and clusters, and thus wider jets [143]. The pT-parametrized cuts were optimized with a method similar to that used for the simple cuts discussed in Section 4.3.2. Possible combinations of critical values for ftrack, and the x variables for REM and Rtrack, were exhaustively evaluated in reasonable steps to achieve approximately 60%/50%/30% signal efficiency for the loose/medium/tight working points (respectively), minimizing the background efficiency under the constraint that the candidates that pass medium are a subset of loose, and tight a subset of medium. Unlike the simple cuts that were optimized against simulated dijet events, the pT-parametrized cuts were the first tau discriminant optimized with a background sample from ATLAS data, using a sample of dijet events collected in period G of the 2010 run. In order to limit the pT-parametrized cuts from indefinitely becoming more strict with pT, the shape of the cut curves are defined piecewise in pT, becoming constant cuts for pT ≥ 80 GeV. Figure 4.9 shows the final optimized cut curves for each working point. It shows that while REM is the most effective discriminating variable for 1-prong decays, Rtrack radius becomes more important for 3-prong. Table 4.2 shows the parametrizations of the cuts for each working point. Figures 4.10 and 4.11 show the signal and background efficiencies of both the simple cut-based tau identification and the pT-parametrized cuts, estimated using a cross-section-weighted sample of fully simulated W → τν and Z → ττ decays for signal, and a sample of dijet events from ATLAS data for background. They show that the pT-parametrization achieves efficiencies that are more flat in pT for both signal and background, correcting the rising fake rates that were problematic for the simple cut-based identification. The medium working point of the pT-parametrized cuts was used to identify tau candidates for Z → ττ cross section measurement with the 2010 ATLAS dataset [113] (as discussed in Chapter 5). 4.3 tau identification 63 [GeV] T p 20 30 40 50 60 70 80 90 100 [G e V ] 〉 T p × E M R〈 0 2 4 6 8 10 12 14 16 0.073± = 0.22 0 a 0.0036± = 0.155 1a 3.6e-05± = -0.000489 2a / NDF = 26.5 / 14 = 1.892χ 0.017± = 0.741 0a 0.0012± = 0.0468 1 a 1.9e-05± = -0.000154 2 a / NDF = 52 / 14 = 3.722χ [GeV] T p 20 30 40 50 60 70 80 90 100 [G e V ] 〉 T p × E M R〈 0 2 4 6 8 10 12 14 16 0.065± = 0.554 0a 0.0027± = 0.144 1 a 2.5e-05± = -0.000407 2 a / NDF = 20 / 14 = 1.432χ 0.032± = 1.09 0 a 0.0021± = 0.0572 1 a 3.3e-05± = -0.000133 2 a / NDF = 11.7 / 14 = 0.8362χ [GeV] T p 20 30 40 50 60 70 80 90 100 [G e V ] 〉 T p × tr a c k R〈 0 2 4 6 8 10 12 14 16 0.11± = -0.24 0 a 0.0056± = 0.179 1a 5.6e-05± = -0.000309 2a / NDF = 17.3 / 14 = 1.232χ 0.016± = 0.668 0 a 0.001± = 0.0282 1a 1.6e-05± = -0.000185 2a / NDF = 24.3 / 14 = 1.742χ [GeV] T p 20 30 40 50 60 70 80 90 100 [G e V ] 〉 T p × tr a c k R〈 0 2 4 6 8 10 12 14 16 0.083± = 0.418 0 a 0.0035± = 0.119 1a 3.3e-05± = -0.000251 2a / NDF = 14.8 / 14 = 1.062χ 0.016± = 0.879 0 a 0.0011± = 0.0146 1a 1.6e-05± = -7.21e-05 2a / NDF = 15.1 / 14 = 1.082χ Figure 4.8: Profile plots of 〈R × pT〉 vs the candidate pT, separately for 1-prong (left) and 3prong (right) tau candidates, for REM (top) and Rtrack (bottom). The points indicate the means in each bin. The colored bands indicate the standard deviation. The blue points correspond to tau candidates matched to hadronically decaying taus in simulated W → τν and Z → ττ events. The red points are for the dijet sample from data (mc09) [147]. 4.3.4 Multivariate techniques There have been many efforts to use more sophisticated techniques to identify hadronic tau decays than a cut-based approach, taking advantage of more calorimeterand tracking-related variables, especially the significance of the transverse displacement of secondary vertex that can be found in multi-prong decays. The two main competing approaches involve using a likelihood ratio based on the combined distributions of the tau identification variables, and the use of boosted decision trees, and are described briefly in this section. Distributions of all of the identification variables used by the discriminants for the 2010 dataset are shown in Figures 4.12-4.14. Table 4.3 compares which variables were used by each discriminant. In 2011, as experience with ATLAS tau identification grew, identification based on likelihoods and boosted decision trees became the preferred techniques. 64 4. tau reconstruction and identification [GeV] T p 20 30 40 50 60 70 80 90 100 〉 E M R〈 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 [GeV] T p 20 30 40 50 60 70 80 90 100 〉 E M R〈 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 [GeV] T p 20 30 40 50 60 70 80 90 100 〉 tr a c k R〈 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 [GeV] T p 20 30 40 50 60 70 80 90 100 〉 tr a c k R〈 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 trk,1f 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 Monte Carlo taus Data JetTauEtMiss-DESD_CALJET Period G trk,1f 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.01 0.02 0.03 0.04 0.05 0.06 Monte Carlo taus Data JetTauEtMiss-DESD_CALJET Period G Figure 4.9: The cut values for the working points for the updated pT-parametrized cut-based ID with the 2010 dataset are shown by the dashed lines. Note that the piecewise parts with constant cut values for pT ≥ 80 GeV are not shown, but would simply be a flat continuation of the curves shown, beginning at 80 GeV. The same cut values are given in Table 4.2 (mc09) [147]. 4.3 tau identification 65 Table 4.2: Parametrized cut values for the updated 2010 working points. The formulas for the parametrized cuts use pT in units of GeV. Currently, 1/ftrack, and not its inverse, is the variable stored in the tau Event Data Model (EDM) [147]. pT < 80 GeV pT ≥ 80 GeV 1-prong loose REM < 0.663/pT + 0.063− 2.04× 10−4pT 0.055 Rtrack < 0.0328/pT + 0.134− 2.72× 10−4pT 0.113 1/ftrack no cut no cut medium REM < 0.715/pT + 0.0522− 1.71× 10−4pT 0.0475 Rtrack < 0.0328/pT + 0.134− 2.72× 10−4pT 0.113 1/ftrack < 8.33 8.33 tight REM < 0.819/pT + 0.0306− 1.03× 10−4pT 0.0325 Rtrack < 0.0328/pT + 0.134− 2.72× 10−4pT 0.113 1/ftrack < 7.14 7.14 3-prong loose REM < 0.339/pT + 0.179− 5.17× 10−4pT 0.142 Rtrack < 0.695/pT + 0.0565− 1.44× 10−4pT 0.0536 1/ftrack < 4.55 4.55 medium REM < 0.447/pT + 0.162− 4.62× 10−4pT 0.13 Rtrack < 0.810/pT + 0.0303− 9.90× 10−5pT 0.0325 1/ftrack < 3.33 3.33 tight REM < 0.930/pT + 0.0833− 2.15× 10−4pT 0.0777 Rtrack < 0.879/pT + 0.0146− 7.21× 10−5pT 0.0198 1/ftrack < 2.5 2.5 E!ciency/Rejection: 1-prong Simple cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong ET-parametrized cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 loose medium tight 1-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 21 / 31 E!ciency/Rejection: 3-prong Simple cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 3-prong ET-parametrized cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 loose medium tight 3-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 22 / 31 E!ciency/Rejection: -prong Simple cu s [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong ET-parametrized c t [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -10 1 loose medium tight 1-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 21 / 31 E!ciency/Rejection: 3-prong Simple cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 lo se medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 3-prong ET-parametrized c t [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 lo se medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 loose medium tight 3-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 22 / 31Figure 4.10: The effici n y of the 2010 simple cut-based ID (top) th pT-parametrized cuts (bottom), for both 1-prong (left) and 3-prong (right) true hadronic tau decays (mc09) [143]. 66 4. tau reconstruction and identification E!ciency/Rejection: 1-prong Simple cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong ET-parametrized cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 loose medium tight 1-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 21 / 31 E!ciency/Rejection: 3-prong Simple cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 3-prong ET-parametrized cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 lo se medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 loose medium tight 3-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 22 / 31 E!ciency/Rejection: 1-prong Simple cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong ET-parametrized cut [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 loose medium tight 1-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 21 / 31 E!ciency/Rejection: 3-prong Simple cuts [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 lo se medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose medium tight 3-prong ET-parametrized c t [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 10 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 lo se medium tight 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 loose medium tight 3-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 22 / 31Fig re 4.11: The fak rate of t e 2010 simpl cut-based ID (top) and the pT-parametrized cuts (bottom), for both 1-prong (left) and 3-prong (right) tau candidates in a dijet sample from the 2010 dataset. Table 4.3: Comparison of variables used by each discriminant for the 2010 dataset [100]. REM Rtrack ftrack fcore fEM mclusters mtracks S flight T fHT Cuts • • • Llh single-prong • • • Llh multi-prong • • • • • BDT single-prong • • • • • • BDT multi-prong • • • • • • • • e-BDT single-prong • • • • • • • 4.3 tau identification 67 EMR 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary EMR 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary trackR 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary trackR 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 A rb it ra ry U n it s 0 0.05 0.1 0.15 0.2 0.25 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary trackf 0 0.2 0.4 0.6 0.8 1 1.2 1.4 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary trackf 0 0.2 0.4 0.6 0.8 1 1.2 1.4 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary Figure 4.12: Distributions for REM, Rtrack, and ftrack, for 1-prong (left) and 3-prong (right) candidates. Note that the discontinuity in Rtrack for 1-prong candidates is due to the fact that they can optionally have additional tracks in the isolation annulus (see the definition of Rtrack in Section 4.3.1). The dashed lines indicate the cut boundaries for the tight pT-parameterized cut-based ID, discussed later in Section 4.3.3. Since the cuts on REM and Rtrack are parameterized in pT, the characteristic range of the cut values is demonstrated by showing lines for the cuts for candidates with pT = 20 GeV, and then an arrow pointing to the cut for candidates with pT = 60 GeV (mc09) [100]. 68 4. tau reconstruction and identification coref 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary coref 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary EMf 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary EMf 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary [GeV]clustersm 0 1 2 3 4 5 6 7 8 9 10 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary [GeV]clustersm 0 1 2 3 4 5 6 7 8 9 10 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary Figure 4.13: Distributions for fcore, fEM, and mclusters, for 1-prong (left) and 3-prong (right) candidates (mc09) [100]. 4.3 tau identification 69 [GeV]trackm 0 1 2 3 4 5 6 A rb it ra ry U n it s 0 0.05 0.1 0.15 0.2 0.25 0.3 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary flight T S -6 -4 -2 0 2 4 6 8 10 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary Likelihood Score -20 -15 -10 -5 0 5 10 15 20 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary Likelihood Score -20 -15 -10 -5 0 5 10 15 20 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary BDT Score 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 1 prong 15 GeV<p ATLAS Preliminary BDT Score 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A rb it ra ry U n it s 0 0.02 0.04 0.06 0.08 0.1 0.12 ττ→+Zντ→W dijet Monte Carlo -1dt L = 23 pb∫2010 dijet data <60 GeV T 3 prongs 15 GeV<p ATLAS Preliminary Figure 4.14: Distributions of mtracks (top-left) and S flight T (top-right) for 3-prong candidates, the loglikelihood-ratio for 1-prong (center-left) and 3-prong (center-right) tau candidates, and the jet BDT score for 1-prong (bottom-left) and 3-prong (bottom-right) tau candidates (mc09) [100]. 70 4. tau reconstruction and identification Likelihood-based identification Likelihood-based tau identification has been explored by the ATLAS Collaboration for several years, well before first collision data [148]. The method relies on having well-modeled distributions for each of the identification variables, for both signal and background, and constructing a likelihood function based on the product of those distributions. The likelihood function, LS(B), for signal(background) is defined as the product of the distributions of the identification variables: LS(B) = N∏ i=1 p S(B) i (xi), where p S(B) i (xi) is the signal (background) probability density function of identification variable xi of N variables. The likelihood function represents the joint probability distribution for the identification variables, neglecting correlations between the variables. The discriminant used by the likelihood method is defined as the log-likelihood-ratio between signal and background: d = ln ( LS LB ) = N∑ i=1 ln ( pSi (xi) pBi (xi) ) . The likelihood has been constructed in separate categories based on the tau candidate's transverse momentum (pT < 45, 45−100, > 100 GeV), track multiplicity (single-prong or multi-prong), track quality criteria (presence of a track with pT > 6 GeV or not) and the pile-up activity in the event (12, or more than 2 reconstructed primary vertices). A linear interpolation of the log-likelihood-ratio between neighbouring pT bins is applied if the distance to the bin border is less than 10 GeV [100]. The variables used to construct the likelihood are listed in Table 4.3. Distributions of the loglikelihood-ratio for signal and background are shown in Figure 4.14. Identification with boosted decision trees Decision trees [149] perform a sequence of cuts on multiple variables to classify objects as signal or background. The exact sequence of cuts, or path through a tree, can depend on which previous cuts are passed, such that the decision can have many branches like a tree. A tree is constructed from multiple nodes, where each node represents a specific cut on a variable. A sample of signal and background objects are required to train a set of trees. The algorithm begins with the entire training sample at the root node. The optimal cut, separating signal from background, is then determined separately for each variable. The best of these optimal cuts is chosen and two child nodes are constructed. All objects which fall below the cut are passed to the left node, and all objects which fall above the cut are passed to the right node. This cut improves the signal purity in one of the child nodes. The same algorithm is then applied recursively on each child node 4.3 tau identification 71 8 Identification with boosted decision trees TMVA [32] version 4.0.4 (available as part of ROOT version 5.26) was used to train boosted decision trees (BDTs), described in detail below. 8.1 Introduction Like a simple cut-based technique, a (univariate) decision tree makes a series of orthogonal cuts on a set of identification variables. A decision tree, though, is inherently a much more powerful technique, especially in a highly multivariate situation, since it does not immediately discard objects failing a cut but determines cuts on other variables to save signal which failed a cut in error. Another important di!erence is that a decision tree is not attempting to yield a certain level of signal e"ciency, but rather produces a continiuous score between 0 and 1 which a user may cut on to yield the desired signal (or background) e"ciency. Decision trees apply cuts on multiple variables in a recursive manner to classify objects as signal or background. As with any supervised machine learning algorithm, decision trees are first constructed or "trained" using a sample of known composition. An algorithm then attempts to optimally split the sample into two classes: signal and background. The algorithm begins with the entire training sample at the root node. Then, the optimal cut which separates signal from background is determined separately for each variable. The best of these optimal cuts is chosen and two child nodes are constructed. All objects which fall below the cut are passed to the left node and all objects which fall above the cut are passed to the right node. This cut improves the signal purity in one of the child nodes. The same algorithm is then applied recursively on each child node until a stopping condition is satisfied (in our case, a minimum number of tau candidates contained within a node). This leads to a binary tree structure like the one shown in Figur 19. Figure 19: A simple example of a decision tree training process where we have two distributions labelled signal (S) and background (B) over two variables X and Y . The process begins at (1). by determining the best value of the best variable to cut on, which in this case is Y at a. All objects with Y > a are passed to the right node and all objects with Y ! a are passed to the left. This process continues recursively until a stopping condition is satisfied such as a minimum number of objects contained by a node. A single decision tree is not stable across independent testing samples and is also not a particularly strong classifier. The AdaBoost (Adaptive Boost) algorithm significantly improves decision tree stability 38 8 Identification with boosted decision trees TMVA [32] version 4.0.4 (available as part of ROOT version 5.26) was used to train boosted decision trees (BDTs), described in detail below. 8.1 Introduction Like a simple cut-based technique, a (univariate) decision tree makes a series of orthogonal cuts on a set of identification variables. A decision tree, though, is inherently a much more powerful technique, especially in a highly multivariate situation, since it does not immediately discard objects failing a cut but determines cuts on other variables to save signal which failed a cut in error. Another important di!erence is that a decision tree is not attempting to yield a certain level of signal e"ciency, but rather produces a continiuous score between 0 and 1 which a user may cut on to yi ld the d sired signal (or background) e"ciency. Decision trees apply cuts on multiple variables in a recursive manner to classify objects as signal or background. As with any supervised machine learning algorithm, decision trees are first constructed or "trained" using a sample of known composition. An algorithm then attempts to optimally split the sample into two classes: signal and background. The algorithm begins with the entire training sample at the root node. Then, the optimal cut which separates signal from background is determined separately for each variable. The best of these optimal cuts is chosen and two child nodes are constructed. All objects which fall below the cut are passed to the left node and all obj cts which fall abov the cut are passed to the right node. This cut improves the signal purity in one f the child nodes. The same algorithm is then applied recursively on each child node until a stopping condition is satisfied (in our case, a minimum number of tau candidates contained within a node). This leads to a binary tree structure like the one shown in Figure 19. Figure 19: A simple example of a decision tree training process where we have two distributions labelled signal (S) and background (B) over two variables X and Y . The process begins at (1). by determining the best value of the best variable to cut on, which in this case is Y at a. All objects with Y > a are passed to the right node and all objects with Y ! a are passed to the left. This process continu s r cursively until a stopping condition is atisfi d uch as minimum number of objects contained by a node. A single decision tree is not stable across independent testing samples and is also not a particularly strong classifier. The AdaBoost (Adaptive Boost) algorithm significantly improves decision tree stability 38 Figure 4.15: A simple xample of a decision t raining process wh re t ere are two distributions labeled signal (S) and background (B) over two variables X and Y . The proces begins at point 1, by determining the best value of the best variable to cut on, wh ch in this case is Y at . All objects with Y > a re pas ed to the right node and all objects with Y ≤ a are passed to the left. This process continues recursively until a stopping condition is satisfied, such as a minimum number of objects contained by a node [147]. until a stopping condition is satisfied (in this case, minimum number of tau candidates contained within a node). This leads to a binary tree structure, like the example shown in Figure 4.15. TMVA [150], a package f r multivariate analy is that is part of the ROOT analysis toolkit [133], is used for training [147]. During classification, an object begins at the root node and is passed down the tree according to the cut made by each node until a final leaf node is reached. The response of the decision tree is then the signal purity of the leaf node. A Boosted Decision Tree (BDT) [151] takes advantage of multiple decision trees and forms a normalized weighted sum of their outputs, resulting in a final score that is between 0 (background-like) and 1 (signal-like) [152]. BDTs for jet rejection are trained separately for candidates with one track and candidates with three tracks. The BDT trained on candidates with three tracks is then used for classifying any candidate with two or more tracks. Distributions of the BDT score for discriminating taus from jets are shown in Figure 4.14, for both signal and background. Loose, medium, and tight working points, similar to the cut-based identification, are defined for both the likelihoodand BDT-based identification. A cut is made on the final log-likelihood-ratio or BDT score to discriminate signal from background. The working points have been tuned with pT-dependent selections to compensate for the pT-dependence of the log-likelihood-ratio and BDT scores, yielding roughly flat27 signal and background efficiencies as a function of pT [100]. The 27 See Figures 4.20 and 4.21, which show the pT-dependence of the performance of the discriminants used with the 72 4. tau reconstruction and identification performance of the ATLAS tau identification is discussed in more detail in Section 4.4.3. 4.3.5 Electron-tau discrimination Providing both a track and a well-matched cluster, electrons readily produce tau candidates. Much of this background can be suppressed by overlap-removing tau candidates which pass some electron identification. Figure 4.16 (top-left) shows the efficiency for true hadronic decays of tau leptons in 2010 Z → ττ MC events to be identified as loose/medium/tight electrons. It demonstrates that one can safely remove tau candidates which pass medium ID with only removing ∼ 1% of true tau decays. Since electron ID improved, in 2011 and 2012 it is reasonable to remove loose++ candidates. To further suppress electrons faking tau candidates after overlap-removing identified electrons, electron-tau discriminants have been developed, first a simple cut-based method [153], which was later superseded by a BDT-based electron-veto (e-veto) [102]. The e-vetoes use a list of variables similar to those used by the jet-tau discriminants, but with additional variables like the TRT highthreshold-hit fraction (see Figure 4.16 (top-right)) targeted at discriminating electrons from charged pions. The distribution of the BDT score for the e-veto for 2011 is shown in Figure 4.16 (bottomleft). Loose/medium/tight working points with signal efficiencies of approximately 95%/85%/75% are defined, the efficiency and rejection of which are shown in Figure 4.16 (bottom-right). The measurement of the performance and its uncertainty for the BDT e-veto is discussed in Section 4.4.4. 4.4 Performance and systematic uncertainties 4.4.1 First data-MC comparisons While considerable progress was made in developing the core of the ATLAS tau reconstruction algorithm and preliminary versions of the identification before the LHC circulated any beam, first collisions brought the first concrete evaluations of that software with real data, and the first tests of the modeling of tau-related variables in the ATLAS simulation. In November and December of 2009, following the single-beam commissioning of the LHC, ATLAS collected data from the first proton-proton collisions at the LHC at √ s = 900 GeV. The peak luminosity ranged between 1025 and 1027 cm−2 s−1, resulting in a few μb−1 of integrated luminosity. The following year, the LHC produced the first record-energy proton-proton collisions at √ s = 7 TeV. Between March and May 2010, the peak luminosity ranged from 1027 to 1029 cm−2 s−1, and 15.6 nb−1 of integrated luminosity were collected. 2010 dataset. 4.4 performance and systematic uncertainties 73 [GeV] T pτ 10 20 30 40 50 60 70 80 ∈ 0 0.1 0.2 0.3 0.4 0.5 0.6 All Electrons Match Loose Match Medium Match Tight HTf ATLAS Preliminary 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 S a m p le F ra c ti o n / 0 .0 2 0 0.05 0.1 0.15 0.2 0.25 ττ→Z ee→Z >20 GeV T p ±π EMf -2 -1 0 1 2 3 Ar bi tra ry U ni ts 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 | < 1.37η| τ τ →Z e e→Z ATLAS Preliminary Simulation EM Pf 0 1 2 3 4 5 6 7 Ar bi tra ry U ni ts 0 0.1 0.2 0.3 0.4 0.5 | < 1.37η| τ τ →Z e e→Z ATLAS Preliminary Simulation PSf 0 0.2 0.4 0.6 0.8 1 Ar bi tra ry U ni ts 0 0.02 0.04 .06 0.08 0.1 0.12 0.14 0.16 | < 1.37η| τ τ →Z e e→Z ATLAS Preliminary Simulation Figure 6: The distributions of the three new variables used in this current version of the electron BDT training, for the barrel region of ATLAS (|!| < 1.37). Electron BDT Score 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ar bi tra ry U ni ts 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 | < 2.0η> 20 GeV, | T 1-prong, p τ τ →Z e e→Z ATLAS Preliminary Simulation Figure 7: Score of the BDT-based electron veto for MC simulated "1-prong and electrons both reconstructed as 1-prong "had-vis candidates with |!| < 2.0. reduce backgrounds from muon fakes, as described here. Muons mis-reconstructed as "had-vis candidates can be classified according to the source of the associated calorimeter clusters: • Case 1: The muon itself leaves anomalously large energy deposits in the calorimeter. • Case 2: The energy comes from elsewhere, either collinear radiation from the muon prior to entering the calorimeter, or coincidental overlap with some other calorimeter clusters. 9 Ryan Reece (Penn) El ctro veto 15 HTf ATLAS Preliminary 0 0.1 0.2 0.3 . . .6 0.7 0.8 0.9 1 Sa m pl e Fr ac tio n / 0 .0 2 0 0.05 0.1 0.15 0.2 0.25 ττ→Z ee→Z >20 GeV T p Signal Efficiency 0.5 0.6 0.7 0.8 0.9 1 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 ATLAS Preliminary Simulation | < 2.0η> 20 GeV, | T 1-prong, p BDT-based electron veto [ATLAS-CONF-2011-152, ATLAS-CONF-2012-142] • Electrons provide a track and calorimeter deposit that can fake hadronic tau decay identification. • ATLAS provides a BDT to discriminate electrons from tau candidates, even after removing overlaps with selected electrons. • Tight/Medium/Loose working points are defined (≈75%, 85%, 95% e!cient). • In 2012, the BDT is being reoptimized to have better e!ciency at high-pT. Figure 4.16: (top-left) The efficiency for true hadronic tau decays to the identified with by an overlapping electron candidates with the 2010 ID. (top-right) The distributions of the TRT high-threshold-fraction for tau candidates in MC Z → ττ and Z → ee events, a variables used to discriminant electrons from hadronic decays of taus [101]. (bottomleft) The distribution of the BDT score for the e-veto used to veto real electrons faking tau candidates. (bottom-right) The inverse background efficiency vs signal efficiency for various cuts on the BDT score for the e-veto [102]. The events in the 2009 sample were collected according to a minimum-bias trigger, and are dominated by soft, non-diffractive interactions. In the 2010 dataset, the higher luminosity and collision energy allowed for the production of a more substantial sample of high-pT jets for seeding tau candidates. While the number of real tau leptons produced in the momentum range relevant to the ATLAS physics program is expected to be negligible in both samples, the data have been used to commission the operation of the tau reconstruction algorithm and to validate the modeling of several identification variables for background candidates. Figure 4.17 shows data-MC comparisons of some of the tau-related variables with both of these datasets [154, 144]. In the plot of REM, Figure 4.17 (bottom-right), note that one could already see signs of the mismodeling of the jet width in the ATLAS simulation. PYTHIA [125], specially tuned for minimumbias events at ATLAS [129], was used to generate the simulated background events, producing jets 74 4. tau reconstruction and identification ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC -candidatesτMultiplicity of 0 1 2 3 4 5 N um be r o f e ve nt s 10 210 310 N um be r o f e ve nt s ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC -candidatesτMultiplicity of 0 1 2 3 4 5 N um be r o f e ve nt s 1 10 210 N um be r o f e ve nt s Figure 1: Number of reconstructed τ candidates for the inclusive sample (left) and the jet–enriched sample (right). ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC [GeV]TE 5 10 15 20 25 30 -c an di da te s / 1 G eV τ N um be r o f 0 50 100 150 200 250 300 350 -c an di da te s / 1 G eV τ N um be r o f ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC [GeV]TE 5 10 15 20 25 30 -c an di da te s / 1 G eV τ N um be r o f 0 5 10 15 20 25 30 35 40 45 -c an di da te s / 1 G eV τ N um be r o f Figure 2: Uncalibrated transverse energy, ET, of τ candidates for the inclusive sample (left) and the jet–enriched sample (right). (see Eq. 3), a measure of the longitudinal shower profile, the energy in the electromagnetic calorimeter over the total calorimeter energy EEMT /ET and the ratio of the calibrated transverse τ energy with respect to the leading track momentum ET/pT. The strongest discrimination is expected from REM, especially for 1–prong τ decays, with significant contributions from the other variables. For a detailed description of the variables and their expected discrimination, see [7]. In the following, these basic quantities are compared between simulation and data together with other candidates for discriminating variables. While the shape of the distributions for the available data at a centre-of-mass energy of 900 GeV does not always exactly resemble the background distributions expected at higher centre-of-mass energies and tighter selections, good agreement between data and simulation is observed giving confidence in the performance estimate described in [7]. Figures 1-3 show the number of reconstructed τ candidates per event, the uncalibrated transverse 4 Core energy fraction: Fraction of transverse energy in the core (!R < 0.1) of the ! candidate: fcore = !!R<0.1 i ET,i!!R<0.4 i ET,i , where i runs over all cells associated to the ! candidate within the specified radius. Since the instantaneous luminosities for these datasets are quite low, pile-up e"ects are expected to be negligible for the distributions shown here. With higher luminosity, pile-up will a"ect the distributions of these variables for both fake and true ! candidates, reducing their separation power. Variables that are more robust under pile-up conditions are also being studied, in preparation for the anticipated higher instantaneous luminosities at the LHC. After the selection described in Section 2, the number of ! candidates in MC samples are normalised to the number of ! candidates selected in data. The shapes from ! candidates reconstructed in a signal Z ! !!MC sample and matched to true hadronically decaying ! leptons are also overlaid to show what it will look like once true ! leptons are visible in ATLAS. Figure 1 shows the pT and " of ! candidates, as well as the number of associated tracks within !R < 0.2 (a real ! lepton is expected to have mostly one or three such tracks) and the number of topoclusters: the data are very well described by the QCD dijet MC distributions. [GeV] T p 10 15 20 25 30 35 40 45 50 55 60 c a n d id a te s / G e V ! N u m b e r o f 0 20 40 60 80 100 120 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets -1Integrated Luminosity 15.6 nb (a) # -4 -3 -2 -1 0 1 2 3 4 c a n d id a te s /0 .3 2 ! N u m b e r o f 0 20 40 60 80 100 120 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets -1Integrated Luminosity 15.6 nb (b) Track Multiplicity 0 1 2 3 4 5 6 7 8 9 c a n d id a te s ! N u m b e r o f 0 100 200 300 400 500 600 700 800 900 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets !!Pythia Z-> -1Integrated Luminosity 15.6 nb (c) Number of topoclusters 2 4 6 8 10 12 14 16 18 20 c a n d id a te s ! N u m b e r o f 0 20 40 60 80 100 120 140 160 180 200 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets !!Pythia Z-> -1Integrated Luminosity 15.6 nb (d) Figure 1: (a) Transverse momentum, (b) pseudorapidity, (c) number of associated tracks and (d) number of associated topoclusters of ! candidates. The number of ! candidates in MC samples are normalised to the number of ! candidates selected in data. Most variables built on calorimeter or tracking measurements that describe the properties of ! candidates show very good agreement between data and MC events. This is illustrated in Fig. 2, which shows 3 ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC Mass [GeV] 0 1 2 3 4 5 6 -c an di da te s / 0 .2 G eV τ N um be r o f 0 10 20 30 40 50 60 70 80 90 -c an di da te s / 0 .2 G eV τ N um be r o f ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC Mass [GeV] 0 1 2 3 4 5 6 -c an di da te s / 0 .2 G eV τ N um be r o f 0 2 4 6 8 10 12 14 16 18 20 22 -c an di da te s / 0 .2 G eV τ N um be r o f Figure 11: Invariant mass calculated from the calorimeter clusters of reconstructed τ candidates for the inclusive sample (left) and the jet–enriched sample (right). ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC Track multiplicity 0 1 2 3 4 5 -c an di da te s τ N um be r o f 0 50 100 150 200 250 300 -c an di da te s τ N um be r o f ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC Track multiplicity 0 1 2 3 4 5 -c an di da te s τ N um be r o f 0 10 20 30 40 50 -c an di da te s τ N um be r o f Figure 12: Distribution of the number of tracks associated to the reconstructed τ candidates for the inclusive sample (left) and the jet–enriched sample (right). distributions for both selections are shown in Fig. 12. While the track multiplicity distribution of the τ candidates from the inclusive sample may provide a hint of a deviation from the simulation, there is good agreement for the di-jet sample distribution. The excellent agreement obtained, both in the inclusive selection as well as in the enriched sample of QCD jets following the di-jet selection, gives confidence in the performance estimates for physics with τ leptons [7]. 5 Electron Veto Narrowness and isolation of calorimeter showers as well as low track multiplicity are common signatures for both hadronically decaying τ leptons and electrons. Without the use of a dedicated veto algorithm, the majority of electrons would be identified as single-prong hadronic τ candidates. These studies of 9 Core energy fraction: Fraction of transverse energy in the core (!R < 0.1) of the ! candidate: fcore = !!R<0.1 i ET,i .4 i ,i , where i runs over all cells associated to the ! candidate within the specified radius. Since the instantaneous luminosities for these datasets are quite low, pile-up e"ects are expected to be negligible for the distributions shown here. With higher luminosity, pile-up will a"ect the distributions of these variables for both fake and true ! candidates, reducing their separation power. Variables that are more robust under pile-up conditions are also being studied, in preparation for the anticipated higher instantaneous luminosities at the LHC. After the selection described in Section 2, the number of ! candidates in MC samples are normalised to the number of ! candidates selected in data. The shapes from ! candidates reconstructed in a signal Z ! !!MC sample and matched to true hadronically decaying ! leptons are also overlaid to show what it will look like once true ! leptons are visible in ATLAS. Figure 1 shows the pT and " of ! candidates, as well as the number of associated tracks within !R < 0.2 (a real ! lepton is expected to have mostly one or three such tracks) and the number of topoclusters: the data are very well described by the QCD dijet MC distributions. [GeV] T p 10 15 20 25 30 35 40 45 50 55 60 c a n d id a te s / G e V ! N u m b e r o f 0 20 40 60 80 100 120 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets -1Integrated Luminosity 15.6 nb (a) # -4 -3 -2 -1 0 1 2 3 4 c a n d id a te s /0 .3 2 ! N u m b e r o f 0 20 40 60 80 100 120 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets -1Integrated Luminosity 15.6 nb (b) Track Multiplicity 0 1 2 3 4 5 6 7 8 9 c a n d id a te s ! N u m b e r o f 0 100 200 300 400 500 600 700 800 900 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets !!Pythia Z-> -1Integrated Luminosity 15.6 nb (c) Number of topoclusters 2 4 6 8 10 12 14 16 18 20 c a n d id a te s ! N u m b e r o f 0 20 40 60 80 100 120 140 160 180 200 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets !!Pythia Z-> -1Integrated Luminosity 15.6 nb (d) Figure 1: (a) Transverse momentum, (b) pseudorapidity, (c) number of associated tracks and (d) number of associated topoclusters of ! candidates. The number of ! candidates in MC samples are normalised to the number of ! candidates selected in data. Most variables built on calorimeter or tracking measurements that describe the properties of ! candidates show very good agreement between data and MC events. This is illustrated in Fig. 2, which shows 3 ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC η -3 -2 -1 0 1 2 3 -c an di da te s / 0 .2 5 τ N um be r o f 0 10 20 30 40 50 60 70 80 -c an di da te s / 0 .2 5 τ N um be r o f ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC η -3 -2 -1 0 1 2 3 -c an di da te s / 0 .2 5 τ N um be r o f 0 2 4 6 8 10 12 14 16 18 20 -c an di da te s / 0 .2 5 τ N um be r o f Figure 3: Pseudorapidity, η , of reconstructed τ candidates for the inclusiv sample (left) and the jet– enriched sa ple (right). ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC EMR -0.1 0 0.1 0.2 0.3 0.4 0.5 -c an di da te s / 0 .0 4 τ N um be r o f 0 20 40 60 80 100 120 140 160 180 200 220 -c an di da te s / 0 .0 4 τ N um be r o f ATLAS Preliminary = 900 GeV )sData 2009 ( Non-diffractive minimum bias MC EMR -0.1 0 0.1 0.2 0.3 0.4 0.5 -c an di da te s / 0 .0 4 τ N um be r o f 0 5 10 15 20 25 30 35 40 45 -c an di da te s / 0 .0 4 τ N um be r o f Figure 4: Electromagnetic radius of reconstructed τ candidates for the inclusive sample (left) and e j t–enriched sample (right). energy ET, and the pseudorapidity η . Good agreement is observed between data and simulation for these kinematic distributions within the present statistical uncertainties. Figures 4 and 5 show the electromagnetic radius REM and the hadronic radius RHad, respectively. Based on simulation results [7], these are powerful discriminating variables discrimination for τ–lepton identification for calibrated ET > 10 GeV. Since hadronic τ decays have a low multiplicity of final state particles in a narrow cone, and one particle is often carrying a large fraction of the total energy, τ leptons show a much smaller transverse shower size than jets. They reflect the shower width transverse to the shower and are defined as: REM/Had = ∑ΔR!0.4i E EM/Had T,i ΔR(i,tau) ∑ΔR!0.4i E EM/Had T,i , (1) where the cell index i loops over the calorimeter cells associated to clusters [8] within the τ cone of 5 EMR 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 c a n d id a te s / 0 .0 1 ! N u m b e r o f 0 20 40 60 80 100 120 140 160 180 200 220 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets !!Pythia Z-> -1Integrated Luminosity 15.6 nb (a) coref 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 c a n d id a te s / 0 .0 2 5 ! N u m b e r o f 0 20 40 60 80 100 120 3 10" ATLAS Preliminary = 7 TeV )sData 2010 ( Pythia QCD Jets !!Pythia Z-> -1Integrated Luminosity 15.6 nb (b) Figure 3: (a) EM radius and (b) core energy fraction of ! candidates. The number of ! candidates in MC samples are normalised to the number of ! candidates selected in data. NHT/NLT: the ratio of high threshold to low threshold hits in the Transition Radiation Tracker [1]. Distributions of these variables in data and MC are shown in Fig. 4. Due to the lepton match requirement, the available statistics are strongly reduced with respect to the selection in Section 2. /pEME 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -c a n d id a te s / 0 .0 8 ! N u m b e r o f 0 200 400 600 800 1000 1200 1400 1600 1800 -1Integrated Luminosity 15.6 nb = 7 TeV ) sData 2010 ( Pythia QCD Jets ATLAS Preliminary (a) LT/NHTN 0 0.1 0.2 0.3 0.4 0.5 -c a n d id a te s / 0 .0 2 ! N u m b e r o f 0 100 200 300 400 500 600 700 800 -1Integrated Luminosity 15.6 nb = 7 TeV ) sData 2010 ( Pythia QCD Jets ATLAS Preliminary (b) Figure 4: (a) EEM/p and (b) NHT/NLT of ! candidates matched to well identified electrons. The yellow (light shaded) band around the MC expectation indicates the statistical uncertainty on simulated samples. The number of ! candidates in MC samples are normalised to the number of ! candidates selected in data. 4 Systematic studies We have considered various sources of systematic uncertainties, using MC samples generated with a di!erent shower model, with a di!erent underlying event tune, with a di!erent fragmentation model and with extra material added in the detector geometry. These systematic e!ects are small. Excluding the additional ! candidates present in the event after the selection described in Section 2, or excluding the ! candidate responsible for selecting the event at the trigger level leaves the agreement of MC to data unchanged. The impact of noise in the calorimeter, of nearby activity, of a larger underlying event contribution and of the run-by-run beam spot position variations and detector conditions stability have also been estimated to be small. Their combination with the MC systematic e!ects mentioned above currently 5 Figure 4.17: First data-MC comparison of tau candidates in soft, non-diffractive events from 2009 collisions at √ s = 900 GeV (left), and from dijet events from 2010 collisions at√ s = 7 TeV (right) [154, 144]. 4.4 performance and systematic uncertainties 75 that are systematically more narrow than jets of the same pT in the data. Since tau ID prefers candidates with narrow distributions of clusters and tracks, the jet fake rate is mis-modeled for tau ID. As noted later in Section 5.7 concerning the background estimation for the observation of Z → ττ , this mis-modeling results in a factor ∼ 2 disagreement between data and MC for the W + jets background to events with a selected lepton and a hadronic tau candidate which is faked by a jet. The ATLAS Jet Performance Group also noted the mis-modeling of the jet width [155], and made detailed data-MC comparisons of measures of jet width with different MC generators [156, 157]. As a result of the sensitivity of the fake rate of tau ID on measures of jet width and the mismodeling of such measures in ATLAS MC, analyses using hadronic decays of taus generally require data-driven methods to model the rate of fake backgrounds28. The rate of identifying true hadronic tau decays, on the other hand, is modeled reasonably well with the ATLAS MC, as demonstrated in samples like selections of W → τhν or Z → ττ events, such as discussed in the following section on the observation of W → τhν at ATLAS. Indeed, scale factors have been measured for the rates of true hadronic decays of tau leptons, both in samples of W → τhν and Z → ττ events, which are generally consistent with 1 within their uncertainties [101, 102]. 4.4.2 Observation of W → τν The initial data-MC comparisons, discussed in the previous section, offered the first tests of the tau reconstruction and modeling of background candidates from QCD jets. The inaugural appearance of real hadronic decays of tau leptons at ATLAS came when sufficient data were collected in 2010 to observe the production W bosons decaying to tau leptons. With 546 nb−1 of integrated luminosity, ATLAS claimed observation of W → τhν decays [145]. Events were triggered which have a L2 tau candidate, which consists of a loosely-isolated calorimeter cluster with at least one matching track with pT > 6 GeV. The EF trigger that was used, required EmissT > 15 GeV. Events were selected if they have a hadronic tau decay with pT between 20 and 60 GeV, selected according to the tight cut-based selection described in Section 4.3.2; EmissT > 30 GeV; estimated significance 29 of the EmissT , SEmissT > 6; and no electrons or muons with pT > 15 GeV. The background is dominated by QCD multijet events. The E miss T significance requirement substantially purifies the W → τhν sample, and a clear peak can be seen in the distribution of the transverse mass between the tau candidate and the EmissT near the W mass as expected (see Figure 4.18). 28 Modeling backgrounds that fake tau ID is a theme that will be returned to many times in this thesis. For example, the use of the kW scale factor for the Z → ττ cross section measurement discussed in Section 5.7.2, and the fake factor method used to predict the W + jets background for the search for Z′ discussed in Section 6.4.4. 29 SEmissT = EmissT 0.5 √ GeV √∑ ET 76 4. tau reconstruction and identification T miss E S 0 2 4 6 8 10 12 14 N u m b e r o f E v e n ts / 0 .5 1 10 210 310 N u m b e r o f E v e n ts / 0 .5 -ID) h τ = 7 TeV ) (Tight sData 2010 ( -ID)hτQCD background (Loose EW background τ ν h τ →W -1Integrated Luminosity 546 nbATLAS Preliminary [GeV]Tm 0 20 40 60 80 100 120 N u m b e r o f E v e n ts / 1 0 G e V 0 5 10 15 20 25 30 35 40 N u m b e r o f E v e n ts / 1 0 G e V = 7 TeV )sData 2010 ( QCD background EW background τ ν h τ →W -1Integrated Luminosity 546 nb ATLAS Preliminary -IDτ Loose and fail Tight Tight Tm is s E S 0 2 4 6 8 10 12 14 16 18 20 AC BD = 7 TeV )sData 2010 ( -1Integrated Luminosity 546 nbATLAS Preliminary trackR 0 0.02 0.04 0.06 0.08 0.1 0.12 N u m b e r o f E v e n ts / 0 .0 0 5 0 20 40 60 80 100 N u m b e r o f E v e n ts / 0 .0 0 5 >6) miss TE = 7 TeV ) (SsData 2010 ( <6) miss T E QCD background (S EW background τ ν h τ →W -1Integrated Luminosity 546 nbATLAS Preliminary Figure 4.18: From the W → τhν observation, distributions of the the SEmissT with the full event selection except for the SEmissT cut (top-left), the mT distribution in the full event selection (top-right), the Rtrack distribution in the full event selection except with tau ID relaxed to loose (bottom-right), and an illustration of the ABCD control regions (bottom-left) [145]. The multijet background is estimated with a data-driven technique using the so-called "ABCD method". Four regions of the sample are selected, depending on if the events have a tau candidate that passes the tight tau identification or fails tight and passes loose, and if the events fail or pass the EmissT significance requirement as shown in Figure 4.18 (bottom-left). The shapes of the QCD background distributions in the signal region, A, are modeled with the data in region CD, scaled by the ratio of numbers of events in region B to D, corrected with Monte-Carlo-based estimates of the electroweak contamination. The sample contains an estimated 55.3 W → τhν events with a 70% purity. Figure 4.18 (bottomright) shows the distribution of one of the tau identification variables, Rtrack, in events with the tau identification requirement relaxed to passing loose, showing an excess of events above the backgrounds at low values of Rtrack, consistent with real hadronic decays of tau leptons. The next process producing tau leptons to emerge in the ATLAS data was Z → ττ , the observation and cross section measurement of which are discussed in Chapter 5. It includes a more 4.4 performance and systematic uncertainties 77 throughly explained example of using the ABCD method to the estimate the multijet background to Z → ττ → `τh. After the completion of the 2010 run, the cross sections for the production of W → τν [138] and Z → ττ [113] were measured with approximately 35 pb−1 of integrated luminosity. 4.4.3 Jet discrimination performance As an illustration of the kind of performance one can expect for the jet-tau discriminants, Figure 4.19 shows plots of the tau signal and jet background efficiencies for each of the identification methods used with the 2010 dataset. The background sample is taken from a selection of dijet events in the ATLAS data taken in late 2010 (period G). The signal is a combination of W → τν and Z → ττ simulation [147]. One should note that in practice, the background efficiency will depend on the event selection, as it depends on the pT distribution of the candidates considered and the type of partons that initiated the jets (i.e. the gluon/light-quark/b-quark fractions). Background efficiencies can differ by as much as a factor of five, depending on whether the jet is quark or gluon initiated [158]. The variation of the jet fake rate with composition is discussed in more detail in Section 4.4.8. The evaluation shown in Figure 4.19 gives an estimate of the performance30 for discriminating hadronic decays of tau leptons from QCD jets, independent of the optional requirements for discriminating taus from electrons, the performance of which is discussed in Section 4.4.4. Typically one can expect a medium working point to have a signal efficiency of ≈ 50%, with background efficiencies being less than 10% for the cut-based identification and a few percent for the likelihoodor BDTbased ID. Figures 4.20 and 4.21 show the pT-dependence of the performance of the discriminants. The upper bound on the signal efficiency is limited by the tracking reconstruction efficiency and therefore, is worse for 3-prong candidates. Note that being binned in the number of reconstructed tracks, these background efficiencies reported are with respect to tau candidates that have already been reconstructed with either 1 or 3 tracks, a small subset of reconstructed jets which generally have a broader distribution of number of tracks, as shown previously in Figure 4.4. The signal and background efficiencies are defined as the following. 30 There was a bug in TauDiscriminant at the time of release of this conference note [100]. The tight working point of the 1-prong cuts was not ∼ 15% efficient for 1-prong tau decays. As one can see in the plot of efficiency vs pT in Figure 4.21, the efficiency is consistently between 30 and 40%. TauDiscriminant was patched for physics use with the 2010 dataset and the working point decisions could be re-calculated real-time. 78 4. tau reconstruction and identification Signal Efficiency 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood >20GeV T 1-Prong p ATLAS Preliminary Signal Efficiency 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood >20GeV T 3-Prong p ATLAS Preliminary Signal Efficiency 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood >60GeV T 1-Prong p ATLAS Preliminary Signal Efficiency 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood >60GeV T 3-Prong p ATLAS Preliminary Figure 4.19: The inverse background efficiency versus signal efficiency for the jet-tau discriminants for 1-prong (left) and 3-prong (right) candidates, with pT > 20 GeV (top) and pT > 60 GeV (bottom), used with the 2010 dataset [100]. Signal efficiency: ε 1/3-prong sig =   # of tau candidates with 1/3 reconstructed track(s), passing ID, and truth-matched to a simulated 1/3-prong decay   (# of simulated visible hadronic taus with 1/3 prong(s)) Background efficiency: ε 1/3-prong bkg = (# of tau candidates with 1/3 reconstructed track(s), passing ID) (# of tau candidates with 1/3 reconstructed track(s)) 4.4.4 Electron discrimination performance Figure 4.16 showed the signal and background efficiencies of the BDT e-veto, previously introduced in Section 4.3.5. To constrain an uncertainty on the background efficiency, a modified tag-andprobe31 method with Z → ee events was used to measure the efficiency for real electrons to pass the e-veto. 31 See the discussion of the tag-and-probe method in Section 3.6.3. 4.4 performance and systematic uncertainties 79 [GeV]TE 20 30 40 50 60 70 80 90 100 Ba ck gr ou nd E ffi cie nc y / 5 G eV -310 -210 -110 1 10 Cuts BDT Likelihood 1-Prong Loose [GeV] (of match)T visE 20 30 40 50 60 70 80 90 100 Si gn al E ffi cie nc y / 5 G eV 0 0.2 0.4 0.6 0.8 1 Cuts BDT Likelihood 1-Prong Loose [GeV]TE 20 30 40 50 60 70 80 90 100 Ba ck gr ou nd E ffi cie nc y / 5 G eV -510 -410 -310 -210 -110 1 10 Cuts BDT Likelihood 1-Prong Medium [GeV] (of match)T visE 20 30 40 50 60 70 80 90 100 Si gn al E ffi cie nc y / 5 G eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Cuts BDT Likelihood 1-Prong Medium [GeV]TE 20 30 40 50 60 70 80 90 100 Ba ck gr ou nd E ffi cie nc y / 5 G eV -410 -310 -210 -110 1 10 Cuts BDT Likelihood 1-Prong Tight [GeV] (of match)T visE 20 30 40 50 60 70 80 90 100 Si gn al E ffi cie nc y / 5 G eV 0 0.1 0.2 0.3 0.4 0.5 0.6 Cuts BDT Likelihood 1-Prong Tight Figure 21: Loose, medium, and tight signal and background 1-prong e!ciencies over ET on release 15 samples where variables have been recalculated to look as predicted in release 16. 41 Figure 4.20: The background efficiency (left) and signal efficiency (right) vs pT for the loose/medium/tight working points (top/center/bottom) of the jet-tau discriminants for 1-prong candidates, used with the 2010 dataset [147]. 80 4. tau reconstruction and identification [GeV]TE 20 30 40 50 60 70 80 90 100 Ba ck gr ou nd E ffi cie nc y / 5 G eV -310 -210 -110 1 10 Cuts BDT Likelihood 3-Prong Loose [GeV] (of match)T visE 20 30 40 50 60 70 80 90 100 Si gn al E ffi cie nc y / 5 G eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Cuts BDT Likelihood 3-Prong Loose [GeV]TE 20 30 40 50 60 70 80 90 100 Ba ck gr ou nd E ffi cie nc y / 5 G eV -510 -410 -310 -210 -110 1 10 CutsBDT Likelihood 3-Prong Medium [GeV] (of match)T visE 20 30 40 50 60 70 80 90 100 Si gn al E ffi cie nc y / 5 G eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Cuts BDT Likelihood 3-Prong Medium [GeV]TE 20 30 40 50 60 70 80 90 100 Ba ck gr ou nd E ffi cie nc y / 5 G eV -510 -410 -310 -210 -110 1 10 CutsBDT Likelihood 3-Prong Tight [GeV] (of match)T visE 20 30 40 50 60 70 80 90 100 Si gn al E ffi cie nc y / 5 G eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CutsBDT Likelihood 3-Prong Tight Figure 22: Loose, medium, and tight signal and background 3-prong e!ciencies over ET on release 15 samples where variables have been recalculated to look as predicted in release 16. 42 Figure 4.21: The background efficiency (left) and signal efficiency (right) vs pT for the loose/medium/tight working points (top/center/bottom) of the jet-tau discriminants for 3-prong candidates, used with the 2010 dataset [147]. 4.4 performance and systematic uncertainties 81 ) [GeV]had-visτm(e, 50 60 70 80 90 100 110 120 130 140 150 En tri es / G eV 0 10 20 30 40 50 60 70 310× Data 2011 ee→Z -1dt L = 4.3 fb∫= 7 TeV, s ATLAS Preliminary ) [GeV]had-visτm(e, 50 60 70 80 90 100 110 120 130 140 150 En tri es / G eV 0 20 40 60 80 100 120 140 160 180 Data 2011 ee→Z -1dt L = 4.3 fb∫= 7 TeV, s ATLAS Preliminary loose BDT tau ID medium BDT electron ID Figure 11: Invariant mass of the electron-!had-vis pair in the selected events. On the left plot, no discrimination is applied on the probe !had-vis. The right plot shows only those events where the probe !had-vis has passed the BDT loose !had-vis identification and BDTmedium electron veto. and Z ! ee Monte Carlo simulations even without any background subtraction, as shown in Figure 11 (left). However, after the application of the jet and the electron discrimination, the purity of electron events in data is significantly reduced, as shown in Figure 11 (right), and an estimation of the background events is needed to measure correctly the mis-identification probability. After the background subtraction, the mis-identification probability is measured in data and compared with that estimated in Z ! ee Monte Carlo simulations. The data/MC correction factors are then extracted from the ratio of the two probabilities. The main source of systematic uncertainties is the background subtraction and this is estimated in a conservative way by comparing the data/MC correction factors with and without the background subtraction and taking the di!erence as uncertainty. Another source of systematic uncertainty comes from the event selection. The identification requirement and the energy scale of the tagging electron have been varied and the observed di!erences in the data/MC correction factors are also taken as a systematic uncertainty. The measurement has been performed in four pseudorapidity regions, which are defined using the !had-vis leading track direction: barrel (|"trk| < 1.37), crack (1.37 < |"trk | < 1.52), endcap (1.52 < |"trk| < 2.0) and forward endcap (|"trk | > 2.0). The estimated data/MC correction factors are found to be independent of the tightness of the !had-vis identification applied to the probe !had-vis and of the type of electron overlap removal. For this reason only correction factors for di!erent working points of the electron discrimination are reported in Table 1. electron BDT veto |"trk| < 1.37 1.37 < |"trk| < 1.52 1.52 < |"trk| < 2.00 |"trk| > 2.00 loose 0.96±0.22 0.8±0.3 0.47±0.14 1.7 ±0.4 medium 1.3 ±0.5 0.5 ±0.4 2.8 ±1.3 Table 1: The data/MC correction factors for the e"ciency of the electron discrimination applied to electrons mis-identified as !had-vis with pT > 20 GeV. The correction factors are not dependent on the tightness of the !had-vis identification or on the type of electron overlap removal. The quoted uncertainties are the sum in quadrature of statistical and systematic uncertainties. Some measurements are not available due to lack of su"cient data statistics. 12 Figure 4.22: Visible mass distributions of eτh candidates from the Z → ee tag-and-probe measurement of e-veto efficiency, for the selection without (left) and with (right) the medium BDT e-veto applied, using the 2011 dataset [102]. Figure 4.22 shows the visible mass of eτh pairs i the ta -and-probe selection, with and witho t the e-veto applied to the probe. In the selection without the veto, the Z → ee contribution is very pure. In the selection with the veto applied, the background contamination that is subtracted in the efficiency measurement becomes significant. The estimation of that background is the largest contribution to the systematic error on the e-veto scale factor. The mul ij t background is estimated from the statistically limited same-sign (SS) sample of `τh events in data, assuming the multijet background to be OS/SS symmetric. The remaining backgrounds from W → eν and tt events are estimated with MC [102]. Table 4.4 summarizes the results of the e-veto scale factor measurement with the 2011 dataset. Note that for the medium working point used by many analyses, the scale factors range from 0.5–2.3 in η-bins, with uncertainties ranging from 40–80%. 4.4.5 Energy calibration The clusters associated with a tau candidate are calibrated using the local hadron calibration (LC) [95], which should correctly bring the energy scale of the charged pions to the hadronic scale from the EM energy scale. The transverse energy of a tau candidate is calculated as the sum of the Table 4.4: The 2011 e-veto scale factors derived from the Z → ee tag-and-probe measurement [102]. ) [GeV]had-visτm(e, 50 60 70 80 90 100 110 120 130 140 150 En tri es / G eV 0 10 20 30 40 50 60 70 310× Data 2011 ee→Z -1dt L = 4.3 fb∫= 7 TeV, s ATLAS Preliminary ) [GeV]had-visτm(e, 50 60 70 80 90 100 110 120 130 140 150 En tri es / G eV 0 20 40 60 80 100 120 140 160 180 Data 2011 ee→Z -1dt L = 4.3 fb∫= 7 TeV, s ATLAS Preliminary loose BDT tau ID medium BDT electron ID Figure 11: Invariant mass of the electron-!had-vis pair in the selected events. On the left plot, no discrimination is applied on the probe !had-vis. The right plot shows only those events where the probe !had-vis has pa sed the BDT loo e !had-vis identification a d BDTmedium electron veto. and Z ! ee Monte Carlo simulations even without any background subtraction, as shown in Figure 11 (left). However, after the application of the jet and the electron discrimination, the purity of electron events in data is sign ficantly d c d, as shown in Figure 11 (right), and an estimation f the b ckground events is needed to measure correctly the mis-identification probability. After the background subtraction, the mis-identification probability is measured in data and compared with that estimated in Z ! ee Monte Carlo s mulations. The data/MC correction factors are then extracted from the ratio of the two probabilities. The main source of systematic uncertainties is the background subtraction and this is estimated in a conservative way by comparing the data/MC correction factors with and without the background subtraction and taking the di!erence as uncertainty. Another source of systematic uncertainty comes from the event selection. The identification requirement and the energy scale of the tagging electron have been varied and the observed di!erences in the data/MC correction factors are also taken as a systematic uncertainty. The measurement has been performed in four pseudorapidity regions, which are defined using the !had-vis leading track direction: barrel (|"trk| < 1.37), crack (1.37 < |"trk | < 1.52), endcap (1.52 < |"trk| < 2.0) and forward endcap (|"trk | > 2.0). The estimated data/MC correction factors are found to be independent of the tightness of the !had-vis identification applied to the probe !had-vis and of the type of electron overlap removal. For this reason only correction factors for di!erent working points of the electron discrimin tion are repo ted in Table 1. electron BDT veto |"trk| < 1.37 1.37 < |"trk| < 1.52 1.52 < |"trk| < 2.00 |"trk| > 2.00 loose 0.96±0.22 0.8±0.3 0.47±0.14 1.7 ±0.4 medium 1.3 ±0.5 0.5 ±0.4 2.8 ±1.3 Table 1: The data/MC correction factors for the e"ciency of the electron discrimination applied to electrons mis-identified as !had-vis with pT > 20 GeV. The correction factors are not dependent on the tightness of the !had-vis identification or on the type of electron overlap removal. The quoted uncertainties are the sum in quadrature of statistical and systematic uncertainties. Some measurements are not available due to lack of su"cient data statistics. 12 82 4. tau reconstruction and identification 20 100 200 re sp on se 1-prong tau candidates ATLAS Preliminary [GeV] T p LC 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 | < 0.3η0 < | | < 0.6η0.3 < | | < 1η0.6 < | | < 1.3η1 < | | < 1.6η1.3 < | |η1.6 < | 20 100 200 re sp on se multi-prong tau candidates ATLAS Preliminary [GeV] T p LC 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 | < 0.3η0 < | | < 0.6η0.3 < | | < 1η0.6 < | | < 1.3η1 < | | < 1.6η1.3 < | |η1.6 < | Figure 11: The response curves as a function of reconstructed tau pT at the LC scale for 1-prong (left) and multi-prong (right) tau candidates in various ! bins. leptons, which restores the tau energy to the true value. The initial direction is taken from the four-vector sum of clusters associated with the seed jet. All clusters within a cone of !R < 0.2 around this initial direction are used for tau energy calculation. The smaller cone radius reduces the dependence of the tau energy scale on pileup conditions and provides good energy resolution. The four-vector sum of the selected clusters defines the tau momentum at the LC scale. The additional tau energy calibration factor is then applied to this four-vector. The calibration factors are determined from MC simulated Z ! "" and Z" ! "" samples. Reconstructed tau candidates are required to match to a true hadronically decaying tau within !R < 0.2 and to pass the loose cutbased identification. No other kinematic selection is applied. The tau response is defined as the ratio of reconstructed tau energy at the LC scale divided by true tau visible energy. The response is binned in true visible energy, reconstructed |!| and for 1-prong and multi-prong candidates. In each bin, the core of the response distribution is fitted with a Gaussian. A response curve is constructed as a function of the LC scale energy, in bins of ! and Ntrack. The response is taken as the mean of the Gaussian fit and the LC scale energy is taken as the mean of the LC scale energy distribution in the given true energy bin. The e"ect of tau polarisation on the energy scale is also studied, but is found to have negligible e"ect. The response curves for 1-prong and multi-prong taus are shown in Fig. 11. At very low and high energies, the value of the response at the low and high end-points of the response curve are taken, respectively. 4 Performance This section describes the evaluation of systematic uncertainties associated with the performance of the tau reconstruction and identification algorithms. The performance of the identification algorithms is evaluated using tau candidates selected from data using tag and probe methods. The uncertainty on the energy scale is evaluated using MC simulation. The tag and probe methods rely on the ability to select a high purity sample of signal candidates (probes) from data without applying identification to the probe itself. This is achieved by tagging events from a process that has a very distinct signature, typically either an isolated lepton or a large amount of EmissT , which also contains a real signal candidate. In general, strict selection is applied to the tag, while selection on the probe is avoided if possible, to minimise bias on the identification variables of the probe. 17 ATLAS Preliminary [GeV]truth Tau candidates T p 20 40 60 80 100 )[% ] tru th T /p TE S T (p Δ -6 -4 -2 0 2 4 6 8 | < 1.3η1 prong: | Underlying event Hadronic shower Non closure Detector Material Pile up EM scale Noise Threshold Total sys. error ATLAS Preliminary [GeV]truth Tau candidates T p 20 40 60 80 100 )[% ] tru th T /p TE S T (p Δ -8 -6 -4 -2 0 2 4 6 8 10 | < 1.3ηMulti prong:| Underlying event Hadronic shower Non closure Detector Material Pile up EM scale Noise Threshold Total sys. error ATLAS Preliminary [GeV]truth Tau candidates T p 20 40 60 80 100 )[% ] tru th T /p TE S T (p Δ -6 -4 -2 0 2 4 6 8 10 12 | < 1.6η1 prong: 1.3 < | Underlying event Hadronic shower Non closure Detector Material Pile up EM scale Noise Threshold Total sys. error ATLAS Preliminary [GeV]truth Tau candidates T p 20 40 60 80 100 )[% ] tru th T /p TE S T (p Δ -10 -5 0 5 10 | < 1.6ηMulti prong: 1.3 < | Underlying event Hadronic shower Non closure Detector Material Pile up EM scale Noise Threshold Total sys. error ATLAS Preliminary [GeV]truth Tau candidates T p 20 40 60 80 100 )[% ] tru th T /p TE S T (p Δ -6 -4 -2 0 2 4 6 8 10 | > 1.6η1 prong: | Underlying event Hadronic shower Non closure Detector Material Pile up EM scale Noise Threshold Total sys. error [GeV]truth Tau candidates T p ATLAS Preliminary 20 40 60 80 100 )[% ] tru th T /p TE S T (p Δ -8 -6 -4 -2 0 2 4 6 8 10 12 | > 1.6ηMulti prong: | Underlying event Hadronic shower Non closure Detector Material Pile up EM scale Noise Threshold Total sys. error Figure 22: Final systematic uncertainty on the tau energy scale for 1-prong (left) and multi-prong (right) candidates, in the barrel (top), crack (middle) and endcap (bottom) regions. Each di!erent marker represents a separate source of uncertainty as indicated in the legend. The yellow band shows the combined uncertainty from all sources. 33 Figure 4.23: (left) Response functions for the 2011 TES. (right) The uncertainty on the 2011 TES as a function of pT derived with systematically shifted MC [101]. ET of each cluster associated to the tau in the core cone (∆R < 0.2). As a final correction to this energy, response functions are constructed based on Monte Carlo simulation of hadronic tau decays: response(pLCT ) = pLCT ptruthT . Then the reconstructed energy of a tau candidate is calculated by dividing the energy from the LC calibration by the response to bring it to the tau energy scale (TES). For example, Figure 4.23 (left) shows the response curves derived for tau candidates with the 2011 simulation and calibration. The corrections are generally small (∼ 1%) but drop from 1 more significantly at low-pT. Since the method of calibration relies on Monte Carlo, errors in the modeling need to be accounted for in the systematic uncertainties on the tau energy scale. Monte Carlo samples dedicated to evaluating systematics were generated and fully simulated with systematic shifts or changes of: the event generator, underlying event model, hadronic shower model, amount of detector material, and the topological clustering noise thresholds [100]. The uncertainty due to the changes in pile-up in 2011 dataset (with μ typically in the range of 3–20) is taken as the largest deviation in response in bins of μ resulting in 2% (1-prong) and 1.5% (3-prong). The uncertainty o the EM energy scale is 3% for all candidates, taken from test-beam measurements [90]. Finally an uncertainty is accounted for the n n-closure of he nominal MC sample evaluated as the deviation in the mean of the response from unity in bins of pT. The largest uncertainties come from the hadro ic showe model whi h range from 2–4% (1-prong) and 2–6% (3-prong) as a function of pT, and from non-closure which range from 1–5% as a function of pT, with largest total uncertainty being for low-pT 3-prong candidates (see Figure 4.23) [101]. Later in 2012, the TES was updated for the 2011 dataset with studies propagating single-particle4.4 performance and systematic uncertainties 83 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<0.3η| 1 prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (a) one-prong, |⌘⌧| < 0.3 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<0.3η| multi-prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (b) multi-prong, |⌘⌧| < 0.3 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<0.8η0.3<| 1 prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (c) one-prong, 0.3 < |⌘⌧| < 0.8 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<0.8η0.3<| multi-prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (d) multi-prong, 0.3 < |⌘⌧| < 0.8 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<1.3η0.8<| 1 prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty Hadronic shower model 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (e) one-prong, 0.8 < |⌘⌧| < 1.3 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<1.3η0.8<| multi-prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty Hadronic shower model 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (f) multi-prong, 0.8 < |⌘⌧| < 1.3 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<1.6η1.3<| 1 prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty Hadronic shower model 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (g) one-prong, 1.3 < |⌘⌧| < 1.6 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<1.6η1.3<| multi-prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty Hadronic shower model 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (h) multi-prong, 1.3 < |⌘⌧| < 1.6 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<2.5η1.6<| 1 prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty Hadronic shower model 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (i) one-prong, 1.6 < |⌘⌧| < 2.5 [GeV]τTP 20 30 40 50 60 70 80 100 200 Fr ac tio na l u nc er ta in ty 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 |<2.5η1.6<| multi-prong decays Single particle resp. Material modeling Underlying event Non-closure Pile-Up Total uncertainty Hadronic shower model 2011 Data + Simulation PreliminaryATLAS = 7 TeV s (j) multi-prong, 1.6 < |⌘⌧| < 2.5 Figure 9: TES uncertainty for one and multi-prong decays. The individual contributions are shown as points and the combined uncertainty is shown as a filled band. 15 ) [GeV]hadτ, l(vism 0 20 40 60 80 100 120 140 160 180 200 En tri es /5 G eV 0 200 400 600 800 1000 1200 1400 tt ν τ →W μ μ →Z ν μ →W Multijet τ τ →Z Data ATLAS Preliminary = 7 TeVs Data 2011-1 L dt = 4.26 fb∫ (a) |⌘⌧| < 0.8, ↵ =  10% ) [GeV]hadτ, l(vism 0 20 40 60 80 100 120 140 160 180 20 En tri es /5 G eV 0 200 400 600 800 1000 1200 1400 tt ν τ →W μ μ →Z ν μ →W Multijet τ τ →Z Data ATLAS Preliminary = 7 TeVs Data 2011-1 L dt = 4.26 fb∫ (b) |⌘⌧| < 0.8, ↵ =  1.5% ) [GeV]hadτ, l(vism 0 20 40 60 80 1 0 120 140 160 180 200 En tri es /5 G eV 0 200 400 600 800 1000 1200 1400 tt ν τ →W μ μ →Z ν μ →W Multijet τ τ →Z Data ATLAS Preliminary = 7 TeVs Data 2011-1 L t = 4.26 fb∫ (c) |⌘⌧| < 0.8, ↵ = 10% ) [GeV]hadτ, l(vism 0 20 40 60 80 100 120 140 160 180 200 En tri es /5 G eV 0 200 400 600 800 1000 1200 1400 1600 1800 2000 tt ν τ →W μ μ →Z ν μ →W Multijet τ τ →Z Data ATLAS Preliminary = 7 TeVs Data 2011-1 L dt = 4.26 fb∫ (d) 0.8 < |⌘⌧| < 2.5, ↵ =  10% ) [GeV]hadτ, l(vism 0 20 40 60 80 100 120 140 160 180 200 En tri es /5 G eV 0 200 400 600 800 1000 1200 1400 1600 1800 2000 tt ν τ →W μ μ →Z ν μ →W Multijet τ τ →Z Data ATLAS Preliminary = 7 TeVs Data 2011-1 L dt = 4.26 fb∫ (e) 0.8 < |⌘⌧| < 2.5, ↵ = 1.5% ) [GeV]hadτ, l(vism 0 20 40 60 80 100 120 140 160 180 200 En tri es /5 G eV 0 200 400 600 800 1000 1200 1400 1600 1800 2000 tt ν τ →W μ μ →Z ν μ →W Multijet τ τ →Z Data ATLAS Preliminary = 7 TeVs Data 2011-1 L dt = 4.26 fb∫ (f) 0.8 < ⌘⌧| < 2.5, ↵ = 10% Figure 10: Templates for |⌘⌧| < 0.8 nd 0.8 < |⌘⌧| < 2.5 for values for ↵ of -10% (left plots), +10% (right plots) and the best match with the data (middle plots). respect to statistical fluctuations than other methods. Figure 10 shows a selection of the templates, with data superimposed, for the two ⌘⌧ regions considered. Table 3 shows the value of ↵ obtained for th se |⌘⌧| regions. Here ↵ can be interpreted as th percentage scale to be applied to the TES such that the simulation matches the data. The di↵erence in the ↵ values extracted in |⌘⌧| < 0.8 and 0.8 < |⌘⌧| < 2.5 is found to be 3.0%. ↵ values |⌘⌧| < 0.8 -1.5% 0.8 < |⌘⌧| < 2.5 1.5% Table 3: ↵ values for the data visible mass distributions for the di↵erent ⌧h ⌘ regions. The following procedure is employed to evaluate the e↵ect of the statistical uncertainty in the data sample on the derivation of ↵. For each ⌘⌧ region, each bin of the observed visible mass distribution is varied within statistical error; then, the new distribution is re-matched to the templates. This is repeated in 1000 toy experiments, leading to a distribution of matched ↵ values. The statistical uncertainties, computed as standard deviations of the distributions of preferred templates, are 0.9% for |⌘⌧| < 0.8 and 0.7% for 0.8 < |⌘⌧| < 2.5. The uncertainty due to the limited statistics in the simulated distributions used to generate the template is evaluated in a similar way and found to be 1.0% for |⌘⌧| < 0.8 and 0.7% for 0.8 < |⌘⌧| < 2.5. 4.4 Systematic Uncertainties There are four main contributions to the systematic uncertainty on this method. They are the uncertainties on the scale factors for the identification e ciency of ⌧ leptons and muons, the muon energy resolution, the uncertainty on the embedding procedure and uncertainty in the pileup simulation. Each of these uncertainties is evaluated by generating new templates that are systematically varied. The systematic uncertainty on the measured ⌧ identification scale factors is ± 4% for P⌧T > 22 GeV and ± 8% for 20 GeV < P⌧T < 22 GeV. Muon identification and energy resolution scale factors are each 18 Figure 4.24: (left) The uncertainty on the updated 2011 TES as a function of pT derived with single-particle-response uncertainties. (right) The visible mass of μτh candidates in a Z → ττ selection with he TES shifted by +10%, for example, which can be constrained by the poor agreement between data and MC in the Z → ττ peak [159]. response uncertainties constrained separately for low-pT hadrons (from in situ 〈E/p〉measurements), high-pT hadrons (from test-beam measurements), and neutral pions (EM scale from Z → ee measurements), directly to simulated hadronic decays of tau leptons, constraining the TES to 2–3% (see Figure 4.24 (left)). A data-driven method has also been tested, directly measuring the shift of the vi ible mass peak of a sample of Z → ττ → μτh events, which resulted in an uncertainty of ≈ 3% with the 2011 dataset of 4.26 fb−1 (see Figure 4.24 (right)). This data-driven method is expected to improve in precision as it is updated with the 2012 dataset [159, 160]. 4.4.6 Tau identification efficiency Like the first systematic uncertainty on the tau energy scale described in the previous section, the first recommended systematic on the tau identification efficiency was derived with dedicated Monte Carlo samples with systematic shifts or changes of: the event generator, underlying event model, hadronic shower model, amount of detector material, and the topological clustering noise thresholds. This constrains the efficiency scale factor t ≈ 10%, consistent with 1 [100]. Figure 4.25 shows the efficiency tur -on vs pT for true hadronic taus passing the 2010 me ium cut-based identification, illustrating the change in efficiency for each systematic shift. Later, the tau identification efficiency was measured with a tag-and-probe sample of W → τν events in the 2010 data [161], and tag-and-probe samples of W → τν and Z → ττ → μτh events in the 2011 data [101]. Figure 4.26 shows the 2011 Z → ττ → μτh tag-and-probe events before and after the medium BDT identification is applied. In 2012, the Z → ττ tag-and-probe study has constrained the efficiency to 2–3% for true 1-prong hadronic tau decays and 5–6% for 3-prong [103]. 84 4. tau reconstruction and identification 20 40 60 80 100 Ta u ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Looser Cuts working point 1 prong ATLAS Preliminary Nominal Detector Material Hadronic Shower Underlying Event Noise threshold Total sys. error of truth tau [GeV] T Visible p 20 40 60 80 100 R at io 0.8 0.9 1 1.1 1.2 20 40 60 80 100 Ta u ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Looser Cuts working point 3 prongs ATLAS Preliminary Nominal Detector Material Hadronic Shower Underlying Event Noise threshold Total sys. error of truth tau [GeV] T Visible p 20 40 60 80 100 R at io 0.8 0.9 1 1.1 1.2 20 40 60 80 100 Ta u ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Looser Likelihood working point 1 prong ATLAS Preliminary Nominal Detector Material Hadronic Shower Underlying Event Noise threshold Total sys. error of truth tau [GeV] T Visible p 20 40 60 80 100 R at io 0.8 0.9 1 1.1 1.2 20 40 60 80 100 Ta u ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Looser Likelihood working point 3 prongs ATLAS Preliminary Nominal Detector Material Hadronic Shower Underlying Event Noise threshold Total sys. error of truth tau [GeV] T Visible p 20 40 60 80 100 R at io 0.8 0.9 1 1.1 1.2 20 40 60 80 100 Ta u ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Looser BDT working point 1 prong ATLAS Preliminary Nominal Detector Material Hadronic Shower Underlying Event Noise threshold Total sys. error of truth tau [GeV] T Visible p 20 40 60 80 100 R at io 0.8 0.9 1 1.1 1.2 20 40 60 80 100 Ta u ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Looser BDT working point 3 prongs ATLAS Preliminary Nominal Detector Material Hadronic Shower Underlying Event Noise threshold Total sys. error of truth tau [GeV] T Visible p 20 40 60 80 100 R at io 0.8 0.9 1 1.1 1.2 Figure 10: Signal e!ciencies for the looser example working points as a function of pT, and the ratio of the signal e!ciency of the di"erent systematics sources to the nominal signal Monte Carlo. E!ciencies for 1-prong candidates are on the left, and 3-prong is on the right. The first row shows the e!ciency for the cuts; the second shows the likelihood; the third shows the BDT. The yellow band shows the total systematic uncertainty. 21 Figure 4.25: The tau identification efficiency uncertainty for the 2010 cut-based ID, using dedicated Monte Carlo samples with systematic shifts or changes of: the event generator, underlying event model, had onic shower model, amount of detector material, and the topological clustering noise thresholds, [100]. 5. Tau reconstruction and identification 67 uncertainty is obtained from pseudo-experiments treating all uncertainties as uncorrelated. For both the 1-prong and 3-prong measurements the statistical uncertainty is comparable to the uncertainty from the QCD multi-jet normalisation, while for the combined measurement the QCD multi-jet uncertainty dominates. The data/MC correction factors for inclusive, 1-prong and 3-prong  had-vis candidates for the low pile up period are found to be consistent with unity, as summarised in Table 6. The correction factors measured in the high pile up period are also consistent with unity. ) [GeV]had-visτ,μm( 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / 5 G eV 0 500 1000 1500 2000 2500 3000 3500 4000 4500 ATLAS Preliminary -1dt L = 1.8 fb∫ = 7 TeVs Before Tau ID Inclusive Data early 2011 ττ→Z νμ→W Multi-jet μμ→Z ντ→W (mis-ID)ττ→Z tt ) [GeV]had-visτ,μm( 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / 5 G eV 0 200 400 600 800 1000 1200 1400 ATLAS Preliminary -1dt L = 1.8 fb∫ = 7 TeVs After medium BDT ID Inclusive Data early 2011 ττ→Z νμ→W Multi-jet μμ→Z ντ→W (mis-ID)ττ→Z tt Figure 13: Z      (side-band extrap.) measurement: Visible mass distributions before applying  had-vis ID (left) and after applying the BDT medium identification (right) to the probe  had-vis for the low pile up period. Uncertainty contributions (%) ID  MC(±stat)  Data   stat   W+jets   QCD   exp.   Total BDT loose 0.748±0.003 822 2.3 0.3 3.9 2.2 5.1 BDT medium 0.534±0.003 0.574 .5 0.3 4.2 2.2 5.4 BDT tight 0.282±0.003 0.297 2.9 0.3 4.3 2.2 5.8 LLH loose 0.833±0.002 0.936 2.0 0.3 3.3 2.2 4.5 LLH medium 0.607±0.003 0.669 2.3 0.3 3.9 2.2 5.1 LLH tight 0.332±0.003 0.358 2.8 0.3 4.3 2.2 5.6 Table 5: Z      (side-band extrap.) measurement: Inclusive  had-vis identification e ciencies in MC and measured from data for the low pile up period with all measurement uncertainties. The total uncertainty is obtained from pseudo-experiments treating all uncertainties as uncorrelated. 5.2.4 The pT-binned Measurement In this section, the study is repeated in bins of the pT of the probe  had-vis candidate. The method is identical, except that a sliding window on the visible mass is used to increase the signal purity in each  had-vis pT bin: x < m(μ,  had-vis) < x + 25 GeV, where x is the sum of the lower thresholds on the tag muon and probe  had-vis. The threshold on the muons is 20 GeV and the  had-vis pT bins are: 20, 25, 30, 35, 40, 50, 60 GeV. To increase the sample size in each bin, the low and high pile up periods are combined together. Figure 14 shows the  had-vis identification e ciencies measured in data and estimated in Monte Carlo simulation for 1-prong and 3-prong candidates for the BDT medium identification working point. 18 ID inclusive 1-prong 3-prong BDT loose 1.10±0.06 1.07±0.04 1.18±0.13 BDT medium 1.07±0.06 1.05±0.05 1.16±0.13 BDT tight 1.05±0.06 1.00±0.05 1.19±0.14 LLH loose 1.12±0.05 1.09±0.04 1.23±0.11 LLH medium 1.10±0.06 1.06±0.05 1.23±0.13 LLH tight 1.08±0.06 1.04±0.05 1.19±0.14 Table 6: Z      (side-band extrap.) measurement: pT-inclusive data/MC correction factors including the combined syste atic and statistical uncertainty measured in the low pile up period. 152025303540450560 IDε 0.4 0.6 0.8 1 1.2 1.4 1.6 Data 2011 ττ→Z MC Stat. + Measur. Syst. Uncert. ATLAS Preliminary 1-Prong, BDT Medium =7 TeV, -1 dt L = 3.6 fb∫ ) [GeV]had-visτ(Tp 15 20 25 30 35 40 45 50 55 60 M C IDε/ D at a IDε 0.5 1 1.5 152025303540450560 IDε 0.4 0.6 0.8 1 1.2 1.4 1.6 Data 2011 ττ→Z MC Stat. + Measur. Syst. Uncert. ATLAS Preliminary 3-Prong, BDT Medium =7 TeVs, -1 dt L = 3.6 fb∫ ) [GeV]had-visτ(Tp 15 20 25 30 35 40 45 50 55 60 M C IDε/ D at a IDε 0.5 1 1.5 Figure 14: Z      (side-band extrap.) measurement:  had-vis identification e ciencies in bins of the  had-vis pT for 1-prong (left) and 3-prong (right) candidates for the BDT medium identification working point. The errors on the measured e ciencies include systematic and statistical unc rtainties, while the errors o the simulated e ciencies are only statistical uncertainties. The data/MC correction factors are shown at the bottom and their error bars include only the statistical uncertainty. The yellow band includes the systematic uncertainty of the measurement and the statis ical uncertainty of the simulated e ciencies. 19 uncertainty is obtained from pseudo-experiments treating all uncertainties as uncorrelated. For both the 1-prong and 3-prong measurements the statistical uncertainty is comparable to the uncertainty from the QCD multi-jet normalisation, while for the combined measurement the QCD multi-jet uncertainty dominates. The data/MC correction factors for inclusive, 1-prong and 3-prong  had-vis candidates for the low pile up period are found to be consistent with unity, as summarised in Table 6. The correction factors measured in the high pile up period are also consistent with unity. ) [GeV]had-visτ,μm( 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / 5 G eV 0 500 1000 1500 2000 2500 3000 3500 4000 4500 ATLAS Preliminary -1dt L = 1.8 fb∫ = 7 TeVs Before Tau ID Inclusive Data early 2011 ττ→Z νμ→W Multi-jet μμ→Z ντ→W (mis-ID)ττ→Z tt ) [GeV]had-visτ,μm( 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / 5 G eV 0 200 400 600 800 1000 1200 1400 ATLAS Preliminary -1dt L = 1.8 fb∫ = 7 TeVs After medium BDT ID Inclusive Data early 2011 ττ→Z νμ→W Multi-jet μμ→Z ντ→W (mis-ID)ττ→Z tt Figure 13: Z      (side-band extrap.) measurement: Visible mass distributions before applying  had-vis ID (left) and after applying the BDT medium identification (right) to the probe  had-vis for the low pile up period. Uncertainty contri utions (%) ID  MC(±stat)  Data   stat   W+jets   QCD   exp.   Total BDT loose 0.748±0.003 0.822 2.3 0.3 3.9 2.2 5.1 BDT medium 0.534±0.003 0.574 2.5 0.3 4.2 2.2 5.4 BDT tight 0.282±0.003 0.297 2.9 0.3 4.3 2.2 5.8 LLH loose 0.833±0.002 0.936 2.0 0.3 3.3 2.2 4.5 LLH medium 0.607±0.003 0.669 2.3 0.3 3.9 2.2 5.1 LLH tight 0.332±0.003 0.358 2.8 0.3 4.3 2.2 5.6 Table 5: Z      (side-band extrap.) measurement: Inclusive  had-vis identification e ciencies in MC and measured from data for the low pile up period with all measurement uncertainties. The total uncertainty is obtained from pseudo-experiments treating all uncertainties as uncorrelated. 5.2.4 The pT-binned Measurement In this section, the study is repeated in bins of the pT of the probe  had-vis candidate. The method is identical, except that a sliding window on the visible mass is used to increase the signal purity in each  had-vis pT bin: x < m(μ,  had-vis) < x + 25 GeV, where x is the sum of the lower thresholds on the tag muon and probe  had-vis. The threshold on the muons is 20 GeV and the  had-vis pT bins are: 20, 25, 30, 35, 40, 50, 60 GeV. To increase the sample size in each bin, the low and high pile up periods are combined together. Figure 14 shows the  had-vis identification e ciencies measured in data and estimated in Monte Carlo simulation for 1-prong and 3-prong candidates for the BDT medium identification working point. 18 Figure 5.42: TODO [115]. e ciency with 2011 dataset is suggested to be: • pT  100 GeV:  " = 4% (taken from the Z ! ⌧⌧ measurement) • 100 < pT < 350 GeV:  " = 4 + 0.016 * (pT   100)%, with pT in GeV (taken from the linear fit in the dijets m asurement). • pT   350 GeV:  " = 8%, (taken from the largest deviation in the dijets measurement). This prescription details a low uncertainty at low-pT (coming from the tag and probe measurements), foll ed by a linear inflation in the uncertainty as a function of pT (quantifying the limitation of our kn wledge from the ijets measu ement), with a maximum uncertainty of 8% reached at pT = 350 GeV (which is the maximum deviation in the dijets measurement) [110]. Table 5.7: TODO. Data/MC tau ID e ciency ratio (SF) measured in bin of tau-pT in the Z ! ⌧⌧ tag and probe analysis. The individual contributions to the uncertainty are: the statistical uncertainty,  SFstat; the normalisation uncertainties on the W+jets and multijet backgrounds,  SFW+jets and  SFQCD; and the experimental uncertainties on the muon, tau and the integrated luminosity,  SFexp [110]. Data/MC Scale factor uncertainty contributions (%) pT [GeV] SF  SFstat  SFW+jets  SFQCD  SFexp  SFTotal 20–25 1.112±0.107 5.3 1.2 7.4 1.8 9.6 25–30 1.054±0.060 3.7 0.7 3.5 1.9 5.7 30–35 1.000±0.045 3.3 0.6 1.9 2.0 4.5 35–40 1.018±0.045 3.5 0.6 1.3 2.0 4.4 40–50 1.022±0.047 3.8 0.5 1.2 2.0 4.6 50–60 1.301±0.190 13.8 2.1 2.6 1.5 14.6 ID inclusive 1-prong 3-prong BDT loose 1.10±0.06 1.07±0.04 1.18±0.13 BDT medium 1.07±0.06 1.05±0.05 1.16±0.13 BDT tight 1.05±0.06 1.00±0.05 1.19±0.14 LLH loose 1.12±0.05 1.09±0.04 1.23±0.11 LLH medium 1.10±0.06 1.06±0.05 1.23±0.13 LLH tight 1.08±0.06 1.04±0.05 1.19±0.14 Table 6: Z ! !! (side-band extrap.) measurement: pT-inclusive data/MC correction factors including the combined systematic nd statistical uncertainty measured in the low pile up period. 4 6 IDε 0.4 0.6 0.8 1 1.2 1.4 1.6 Data 2011 ττ→Z MC Stat. + Measur. Syst. Uncert. ATLAS Preliminary 1-Prong, BDT Medium =7 TeVs, -1 dt L = 3.6 fb∫ ) [GeV]had-visτ(Tp 15 20 25 30 35 40 45 50 55 60 M C IDε/ D at a IDε 0.5 1 1.5 12 50 IDε 0.4 0.6 0.8 1 1.2 1.4 1.6 Data 2011 ττ→Z MC Stat. + Measur. Syst. Uncert. ATLAS Preliminary 3-Prong, BDT Medium =7 TeVs, -1 dt L = 3.6 fb∫ ) [GeV]had-visτ(Tp 15 20 25 30 35 40 45 50 55 60 M C IDε/ D at a IDε 0.5 1 1.5 Figure 14: Z ! !! (side-band extrap.) measurement: !had-vis identification e!ciencies in bins of the !had-vis pT for 1-prong (left) and 3-prong (right) candidates for the BDT medium identification working point. The errors on the measured e!ciencies include systematic and statistical uncertainties, while the errors on the simulated e!ciencies are only statistical uncertainties. The data/MC co rection factors are shown at the bottom and their rror bars n lude only the statistical uncertainty. The yellow b n includ s the systematic un ertainty of the measurement and the statistical uncertainty of the simulated e!ciencies. 19 Figure 4.26: The visible mass of μτh candidates in the Z → ττ tag-and-probe selection without tau ID required (left-top), and after medium BDT ID (left-bottom). (right) Th scale factors derived after subtracting background and dividing those selections [1 2]. 4.4 performance and systematic uncertainties 85 4.4.7 Performance at high-pT Primarily in the course of the analysis of the 2011 dataset for the Z ′ → ττ search reported in Chapter 6, several issues arose concerning the high-pT behavior of reconstructed hadronic decays of taus. These include specific degradations in the performance of parts of the reconstruction and identification, and uncertainties on the modeling of the high-pTbehavior. The issues discussed here are documented in more detail in the 2011 Z ′ → ττ search support note [97]. High-pT tau ID performance with Z ′ Monte Carlo Figure 4.27 shows the tau identification efficiency measured with a sample of high-pT tau decays from Monte Carlo simulation of a Sequential Standard Model (SSM) Z ′ boson with a mass of 1000 GeV. It shows that the tau reconstruction and identification efficiency is flat vs pT for the 1-prong identification, but falls gradually for the 3-prong identification. Figure 4.28 shows the reconstruction efficiency for true 3-prong hadronic tau decays to be reconstructed with 2, 3, or 4 tracks. It demonstrates that the falling 3-prong efficiency is due to miscounting the number of tracks at high pT, and not due to the tau discriminants themselves [162]. The effect is most likely due to highly collimated tracks having overlapping hits and not being resolvable, but this hypothesis needs additional study. Figures 4.29 and 4.30 show the efficiencies for the tau discriminants for 1-prong hadronic tau decays for the 2011 dataset, measured with Monte Carlo simulation of a SSM Z ′ with a mass of 1000 GeV. They show that the jet and muon discrimination is flat vs pT, while the electron vetoes are more harsh on the signal at high pT. Table 4.5: Data/MC tau ID efficiency ratio (SF) measured in bin of tau-pT in the Z → ττ tag and probe analysis. The individual contributions to the uncertainty are: the statistical uncertainty, ∆SFstat; the normalisation uncertainties on the W+jets and multijet backgrounds, ∆SFW+jets and ∆SFQCD; and the experimental uncertainties on the muon, tau and the integrated luminosity, ∆SFexp [97]. Data/MC Scale factor uncertainty contributions (%) pT [GeV] SF ∆SFstat ∆SFW+jets ∆SFQCD ∆SFexp ∆SFTotal 20–25 1.112±0.107 5.3 1.2 7.4 1.8 9.6 25–30 1.054±0.060 3.7 0.7 3.5 1.9 5.7 30–35 1.000±0.045 3.3 0.6 1.9 2.0 4.5 35–40 1.018±0.045 3.5 0.6 1.3 2.0 4.4 40–50 1.022±0.047 3.8 0.5 1.2 2.0 4.6 50–60 1.301±0.190 13.8 2.1 2.6 1.5 14.6 86 4. tau reconstruction and identification ) [GeV] h τ( T p 0 100 200 300 400 500 600 700 800 E ff ic ie n c y / 2 0 G e V 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Loose Cut Loose LLH Loose BDT Medium Cut Medium LLH Medium BDT Tight Cut Tight LLH Tight BDT ) [GeV] h τ( T p 0 100 200 300 400 500 600 700 800 E ff ic ie n c y / 2 0 G e V 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Loose Cut Loose LLH Loose BDT Medium Cut Medium LLH Medium BDT Tight Cut Tight LLH Tight BDT Figure 4.27: The efficiency for true 1-prong (left) and 3-prong (right) hadronic tau decays to be reconstructed with the correct number of tracks and pass the tau discriminants for rejecting jets, measured with Monte Carlo simulation for a SSM Z ′ with a mass of 1000 GeV [97]. Figure 4.28: The efficiency for true 3-prong hadronic tau decays to be reconstructed with 2, 3, or 4 tracks, measured with Monte Carlo simulation for a SSM Z ′ with a mass of 1000 GeV [97]. High-pT tau ID efficiency uncertainty In support of the Z ′ → ττ analysis, studies were done to quantify the fidelity of the simulation in modelling the tau identification at high-pT. The conclusion of these studies is that while no degradation of the modeling at high-pT is observed (within the uncertainty of the measurements), the uncertainty on the tau ID efficiency should be inflated linearly with pT, up to a maximum uncertainty, to account for the increased uncertainty from the extrapolation technique used in the studies. The tau ID efficiency is constrained to within about 4% with a tag-and-probe32 measurement selecting Z → ττ events [101], but that quantifies the performance only with candidates pT . 60 GeV. 32 See the discussion of the tag-and-probe method in Section 3.6.3. 4.4 performance and systematic uncertainties 87 ) [GeV] h τ(truth T p 0 100 200 300 400 500 600 e ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 JetBDTSigLoose JetBDTSigMedium JetBDTSigTight ATLAS Internal ) [GeV] h τ(truth η -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 e ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 JetBDTSigLoose JetBDTSigMedium JetBDTSigTight ATLAS Internal Figure 4.29: The efficiency true for 1-prong hadronic tau decays to be reconstructed and pass the tau discriminants for rejecting jets, in Monte Carlo simulation for a SSM Z ′ with a mass of 1000 GeV, as a function of the true visible pT (left) and η of hadronic tau decays [97]. ) [GeV] h τ(truth T p 0 100 200 300 400 500 600 e ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 EleBDTLoose EleBDTMedium EleBDTTight MuonVeto ATLAS Internal ) [GeV] h τ(truth η -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 e ff ic ie n c y 0 0.2 0.4 0.6 0.8 1 1.2 EleBDTLoose EleBDTMedium EleBDTTight ATLAS Internal Figure 4.30: The efficiency true for 1-prong hadronic tau decays to be reconstructed with the corrected number of tracks and pass the tau discriminants for rejecting leptons, in Monte Carlo simulation for a SSM Z ′ with a mass of 1000 GeV, as a function of the true visible pT (left) and η of hadronic tau decays [97]. The difficulty in quantifying the fidelity of tau ID at high-pT is that there are no abundant sources of hadronic tau decays with pT & 80 GeV in the data. This disqualifies the possibility of a direct measurement, however, one can ask whether the modeling of tau ID in simulation at high-pT is any poorer than at low-pT. To answer this question, the assumption is made that data-MC mis-modelling can be attributed to incorrect modelling of either 1) the tau decay, or 2) the detector response. Since the simulation of tau decay branching-fractions and kinematics done by TAUOLA [127] has been well constrained for low-pT candidates, boosting taus to higher pT should not introduce mis-modelings. Therefore, the most important aspect of the study is to show that the detector response is modelled accurately 88 4. tau reconstruction and identification at high-pT. To establish an estimate of the uncertainty of the high-pT tau ID efficiency, first the tag-andprobe efficiency measurement using Z → ττ was performed in a number of pT-bins to investigate the behaviour of the data-MC efficiency scale factors as a function of pT. Figure 4.26 and Table 4.5 show the results of the scale factor measurements, giving no suggestion of a trend [97]. Second, a comparison was made of the tau ID variables for high-pT candidates between simulated dijet events and dijet events selected from data, since a sample of fake taus still provides plenty of pions to test detector modeling. The scale factor for the fake rate was evaluated as a function of pT and found not to have a significant trend. The scale factor vs pT was fit to a line, with the slope constrained to 0.016% per 100 GeV. Given these observations, the uncertainty on the tau identification efficiency with 2011 dataset is suggested to be: • pT ≤ 100 GeV: ∆ε = 4% (taken from the Z → ττ measurement) • 100 < pT < 350 GeV: ∆ε = 4 + 0.016 * (pT − 100)%, with pT in GeV (taken from the linear fit in the dijets measurement). • pT ≥ 350 GeV: ∆ε = 8%, (taken from the largest deviation in the dijets measurement). This prescription details a low uncertainty at low-pT (coming from the tag and probe measurements), followed by a linear inflation in the uncertainty as a function of pT (quantifying the limitation of our knowledge from the dijets measurement), with a maximum uncertainty of 8% reached at pT = 350 GeV (which is the maximum deviation in the dijets measurement) [97]. High-pT 3-prong reconstruction efficiency uncertainty As shown in Figure 4.28, the reconstruction efficiency for 3-prong taus decreases at high-pT. The effect is due to track merging, which becomes more probable as the tracks in the tau decay become more collimated, hence a large number of 3-prong taus are reconstructed with only two tracks. Track merging in hadronic jets has been studied [163, 164]. In general, the modelling of shared and merged hits in MC simulation is observed to be in very good agreement with data. However, a conservative uncertainty of 50% on the tracking efficiency loss due to shared hits in MC simulation is assumed, as a direct measurement of the data/MC efficiency ratio was not possible. The same prescription is used to derive an uncertainty on the 3-prong reconstruction efficiency in this analysis. Firstly, it is observed from Figure 4.28 that above ≈ 150 GeV, the 3-prong reconstruction efficiency in MC drops by ≈ 12% every 100 GeV. Taking 50% of this efficiency drop as the uncertainty on the 3-prong reconstruction efficiency leads to the following prescription: • pT ≤ 150 GeV: no additional uncertainty 4.4 performance and systematic uncertainties 89 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 142 significantly among di!erent types of samples with jets. For example, the fake rate is known to be2259 ! 2 times larger in W+jets events than in multijet events with a muon (see Figure 88). A reasonable2260 hypothesis for explaining the observed variance in fake rates is that the parton composition of the jets2261 varies among the samples, that is, the relative mix of quarks and gluons that initiated the jets. Gluons2262 are known to produce wider jets than quarks of the same energy [99, 100], and should therefore have a2263 smaller rate to fake tau identification, which prefers narrow candidates.2264 Since the multijet background falls more quickly at high mass than the W+jets background, and2265 because the multijet background can be independently estimated from non-isolated leptons (see Sec-2266 tion 5.5.2), we correct for the multijet contamination and only apply tau identification fake rates that are2267 appropriate for W+jets events.2268 ) [GeV]hτ(Tp 0 50 100 150 200 250 )+ je ts ν μ → : W ( τ f 0 0.02 0.04 0.06 0.08 0.1 Inclusive ) h τ, μOS( ) h τ, μSS( ATLAS Internal ) [GeV]hτ(Tp 0 50 100 150 200 250 : m ul tije t τ f 0 0.02 0.04 0.06 0.08 0.1 Inclusive ) h τ, μOS( ) h τ, μSS( ATLAS Internal Figure 88: Comparison of tau identification fake factors measured in the W+jets (left) and mulitjet (right) control regions, for the BDT medium tau-jet discriminant. G.5.2 W+jets control region2269 Section 5.5.3 discussed the W+jets control region used to derive tau identification fake factors. It is2270 • exactly one preselected lepton,2271 • exactly one isolated lepton,2272 • at least one preselected hadronic tau candidate,2273 • mT(!, EmissT ) > 70 GeV,2274 Most of the electroweak and multijet contamination in this control region is removed by the cut on2275 mT(!, EmissT ). Figure 89 shows the distribution of mT(μ, E miss T ) near the W(" μ")+jets control region,2276 before the restriction on mT(μ, EmissT ) > 70 GeV.2277 This method assumes that regions of the event selection where tau identification is inverted are dom-2278 inated by W(" !")+jets events. These selections are contaminated by non-W(" !")+jets events at2279 ! 25%, ! 25%, and ! 20% after event preselection, baseline event selection, and signal region event2280 selection, respectively. These selections are described in Section 5.4. Figures 90–91 show kinematic2281 distributions after event preselection, baseline event selection and signal event selection, respectively,2282 with tau identification inverted and tau identification fake factors weighting applied. In these figures, the2283 di!erence between data and Monte Carlo comprises the W+jets estimation in that kinematic variable. If2284 the Monte Carlo estimated contamination exceeds the data, the W+jets estimation is set to zero.2285 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 142 significantly a ong di!erent types of sa ples ith jets. For exa ple, the fake rate is kno n to be2 59 ! 2 ti es larger in +jets events than in ultijet events ith a uon (see Figure 88). reasonable2 60 hypothesis for explaining the observed variance in fake rates is that the parton co position of the jets2 61 varies a ong the sa ples, that is, the relative ix of quarks and gluons that initiated the jets. luons2 62 are kno n to produce ider jets than quarks of the sa e energy [99, 100], and should therefore have a2 63 s al er rate to fake tau identification, hich prefers nar o candidates.2 64 Since the ultijet background fal s ore quickly at high ass than the +jets background, and2 65 because the ultijet background can be independently esti ated fro non-isolated leptons (see Sec-2 6 tion 5.5.2), e cor ect for the ultijet conta ination and only apply tau identification fake rates that are2 67 appropriate for +jets events.2 68 ) [GeV]hτ(Tp 0 50 100 150 200 250 )+ je ts ν μ → : W ( τ f 0 0.02 0.04 0.06 0.08 0.1 Inclusive ) h τ, μOS( ) h τ, μSS( ATLAS Internal ) [GeV]hτ(Tp 0 50 100 150 200 250 : m ul tije t τ f 0 0.02 0.04 0.06 0.08 0.1 Inclusive ) h τ, μOS( ) h τ, μSS( ATLAS Internal Figure 88: Co parison of tau identification fake factors easured in the +jets (left) and ulitjet (right) control regions, for the B T ediu tau-jet discri inant. .5.2 jets control region2 69 Section 5.5.3 discussed the +jets control region used to derive tau identification fake factors. It is2 70 • exactly one preselected lepton,2 71 • exactly one isolated lepton,2 72 • at least one preselected hadronic tau candidate,2 73 • T(!, EmisT ) > 70 e ,2 74 ost of the electro eak and ultijet conta ination in this control region is re oved by the cut on2 75 T(!, EmisT ). Figure 89 sho s the distribution of T(μ, E mis T ) near the ( μ")+jets control region,2 76 before the restriction on T(μ, EmisT ) > 70 e .2 7 This ethod assu es that regions of the event selection here tau identification is inverted are do -2 78 inated by ( !")+jets events. These selections are conta inated by non- ( !")+jets events at2 79 ! 25 , ! 25 , and ! 20 after event preselection, baseline event selection, and signal region event2 80 selection, respectively. These selections are described in Section 5.4. Figures 90–91 sho kine atic2 81 distributions after event preselection, baseline event selection and signal event selection, respectively,2 82 ith tau identification inverted and tau identification fake factors eighting applied. In these figures, the2 83 di!erence bet een data and onte Carlo co prises the +jets esti ation in that kine atic variable. If2 84 the onte Carlo esti ated conta ination exceeds the data, the +jets esti ation is set to zero.2 85 Figure 4.31: Fake fact rs derived for the medium BDT t ID i a sample of events fro the 2011 dataset rich in W → μν+jets events (left) and dijet events (right) with the 2011 data [97]. • pT > 150 GeV: ∆ε3-prong = 0.06 * (pT − 150)% with pT in GeV. 4.4.8 Variation of jet fake rates with composition As previously noted in Section 4.4.1, fake rates for jet-tau discrimination are strongly correlated with measures of th width the tau c ndidate, in both the calorimeter and among its associated tracks. Misodeling of the width of jets and the distribution of tracks in the ATLAS MC motivates the use of data-driven estimates of fake backgrounds to hadronic tau decays. An additional challenge w n modeling fake backgrounds is t at the width of jets can vary among samples in the data, depending on the kinematics and composition of the jets that are selected. Figure 4.31 shows distributions of fake factors33 measured samples enriched in W + jets and dijet events. Note that th fake factor can be significa tly higher in a sample of W + jets ev nts than in dijet events. An explanation for the variance in these fake rates, even within a given pT-bin, is that the composition of the hard partons that initiated t jets (th fracti outgoing of quarks or gluons) are different among the samples, and moreover, quarkand gluon-initiated jets have different distributions of tracks and jet width for jets of the same pT. This suggests one to ask how quarkgluon-composition can effect tau ID fake rates. Why do quarks and gluons have different fake rates? Studies of the properties of quarkand gluon-initiated jets within the ATLAS Jet Performance Group show that, while measures of jet width are not perfectly modeled in MC, the salient features that 33 Fake factors are discussed in more detail in Section 6.4.4 on their use in the Z′ → ττ search. 90 4. tau reconstruction and identification 6 Study of variables for light-quark and gluon jet discrimination The di!erences between light quarks and gluons lead to di!erences in observable final state jet properties on average. Jets initiated by gluons are expected to be broader, with more low-pT particles than those initiated by light quarks. The jet width and number of tracks have already been used to measure the average flavor fractions in di!erent data samples [2], and they have been identified as powerful discriminators for the purpose of understanding partonic flavor in previous studies [3]. The significant pile-up at the LHC in 2011 means that any measurement of jet properties may be a!ected by particles from other interactions. Calorimetric properties are particularly sensitive to the e!ects of pile-up. However, since charged particle tracks can be associated to a specific proton-proton collision via vertex association, jet properties calculated from tracks associated to one primary vertex are inherently less sensitive to pile-up. Thus, for this study, the properties used to distinguish di!erent classes of jets are the number of charged tracks associated to the jet and the jet width, W , defined as W = ! pT,i ! "Ri! pT,i , (3) where the sum is over the tracks associated to the jet, pT,i is the pT of the track, and "Ri is the opening angle in !–" between the jet axis and the track. Properties of jets based on tracks depend upon a good description of hadronization and fragmentation. Although the phenomenological models used in various generators have been tuned to match measurements of correlated properties (such as the fragmentation function and di!erential jet shapes) [16, 22], the charged particle spectra within a jet remain di#cult to describe. This is illustrated in Figure 2, where the mean value of each property is shown as a function of pT for PythiaMC11, Pythia Perugia2011 and Herwig++. 50 100 150 200 250 300 350 〉 trk n〈 5 10 15 20 25 30 ATLAS Simulation Preliminary = 7 TeVs R = 0.4, tanti-k |<0.8η| PYTHIA MC11 PYTHIA Perugia2011 Herwig++ Solid Markers: Light-quark Jets Empty Markers: Gluon Jets [GeV]jet T p 50 100 150 200 250 300 350 M C/ Py t. M C1 1 0.8 0.9 1 1.1 (a) < ntrk > 50 100 150 200 250 300 350 〉 T ra ck W id th 〈 0.05 0.1 0.15 0.2 0.25 0.3 ATLAS Simulation Preliminary = 7 TeVs R = 0.4, tanti-k |<0.8η| PYTHIA MC11 PYTHIA Perugia2011 Herwig++ Solid Markers: Light-quark Jets Empty Markers: Gluon Jets [GeV]jet T p 50 100 150 200 250 300 350 M C/ Py t. M C1 1 0.9 1 1.1 (b) < W > Figure 2: Average ntrk and track width for light-quark-induced (closed markers) and gluon-induced (empty markers) jets as a function of the reconstructed jet pT for isolated jets with |!| < 0.8. Results are shown for Pythia MC11 (black circles), Pythia Perugia2011 (red triangles) and Herwig++ (blue squares). The error bars represent only statistical uncertainties. Di!erences are most significant for the charged particle multiplicity of gluon jets, for which Pythia 6 6 Study of variables for light-quark and gluon jet discrimination The di!er nces between light quarks and gluons lead to di!er nces in observable final state j t properties on average. Jets initiated by gluons are expected to be broader, with more low-pT particles than those initiated by light quarks. The j t width and number of tracks have already been used to measure the average flavor f actions in di!er nt data samples [2], and they have been identified as powerful discriminators for the purpose of understanding partonic flavor in previous studies [3]. The significant pile-up at the LHC in 2011 means that any measurement of jet properties may be a!ected by particles from other interactions. Calorimetric properties are particularly sensitive to the e!ects of pile-up. Howev r, since charged particle tracks can be associated to a specific prot n-prot n collision via vertex association, jet properties calculated from tracks associated to ne primary vertex are inher ntly less sensitive to pile-up. Thus, for this study, the properties used to dist nguish di!er nt classe of jets are the number of charged tracks associated to the j t and the j t width, W , defined as W = ! pT,i ! "Ri! pT,i , (3) wher the sum is over the tracks associated to the j t, pT,i is the pT of the track, and "Ri is the openi g angle in !–" between the j t axis and the track. Properties of jets based on tracks dep nd upon a good description of hadronization and fragmentation. Although the phenomenol gical models used in various gen rators have been tuned to match measurements of correlated properties (such as the fragmentation function and i!er ntial jet shapes) [16, 22], the charged particle spectra within a jet remain di#cult to describe. This llustrated in Figure 2, wher the mean value of each property is shown as a function of pT for PythiaMC11, Pythia Perugia2011 and Herwig++. 50 100 150 200 250 300 350 〉 trk n〈 5 10 15 20 25 30 ATL S Simulation Preliminary = 7 TeVs R = 0.4, tanti-k |<0.8η| PYTHIA MC11 PYTHIA Perugia2011 Herwig++ Solid Markers: Light-quark Jets Empty Markers: Gluon Jets [GeV]jet T p 50 100 150 200 250 300 350 M C/ Py t. M C1 1 0.8 0.9 1 . (a) < ntrk > 50 100 150 200 250 300 350 〉 T ra ck W id th 〈 0. 5 0.1 0.15 0.2 0.25 0.3 ATL S Simulation Preliminary = 7 TeVs R = 0.4, tanti-k |<0.8η| PYTHIA MC11 PYTHIA Perugia2011 Herwig++ Solid Markers: Light-quark Jets Empty Markers: Gluon Jets [GeV]jet T p 50 100 150 200 250 300 350 M C/ Py t. M C1 1 0.9 1 . (b) < W > Figure 2: Average ntrk and track width for light-quark-induced (closed markers) and gluon-induced (empty markers) jets as a function of the reconstructed jet pT for isolated jets with |!| < 0.8. Results are shown for Pythia MC11 (black circles), Pythia Perugia2011 (red triangles) and Herwig++ (blue squares). The erro bars epres nt only statis cal uncertainties. Di!er nces are most ignificant for the charged particle multiplicity of gluon jets, for which Pythia 6 Figure 4.32: Profile plots of the number of tracks associated to a jet (left) and the track width (defined the same as Rtrack) (right) vs pT of jets in ATLAS simulation. Note that gluon-initiated jets are systematically wider and have a higher track multiplicity than quark-initiated jets (mc11) [166]. distinguish quark jets from gluon jets can be seen [165, 166, 167]. Figure 4.32 shows profile plots34 of the average number of tracks associated to a jet within ∆R < 0.4 and track width vs pT of the jet. Track width is identical to what is called Rtrack in ATLAS tau identification (see Section 4.3.1). Quark-initiated jets are also more narrow in calorimeter-based measures of width. Figure 4.33 shows distributions of the integrated jet shape, Ψ(r), defined as the fraction of the jet constituent pT that lies inside a cone of radius r concentric with the jet cone: Ψ(r) ≡ ∑ i p i T ∣∣∆Ri < r∑ j p j T , where the indexes i and j run over the constituents of the jet (either clusters in the case of a reconstructed jet, or the generator-level truth particles in simulation). Figure 4.33 (left) shows that jets get more narrow with pT, and that quark-initiated jets are significantly more narrow than gluon-initiated. The figure on the right shows a similar generator-level study by Gallicchio and Schwartz, who discuss the phenomenological differences among quarkand gluon-initiated jets [168] and suggest how to select control samples in the data enriching either quarks or gluons [169]. In general, gluon-initiated jets tend to have higher track and cluster multiplicities, and wider angles among their constituents than quark-initiated jets. This results in lower tau ID fake rates in samples enriched with gluon-initiated jets, and higher for quarks. 34 Profile plots were first discussed in Section 4.3.3. 4.4 performance and systematic uncertainties 91 13 (GeV) T p 0 100 200 300 400 500 600 (r = 0. 3) Ψ 1

.05 0.1 0.15 0.2 0.25 0.3 jets R = 0.6tanti-k | y | < 2.8 ATLAS -1 3 pb-1 dt = 0.7 nbL∫Data PYTHIA-Perugia2010 Perugia2010 (di-jet) gluon-initiated jets Perugia2010 (di-jet) quark-initiated jets FIG. 6: The measured integrated jet shape, 1 ! !(r = 0.3), as a function of pT for jets with |y| < 2.8 and 30 GeV < pT < 600 GeV. Error bars indicate the statistical and systematic uncertainties added in quadrature. The predictions of PYTHIAPerugia2010 (solid line) are shown for comparison, together with the prediction separately for quark-initiated (dashed lines) and gluon-initiated jets (dotted lines) in dijet events. 2 was that b-jets were more similar to gluon jets than to light-quark jets [7, 8]: due to the longer decay chain of B-hadrons, the number of particles and angular spread is larger for a b-jet than a light-quark jet. The similarity of b-jets to gluon jets should be lessened in the LHC's higher pT jets because the QCD shower produces more particles, whereas the particle multiplicity is relatively fixed in the B-hadron decay. There are already sophisticated and very detector-specific methods for b-tagging. Current b-taggers rely mostly on impact parameters or a secondary vertex, so they are independent of the observables we consider. Therefore, we restrict our study to discriminating light quarks (uds) from gluons. The accumulated knowledge from decades of experiments and perturba iv QCD calculatio s have been incorporated into Monte Carlo event generators, in p rticular Pythia [9] and Herwig [10]. These programs also include sophisticated hadronization and underlying event models which have also been tuned to data. Small differences still exist between these tools (and between the tools and data), but they provide an excellent starting point to characterize which observables might be useful in gluon-tagging. The approach to gluon-tagging discussed here is to find observables which appear promising and then can be measured and calibrated on samples of mixed or pure quark or gluon jets at the LHC [3]. To understand the structure of a jet, it is important to distinguish observables which average over all events from observables which are useful on an event-by-event basis. One example of an averaged observable is the classic integrated jet shape, !(r), which has already been measured at the LHC [11]. This jet shape is defined as the fraction of a jet's pT within a cone of radius r. Traditionally, jet shapes are presented as an average over all jets in a particular pT or ! range. For any r, the averaged jet shape becomes a single number, which is generally larger for quarks than for gluons because a greater fraction of a typical quark jet's pT is at the center of the jet. On traditional jet shape plots, error bars for each r are proportional to the standard deviation of the underlying distribution, but that distribution is not a narrow Gaussian around the average. For example, the event-byevent distributions for !(r = 0.1) are shown in Figure 1 for quarks and gluons. Jet shapes averaged over these distributions throw out useful information about the location and pT 's of particles within the jet, along with their correlations. For event-by-event discrimination, it is crucial to have distributions, whereas most public data only describes averages. In this study we consider !(r) and many other variables to see which are best suited to quark/gluon tagging. To generate samples of quark and gluon jets we considered samples of dijet events and "+jet events. These were generated with madgraph v4.4.26 [12] and showered through both pythia v8.140 [9] and herwig++ FIG. 1: Data on the integrated jet shape !(r) is usually published only when averaged over all events. Here we show the distribution of !(0.1), for quarks (blue, solid) and gluons (red, hollow). The event-by-event distributions of !(r) and other observables are much more important for gluon tagging than average values. v2.4.2 [10] with the default tunes. Jets, reconstructed using fastjet v2.4.2 [13], were required to have |!| < 1. We needed to isolate samples of quark and gluon jets with the similar jet pT 's. Unfortunately, we cannot get similar jet pT 's by having similar pT 's at the hard parton level, since the showering changes the pT significantly, and di"erently for quarks and gluons. This is an unphysical di"erence, since the parton pT is set artificially, and we have to avoid our tagger picking up on it. The solution we chose was to generate and shower a wide spectrum of dijet and "+jet events, and require the resulting Anti-kT R=0.5 jets to lie within 10% of the central value for each of six pT windows, centered around 50, 100, 200, 400, 800, and 1600GeV. (The underlying hard partons spanned a range from half to twice the central value.) The pT spectrum within each window matches the falling spectrum of the underlying dijet or "+jet samples, which are nearly identical for quarks and gluons in narrow windows chosen. When the entire event is reclustered with a di"erent jet size, as was done when examining how the observables change with R, the resulting jet pT no longer necessarily lies within the narrow ±10% window. In fact, how the jet pT changes with R forms a quark/gluon discriminant similar to integrated jet shape. With each sample of similar-pT jets, there are two main types of observables useful in separating quarks from gluons: discrete ones, which try to distinguish individual particles/tracks/subjets, and continuous ones that can treat the energy or pT within the jet as a smooth function of (#!, #$) away from the jet axis in order to form combinations like geometric moments. The discrete category includes the number of distinguishable tracks, small subjets, or reconstructed partiFigure 4.33: (left) A profile plot of 1−Ψ(0.3) vs pT using 2010 ATLAS data. Such a quantity is a measure of the jet width, quantifying the fraction of the jet energy not within ∆R < 0.3 [157]. (right) The generator-level distribution for Ψ(0.1) separately for quarkand gluon-initiated jets with pT = 200 GeV [168]. Note that while both have significant tails with Ψ approaching 0, quark-initi t d jet have Ψ peaked much closer to 1, meaning that quark-initiated jets are more likely to be tightly collimated. How do s the quark/gluon fraction vary among samples? It being clear that the quark/gluon fraction can have a large effect on tau ID fake rates, next one is lead to question how the quark/gluon fraction can vary among selections. Figure 4.34 shows the leading order diagrams for W + jet production at hadron-hadron colliders. Note that the first two diagrams have a quark-initiated jet in the final state, while the third diagram has a gluon-initiated jet. The exact details behind the hadronization of these jets are complicated, but studies with MC truth have shown [167] that the sign of the charge of a reconstruc ed tau candidate, counted rom the sum of the charges of the associated tracks, is anti-correlated with the sign of the W boson emitted, presumably because the sign of the charge of the out-going quark is correlated with the final reconstructed charge of the resulting tau candidate. Therefore the W + jets processes with quark-initiated jets are more likely to counted with the tau candidate and lepton having oppositesign charges (OS) Gluon-initiated jets, on the other hand, show no bias towards a reconstructed charge. This results in a more quark-enriched W + jet sample in OS an in same-sign (SS), explaining why the fake factor is highest for OS W + jet in Figure 4.31, and why the dijet sample, which is more gluon dominated, is more OS/SS symmetric. Figure 4.35 shows the estimat d q ark/gluon fraction for samples of W/Z + jets and dijet events as a function of the jet pT at the generator-level from Gallicchio and Schwartz [169], demonstrating that W/Z + jets events are dominated by quark-init ated jets, while dijet events are more gluon92 4. tau reconstruction and identification  g q± W± q∓  q± g W± q∓  q± q∓ W± g Figure 4.34: Leading order Feynman diagrams for production of W + jets at hadron-hadron colliders. Note that the ± simply denotes the sign of the electric charge, and that quarks have fractional magnitudes of charge. The diagrams with the quark current flipped also contribute, but diagrams with a q in the initial state will be suppressed by the proton PDFs. 50 100 200 400 800 1600 Q G 0% 100% 80% 60% 40% 20% γ+1jet pT Cut on All Jets (GeV) 50 100 200 400 800 1600 Q G 0% 100% 80% 60% 40% 20% Z/W+1jet pT Cut on All Jets (GeV) 50 100 200 400 800 1600 G Q 0% 100% 80% 60% 40% 20% b+1jet pT Cut on All Jets (GeV) Figure 2: Fraction of X+1jet events where the jet is uds quark (bottom and blue in each plot) as compared to gluon (top and red). The horizontal axis is a pT cut on the jet, which in these events translates into an identical pT cut on the other object. 50 100 200 400 800 1600 QQ QG GG 0% 100% 80% 60% 40% 20% γ+2jets pT Cut on All Jets (GeV) 50 100 200 400 800 1600 QQ QG GG 0% 100% 80% 60% 40% 20% Z/W+2jets pT Cut on All Jets (GeV) 50 100 200 400 800 1600 0% 100% 80% 60% 40% 20% b+2jets QQ QG GG pT Cut on All Jets (GeV) Figure 3: Fraction of X+2jet events where the jets are both light quark 'QQ' (bottom blue) vs one light quark one gluon 'QG' (middle purple) vs both gluon 'GG' (top red). Notice ! +GG almost never happens, nor does b+ QQ. These are starting points for quark and gluon purification. The horizontal axis is a pT cut on all jets, while the other objects (b, !, and leptons from Z/W ) have pT > 20GeV. 50 100 200 400 800 1600 2 Jets 0% 100% 80% 60% 40% 20% GG QG QQ pT Cut on All Jets (GeV) 50 100 200 400 800 1600 0% 3 Jets 100% 80% 60% 40% 20% GGG QGG QQG QQQ pT Cut on All Jets (GeV) 50 100 200 400 800 1600 4 Jets GGGG QGGG QQGG QQQG QQQQ 0% 100% 80% 60% 40% 20% pT Cut on All Jets (GeV) Figure 4: Division of the multijet (dominantly QCD) sample. The horizontal axis is a pT cut on all jets. Notice that all three jets are almost never all quark, and in the 4-jet sample, there are almost always at least two gluons. The 3-jet sample will be a staring point for gluon purification. – 5 – 50 100 200 400 800 1600 Q G 0% 100% 80% 60% 40% 20% γ+1jet pT Cut on All Jets (GeV) 50 100 200 400 800 1600 Q G 0% 100% 80% 60% 40% 20% Z/W+1jet pT Cut on All Jets (GeV) 50 100 200 400 800 1600 G Q 0% 100% 80% 60% 40% 20% b+1jet pT Cut on All Jets (GeV) Figure 2: Fraction of X+1jet events where the jet is uds quark (bottom and blue in each plot) as compared to gluon (top and red). The horizontal axis is a pT cut on the jet, which in these events translates into an identical pT cut on the other object. 50 100 200 400 800 1600 QQ QG GG 0% 100% 80% 60% 40% 20% γ+2jets pT Cut on All Jets (GeV) 50 100 200 400 800 1600 QQ QG GG 0% 100% 80% 60% 40% 20% Z/W+2jets pT Cut on All Jets (GeV) 50 100 200 400 800 1600 0% 100% 80% 60% 40% 20% b+2jets QQ QG GG pT Cut on All Jets (GeV) Figure 3: Fraction of X+2jet events where the jets are both light quark 'QQ' (bottom blue) vs one light quark one gluon 'QG' (middle purple) vs both gluon 'GG' (top red). Notice ! +GG almost never happens, nor does b+ QQ. These are starting points for quark and gluon purification. The horizontal axis is a pT cut on all jets, while the other objects (b, !, and leptons from Z/W ) have pT > 20GeV. 50 100 200 400 800 1600 2 Jets 0% 100% 80% 60% 40% 20% GG QG QQ pT Cut on All Jets (GeV) 50 100 200 400 800 1600 0% 3 Jets 100% 80% 60% 40% 20% GGG QGG QQG QQQ pT Cut on All Jets (GeV) 50 100 200 400 800 1600 4 Jets GGGG QGGG QQGG QQQG QQQQ 0% 100% 80% 60% 40% 20% pT Cut on All Jets (GeV) Figure 4: Divisio of t e multijet (dominantly QCD) sample. The horizontal axis is a pT cut on all jets. Notice t at all three j ts are almost never all quark, and in the 4-jet sample, there are almost always at least two gluons. The 3-jet sample will be a staring point for gluon purification. – 5 – Figure 4.35: Distributions of the predicted quark/gluon fraction of jets in W/Z + jets events (left) and dijet events (right) [169]. dominated but with quarks contributing more significantly for jets with pT & 100 GeV. Figure 4.36 plots the generator-level quark-gluon fraction for the true outgoing parton matched to a tau candidate in Alpgen W + jets Monte Carlo, showing that the fake tau candidates get more quark-rich at high-pT. 4.4.9 Pile-up robustness Motivation for pile-up concerns Following the initial success of the tau identification for the 2010 dataset, tau performance efforts in 2011 quickly shifted to focus on evaluating the pile-up robustness of the reconstruction and identification, in anticipation of the coming climb in instantaneous luminosity that year. In the later runs of the 2010 dataset in October and November, the peak average number of hard interactions 4.4 performance and systematic uncertainties 93 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 144 ) [GeV]missT, Ehτ, μ(TM 0 50 100 150 200 250 300 350 400 Ev en ts / (1 0 G eV ) 0 50 100 150 200 250 300 350 data 2011 τ τ →Z multijet μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140 Ta u Ca nd id at es / (5 G eV ) 0 100 200 300 400 500 600 700 800 900 data 2011 τ τ →Z multijet μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 91: (left) The distribution of MT(μ, !h, EmissT ) after baseline event selection, with tau identification inverted and fake factor weighting applied. (right) The distribution of the transverse momentum of the selected hadronic tau after baseline event selection, with tau identification inverted and fake factor weighting applied. G.5.3 Systematic error for the tau identification fake factor2286 This method also assumes that high mT requirement for the W control region does not significantly bias2287 the fake factor measured there. Figure 89 shows that the tau identification fake factor does not change2288 significantly when the cut on mT(", EmissT ) is varied.2289 ) [GeV]miss T , Eμ(Tm 0 20 40 60 80 100 )+ je ts M C ν μ → fl av or fr ac tio n: W ( 0 0.2 0.4 0.6 0.8 1 Light flavor Gluon flavor ATLAS Internal ) [GeV]hτ(Tp 0 50 100 150 200 250 )+ je ts M C ν μ → fl av or fr ac tio n: W ( 0 0.2 0.4 0.6 0.8 1 Light flavor Gluon flavor ATLAS Internal Figure 92: The distribution of the quark/gluon fraction of the true high-pT parton matched to the reconstructed tau candidate in Alpgen W+jets Monte Carlo, vs mT(μ, EmissT ) (left) and pT(!h) (right). Since the quark-gluon fraction of jets is strongly correlated with the tau fake rate, the stability of the2290 quark-gluon fraction as a function of mT(", EmissT ), shown in Figure 92, as predicted with Alpgen W+jets2291 Monte Carlo, supports that the fake rate does not vary much due to a change in quark-gluon composition2292 between the W control region and the signal region.2293 Tomotivate a systematic error on the tau identification fake factor method used in the μ!h channel, tau2294 identification fake factors are derived in complementary but orthogonal regions of data and compared to2295 the tau identification fake factors used in this channel. The regions are Z(! ee)+jets and Z(! μμ)+jets.2296 Jets in these regions are viable comparisons to jets from the W(! "#)+jets control region because the2297 expected fractions of quarkand gluon-initiated jets in these regions are comparable to the fractions of2298 re 4.36: The t ue leading quark/gluon fraction of a jet in Alpgen W + je s Monte Carlo events plo ted as function of the transverse mass, mT, of the selected muon and E miss T (left), and as a function of the pT of the tau candidate seeded by the jet (right) [97]. per bunch-crossing exceeded 3, providing significant samples of events with up to 5 reconstructed vertices per bunch-crossing for evaluating the effects of pile-up. In 2011, the peak average number of hard interactions would climb to nearly nearly 20, and surpass 30 in 201235. With the first samples of events with many vertices per bunch-crossing taken in later 2010, one could alr ady see significant degradation in the efficiency to select true tau signal with the ut-based ID. As shown in Figure 4.37, the tight cut-based ID for 1-prong candidates, for example, falls from being ≈ 40% efficient for tau candidates with pT ≈ 30 GeV in events with 1 reconstructed vertex, to ≈ 25% in events with 4 vertices, an alarming sensitivity to pile-up that would soon increase. The main improvement to the tau reconstruction in 2011 to mitigate the effects of pile-up concern the procedure for associating a vertex to a tau candidate, discussed previously in Section 4.2.5. Instead of selecting tracks with d0 and z0 selection requirements with respect to the primary vertex with the highest ∑ p2T of tracks, the vertex with the highest JVF for a tau candidate is associated to that candidate, which improves the efficiency to select the correct tracks in high-pile-up events. Selecting the proper vertex for a tau candidate with the highest JVF, which selects the vertex with tracks that are most correlated with the jet seeding that candidate, and then only selecting tracks consistent with that vertex, stabilized the tracking-related variables used with tau identification, with respect to pile-up. The other improvements to the reconstruction concerned correcting calorimeter-related variables to dampen the effects of pile-up. First, explorations to mitigate pile-up in the cut-based ID are discussed. Then, the current corrections to the multivariate-based ID for the 2012 dataset will be reviewed. 35 See the discussion of pile-up in Section 3.5.2. 94 4. tau reconstruction and identificationDependence on Number of Primary Vertices Signal E!ciency, 1-prong [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 = 1vxloose, n = 2vxloose, n = 3vxloose, n = 4vxloose, n = 1vxmedium, n = 2vxmedium, n = 3vxmedium, n = 4vxmedium, n = 1 vx tight, n = 2 vx tight, n = 3 vx tight, n = 4 vx tight, n 1-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 28 / 31 Dependence on Number of Primary Vertices Signal E!ciency, 3-prong [GeV]Ttrue visible E 0 10 20 30 40 50 60 70 80 90 100 Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 = 1vxloose, n = 2vxloose, n = 3vxloose, n = 4vxloose, n = 1vxmedium, n = 2vxmedium, n = 3vxmedium, n = 4vxmedium, n = 1 vx tight, n = 2 vx tight, n = 3 vx tight, n = 4 vx tight, n 3-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 29 / 31 Dependence on Number of Primary Vertices Background E!ciency, 1-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 = 1vxloose, n = 2vxloose, n = 3vxloose, n = 4vxloose, n = 1vxmedium, n = 2vxmedium, n = 3vxmedium, n = 4vxmedium, n = 1 vx tight, n = 2 vx tight, n = 3 vx tight, n = 4 vx tight, n 1-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 26 / 31 Dependence on Number of Primary Vertices Background E!ciency, 3-prong [GeV]Treco E 0 10 20 30 40 50 60 70 80 90 100 Fa ke R at e -410 -310 -210 -110 1 = 1vxloose, n = 2vxloose, n = 3vxloose, n = 4vxloose, n = 1vxmedium, n = 2vxmedium, n = 3vxmedium, n = 4vxmedium, n = 1 vx tight, n = 2 vx tight, n = 3 vx tight, n = 4 vx tight, n 3-prong Ryan Reece | Penn | ryan.reece@cern.ch | Cut Based Tau ID: Status and Plans 27 / 31Figure 4.37: Distributions showing the pile-up dependence of the signal efficiency (top) and fake rate (bottom) of the 2010 pT-parametrized cut-based tau ID, using ATLAS simulation. There is a distribution for each loose/medium/tight working point, and binned in the number of reconstructed vertices, showing a dramatic drop in efficiency as the number of vertices increases (mc09) [147]. Calorimeter-related variables are susceptible to pile-up, because unlike tracking-related variables which can be constructed to consider only the tracks consistent with a certain vertex, the calorimeter experiences the sum of activity from all interactions in an event36. Figure 4.38 illustrates that calorimeter-related variables, such as the number of clusters or REM, will be affected by pile-up activity that happens to fall near a tau candidate. Exploring pile-up corrections with the cut-based ID The cut-based tau identification was updated in 2011 from its previous version [100], with the main goal of reducing pile-up dependence [101]. The previous version used cuts on only three variables: REM, Rtrack, and ftrack, binned in 1-prong and multi-prong candidates. The cuts on REM and Rtrack were parameterized by the pT of the tau candidate to remove the pT dependence from the identification efficiency. In addition to the pT-dependence, the pile-up-dependence of the tau ID 36 And in some ways, is effected by events in the recent past, called out-of-time pile-up, discussed in Section 3.5.2. 4.4 performance and systematic uncertainties 95 0.4 0.2 pile-up tau underlying event calculate REM, Rtrack in cone count # tracks in cone ∆R fcore 0.1 Figure 4.38: A sketch illustrating that fcore is calculated as the ratio of energies in ∆R < 0.1 to ∆R < 0.2, smaller than the REM size of 0.4, to be more pile-up robust. variables was investigated. These dependences are summarized for some of the key ID variables in Table 4.6. A new pile-up-corrected calorimeter isolation variable was developed to replace REM, and additional cuts on tracking isolation and transverse flight path significance were added. Two of the three variables (REM and Rtrack) used by the previous cut-based ID quantify the width of the hadronic shower, which tends to be larger for QCD jets than for taus of the same energy. The track-based variable Rtrack is robust against pile-up because the tracks are required to be consistent Table 4.6: An accounting of the pT and pile-up dependence of some of the key tau ID variables. A '+' indicates a positive correlation of that variable with pT or Nvertex. A '-' indicates a negative correlation. Tau++ refers to the experimental version of the cut-based ID discuss in Section 4.4.9 [170]. Ryan Reece Penn ryan.reece@cern.ch Introducing Tau++: A more natural pile-up-proof tau Momentum and pile-up dependence of ID variables 8 Cuts: 1-prong dependence variable used pT pile-up 1-prong 3-prong REM - + Rtrack 0 • • ftrack weak0 • •! EisoT (cluster) weak- + • •! pisoT (track) 0 0 • • Ne!(clusters) - + mclusters + + m(core clusters) + + mtracks bkg weak+ 0 SflightT 0 0 • Ryan Reece | Penn | ryan.reece@cern.ch | Cut-based Tau ID Optimization Status 3 / 22 • 0 indicates little or no correlation ⇒ robustness. • Rtrack and track isolatio are robust against pile-up, even out to ΔR < 0.4, because of the of |Δz sin θ| < 1.5 mm requirement in the tau track selection. Among the chosen variables, the largest dependencies are acounted for: • Rtrack cut is pT parametrized • Calorimeter isolation is pile-up corrected in Tau++ 96 4. tau reconstruction and identification with the primary vertex by demanding (|z0 sin θ| < 1.5 mm). By contrast, the calorimeter-based quantity REM is more sensitive to pile-up since by using calorimeter information alone one cannot measure z0 at the precision required to distinguish different proton-proton collisions. Additional contributions from pile-up bias the REM distribution for real hadronic tau decays, making them wider, and more like QCD jets. This can be seen in Figure 4.40, which shows REM as a function of the number of reconstructed vertices. One might consider that discriminating hadronic tau decays from QCD jets by requiring a small REM within the arbitrary cone of ∆R < 0.4 is not the most natural use of the calorimeter information. One can accurately predict the transverse width of true hadronic tau decays with Monte Carlo as a function of pT. Figure 4.7 shows that the spread of calorimeter deposits and tracks for true hadronic tau decays is well within ∆R < 0.2. Having tracks or clusters at wider ∆R is more consistent with a tau candidate being a QCD jet, and hence the discriminating power of REM. But tracks or clusters at wider ∆R can also be due to activity from pile-up or the underlying event falling on a true hadronic tau decay (see Figure 4.38). The challenge is to distinguish true hadronic tau decays covered in the noise of pile-up from QCD jets. Requiring a narrow REM is indirectly requiring a tau candidate to be isolated in the calorimeter, that is, without much energy deposited in the annulus of 0.2 < ∆R < 0.4. By directly cutting on the energy deposited in this isolation annulus one can exploit the same discriminating information as REM, but with a quantity that can be more readily corrected by subtracting an estimate of the isolation energy due to pile-up, than could done to correct the pile-up effects on a width variable like REM. A new calorimeter isolation variable (EisoT,corr) is defined as the sum of the ET of the clusters in the isolation annulus and a pile-up correction term: EisoT,corr = ∑ 0.2<∆R<0.4 ET(cluster)− Epile-upT , with a pile-up correction term to be defined. In order to mitigate pile-up dependence, the newest version of the cut based identification drops cuts on REM, in favor of making cuts on the E iso T,corr. The jet-vertex fraction (JVF) reconstructed for each tau candidate, is calculated as the fraction of the summed pT of tracks associated to the seed jet that are consistent with the selected vertex 37. Not only can JVF be used to tell if a vertex is consistent with the jet activity, it can indicate the degree of pile-up activity on a candidate. Figure 4.39 shows the distribution of JVF in a 2011 data sample with μ ≈ 5. A JVF-based correction to suppress the effects of pile-up on the calorimeter isolation is calculated as follows [170]. When JVF = 1, all tracks falling in a jet are consistent with the primary vertex and not pile-up. If JVF is 95%, then 5% of the sum of the pT of tracks that fall 37 JVF is discussed in some detail in Section 3.3.6. 4.4 performance and systematic uncertainties 97 JVF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 T a u C a n d id a te s / 0 .0 2 0 0.02 0.04 0.06 0.08 0.1 (track) [GeV] T p∑(1-JVF) 0 2 4 6 8 10 12 14 16 18 20 T a u C a n d id a te s / ( 0 .5 G e V ) -410 -310 -210 -110 1 Figure 4.39: Distributions of JVF (left) and ppile-upT = (1 − JVF) ∑ pT(track) (right), for true Monte Carlo hadronic tau decays (blue) and jets from a dijet sample of 2011 ATLAS data (red). in a jet are from pile-up vertices. Therefore, 1− JVF, estimates the fraction of pT of tracks in a jet that is from pile-up. Multiplying this by the denominator of JVF gives an estimate of the pT of tracks in a jet from pile-up: ppile-upT = (1− JVF) ∑ pT(track) . This quantity gives a local measure of the charged pile-up contribution to a jet, in contrast to other measures of pile-up like Nvertex, which only quantify the pile-up activity globally in the event. Note that ppile-upT , as defined above, does not account for pile-up energy deposits from neutral particles. To the degree that charged and neutral pile-up are correlated, the neutral pile-up can still be estimated from the charged. Ideally one should only correct EisoT for the pile-up energy deposited in the isolation annulus, which takes up 3/4 of the area of a cone of ∆R < 0.4. To calibrate the isolation correction, parameterizing to correct for neutrals and for the mismatch in areas for calculating JVF and EisoT , we introduce a dimensionless parameter α: Epile-upT = min ( α (1− JVF) ∑ pT(track), 4 GeV ) . Several values of α are considered, and a value of α = 1 is chosen based on considerations of efficiency and pile-up insensitivity. To keep the correction conservative, the pile-up correction is limited to a maximum of 4 GeV. Only ≈1% of the jets in the training sample with μ ≈ 5 would otherwise have exceeded this limit. Figure 4.41 shows that the uncorrected 〈EisoT 〉 clearly depends linearly on ppile-upT , while the dependence is reduced for 〈EisoT,corr〉. Figure 4.40 shows that the correction term largely succeeds in removing the bias in 〈EisoT 〉 as a function of Nvertex and ppile-upT . Figure 4.42 shows the cut-based identification efficiency as a function of pT in bins of the number of pile-up vertices. In addition to introducing pile-up-corrected calorimeter isolation, the cuts have been improved by adding cuts on N isotrack and S flight T . Tight and medium levels of the cut-based identification require 98 4. tau reconstruction and identification N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 〉 E M R〈 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 〉 E M R〈 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 〉 tr a c k R〈 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 〉 tr a c k R〈 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 [G e V ] 〉 (c lu s te r) is o T E ∑〈 0 2 4 6 8 10 12 14 16 18 N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 [G e V ] 〉 (c lu s te r) is o T E ∑〈 0 2 4 6 8 10 12 14 16 18 N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 [G e V ] 〉 (c lu s te r) c o rr e c te d is o T E ∑〈 0 2 4 6 8 10 12 14 N(vertex) ATLAS Preliminary 2 4 6 8 10 12 14 [G e V ] 〉 (c lu s te r) c o rr e c te d is o T E ∑〈 0 2 4 6 8 10 12 14 Figure 4.40: The dependence of key tau identification variables as a function of the number of reconstructed vertices, separately for 1-prong (left) and 3-prong (right) tau candidates. The points indicate the means in each bin. The coloured bands indicate the standard deviation. The blue (filled) points correspond to tau candidates matched to hadronically decaying taus in simulated W → τν and Z → ττ events. The red (open) points are for the dijet sample from data [101]. 4.4 performance and systematic uncertainties 99 ATLAS Preliminary (track) [GeV] T p∑(1-JVF) 0 1 2 3 4 5 6 [G e V ] 〉 (c lu s te r) is o T E ∑〈 0 2 4 6 8 10 12 14 16 ATLAS Preliminary (track) [GeV] T p∑(1-JVF) 0 1 2 3 4 5 6 [G e V ] 〉 (c lu s te r) is o T E ∑〈 0 2 4 6 8 10 12 14 16 ATLAS Preliminary (track) [GeV] T p∑(1-JVF) 0 1 2 3 4 5 6 [G e V ] 〉 (c lu s te r) c o rr e c te d is o T E ∑〈 -4 -2 0 2 4 6 8 10 12 14 ATLAS Preliminary (track) [GeV] T p∑(1-JVF) 0 1 2 3 4 5 6 [G e V ] 〉 (c lu s te r) c o rr e c te d is o T E ∑〈 -2 0 2 4 6 8 10 12 14 Figure 4.41: The dependence of key tau identification variables as a function of (1 − JVF) ∑ pT(track), a local measure of the summed pT from pile-up tracks that contribute to the tau candidate, separately for 1-prong (left) and 3-prong (right) tau candidates. The points indicate the means in each bin. The coloured bands indicate the standard deviation. The blue (filled) points correspond to tau candidates matched to hadronically decaying taus in simulated W → τν and Z → ττ events. The red (open) points are for the dijet sample from data [101]. N isotrack = 0. This selection performs better than applying selection based on the sum of track pT in the isolation annulus. For 3-prong candidates, a minimum SflightT of 0 and 0.5 is required for the medium and tight-level cuts, respectively. Table 4.7 shows the re-tuned cuts using the pile-up corrected calorimeter isolation. Figure 4.43 shows the performance of the jet-tau discriminants re-optimzed in 2011. The likelihoodand BDT-based ID methods did not yet use any directly pile-up corrected ID variables, but binned the working points in the number of reconstructed vertices for stability. One can see that for pT & 40 GeV the candidates are sufficiently Lorentz collimated that the experimental new cuts suffer from not using any calorimeter information in ∆R < 0.2, and have lower discriminating power. Instead of using JVF to measure the amount of pile-up on a candidate, a more direct approach would be make a correction for each individual pile-up track that falls near a candidate. Further 100 4. tau reconstruction and identification ) [GeV] h true vis. τ( T p 0 20 40 60 80100120140160180200 E ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose, vxp1-3 loose, vxp4-6 loose, vxp7+ medium, vxp1-3 medium, vxp4-6 medium, vxp7+ tight, vxp1-3 tight, vxp4-6 tight, vxp7+ ) [GeV] h true vis. τ( T p 0 20 40 60 80100120140160180200 E ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose, vxp1-3 loose, vxp4-6 loose, vxp7+ medium, vxp1-3 medium, vxp4-6 medium, vxp7+ tight, vxp1-3 tight, vxp4-6 tight, vxp7+ ) [GeV] h true vis. τ( T p 0 20 40 60 80100120140160180200 E ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose, vxp1-3 loose, vxp4-6 loose, vxp7+ medium, vxp1-3 medium, vxp4-6 medium, vxp7+ tight, vxp1-3 tight, vxp4-6 tight, vxp7+ ) [GeV] h true vis. τ( T p 0 20 40 60 80100120140160180200 E ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose, vxp1-3 loose, vxp4-6 loose, vxp7+ medium, vxp1-3 medium, vxp4-6 medium, vxp7+ tight, vxp1-3 tight, vxp4-6 tight, vxp7+ ) [GeV] h true vis. τ( T p 0 20 40 60 80100120140160180200 E ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose, vxp1-3 loose, vxp4-6 loose, vxp7+ medium, vxp1-3 medium, vxp4-6 medium, vxp7+ tight, vxp1-3 tight, vxp4-6 tight, vxp7+ ) [GeV] h true vis. τ( T p 0 20 40 60 80100120140160180200 E ff ic ie n c y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 loose, vxp1-3 loose, vxp4-6 loose, vxp7+ medium, vxp1-3 medium, vxp4-6 medium, vxp7+ tight, vxp1-3 tight, vxp4-6 tight, vxp7+ Figure 4.42: Signal efficiency of the experimental Tau++ cut-based identification for 1-prong (left) and 3-prong (right) candidates using the chosen value of the parameter, α = 0.0/0.6/1.0 for (top/center/bottom) [117]. 4.4 performance and systematic uncertainties 101 investigation was done using track extrapolation tools to find each pile-up track falling near a tau candidate, and to use each one to make a correction to the isolation. Although the principle is attractive, manpower and time constraints left the study with only preliminary results [171]. Pile-up tracks that are not consistent with the selected vertex of the tau candidate are extrapolated to layer-2 of the EM calorimeter and the sum of their pT is counted if the tracks fall within the isolation annulus (0.2 < ∆R < 0.4). This sum is used to make a correction term to the isolation with a second correction depending on the number of reconstructed vertices: EisoT ′ = ∑ 0.2<∆R<0.4 ET(cluster)− a ∑ 0.2<∆R<0.4 pT(track extrap.)− b Nvertex , where a and b are parameters that can be tuned to slope of the dependence of EisoT on the respective terms. Figure 4.44 shows that the uncorrected calorimeter isolation shows a strong dependence on the number of reconstructed vertices, adding approximately 320 MeV per vertex. The first correction using the extrapolated pile-up tracks succeeds in suppressing the dependence on Nvertex to approximately 190 MeV per vertex. Part of the remaining dependence is because only approximately 50% of the candidates in the Z → ττ MC used with μ ≈ 5 do not have any pile-up tracks matched to them. The remaining dependence is removed with the second term. The performance of the experimental cut-based tau ID with this correction was comparable to the cuts using the JVF-based correction. Table 4.7: Cut values for the working points for the experimental Tau++ ID, using the JVFcorrected EisoT,corr [117]. 1-prong Rtrack < { 417/pT + 0.0824− 2.61× 10−7pT for pT < 80 GeV 0.0667 for pT ≥ 80 GeV loose or medium { 417/pT + 0.0724− 2.61× 10−7pT for pT < 80 GeV 0.0567 for pT ≥ 80 GeV tight 1 / ftrack < 4.0, 3.33, 2.5 loose, medium, tight EisoT,corr < 6, 4, 3 GeV N isotrack = no cut, 0, 0 3-prong Rtrack < { 375/pT + 0.0696− 3.28× 10−7pT for pT < 80 GeV 0.048 for pT ≥ 80 GeV loose or medium { 375/pT + 0.0596− 3.28× 10−7pT for pT < 80 GeV 0.038 for pT ≥ 80 GeV tight 1 / ftrack < 3.33, 3.33, 2.5 loose, medium, tight EisoT,corr < 7, 7, 4 GeV N isotrack = no cut, 0, 0 SflightT > no cut, 0, 0.5 102 4. tau reconstruction and identification Signal Efficiency ATLAS Preliminary tau performance 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood 40 GeV≤ T 1-prong, 20 GeV < p -1dt L = 130 pb∫2011 dijet data Signal Efficiency ATLAS Preliminary tau performance 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood 40 GeV≤ T 3-prong, 20 GeV < p -1dt L = 130 pb∫2011 dijet data Signal Efficiency ATLAS Preliminary tau performance 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood 100 GeV≤ T 1-prong, 40 GeV < p -1dt L = 130 pb∫2011 dijet data Signal Efficiency ATLAS Preliminary tau performance 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 In v e rs e B a c k g ro u n d E ff ic ie n c y 1 10 210 310 Cuts BDT Likelihood 100 GeV≤ T 3-prong, 40 GeV < p -1dt L = 130 pb∫2011 dijet data Figure 4.43: Inverse background efficiency as a function of signal efficiency for 1-prong (left) and 3-prong (right) candidates, in low (top) and high (bottom) pT ranges, for the jet-tau discriminants re-optimized in the summer of 2011 [101]. ($&)

 )" ""$$ &        	 320 MeV/vertex 190 MeV/vertex 0 MeV/vertex Figure 4.44: Profile plots of the cluster isolation, EisoT , without a pile-up correction (left), corrected with extrapolated pile-up tracks (center), and corrected with extrapolated pile-up tracks and a term linear in Nvertex (right) [171]. 4.4 performance and systematic uncertainties 103 Pile-up corrections in the 2012 ID It became clear that the experimental versions of the cuts, while aggressively attempting to make a pile-up correction using information local to the tau candidate, had lost performance by not using calorimeter information in the core cone of ∆R < 0.2. For use with the 2012 dataset, a method of reducing the pile-up dependence of the tau identification was developed by using the core energy fraction, fcore, calculated as the ratio of the sum of the calorimeter cells associated to the candidate within ∆R < 0.1 to that of ∆R < 0.2 (see the definition in Appendix B). This variable would replace REM in the multivariate ID methods, having less pile-up dependence because it uses a cones smaller than 0.4 (see Figure 4.38), and the ratio of energies naturally cancels some of the dependence. The remaining pile-up dependence was corrected with a simple global correction depending on the number of reconstructed vertices. Such a linear correction is defined for fcore and ftrack: f corrcore = fcore + 0.003×Nvertex , for pT < 80 GeV, f corrtrack = ftrack + 0.003×Nvertex . Figure 4.45 (left) shows the dependence of fcore and its corrected version on Nvertex, as well as the efficiency of the 2012 BDT-based jet-tau discriminant. Putting the pile-up corrected variables into the training of the BDT and the construction of the likelihood resulted in a much more flat efficiency as a function of the number of reconstructed vertices for both methods. For example, the signal efficiencies for the BDT working points for 1-prong candidates vs Nvertex are shown in Figure 4.45 (right)38. 38 The primary references discussing the topics of this chapter in more detail are • Commissioning of the ATLAS tau lepton reconstruction using 900 GeV minimum bias data ATLAS-CONF-2010-012 [154] – the first note to document the commissioning of the ATLAS tau reconstruction with the first minimum-bias data, • Reconstruction of hadronic tau candidates in QCD events at ATLAS with 7 TeV proton-proton collisions ATLAS-CONF-2010-059 [144] – commissioning note, • Reconstruction, energy calibration, and identification of hadronically decaying tau leptons ATLAS-CONF-2011-077 [100] – the first report of the ATLAS tau performance with the 2010 data, • Performance of the reconstruction and identification of hadronic tau decays with ATLAS ATLAS-CONF-2011-152 [101] – the report of the ATLAS tau performance with the 2011 data, • A search for high-mass resonances decaying to τ+τ− in pp collisions at √s = 7 TeV with the ATLAS detector ATL-COM-PHYS-2012-394 [97] – support note for the Z′ → ττ search, including some of the first recommendations for high-pT taus, • Performance of the reconstruction and identification of hadronic tau decays in ATLAS with 2011 data ATLAS-CONF-2012-142 [102] – an updated report of the ATLAS tau performance with the 2011 data, • Identification of the hadronic decays of tau leptons in 2012 data with the ATLAS detector ATLAS-CONF-2013-064 [172] – report of the ATLAS tau performance with the 2012 data. • Identification of the hadronic decays of tau leptons in 2012 data ATL-COM-PHYS-2012-1821 [103] – the support note for ATLAS-CONF-2013-064. 104 4. tau reconstruction and identification N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly February 8, 2013 – 15 : 03 DRAFT 11 VtxN 0 5 10 15 20 25 30 > co re < f 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 correction Vtx Without N!! "Z correction Vtx With N!! "Z > 20 GeV T 1 prong, p ATLAS Internal VtxN 0 5 10 15 20 25 30 > co re < f 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 correction Vtx Without N!! "Z correction Vtx With N!! "Z > 20 GeV T Multi prong, p ATLAS Internal Figure 1: Pile-up dependence of the uncorrected (black) and corrected (red) core energy fraction for 1-prong (left) and multi prong (right) !had-vis candidates of a Z ! !! signal sample. Variable LLH ID BDT ID BDT e-veto Cut muon-veto prongs 1-prong multi-prong 1-prong multi-prong 1-prong 1-prong f corrcore • • • • • f corr track • • • • • ftrack • inverse ftrack • Rtrack • • • • • S lead track • • Niso track • • !Rmax • • S flight T • • mtracks • • fEM • • fHT • E strip T,max • f leadtrk HCAL • f leadtrk ECAL • fPS • f " ± EM • fiso • RHad • Table 1: Comparison of variables used by the !had-vis identification algorithms: projective likelihood identification (LLH ID), boosted decision tree identification (BDT ID), boosted decision tree based electron veto (BDT e-veto) and cut based muon veto (Cut muon-veto). N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly February 8, 2013 – 15 : 03 DRAFT 16 VtxN 0 5 10 15 20 25 30 S ig n a l E ff ic ie n cy 0 0.2 0.4 0.6 0.8 1 1.2 1 Prong | < 2.3! > 20 GeV, | T p ATLAS Preliminary 2012 Simulation BDT loose BDT medium BDT tight VtxN 0 5 10 15 20 25 30 S ig n a l E ff ic ie n cy 0 0.2 0.4 0.6 0.8 1 1.2 Multi Prong | < 2.3! > 20 GeV, | T p ATLAS Preliminary 2012 Simulation BDT loose BDT medium BDT tight VtxN 0 5 10 15 20 25 30 B a ck g ro u n d E ff ic ie n cy -310 -210 -110 1 1 Prong | < 2.3! > 20 GeV, | T p ATLAS Preliminary -1 dt L = 740 pb"2012 data BDT loose BDT medium BDT tight VtxN 0 5 10 15 20 25 30 B a ck g ro u n d E ff ic ie n cy -310 -210 -110 1 Multi Prong | < 2.3! > 20 GeV, | T p ATLAS Preliminary -1 dt L = 740 pb"2012 data BDT loose BDT medium BDT tight Figure 5: Signal (top) and background (bottom) e!ciencies for 1-prong (left) and multi-prong (right) !had-vis candidates as a function of Nvtx for the three working points loose (green), medium (blue) and tight (red) of the BDT identification. The e!ciencies were obtained using Z, Z! " !! and W " !" Pythia 8 samples for signal and 2012 data dijet samples with an integrated luminosity of 740 pb#1. LLH Score -20 -15 -10 -5 0 5 10 15 20 S a m p le F ra ct io n / 2 .0 0.02 0.04 0.06 0.08 0.1 0.12 #$ % + W $$ %Z,Z' -1 dt L = 370 pb"2012 data > 20 GeV T 1 prong, p ATLAS Internal LLH Score -40 -30 -20 -10 0 10 S a m p le F ra ct io n / 2 .0 0.02 0.04 0.06 0.08 0.1 0.12 #$ % + W $$ %Z,Z' -1 dt L = 370 pb"2012 data > 20 GeV T Multi prong, p ATLAS Internal Figure 6: Log-likelihood ratio for 1-prong (left) and multi-prong (right) !had-vis candidates. While the first signal peak is dominated by !had-vis coming from Z and W events, the second signal peak at higher LLH score values is dominated by very boosted !had-vis coming from Z ! events. Figure 4.45: (left) Profile plot of fcore vs Nvertex for the uncorrected (black) and pile-up corrected (red) versions. (right) The signal efficiency of the BDT working points vs Nvertex, using the pile-up corrected versions of fcore and ftrack, from 2012 ATLAS simulation [103]. Chapter 5 Measurement of the Z → ττ cross section This chapter describes studies of the event kinematics of `τh events with Monte Carlo before the start-up of the LHC, the observation of Z → ττ with the first 8.5 pb−1 of ATLAS data in 2010, and the Z → ττ cross section measurement with the 36 pb−1 dataset collected in 2010. The discussion is focused on the `τh channel because of its interest as a τh control sample, its use in new physics searches, and because it was the focus of my graduate research. 5.1 Introduction 5.1.1 Motivation The production of W → τν and Z → ττ events at the LHC provides the critical control samples for evaluating the performance of the triggering, reconstruction, and identification of hadronically decaying tau leptons. Such events provide true tau leptons with relatively low visible transverse momenta and with genuine missing transverse momentum. The `τh final state is especially interesting because one can trigger on the lepton, leaving an unbiased sample of tau candidates for studying tau performance39. In addition, because the visible mass distribution of the `τh system is sensitive to the energy scale of the reconstructed tau candidates, a measurement of the tau energy scale can be made with this sample. Additionally, the ττ invariant mass distribution, using the collinear approximation40, is sensitive to the EmissT scale. Therefore, Z → ττ events can be used as a control sample for the EmissT reconstruction in events with genuine E miss T [173, 174, 159]. 39 For example, the Z → ττ tag-and-probe study, discussed briefly in Section 4.4.7, takes advantage of this sample of tau decays. 40 The collinear approximation is a mass-reconstruction technique for ditau systems where the components of the EmissT are projected along the visible decay products. The fractions of the momenta carried by neutrinos for each tau decay can be solved for analytically if the decays are not back-to-back. The method is described in more detail in Refs. [69, 173]. 105 106 5. measurement of the z → ττ cross section Moreover, Z → ττ will often dominate control regions and/or the signal region in searches for new physics with the ττ final state like H → ττ and Z ′ → ττ . The Z → ττ process forms the main irreducible background that must be understood in order to search for new physics in this channel [69]. 5.1.2 Backgrounds When trying to select the Z → ττ process itself, in the `τh channel, there is a complicated background composition dominated by processes that produce a real lepton and a real or fake hadronic tau decay. They include: • W (→ `ν) + jets Decays of W bosons produce a real lepton and missing transverse momentum, and jets produced in association with the W are mis-identified as hadronic tau decays at a rate of a few percent. The relatively large cross section for these events make W+jets events the largest background in the signal region. The process W → τν → `ννν, where the electron or muon comes from the tau decay, also contributes a few percent to the total W → `ν background. • Z/γ∗(→ ``) + jets If one of the electrons or muons from Z/γ∗(→ ``) does not pass the object preselection, this process will pass the dilepton veto, and jets produced in association with the Z are mis-identified as hadronic tau decays at a rate of a few percent. One of the leptons can also be mis-identified as a tau candidate. Z → ee is a more challenging background in the eτh channel than Z → μμ is for the μτh channel because it is much more rare for a muon to deposit significant energy in the calorimeter, while electrons readily make a track and an isolated cluster. • Multijet Multijet events are a challenge at hadron colliders because the cross section for multijet events produced in strong interactions is many orders of magnitude above the electroweak processes that produce tau leptons41. This background is dominated by B-meson and kaon in-flight decays within a jet, which provide sources of real leptons, but there is also a contribution from mis-identified leptons that is more significant in the eτh channel. The multijet background can be suppressed with lepton isolation, and a pure control sample of the multijet background can be selected by requiring a non-isolated lepton candidate. • tt and single top The decay of top quarks provides sources of leptons, real and fake hadronic taus, and often significant EmissT . 41 Recall the introductory discussion of hadronic tau decays and fakes in Section 3.3.7 and the review of tau reconstruction in Chapter 4. 5.2 mc studies of `τh event kinematics 107 • Diboson The production of vector boson pairs (WW , WZ, ZZ) provides sources of leptons, real and fake hadronic taus, and often significant EmissT . 5.2 MC studies of `τh event kinematics In order to better understand the background composition and optimal selection criteria, studies of Z → ττ were performed prior to the start-up of the LHC42, the results of which are reviewed in this section. 5.2.1 Multijet background Without data to employ a data-driven technique, it was a challenge to model the estimated multijet background. Independent of the issues of Monte Carlo modeling of QCD hadronization, the resulting distributions of jet-shapes, and their consequences on the modeling of the efficiency for jets to pass tau identification43, the multijet background is especially difficult to estimate with Monte Carlo because it has the worst combination of having a high event-rate and low selection-rate. Therefore, the multijet background of a selection of events at the LHC often has limited Monte Carlo statistics passing object identification and event selection, but is not always clearly negligible. Figure 5.1 concerns the sources of reconstructed muon candidates in a Monte Carlo dijet sample. Figure 5.1 (a) shows that approximately 2/3 of the muons in dijets come from prompt sources, and therefore can be matched to a true generator-level muon. Most of the other third come from the decay of pions or kaons in flight, which happen after generation in the GEANT detector simulation. Since one cannot select events which will have a pion or kaon decay with a generator-level filter, it is not practical to efficiently sample this background with Monte Carlo. Figure 5.1 (b) shows that of the generator-level muons, most of them come from B hadron decays. Therefore it is relevant to focus on the bb background, for which ATLAS produced Monte Carlo samples with a generator-level filter for a muon with pT > 15 GeV. The lepton-pT distribution of the multijet background is steeply falling, and therefore the background may be effectively cut away with a high-pT requirement, but at the cost of much of the Z → ττ sample, which also prefers low-pT leptons (see Figure 5.2). Analyses that require significant EmissT can effectively suppress the multijet background, as shown in Figure 5.3, but Z → ττ events generally have soft EmissT because most often the tau decays are back-to-back and the vector-sum of the neutrino momenta largely cancel. 42 This section uses Monte Carlo from the mc08 ATLAS Monte Carlo before the start-up of the LHC, around the time of ATLAS Full Dress Rehearsal (FDR) in 2008 when large scale Monte Carlo production was being done to exercise the entire ATLAS computing chain [175, 176]. 43 See the discussion of jet-shapes and tau identification in Section 4.4.1 and Section 4.4.8. 108 5. measurement of the z → ττ cross section MET [GeV] 0 20 40 60 80 100 120 140 pb / (2 .5 G eV ) -210 -110 1 10 210 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (a) ) τ φμ φcos( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 pb / (0 .0 5) -210 -110 1 10 210 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (b) Figure 4: Distributions prior to cutting on the muon isolation variables. After requiring the isolation cuts, there were not enough events to require tau ID cuts and continue the cut flow. We needed a more exclusive QCD sample, targeted at the types of events that would pass the cuts in our analysis. This led us to investigate the sources of the muons in dijets. (3 8. 3 % ) + μ (33.7 %)μ (7.7 % ) + K (6.7 % ) +π (6.1 %) -K (5.7 %) -π other (1.9 %) Nearest truth particle to reco muon (a) Nearest generator truth particle to a reconstructed muon (14 .6 % ) +B (1 4. 0 % ) 0 B (13.8 % ) -B (13.5 %)0B (7. 0 % ) 0 D (6 .6 % ) + D (6 .1 % ) 0 D (5.2 % ) 0s B (5.0 % ) -D (4.1 % ) 0s B (2.2 %) 0 b Λ (2.0 %) + sD other (5.9 %) Mother of true muon (b) Parent particle of true generator muons Figure 5: Sources of muons with pT > 15 GeV in dijets Figure 5 concerns the sources of muons in the J2 dijets sample. Plots made from J1 and J3 are very similar. Figure 5(a) shows that approximately 2/3 of the muons in dijets come from prompt sources, and therefore can be matched to a true generator muon. Most of the other third come from the decay of pions or kaons in flight. Since one cannot select events which will have a pion or kaon decay with a generator-level filter, it is not obvious how one can model the background contribution due pion and kaon decay with Monte 8 Figure 5.1: Generator-level truth information for muons in the mc08 PYTHIA J2 dijet sample [177]. The Likelihood variable is actually the sum of the log likelihood ratio of several discriminating variables, discussed in detail in reference [9]. This tau ID criteria was chosen simply as a benchmark identification. Indeed, a standardized cut-based tau identification will probably be more appropriate for analysis done with the first data. Appendix A.3 shows plots of the signal e ciency and jet fake-rate for the tau reconstruction and ID criteria used in this note, determined using the Monte Carlo truth. Additional cuts were designed to suppress specific backgrounds. The characteristics of the backgrounds and the methods of their suppression are the subject of the next two sections. 4 QCD Backgrounds QCD processes are the largest background to Z ! ⌧⌧ ! μ⌧h because they have cross sections which are as much as a million times larger than that of Z ! ⌧⌧ , and the fakerates for jets to pass hadronic tau reconstruction and identification are generally near one percent. The first handle on suppressing these backgrounds is the selection of an isolated muon with some minimum pT. 4.1 Inclusive Dijet Background While the J1-J3 dijet samples are too inclusive to pass th entire cut flow, and have s ale factors t o large to compare next to other samples, we use them to investigate the properties and possible sources of muons from QCD processes. ) [GeV]μ( T p 0 10 20 30 40 50 60 70 80 90 100 pb / (2 .5 G eV ) 1 10 210 310 410 510 610 710 J1 J2 J3 τ τ →Z (a) Without isolation ) [GeV]μ( T p 0 20 40 60 80 100 120 140 pb / (2 .5 G eV ) 1 10 210 310 410 510 610 710 ) < 2 GeVμ(R<0.4Δ T ) = 0, Eμ(R<0.4ΔtracksN J1 J2 J3 τ τ →Z (b) With isolation Figure 2: pT of muons from the dijet samples and from the Z ! ⌧⌧ signal sample. Figure 2(a) reveals that the di↵erential cross section of dijets rapidly increases as the pT of the required muon decreases. While Z ! ⌧⌧ , favors rather low pT muons, a minimum pT threshold will be necessary to avoid being swamped by the dijet background. In our selection we require a minimum muon pT of 15 GeV. The most powerful variables we use for suppressing the QCD background are muon isolation variables. Muons produced in jets will tend to be collimated with the other 6 Figure 5.2: The pT of reconstructed muon candidates, comparing dijet and Z → ττ MC (mc08,√ s = 10 TeV) [177] J1, J2, and J3 denote simulated dijet samples with an out-going parton in the pT ranges 17–35, 35–70, and 70–140 GeV respectively. 5.2 mc studies of `τh event kinematics 109 MET [GeV] 0 20 40 60 80 100 120 140 pb / (2 .5 G eV ) -210 -110 1 10 210 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (a) ) τ φμ φcos( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 pb / (0 .0 5) -210 -110 1 10 210 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (b) Figure 4: Distributions prior to cutting on the muon isolation variables. After requiring the isolation cuts, there were not enough events to require tau ID cuts and continue the cut flow. We needed a more exclusive QCD sample, targeted at the types of events that would pass the cuts in our analysis. This led us to investigate the sources of the muons in dijets. (3 8. 3 % ) + μ (33.7 %)μ (7.7 % ) + K (6.7 % ) +π (6.1 %) -K (5.7 %) -π other (1.9 %) Nearest truth particle to reco muon (a) Nearest generator truth particle to a reconstructed muon (14 .6 % ) +B (1 4. 0 % ) 0 B (13.8 % ) -B (13.5 %)0B (7. 0 % ) 0 D (6 .6 % ) + D (6 .1 % ) 0 D (5.2 % ) 0s B (5.0 % ) -D (4.1 % ) 0s B (2.2 %) 0 b Λ (2.0 %) + sD other (5.9 %) Mother of true muon (b) Parent particle of true generator muons Figure 5: Sources of muons with pT > 15 GeV in dijets Figure 5 concerns the sources of muons in the J2 dijets sample. Plots made from J1 and J3 are very similar. Figure 5(a) shows that approximately 2/3 of the muons in dijets come from prompt sources, and therefore can be matched to a true generator muon. Most of the other third come from the decay of pions or kaons in flight. Since one cannot select events which will have a pion or kaon decay with a generator-level filter, it is not obvious how one can model the background contribution due pion and kaon decay with Monte 8 Figure 5.3: The distribution of the reconstructed missing transverse momentum for the relevant MC samples with preselected μτh events [177]. particles in the jet. Requiring that a muon not be near other tracks or significant energy deposits in the calorimeter will exclude these background events. We make cuts on two muon isolation variables: • N R<0.4tracks (μ) = 0 (nucone40 in Athena) The number of tracks with pT over 1 GeV in a cone of  R < 0.4 around the trajectory of the muon (not including the muon's track) must be zero. • E R<0.4T (μ) < 2 GeV (etcone40 in Athena) The ET deposited in calorimeters in a cone of  R < 0.4 around the trajectory of the muon must be less than 2 GeV. The distributions of these variables are shown in Figure 3. The e↵ects of underlying events on these distributions and the e ciency for the Z ! ⌧⌧ signal to pass these cuts could be modeled dir ctly with data by quiring a second muon in tead of a tau-je , sel cting clearly recognizable Z ! μμ events. )μ(R<0.4ΔtracksN 0 2 4 6 8 10 12 14 pb 1 10 210 310 410 ) > 15 GeVμ( T p J1 J2 J3 τ τ →Z (a) ) [GeV]μ(R<0.4ΔTE 0 2 4 6 8 10 12 14 16 18 20 pb / (0 .5 G eV ) 1 10 210 310 410 ) > 15 GeVμ( T p J1 J2 J3 τ τ →Z (b) Figure 3: Muon isolation variables In order to overcome the QCD backgrounds, we decided that making strong isolation requirements is more suitable than requiring a minimum MET because such a cut is very costly on the signal, as shown in Figure 4(a). Also, being such a heavily derived quantity cutting on MET could introduce unnecessary systematic error. However, not requiring a minimum MET has the disadvantage that one cannot use the collinear approximation to calculate the Z mass, as is used to tune the MET scale in reference [3]. This is because the collinear approximation only gives a reliable result in events with significant MET. Moreover, the system of equations used in the collinear approximation becomes linearly dependent when the tau decay products are back-to-back. One can exclude these events with a cut like | cos( μ    ⌧ )| < 0.9 at the cost of most of the signal, as shown in Figure 4(b). Therefore, with the goal in mind being to select a sizable and relatively pure control sample of hadronic taus, we have forgone the use of MET cuts and the collinear approximation. After our analysis has selected such a control sample, one can use the subset of events suitable for the collinear approximation to make those corresponding measurements. 7 Figure 5.4: Distributions of trackingand calorimeter-based muon isolation variables for Z → ττ and dijet samples [177]. The most effective way to suppress the multijet background in events with a elected lepton is to require that the lepton be isolated. Leptons produced in jets will tend to be collimated with the other particles in the jet. Requiring that a lepton not be near other tracks or significant energy deposits in the calorimeter will exclude th se b ckground events. Figure 5.4 shows examples of two muon isolation variables, one using tracking information and the other being calorimeter-based. • N∆R<0.4tracks (μ) (nucone40 in Athena) The number of tracks with pT > 1 GeV within ∆R < 0.4 around the trajectory of the muon (not including the track of the reconstructed muon). • E∆R<0.4T (μ) (et one40 in Athena44) 44 Also referred to as I0.4ET in Section 5.4.4. 110 5. measurement of the z → ττ cross section ) [GeV]hτ(TE 0 20 40 60 80 100 120 140 ID E ffi ci en cy -510 -410 -310 -210 -110 1 flagsμJ2 + J3, cuts: LLH > 4, e/ all 1-prong 2-prong 3-prong 4-prong 5-prong 6-prong (a) J2+J3 ) [GeV]hτ(TE 0 20 40 60 80 100 120 140 ID E ffi ci en cy -510 -410 -310 -210 -110 1 flagsμ, cuts: LLH > 4, e/bb all 1-prong 2-prong 3-prong 4-prong 5-prong 6-prong (b) bb Figure 7: Tau-jet identification fake-rates the fake-rate for b-jets is enhanced, especially at low ET. Perhaps this indicates the possibility of improving the e/μ flags. ) [GeV]hτ(TE 0 20 40 60 80 100 120 140 ID E ffi ci en cy -310 -210 -110 1 flags, OLRμcuts: LLH > 4, e/ J2 + J3, 1-prong J2 + J3, 3-prong , 1-prongbb , 3-prongbb (a) With overlap removal ) [GeV]hτ(TE 0 20 40 60 80 100 120 140 ID E ffi ci en cy -310 -210 -110 1 flagsμcuts: LLH > 4, e/ J2 + J3, 1-prong J2 + J3, 3-prong , 1-prongbb , 3-prongbb (b) Without overlap removal Figure 8: Overlays of the 1 and 3-prong fake-rates from both the inclusive dijets and bb. After parametrizing the fake-rate, we did not require tau ID cuts for the bb sample, and instead scaled its histogram entries by the fake-rate. We did the scaling tau candidate by tau candidate. If an event had multiple tau candidates, then in histograms it contributes an entry for each candidate scaled by the fake-rate for that candidate. The justification for this approach is discussed in Appendix A.5. Figure 9(a) compares the bb visible mass distribution just following the tau ID cuts, to the distribution determined with the scaling technique, showing good agreement. Following the tau ID scaling, the muon isolation cuts were applied to extinguish the bb background, with a rejection factor of 110. This brings the bb background rate to the order of the other electroweak backgrounds, with the W ! μ⌫ + jets background now dominating (see Figure 9(b)). 10 Figure 5.5: Tau identification fake rates derived with dijet and bb Monte Carlo samples (mc08,√ s = 10 TeV) [177]. The identification used is a preliminary version of the likelihood method [148]. The fake rate in the bb sample is enhanced compared to the inclusive sa ple of dijets, m inly du to the presence of real leptons from B decays, but the effect is not significant after emoving pre-selected leptons. The ET deposited in calorimeters within ∆R < 0.4 around the trajectory of the muon. Requiring that an event pass lepton isolation cuts and tau identification each suppress the multijet background by a factor of 10–100, resulting in poor Monte Carlo statistics for modeling the multijet background. In order to improve the statistics of the multijet model, the rate for jets to fake tau identification was parameterized and used to weight MC events instead of directly applying the tau identification requirements. This method is valid, assuming that the rate to pass tau identification depends on the local properties of the jet forming the tau candidate, and is largely uncorrelated45 with the global event kinematics (invariant masses, ∆φ, etc.) [177]. This method is similar to the fake factor methods developed later for the search for Z ′ → ττ , discussed in Section 6.4.4. First, the fake rate for jets to pass the tau identification cuts, as measured with the dijet Monte Carlo, was parametrized in bins of the reconstructed visible ET and the number of tracks (prongs) associated to a tau candidate. Figure 5.5 shows the fake rate measured with an inclusive dijet sample and a bb sample. These fake-rates are defined46 as ε = number of n-prong candidates in the ET-bin that pass selection number of n-prong candidates in the ET-bin , After parametrizing the fake rate47, when analyzing the bb Monte Carlo sample, the tau identification 45 There is actually some sample dependence in the fake rates for tau identification, mainly due to variations in the quark-gluon fraction of the out-going parton initiating a jet as discussed in Section 4.4.8. 46 Here, "selection" denotes identification and overlap-removal requirements that will be discussed in more detail in Section 5.4.4. 47 The fake rates of the inclusive dijet and bb sample were in statistical agreement after overlap removing preselected leptons, and therefore the fake rates from the large inclusive dijet sample where used. Pre-selection and overlap removal are discussed later in Section 5.4.3. 5.2 mc studies of `τh event kinematics 111 ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 10 20 30 40 50 60 70 80 Passed tau ID cuts Scaled by fake-rate (a) ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 1 2 3 4 5 6 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (b) Figure 9: (a) Comparison of visible mass distribution of the bb events that passed the tau ID cuts, to the distribution determined by the fake-rate scaling. (b) Visible mass distribution following the muon isolation cuts. 5 W + jets Backgrounds Once QCD backgrounds have been suppressed, the largest electroweak background to tackle is W + jets. Due to the recoil of the W o↵ of a jet, a muon produced in the decay of a W is likely to traverse away from the direction of the jet and is therefore likely to survive muon isolation requirements used to suppress QCD backgrounds. 5.1 Opposite Sign vs. Same Sign ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 0.5 1 1.5 2 2.5 3 3.5 OS ν μ →W ν τ →W τ τ →Z (a) Opposite sign ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 0.5 1 1.5 2 2.5 3 3.5 SS ν μ →W ν τ →W τ τ →Z (b) Same sign Figure 10: Visible mass of muon tau-jet combination, including all cuts through the tau ID cuts on the Likelihood and the e/μ flags. (See list of cuts in Table 2.) An important property to note is that the muon and jet from W + jets are biased towards being reconstructed to have oppositely signed charges, like the Z ! ⌧⌧ signal is expected to have (see Figure 10). One can understand the cause of this e↵ect by 11 Figure 5.6: Distributions of the visible mass of the combination of a muon and a selected tau candidate. (left) A comparison of Monte Carlo bb events that pass tau identification with a distribution from scaling candidate by a fake rate (with no lepton isol tion). (right) The combined SM background model for selected μτh events with tau identification and muon isolation requirements. A preliminary likelihood-based tau identification [148] was used by requiring that the likelihood score was greater than 4. The isolation requirements used were: N∆R<0.4tracks (μ) = 0 and E ∆R<0.4 T (μ) < 2 GeV [177]. requirements were not applied and instead the events were weighted by the fake rate, tau candi ateby-candidate. Figure 5.6 shows the predicted distribution of the visible mass of the combination of a muon and a tau candidate passing identification. Figure 5.6 (a) compares the bb estimates when requiring the tau identification and when weighting by the fake rate, showing that the shape looks generally wellmodeled. Figure 5.6 (b) shows the visible mass after requiring muon isolation, which suppresses the bb background by a factor of ≈ 100. Without parametrizing and weighting by the fake rate, the bb model would not have a statistically significant shap . Requiring both tau identification and lepton isolation bring the multijet background rate to the order of the other electroweak backgrounds. 5.2.2 W+jets background After the multijet background has been suppressed by lepton isolation and tau identification, the leading background to tackle isW + jets. There are contributions from bothW → `ν andW → τν → `ννν where a jet in the event is falsely identified as the tau candidate. Opposite-sign vs same-sign An important property of W + jets events to note is that they are biased towards having a lepton and tau candidate with opposite-sign (OS) reconstructed charges (see Figure 5.7). One can explain this feature by noting that the leading order W + jet diagrams are biased towards having an out-going lepton and quark with opposite-sign charges, and quark-initiated jets are biased towards hadronizing 112 5. measurement of the z → ττ cross section ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 10 20 30 40 50 60 70 80 Passed tau ID cuts Scaled by fake-rate (a) ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 1 2 3 4 5 6 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (b) Figure 9: (a) Comparison of visible mass distribution of the bb events that passed the tau ID cuts, to the distribution determined by the fake-rate scaling. (b) Visible mass distribution following the muon isolation cuts. 5 W + jets Backgrounds Once QCD backgrounds have been suppressed, the largest electroweak background to tackle is W + jets. Due to the recoil of the W o↵ of a jet, a muon produced in the decay of a W is likely to traverse away from the direction of the jet and is therefore likely to survive muon isolation requirements used to suppress QCD backgrounds. 5.1 Opposite Sign vs. Same Sign ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 0.5 1 1.5 2 2.5 3 3.5 OS ν μ →W ν τ →W τ τ →Z (a) Opposite sign ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 pb / (5 G eV ) 0 0.5 1 1.5 2 2.5 3 3.5 SS ν μ →W ν τ →W τ τ →Z (b) Same sign Figure 10: Visible mass of muon tau-jet combination, including all cuts through the tau ID cuts on the Likelihood and the e/μ flags. (See list of cuts in Table 2.) An important property to note is that the muon and jet from W + jets are biased towards being reconstructed to have oppositely signed charges, like the Z ! ⌧⌧ signal is expected to have (see Figure 10). One can understand the cause of this e↵ect by 11 Figure 5.7: The visible mass of μτh events with opposite-sign (left) and same-sign (right) reconstructed charges. Note that the W + jets background is OS-biased [177]. and being reconstructed as tau candidates with charge the same sign as the initial out-going quark48. Moreover, the quark-gluon fraction is different among the OS and same-sign (SS) W + jets samples49. EmissT angular correlations The leptons from W + jets events and other electroweak processes tend to be well isolated. To reject the W + jets background, angular correlations of the direction of the EmissT and the directions of the lepton and tau candidate can be exploited. Because the mass of the Z boson is much larger than the mass of the τ lepton, the τ leptons in Z → ττ will be boosted such that their decay products will be collimated along the trajectory of the parent τ lepton. Ignoring underlying interactions in the event and mis-measurements of EmissT , the E miss T will be the vector sum of the pT of the neutrinos, as depicted in Figure 5.8. The majority of Z bosons produced will have low pT, and therefore the taus will be back-to-back, but in the case that the Z has significant nonzero boost in the transverse plane, the EmissT vector will fall in the angle (less than π) between the decay products of the Z. In contrast, in events from the W + jets background, the neutrino, jet, and muon will all tend to point in different directions, balancing pT in the transverse plane. Ignoring underlying interactions in the event and EmissT mis-measurement, the E miss T vector should point along the neutrino which is not in the angle between the fake tau candidate and the muon. In W → τν → μννν events, there are two additional neutrinos, but the EmissT will still point outside of the angle between the muon and the fake tau candidate. The traditional50 variable for suppressing W + jets is the transverse mass of the lepton and EmissT , mT, usually by requiring mT . 30 GeV. Figure 5.9 shows the distribution of mT for Z → ττ and 48 Refer back to Figure 4.34 and the discussion of W + jets fake rates in Section 4.4.8. 49 Therefore the SS sample cannot simply be used to model the background from W + jets events like the method for estimating the multijet background that will be discussed in Section 5.7.3. 50 Previous MC Z → ττ studies in Refs. [173, 178] used mT < 30 and 35 GeV, respectively. 5.2 mc studies of `τh event kinematics 113 (a) Z ! ⌧⌧ ! μ⌧h (b) W ! μ⌫ (c) W ! ⌧⌫ ! μ⌫⌫⌫ Figure 13: Drawings of representative transverse plane orientations of W and Z decay products and the MET. The shaded angles indicate the angle less than ⇡ between the muon and the (fake) tau-jet. (In (a), the Z is depicted to have nonzero pT, which must be balanced on the left by some other activity omitted for clarity.) ) MET φμ φcos( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ) M ET φτφ co s( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1100 pb ν μ →W ν τ →W τ τ →Z (a) ) MET φτ φ) + cos( MET φμ φcos( -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 pb / (0 .0 5) 0 0.5 1 1.5 2 2.5 3 3.5 4 ν μ →W ν τ →W τ τ →Z (b) Figure 14: Plots demonstrating the angular correlations of the MET and the decay products of W ! μ⌫, W ! ⌧⌫ ! μ⌫⌫⌫, and Z ! ⌧⌧ ! μ⌧h. 14 Figure 5.8: Diagrams illustrating representative transverse plane orientations of W and Z decay products and the EmissT . The shaded angles indicate the angle less than π between the lepton and the (fake) tau-jet. τh denotes the visible sum of the decay products of a hadronic decay of a tau lepton. In (a), the Z is depicted to have nonzero pT, which must be balanced on the left by some other activity omitted for clarity [177]. W + jets events. In Z → ττ → `τh events, since there are two neutrinos on the side of the leptonic decay, the EmissT tends to point along the lepton in the transverse plane. Ignoring the masses of the leptons, the transverse mass can be calculated as mT ≡ √ 2 pT(`) EmissT (1− cos ∆φ(`, EmissT )) , which illustrates that the mT goes to zero when the E miss T is along the lepton, explaining the spike in the mT distribution at low mT for Z → ττ . However, there is also some phase-space where the neutrino from the hadronic tau decay has an exceptionally high share of the pT, and the E miss T points along the τh, giving the higher-mT tail for Z → ττ that is lost if requiring low mT. For W → `ν events, mT is maximal when the momentum vectors of the neutrino and lepton have zero z-components, in which case mT is a measurement of the W mass. Using mT to reject W + jets does not take into account the information of the direction of the tau candidate. One way to see that the EmissT tends to point between the decay products in Z → ττ events, rather than away as in W + jets events, is to consider the scatter plot in Figure 5.10(left), which shows cos ∆φ(τh, E miss T ) versus cos ∆φ(`, E miss T ). The up/down dimension of this plot corresponds to the EmissT pointing towards/away from the hadronic tau decay, while the right/left dimension of this plot corresponds to the EmissT pointing towards/away from the muon. The upperright triangle corresponds to the EmissT being within the angle between the muon and hadronic tau, while the bottom-left corresponds to the EmissT being outside of it. The diagonal going from the top-left to the bottom-right corner corresponds to cases where the muon and hadronic tau are backto-back. A cut passing up to a maximum mT will tend to exclude events on the left side of this plot, ignoring the vertical dimension. This cut will favor the Z → ττ events in the bottom-right corner, 114 5. measurement of the z → ττ cross section (a) , MET) [GeV]μ(Tm 0 20 40 60 80 100 120 140 pb / (2 .5 G eV ) 0 0.5 1 1.5 2 2.5 ν μ →W ν τ →W τ τ →Z (b) Figure 12: (a) In Z ! ⌧⌧ ! μ⌧h, the two neutrinos on the side with the muon tend to align the missing transverse energy along the muon. (b) Transverse mass of the combination of the muon and missing transverse energy, including all cuts through the tau ID cuts on the Likelihood and the e/μ flags. (See list of cuts in Table 2.) the side of the hadronic tau decay has large ET, and therefore the MET points closer to the direction of the hadronic tau decay. In the following subsection, we propose a more e↵ective method for separating Z from W decays. 5.3 Angular Correlations As mentioned before, because the mass of the Z boson is much larger than the mass of the tau lepton, the decay products of the taus in Z ! ⌧⌧ will point along the trajectory of their parent tau. Ignoring underlying interactions in the event and MET mismeasurement, the MET will be the vector sum of the ET of the neutrinos, as depicted in Figure 13(a). The majority of Z bosons produced will have low pT, and therefore the taus will be backto-back, but in the case the Z has significant nonzero boost in the transverse plane, the MET vector will fall in the angle (less than ⇡) between the decay products of the Z. In contrast, in events from the W ! μ⌫ + jets background, the neutrino, jet, and muon should all point in di↵erent directions, balancing pT in the transverse plane. Ignoring underlying interactions in the event and MET mismeasurement, the MET vector should point along the neutrino which is not in the angle between the fake tau-jet and the muon. In W ! ⌧⌫ ! μ⌫⌫⌫ events, there are two additional neutrinos, but the MET will still point outside of the angle between the fake tau-jet and the muon. One can see this behavior in the Monte Carlo by scatter plotting the cos( ⌧    MET) versus the cos( μ    MET), shown in Figure 14(a). The up/down dimension of this plot corresponds to the MET pointing towards/away from the hadronic tau decay. The 13 Figure 5.9: (left) In Z → ττ → `τh events, since there are two neutrinos on the side of the leptonic decay, the EmissT tends to point along the lepton in the transverse plane. (right) The transverse mass of the lepton and the EmissT in reconstructe μτh events for Z → ττ and W + jets Monte Carlo samples (mc08, √ s = 10 TeV) [177]. but will tend to lose the top-left corner, corresponding to the case when the neutrino on the side of the τh has large pT. A variable for suppressing W + jets using the directi n of both decay products and the EmissT was introduced [177]. Rotating Figure 5.10 (left) by clockwise by π/4 and projecting down gives the sum of the cosines of the ∆φ between each decay product and the EmissT : ∑ cos ∆φ = cos ∆φ(τh, E miss T ) + cos ∆φ(`, E miss T ) , This variable separates the Z → ττ events with high ∑ cos ∆φ and the EmissT between the decay products, from the W + jets events with low ∑ cos ∆φ and the EmissT outside the angle between the decay products, as shown in Figure 5.10(right). The p ak at zero corresponds to events with lepton and tau candidates that are back-to-back in the transverse plane. Requiring ∑ cos ∆φ > −0.15 accepts the back-to-back events and the upper-right triangle of Figure 5.10(left). Figure 5.11 shows the same scatter plot and the distribution of mT after requiring ∑ cos ∆φ > −0.15. Combining this ∑ cos ∆φ cut with a looser cut on the transverse mass, mT < 50 GeV, gave 9% more signal acceptance and a 15% increase in the signal-to-background ratio compared to just a mT < 30 GeV cut in MC st di s [177]. 5.2 mc studies of `τh event kinematics 115 (a) Z ! ⌧⌧ ! μ⌧h (b) W ! μ⌫ (c) W ! ⌧⌫ ! μ⌫⌫⌫ Figure 13: Drawings of representative transverse plane orientations of W and Z decay products and the MET. The shaded angles indicate the angle less than ⇡ between the muon and the (fake) tau-jet. (In (a), the Z is depicted to have nonzero pT, which must be balanced on the left by some other activity omitted for clarity.) ) MET φμ φcos( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ) M ET φτφ co s( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1100 pb ν μ →W ν τ →W τ τ →Z (a) ) MET φτ φ) + cos( MET φμ φcos( -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 pb / (0 .0 5) 0 0.5 1 1.5 2 2.5 3 3.5 4 ν μ →W ν τ →W τ τ →Z (b) Figure 14: Plots demonstrating the angular correlations of the MET and the decay products of W ! μ⌫, W ! ⌧⌫ ! μ⌫⌫⌫, and Z ! ⌧⌧ ! μ⌧h. 14 Figure 5.10: (left) A scatter plot of the cos ∆φ for the angles between each decay product and the EmissT for μτh events with Monte Carlo. (right) The distribution of ∑ cos ∆φ for the same events [177]. ) MET φμ φcos( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ) M ET φτφ co s( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1100 pb ν μ →W ν τ →W τ τ →Z (a) , MET) [GeV]μ(Tm 0 20 40 60 80 100 120 140 pb / (2 .5 G eV ) 0 0.5 1 1.5 2 2.5 ν μ →W ν τ →W τ τ →Z (b) Figure 15: Plots after the cut: cos( μ    MET) + cos( ⌧    MET) >  0.15 cases with sizable true MET, the addition of a comparatively small fake MET vector will have only a minor e↵ect on the direction of the resultant measured MET vector. 6 Cut Flow and Results Following the transverse mass cut, we further suppress the Z ! μμ and tt backgrounds by requiring that there be only one muon and no tight electrons with pT > 10GeV. Then we require that the number of tau-jet candidates after overlap removal, N(⌧h cand. OLR), be less than or equal to four (see Figure 16(a)). Because these candidates need not pass any ID criteria, this is basically a cut on the jet multiplicity. cand. OLR)hτN( 0 2 4 6 8 10 12 14 pb -210 -110 1 10 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (a) ) h τ charge(×) μcharge( -4 -3 -2 -1 0 1 2 3 4 pb -210 -110 1 10 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb (b) Figure 16: (a) Number of tau-jet candidates after overlap removal, and after all cuts in the cut flow table through the N(e; pT > 10 GeV) = 0 cut. (b) Product of charges of the muon and tau-jet after the cut on N(⌧h cand. OLR). 16 Figure 5.11: (left) A scatter plot of the cos ∆φ for the angles between each decay product and the EmissT for μτh events from Monte Carlo. (right) The distribution of the transverse mass of the combination of the muon and the EmissT . Both of these plots are after requiring∑ cos ∆φ > −0.15 [177]. 116 5. measurement of the z → ττ cross section 5.2.3 Preliminary event selection Figure 5.12 illustrates the effective cross section selected for Z → ττ and background processes, stepping through a preliminary event selection, which is described in detail in Ref. [177]. A detailed discussion of the event selection used for the Z → ττ cross section measurement will be given in Section 5.4.5, but can be briefly summarized as • opposite-sign isolated lepton and selected tau candidate • no other leptons • W + jets suppression cuts on mT and ∑ cos ∆φ • a visible mass window. Figure 5.13 (left) shows the visible mass of the muon and selected tau candidate after all selections except a mass window. Figure 5.13 (right) shows the distribution of the number of tracks associated to the selected tau candidate in events passing all event selection except a cut on this number of tracks. In both figures, to help visualize the expected statistics in 100 pb−1 of data with √ s = 10 TeV, toy data are shown, drawn from Poisson distributions for the expected number of events in each bin. The efforts from other ATLAS preliminary MC investigations of selecting Z → ττ [173, 178] converged in 2009 to define the ATLAS "benchmark analysis" for Z → ττ [174]. These studies demonstrate that with an integrated luminosity of 100 pb−1 at √ s = 10 TeV and using conservative cut-based tau identification and event selection, approximately 1000 Z → ττ events could be selected with about 80% purity, which could be improved with tighter tau identification. The tau identification is the one requirement where the selection efficiency of Z → ττ could be most improved, as it is the step that results in the largest loss of Z → ττ (≈ 30% efficient for tight cuts) after requiring a high-pT lepton and tau candidate. For the benchmark analysis, studies were also done to estimate the multijet background with ATLFAST-II [179] fast Monte Carlo simulation. Since the trigger decisions were not simulated in the fast simulation, the efficiency to pass the single lepton triggers was parametrized as a function of pT, as measured in the full simulation Monte Carlo, and used to weight the fast simulation events (see Figure 5.14). The visible mass distributions are compared for estimates of the multijet background using full simulation weighted by the tau identification fake rate as in Section 5.2.1, and using ATLFAST-II in Figure 5.15. 5.2 mc studies of `τh event kinematics 117 generated ) > 0μN( )/DOF < 4μ( fit 2χ )/DOF < 8μ( match 2χ ) > 15 GeVμ( T p cand.) > 0hτN( Overlap Removal ) = 15-140 GeVhτ(TE 1-5 prong Likelihood > 4 e flag flagμ ) = 0μ(R<0.4ΔtracksN ) < 2 GeVμ(R<0.4ΔTE > -0.15φΔ cos∑ , MET) < 50 GeVμ(Tm > 10 GeV) = 1 T ; pμN( > 10 GeV) = 0 T N(e; p 4≤ cand. OLR) hτN( ) = -1 or 0 h τ chg(×) μchg( ) = 35-80 GeV h τ, μ(vism 1 or 3 prong pb -1 10 1 10 2 10 3 10 4 10 5 10 C ut Flow τ τ → Z ν μ → W ν τ → W μ μ → Z tt b b Figure 18: Cut flow. Note that the bb entries following the Likelihood and e flag cuts do not change because the sample is not scaled until all three tau ID cuts are applied. The same information is presented in Table 2. 19 Figure 5.12: The effective cross section passing successive event selections for a preliminary Z → ττ → μτh event selection (mc08, √ s = 10 TeV) [177]. 118 5. measurement of the z → ττ cross section ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / (5 G eV ) 0 50 100 150 200 250 300 350 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb toy data -1100 pb (a) Stacked visible mass distributions after the cut on charge(μ) ⇥ charge(⌧h). ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / (5 G eV ) 0 50 100 150 200 250 300 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb toy data -1100 pb (b) Final stacked visible mass distributions after the 1 or 3 prong cut. )hτ(tracksN 0 1 2 3 4 5 6 7 8 9 Ev en ts 0 200 400 600 800 1000 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb toy data -1100 pb (c) Stacked number of tracks distributions of the tau-jet, prior to requiring 1 or 3 prong. Figure 17: Plots scaled to the expectation in 100 pb 1 of integrated luminosity. The points with error bars show a fake data sample drawn from Poisson distributions with means determined by the sum in each bin. 18 ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / (5 G eV ) 0 50 100 150 200 250 300 350 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb toy data -1100 pb (a) Stacked visible mass distributions after the cut on charge(μ) ⇥ charge(⌧h). ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / (5 G eV ) 0 50 100 150 200 250 300 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb toy data -1100 pb (b) Final stacked visible mass distributions after the 1 or 3 prong cut. )hτ(tracksN 0 1 2 3 4 5 6 7 8 9 Ev en ts 0 200 400 600 800 1 00 τ τ →Z ν μ →W ν τ →W μ μ →Z tt bb toy data -1100 pb (c) Stacked number of tracks distributions of the tau-jet, prior to requiring 1 or 3 prong. Figure 17: Plots scaled to the expectation in 100 pb 1 of integrated luminosity. The points with error bars show a fake data sample drawn from Poisson distributions with means determined by the sum in each bin. 18 Figure 5.13: The μτh visible mass of events passing the entire analysis selection except for a visibile mass window. The number of reconstructed tracks associated to the tau candidate in events passing the entire selection except relaxing the 1 or 3 and OS requirements [177]. Toy data drawn from a Poisson distribution for the expected value in each bin is shown to give a visualization of the expected statistics. 3.4 Trigger Weighting228 Unlike the full simulation samples, ATLFAST-II samples have no simulated trigger decision. In order to simulate the trigger requirement, the lepton trigger e ciency is parametrised as a function of the lepton pT, using full simulation samples. The events are then weighted by the e ciency given by this parametrisation when running over ATLFAST-II samples. The fit function used for the parametrisation was f(pT) = aplateau 1 2 ✓ 1 + erf ⇣pT   aedge awidth ⌘◆ ✓(pT   acuto↵) . An error function (erf) is expected for trigger e ciency curves, with a width characteristic229 of the pT resolution at the level 1 trigger (worse for muons). Fit p rameters are denoted by230 the symbol a, and ✓(x) denotes a step function. The sharp step function cuto↵ represents231 the selection at the event filter, which has the same resolution as the o✏ine pT, and232 therefore does not have a width. Fig. 4 shows the trigger e ciencies and fitted functions233 for the full simulation QCD J3 sample for muons and electrons. While the J3 sample was234 used because it was the only QCD sample with leptons over the entire relevant pT range,235 the corresponding plots for J1 and J2 agree within the statistical uncertainty.236 (e) [GeV] T p 5 10 15 20 25 30 Tr ig ge r Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.02±Plateau = 0.879 0.05 GeV±Edge = 10.0 0.4 GeV±Width = 2.01 0.02 GeV±Cutoff = 9.58 / NDF = 23.5 / 23 = 1.022χ (a) electrons ) [GeV]μ( T p 5 10 15 20 25 30 Tr ig ge r Ef fic ie nc y 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.008±Plateau = 0.820 0.1 GeV±Edge = 11.9 0.3 GeV±Width = 6.37 0.005 GeV±Cutoff = 9.55 / NDF = 63.0 / 23 = 2.742χ (b) muons Figure 4: E ciency for a preselected lepton to pass the trigger requirement as a function of the o✏ine reconstructed lepton pT, using the full simulation J3 sample. The solid curve shows the entire fit function, while the dashed curve shows the same function without the step function component. The error bars are asymmetric Bayesian error bars given by the ROOT function TGraphAsymmErrors::BayesDivide [14]. 3.5 Lepton Isolation237 The background process with the largest cross section is QCD dijet production. Approx-238 imately 60% of lepton candidates from these processes come from true leptons, most of239 them originating from b-decays. Lepton candidates from these dijet events usually occur240 in the vicinity of other particle production, and therefore lepton isolation provides good241 discrimination between signal and the QCD background.242 11 Figure 5.14: The efficiency for true reconstructed leptons in Monte Carlo to pass the trigger using fu ly simulated Monte Carlo. This efficiency was fit and the parametrtizat on used to weight fast simulation samples (ATLFAST-II) that di not have a simulated trigger decision (mc08) [174]. 5.3 data samples 119 ) [GeV]h!(lep, vism 0 20 40 60 80 100 120 140 160 180 200 Cr os s S ec tio n [p b] / ( 5 G eV ) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Cr os s S ec tio n [p b] / ( 5 G eV ) ! ! "Z # μ "W # e "W # ! "W μ μ "Z e e"Z tt μQCD QCD e Figure 13: The distribution of the visible mass for fully simulated samples. ) [GeV]h!(lep, vism 0 20 40 60 80 100 120 140 160 180 200 Cr os s S ec tio n [p b] / ( 5 G eV ) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Cr os s S ec tio n [p b] / ( 5 G eV ) ! ! "Z # μ "W # e "W # ! "W μ μ "Z e e"Z tt QCD Figure 14: The distribution of the visible mass for ATLFAST-II dijet simulated samples. All other samples shown are from full simulation. 19 ) [GeV]h!(lep, vism 0 20 40 60 80 100 120 140 160 180 200 Cr os s S ec tio n [p b] / ( 5 G eV ) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Cr os s S ec tio n [p b] / ( 5 G eV ) ! ! "Z # μ "W # e "W # ! "W μ μ "Z e e"Z tt μQCD QCD e Figure 13: The distribution of the visible mass for fully simulated samples. ) [GeV]h!(lep, vism 0 20 40 60 80 100 120 140 160 180 200 Cr os s S ec tio n [p b] / ( 5 G eV ) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Cr os s S ec tio n [p b] / ( 5 G eV ) ! ! "Z # μ "W # e "W # ! "W μ μ "Z e e"Z tt QCD Figure 14: The distribution of the visible mass for ATLFAST-II dijet simulated samples. All other samples shown are from full simulation. 19 Figure 5.15: The μτh visible mass of events passing the entire analysis selection except for a visibile mass window as predicted with the full simulation dijet samples, weighted by fake rates (left), and as predicted with ATLFAST-II dijet Monte Carlo (right) [174]. 5.3 Data samples 5.3.1 Data The year 2010 was the year with the first record-energy collision data at the LHC. Collision data at √ s = 7 TeV collected from July to October 2010 were used for the first ATLAS measurement of the Z → ττ cross section. The datasets were processed with the autumn 2010 reprocessing, which uses Athena release 16.0.2.3. The events were triggered with the lowest-pT unprescaled single electron and muon triggers described in Section 5.4.2. In the eτh channel, run periods E3–I2 were used, while in the μτh channel E4–I2 were used. The first periods were not included because initially the trigger conditions varied rapidly. The resulting integrated luminosity [180], after data quality requirements, is about 36 pb−1 in both the eτh and μτh channels, as is shown for each run period in Table 5.1. Table 5.1: The EF e15 medium trigger was required for the eτh channel, including a prescale in part of period E. In the μτh channel the trigger, EF mu10 MG was used for run period 160899–165632, EF mu13 MG for the run period 165703–167576 and EF mu13 MG tight for run period 167607–167844, respectively to avoid the use of prescaled triggers. In period E, the eτh channel is using data from period E3 (160613) and above, while the μτh channel starts at period E4 (160899) [181]. run period run number int. luminosity (pb−1) int. luminosity (pb−1) eτh channel μτh channel period E 160387–161948 0.752 0.514 period F 162347–162882 1.743 1.743 period G 165591–166383 5.531 5.531 period H 166466–166964 6.984 6.984 period I 167575–167844 20.735 20.735 35.745 35.507 120 5. measurement of the z → ττ cross section Nvertex Event weight 1 1.970(8) 2 1.242(4) 3 0.853(3) 4 0.633(2) 5 0.509(3) 6 0.427(4) 7 0.392(6) 8 0.38(1) 9 0.39(2) 10 0.41(5) >=11 0.89(14) Table 3: Number of reconstructed vertices and corresponding pileup weights. N(vertices) 0 2 4 6 8 10 12 14 Ev en ts 10 210 310 410 510 610 Data ττ→Z (a) N(vertices) 0 2 4 6 8 10 12 14 Ev en ts 10 210 310 410 510 610 Data ττ→Z (b) Figure 1: Comaprison of vertex distributions between data and signal Monte Carlo before (left) and after (right) vertex re-weighting. 9 Figure 5.16: Comparison, for data and Monte Carlo, of the distributions of the number of reconstructed vertices in each event before (left) and after (right) vertex re-weighting [181]. 5.3.2 Simulation The Monte Carlo samples51 were from the mc10 production campaign. The W and γ∗/Z backgrounds and Z → ττ signal samples were generated with PYTHIA [125], and were normalized to their corresponding NNLO cross sections [108] calculated using FEWZ [182]. The low-mass γ∗/Z samples were normalized to the NNLO cross sections from Refs. [183, 184]. The diboson samples were generated using Herwig [121]. Other samples used were generated as described in Section 3.6.1. In each event that is recorded by ATLAS, proton-proton interactions in addition to the one which triggered the read-out can occur, resulting in pile-up interactions characterized by having more than one primary vertex reconstructed per event, as described in Section 3.5.2. The Monte Carlo samples were produced with the so-called bunch-train pile-up setup in which simulated minimum bias interactions were overlaid on top of the hard-scattering event with the following timing structure: individual bunches were separated by 150 ns and contained in trains of eight bunches length. A second bunch train followed with a time separation equal to 225 ns, followed by a longer pause before the next bunch train. The average number of reconstructed primary vertices per bunch crossing in the data ranged from 1–2.2, depending on the period used, while the average number of vertices in the Monte Carlo before re-weighting was 2.8. The Monte Carlo samples were re-weighted such that their distributions of the number of reconstructed vertices per event match the distribution in data (see Figure 5.16). 51 All of the simulated samples used are listed in the Appendix of Ref. [181]. 5.4 z → ττ → `τhselection 121 5.4 Z → ττ → `τh selection 5.4.1 Event preselection Primary vertex requirement Candidate events were required to have at least one reconstructed primary vertex with at least 3 reconstructed tracks. Jet cleaning Events may occasionally contain localized high-energy calorimeter deposits not originating from the proton-proton collision. Sources of such apparent energy depositions are, for example, discharges in the hadronic end-cap calorimeter and more rarely, coherent noise in the electromagnetic calorimeter. Cosmic-ray muons undergoing a hard bremsstrahlung are also a potential source of localized energy deposits uncorrelated to the primary proton-proton collisions. The occurrence of these events is very rare, but such spurious energy deposits can have a significant impact on the EmissT measurement (by creating high-energy tails), or be incorrectly reconstructed as a jet and, hence, a tau candidate. To prevent these occurrences, dedicated cleaning requirements were applied to events with indications of noise or poor quality jets [185, 181]. 5.4.2 Triggering The analysis made use of unprescaled single-lepton triggers. Events in the eτh channel were required to pass a trigger for a loosely identified electron with pT & 15 GeV: • EF_e15_medium. For the μτh channel the lowest-pT unprescaled triggers for a single muon with pT & 10–20 GeV, in the individual run periods were used: • EF_mu10_MG (periods E4-G1) • EF_mu13_MG (periods G2-I1, until run 167576) • EF_mu13_MG_tight (remaining period I1). For both channels this resulted in an integrated luminosity of approximately 36 pb−1. Trigger efficiencies were determined using the tag-and-probe52 method using Z → `` (` = e or μ) events, tagging events with a good lepton and a second candidate, and with W → `ν events, tagging events with significant EmissT and a lepton candidate. In Table 5.2 and 5.3, the trigger efficiencies 52 See the discussion of the tag-and-probe method in Section 3.6.3. 122 5. measurement of the z → ττ cross section for electrons and muons are shown as measured from data. Correction factors were applied to the Monte Carlo simulation to make the MC trigger efficiency prediction agree with the data. These correction factors were defined as the ratio between the efficiencies measured in data and in Monte Carlo [181]. 5.4.3 Object preselection Selecting the `τh final state utilizes the suite of ATLAS reconstruction, including muons, electrons, hadronic tau decays, and missing transverse momentum. Electrons, muons and tau candidates are initially preselected using looser criteria. Pre-selected leptons are used to remove overlapping tau candidates and counted for the dilepton veto (Section 5.4.5). A summary of the preselection can be seen in Table 5.5. After the preselection, the full object selection takes place, including lepton isolation requirements, and the selection of tau candidates (Section 5.4.4). The reconstructed EmissT is also utilized in the event selection. Electrons The electron identification is based on variables that can efficiently discriminate between electrons and fakes (mis-identified photons and jets). These variables are based on calorimeter information, tracking information or a combination of the two. Three qualities of electrons are provided, with different levels of signal efficiency and purity, namely loose, medium, and tight, subsequently modified for 2010 data analysis (so called MediumWithTrackMatch and TightWithTrackMatch) [186]. The electrons in this analysis were preselected if they had a cluster with ET > 15 GeV, were within |η| < 2.47 excluding the transition region between the barrel and end-cap calorimeters (1.37 < |η| < 1.52) and passed the MediumWithTrackMatch identification requirements. Additionally information Table 5.2: Electron trigger efficiency measured with respect to offline selected electrons in three pT bins [181]. trigger EF_e15_medium 16− 18 GeV 95.8±2.2(stat.)±0.6(syst.) 18− 20 GeV 96.5±2.1(stat.)±0.4(syst.) > 20 GeV 99.05±0.22(stat.)±0.08(syst.) Table 5.3: Muon trigger efficiency measured with respect to offline selected muons with pT > 15 GeV [181]. trigger efficiency EF_mu10_MG 82.9±0.9(stat.)±0.3(syst.) EF_mu13_MG 84.5±0.4(stat.)±0.1(syst.) EF_mu13_MG_tight 83.1±0.4(stat.)±0.2(syst.) 5.4 z → ττ → `τhselection 123 from the Object Quality maps (OQmaps) [108] was used, removing electrons built from a cluster affected by detector problems53. Muons Muons reconstructed by the Staco algorithm were used in this analysis [69]. Tracks were reconstructed independently by the inner detector and muon spectrometer, and the muon track was formed from the successful combination of a muon spectrometer track with an inner detector one. The preselection of muons required pT > 15 GeV with |η| < 2.4, corresponding to the trigger acceptance. The longitudinal distance from the primary vertex was required to be less than 10 mm. Hadronic tau decays The reconstruction of hadronic tau decays at ATLAS was discussed in detail in Chapter 4. Reconstructed tau candidates were preselected if they had pT > 20 GeV and were located within |η| < 2.47 but not in the crack region (1.37 < |η| < 1.52). Information about the full tau candidate selection can be found in Section 5.4.4. Overlap removal Because multiple candidates (electron, muon, or tau candidates) were often reconstructed from the same localized response in the ATLAS detector, an overlap removal procedure had to be performed to have a unique hypothesis for each object. Since muons and electrons can be selected with a higher purity than hadronic tau decays, any preselected tau candidate was removed from consideration if it lay within ∆R < 0.4 from any preselected lepton. Electrons were removed if they overlapped with muons within ∆R < 0.2. Finally electron and muon candidates were removed if they lay within ∆R < 0.2 from a harder reconstructed lepton of the same kind. 5.4.4 Object selection Electron selection Further requirements were applied on the preselected electrons. The transverse momentum cut was raised to 16 GeV in order to avoid the region immediately surrounding the trigger threshold, which had been found to be poorly modeled by Monte Carlo. Additionally the electron candidates were required to pass the TightWithTrackMatch cut identification. 53 The OQmap for run 167521 was used, for both data and Monte Carlo. 124 5. measurement of the z → ττ cross section Muon selection In addition to the preselection requirements, muons had to fulfill requirements of a good quality inner detector track. The inner detector track was required to have at least 1 hit, if expected, in the B layer and the sum of the hits and dead sensors in the pixel detector was required to be greater than 1. The number of SCT hits and dead sensors had to be greater than 5 while the sum of the pixel and SCT holes had to be less than 2, and an additional cut was applied to the fraction of TRT outlier hits to total TRT hits. Lepton isolation Fake or real leptons produced in multijet events tend to not be isolated because they are accompanied by the other products of hadronization in a jet. Requiring the leptons to pass isolation requirements suprresses the multijet background to electroweak processes, like Z → ττ . I0.4pT denotes the scalar sum of the pT of tracks with pT > 1 GeV and consistent with the primary vertex, within ∆R < 0.4, excluding the track from the lepton candidate itself. I0.4ET is the scalar sum of the ET of calorimeter cells within ∆R < 0.4, excluding the cells near the lepton candidate itself. Figure 5.17 shows the isolation variables used. The isolation requirements, chosen to accept Z → ττ signal and suppress multijet events, are • for electrons: I0.4pT /pT < 0.06 and I0.3ET/pT < 0.1; • for muons: I0.4pT /pT < 0.06 and I0.4ET/pT < 0.06. The efficiency of these isolation cuts was measured in data using a tag-and-probe method and correction factors were applied to the Monte Carlo to correct the efficiency [181]. The corresponding cut efficiencies are given in Table 5.4. Table 5.4: Efficiency of isolation variables for electrons and muons in signal Monte Carlo and multijet background after object selection cuts. In brackets is given the statistical error of the last digit [181]. Isolation variable Z → ττ Multijet muon I0.4pT /pT < 0.06 0.926(2) 0.076(1) muon I0.4ET/pT < 0.06 0.872(3) 0.0309(6) muon combined isolation 0.841(3) 0.0143(4) electron I0.4pT /pT < 0.06 0.941(3) 0.232(3) electron I0.3ET/pT < 0.1 0.814(4) 0.082(2) electron combined isolation 0.781(4) 0.046(1) 5.4 z → ττ → `τhselection 125 )μ( T / p 0.4 T p I 0 0.05 0.1 0.15 0.2 0.25 0.3 m uo ns / 0. 01 -110 1 10 210 310 410 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (a) Muon isolation I0.4pT divided by pT. (e) T / p 0.4 T p I 0 0.05 0.1 0.15 0.2 0.25 0.3 el ec tro ns / 0. 01 -110 1 10 210 310 410 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (b) Electron isolation I0.4pT divided by pT. )μ( T / p 0.4 T E I 0 0.05 0.1 0.15 0.2 0.25 0.3 m uo ns / 0. 01 -110 1 10 210 310 410 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (c) Muon isolation I0.4ET divided by pT. (e) T / p 0.3 T E I 0 0.05 0.1 0.15 0.2 0.25 0.3 el ec tro ns / 0. 01 -110 1 10 210 310 410 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (d) Electron isolation I0.3ET divided by pT. Figure 2: Isolation variables for electroweak Monte Carlo, multijet events and data events after selecting one ! candidate and one lepton with opposite signs. The electroweak background was obtained from Monte Carlo, weighted by cross-section. The multijet background was estimated by reversing the opposite sign requirement. Efficiency Signal 0.8 0.85 0.9 0.95 1 Ef fic ie nc y M ul tije t B ac kg ro un d -110 1 T mu_etcone40/p T mu_etcone30/p T mu_ptcone40/p T mu_ptcone30/p (a) Muon channel. Efficiency Signal 0.4 0.5 0.6 0.7 0.8 0.9 1 Ef fic ie nc y M ul tije t B ac kg ro un d -110 1 T el_Etcone40/p T el_Etcone30/p T el_ptcone40/p T el_ptcone30/p (b) Electron channel. Figure 3: Isolation e!ciencies of signal Monte Carlo and multijet data events for di"erent isolation variables. 15 Figure 5.17: Distributions of the isolation variables used after selecting one tau candidate and an opposite-sign lepton. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. Hadronic tau decay selection The reconstr cti n of hadronic decays of tau leptons, as described in Chapter 4, was used54. From the reconstr cted tau candidates, those passing the simple cut-bas d identification,55, which uses pT-parametrized cuts on the three variables (REM, Rtrack, and ftrack) were selected. The reconstructed tau candidates were required to pass the medium cut-based identification in the 1-prong case or the tight one in the 3-prong case, together with a tight electron veto [187]. In total, these identification requirements result in an efficiency of about 30% for true hadronic tau decays, as determined with Monte Carlo. A correction factor was applied to 1-prong tau candidates in Monte Carlo samples containing true electrons, to correct the probability of electrons being mis-identified as 54 without JVF-corrected vertex-association, pile-up corrected variables, and other improvements that had not been developed in 2010. 55 The Winter 2011 version [187]. 126 5. measurement of the z → ττ cross section tau candidates, as measured in data [187]. The highest pT tau candidate passing these identification criteria, with pT > 20 GeV, and within 0 < |η| < 1.37 or 1.52 < |η| < 2.47, was chosen for the signal selection. Missing transverse momentum The missing transverse momentum (EmissT ) reconstruction used in this analysis was based on clustered energy deposits in the calorimeter and on reconstructed muon tracks, and was based on the following vectorial sum: EmissT = E miss T (LocHadTopo) + E miss T (MuonBoy)− EmissT (RefMuon Track). The calorimeter part EmissT (LocHadTopo) was calculated from the energy deposits of calorimeter cells inside three-dimensional topological clusters [91], calibrated locally to the electromagnetic or hadronic scale depending on the energy deposit classification. EmissT (MuonBoy) refers to the sum of the combined muon momenta from all isolated combined muons and muons in gaps as well as the sum of all non-isolated muons reconstructed as tracks in the muon spectrometer. A muon was considered isolated if the distance ∆R to the nearest jet was at least 0.3. To avoid double counting because of the isolated muons, the sum of the energy of the calorimeter cells crossed by an isolated muon, EmissT (RefMuon Track), was subtracted from the sum of the other two terms. Object selection summary The full preselection and selection requirements are listed in Table 5.5. A summary showing the effect of each of the cuts described in this section on signal Monte Carlo events, normalized to the integrated luminosity used for this study, is listed in Table 5.6. As can be seen, the tau candidate selection is the least efficient step. Figure 5.18 shows the kinematic distributions of the selected objects. 5.4.5 Event selection Following suppression of the multijets background by the tau identification and lepton isolation cuts, W/Z + jets events dominate the background. These background processes are suppressed with further event-level selection, discussed in the following sections. Dilepton veto The background from Z → `` + jets events, where a jet fakes tau identification, can be suppressed if the second lepton can be identified and vetoed. This veto additionally suppresses Z → ττ → ``+ ν 5.4 z → ττ → `τhselection 127 Table 5.5: Selection summary [181]. Event preselection Primary vertex Nvtx ≥ 1 with Ntrk ≥ 3 Jet cleaning Cleaning cuts "medium" with Tau Performance modifications Trigger EF_e15_medium (e channel) EF_mu10_MG, EF_mu13_MG, EF_mu13_MGtight (μ channel) Pre-selection Electrons pT > 15 GeV |η| < 2.47, but excluding 1.37 < |η| < 1.52 not in bad OQmaps region, map of run 167521 author 1 or 3 MediumWithTrackMatch Muons pT > 15 GeV |η| < 2.4 isCombinedMuon |z0| < 10 mm Tau candidates pT > 20 GeV |η| < 2.47, but excluding 1.37 < |η| < 1.52 Overlap removal Order of priority: muon, electrons, tau candidate, jets Object selection Electrons pT > 16 GeV TightWithTrackMatch electron I0.4pT /pT < 0.06 ; I 0.3 ET /pT < 0.1 Muons pT > 15 GeV expectBLayerHit==0 or nBLHits > 0 nPixHits + nDeadPixelSensors > 1 nSCTHits + nDeadSCTSensors > 5 nPixHoles + nSCTHoles < 2 |η| < 1.9: nTRTOutliers / (nTRTHits + nTRTOutliers) < 0.9 and nTRTHits + nTRTOutliers > 5 |η| ≥ 1.9 : (nTRTHits + nTRTOutliers > 5 and nTRTOutliers / (nTRTHits + nTRTOutliers) < 0.9 ) or nTRTHits + nTRTOutliers < 6 I0.4pT /pT < 0.06; I 0.4 ET /pT < 0.06 Tau candidates author 1 or 3 passes e veto 1-prong medium, 3-prong tight cuts τ -ID Event selection W+jets suppression ∑ cos ∆φ > −0.15 mT < 50 GeV Dilepton veto Remove event if N(preselected leptons)> 1 Visible mass cut 35 GeV < mvis < 75 GeV Tau candidate selection Ntracks(τh) = 1 or 3 |charge(τh)| = 1 Opposite sign cut charge(τh)× charge(`) < 0 128 5. measurement of the z → ττ cross section [GeV] T pμ 0 10 20 30 40 50 60 70 80 90 100 E ve nt s / 5 G eV 0 20 40 60 80 100 120 140 160 180 200 dataττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs (a) muon channel [GeV] T e p 0 10 20 30 40 50 60 70 80 90 100 E ve nt s / 5 G eV 0 20 40 60 80 100 120 140 160 dataττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs (b) electron channel η μ -3 -2 -1 0 1 2 3 E ve nt s / 0 .5 0 20 40 60 80 100 120 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs (c) muon channel η e -3 -2 -1 0 1 2 3 E ve nt s / 0 .5 0 20 40 60 80 100 120 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs (d) electron channel [GeV] T pτ 0 10 20 30 40 50 60 70 80 90 100 E ve nt s / 5 G eV 0 50 100 150 200 250 300 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs (e) muon channel [GeV] T pτ 0 10 20 30 40 50 60 70 80 90 100 E ve nt s / 5 G eV 0 50 100 150 200 250 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs (f) electron channel η τ -3 -2 -1 0 1 2 3 E ve nt s / 0 .5 0 20 40 60 80 100 120 140 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs (g) muon channel η τ -3 -2 -1 0 1 2 3 E ve nt s / 0 .5 0 20 40 60 80 100 120 dataττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs (h) electron channel Figure 4: Kinematic distributions for reconstructed leptons and ! candidates following all object selections. A requirement of the charge of the ! candidate to be of opposite sign of that of the lepton has also been applied The predictions for individual processes are taken from Monte Carlo, except for the multijet background, which is estimated by inverting the opposite-sign requirement. 18 Figure 5.18: Kinematic distributions of the selected leptons and tau candidates following all object selections. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. 5.4 z → ττ → `τhselection 129 N leptons -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 E ve nt s 0 200 400 600 800 1000 dataττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs (a) muon channel N leptons -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 E ve nt s 0 100 200 300 400 500 600 700 800 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs (b) electron channel Figure 5: Distributions of the number of preselected leptons, counted for the dilepton veto, following all object selections. A requirement on the charge of the ! candidate to be of opposite sign to that of the lepton has been applied – the multijet background contribution is estimated by inverting this cut; all other processes are estimated using Monte Carlo. 7 Event selection425 Following suppression of the multijets background by the ! identification and lepton isolation cuts,426 W ! "#,W ! !#! "###, and Z ! "" events remained as the dominant background. These background427 processes were suppressed with several event-level cuts, discussed in the following sections.428 7.1 Dilepton veto429 The background from Z ! "" + jets events, where a jet fakes ! identification, can be suppressed if the430 second lepton can be identified and vetoed. This veto additionally suppresses Z ! !! ! "" + # events,431 ensuring that the event selection is orthogonal to that from the analysis studying that decay mode. The432 distribution of the number of preselected leptons can be seen in Figure 5. Any event with more than one433 preselected lepton, as defined in Section 6.1, was vetoed. Preselected rather than selected leptons were434 used for the dilepton veto cut. The reason for this was that using selected leptons instead introduced435 18% and 2% more background in the Z ! ee and μμ channels while only increasing signal e!ciency by436 0.1%.437 7.2 W + jets suppression cuts438 Following the dilepton veto, the largest electroweak background was W + jets production, both W ! "#439 and W ! !#! "### decays, where the lepton from the W was correctly identified and an associated440 jet faked ! identification. These backgrounds were suppressed by cutting on two variables that exploit441 kinematic correlations between the lepton and transverse missing energy, described below.442 Because the mass of the Z boson is much larger than the mass of the ! lepton, the ! leptons in443 Z ! !! are boosted such that their decay products are collimated along the trajectory of the parent !444 lepton. Ignoring underlying interactions in the event and mis-measurements of EmissT , the E miss T is the445 vector sum of the pT of the neutrinos, as depicted in Figure 6(a). The majority of Z bosons produced446 have low pT, and therefore the ! leptons are produced back-to-back, but in the case the Z has significant447 nonzero boost in the transverse plane, the EmissT vector falls in the angle between the decay products of448 the Z.449 20 Figure 5.19: Distributions of the number of preselected leptons, counted for the dilepton veto, following all object selections. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. events, ensuring that the event selection is orthogonal to that from the analysis studying that decay mode. The distribution of the number of preselected leptons can be seen in Figure 5.19. Any event with more than one preselected lepton, as defined in Section 5.4.3, was vetoed. Pre-selected rather than selected leptons were used for the dilepton veto cut. The reason for this was that using selected leptons instead introduced 18% and 2% more background in the Z → ee and μμ channels while only increasing signal efficiency by 0.1%. W + jets suppression cuts TheW + jets background is suppressed by requiring that the direction of the EmissT be corr lated with the direction of the `τh decay products, using the transverse mass and ∑ cos ∆φ variables discussed in Section 5.2.2. Distributions of these variables using the 2010 data are shown in Figure Fig. 5.20. The cuts required are ∑ cos ∆φ = cos ∆φ(τh, E miss T ) + cos ∆φ(`, E miss T ) > −0.15 Table 5.6: Summary of the events pass ng object selection [181]. Selection Events (eτh channel 35.7pb −1) Events (μτh channel 35.5pb −1) Pre-selected lepton and overlap removal 2497(7) 2478(7) Pre-selected tau cand. and overlap removal 1179(5) 1133(5) Selected Lepton 690(4) 1143(5) Isolated Lepton 531(3) 941(5) Selected tau candidate 141(2) 258(2) 130 5. measurement of the z → ττ cross section φΔcos∑ -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Ev en ts / 0. 05 0 20 40 60 80 100 120 140 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS ! (a) muon channel φΔcos∑ -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Ev en ts / 0. 05 0 20 40 60 80 100 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS ! (b) electron channel [GeV]Tm 0 20 40 60 80 100 120 140 E ve nt s / 5 G eV 0 20 40 60 80 100 120 140 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS " (c) muon channel [GeV]Tm 0 20 40 60 80 100 120 140 E ve nt s / 5 G eV 0 20 40 60 80 100 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS " (d) electron channel Figure 7: The distributions of ! cos!! are shown for the muon (a) and electron (b) channels. The distributions of transverse mass, mT, of the combination of the lepton and the EmissT are shown for the muon (c) and electron (d) channels. All of these distributions are shown following the full object selections (Section 6) and dilepton veto (Section 7.1). A requirement on the charge of the " candidate to be of opposite sign to that of the lepton has also been applied – the multijet background contribution is estimated by inverting this cut; all other processes are estimated using Monte Carlo. 22 Figure 5.20: The distributions of ∑ cos ∆φ are shown for the muon (a) and electron (b) channels. The distributions of transverse mass, mT, of the combination of the lepton and the EmissT are shown for the muon (c) and electron (d) channels. All of these distributions are shown following the full object selections, the dilepton veto, and requiring opposite sign. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. and mT < 50 GeV . Final selection A few additional cuts that are characteristic of the Z → ττ signal were applied to increase its purity. Events were selected that had a reconstructed visible mass of the combination of the chosen tau candidate and the chosen lepton between 35–75 GeV. This window was chosen to be inclusive of the bulk of the signal, while avoiding the background contamination from Z → `` accumulating at the Z boson mass near 90 GeV. Figure 5.21 shows distributions of the visible mass. The chosen tau candidate was required to have 1 or 3 associated tracks and a reconstructed 5.5 observation of z → ττ → `τh 131 ) [GeV] h τ, μ(vism 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 10 20 30 40 50 60 dataττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (a) muon channel ) [GeV]hτ(e, vism 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 5 10 15 20 25 30 35 40 45 dataττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (b) electron channel Figure 8: The distributions of the visible mass of the combination of the chosen ! candidate and chosen lepton are shown for the muon (a) and electron (b) channels. These distributions are shown following the full object selections (Section 6) and event selections (Section 7), except for the visible mass window. Only a loose cut on transverse mass mT < 50 GeV was applied as many of W + jets events were478 rejected by the cut on ! cos!".479 7.3 Final selection480 A few more cuts that are characteristic of the Z ! !! signal were applied to increase its purity. Events481 were selected that had a reconstructed visible mass of the combination of the chosen ! candidate and the482 chosen lepton between 35–75 GeV. This window was chosen to be inclusive of the bulk of the signal,483 while avoiding the background contamination from Z ! ## accumulating at the Z boson mass near 90484 GeV. Figure 8 shows distributions of the visible mass.485 The chosen ! candidate was required to have 1 or 3 associated tracks and a reconstructed charge of486 unit magnitude, characteristic of true hadronic ! decays. The ! candidate charge was reconstructed as487 the sum of the charges of the associated tracks.488 Finally, the product of the charges of the chosen ! candidate and the chosen lepton was required to489 be negative. This e"ectively required the chosen ! candidate and the chosen lepton to have opposite sign490 charges, as expected from the products of a Z ! !! decay.491 Table 11 gives a summary of all selections applied, as described in Sections 5 7. Tables 12 and 13492 show the number of events passing the cumulative event selections. In these tables the background has493 been estimated as described in Section 8. It is worth noting that the multijet background in these tables494 was estimated using the method of Section 8.3 (using non-isolated leptons), rather than the method of495 Section 8.2 (using a same sign sample) which is the main method used to obtain the central value of the496 mulitjet backgrounds that enters the cross-section calculation. The reason for this inconsistency lies in497 the fact that the latter method is constructed to only estimate the background after the entire selection,498 whilst the former can be applied at any stage of the cut-flow – and was therefore used here, as the purpose499 of these tables is to illustrate the cut-flow, not only the value obtained at the end of it. As discussed in500 Section 8, the two methods are in very good agreement.501 23 Figure 5.21: The distributions of the visible mass of the combination of the chosen tau candidate and chosen lepton are shown for the muon (a) and electron (b) channels. These distributions are shown following the full object selections and event selections, except for the visible mass window [181]. charge of unit mag itude, characteristic of true hadronic tau decays. The tau candidate charge was reconstructed as the sum of the charges of the associated tracks. Finally, the chosen lepton and tau candidate are required to have opposite-sign charges, as expected from the products of a Z → ττ decay. Table 5.5 gives a summary of all selections applied. Table 5.7 shows the number of events pa sing the cumulative event selections. In these tables the background has been estimated as described in Section 5.7.3. 5.5 Observation of Z → ττ → `τh Once ATLAS had collected the first few pb−1 of integrated luminosity in 2010, a few events were expected to pass the Z → ττ → `τh selections. The first 10 or so selected events were scanned by hand, and an event display was approved for a particularly clean Z → ττ → μτh candidate with a 3-prong hadronic tau decay, which is shown in Figure 5.22. With the first 8.5 pb−1, ATLAS announced observation of Z → ττ → `τh events [189, 146]. While the previous section showed plots from the ev nt selection with the entire 36 pb−1 collected that year, Figure 5.23 shows distributions of the visible mass of the lepton and the tau candidate with the observation data sample. 132 5. measurement of the z → ττ cross section T ab le 5.7: N u m b ers o f even ts p assin g th e cu m u la tiv e even t selectio n s fo r th e μ τ h a n d eτ h ch a n n els. T h e statistical errors on th e least sign ifi can t d ig its a re g iven in th e p a ren th eses. T h e p red ictio n s fo r in d iv id u a l p ro cesses w ere ta ken from M on te C arlo, ex cep t for m u ltijet, w h ich w a s estim ated from th e d ata w ith n on -iso la ted lep to n s a s d escrib ed in S ectio n 5 .7 .3 [181]. μ τ h ch an n el d ata γ ∗/Z → τ τ m u ltijets γ ∗/Z → μ μ W → μ ν W → τ ν tt d ib oson ob ject selectio n 1365 2 6 1 (3 ) 1 6 3 (9 ) 2 1 6 (2 ) 6 4 9(6) 54(3) 38 .9(5) 8 .6(1) d ilep to n veto 1291 2 6 0 (3 ) 1 6 2 (8 ) 1 2 5 (2 ) 6 4 8(6) 54(3) 34 .3(5) 7 .8(1) W su p p ressio n cu ts 462 2 3 1 (3 ) 9 0 (4 ) 5 8 (1 ) 6 6(2) 18(2) 7 .8(2) 1 .34(5) m v is = 35− 7 5 G eV 327 2 0 5 (2 ) 7 1 (3 ) 2 3.1 (9 ) 2 3(1) 10(1) 2 .4(1) 0 .49(3) N trk (τ h ) = 1 or 3,|Q (τ h )| = 1 247 1 8 7 (2 ) 4 2 (3 ) 1 5.3 (7 ) 1 2.1(8) 5(1) 1 .4(1) 0 .32(2) op p osite sign 213 1 8 6 (2 ) 2 3 (3 ) 1 1.1 (5 ) 9.3(7) 3 .6(8) 1.3(1) 0 .28(2) eτ h ch a n n el d ata γ ∗/Z → τ τ m u ltijets γ ∗/Z → ee W → eν W → τ ν tt d ib oson o b ject selectio n 1203 1 4 1 (2 ) 4 0 2 (1 2 ) 1 6 4 (1 ) 4 0 9(4) 24(2) 33 .0(4) 6 .4(1) d ilep ton veto 1144 1 4 0 (2 ) 4 0 0 (1 1 ) 1 1 6 (1 ) 4 0 9(4) 24(2) 29 .1(4) 5 .9(1) W su p p ressio n cu ts 449 1 2 5 (2 ) 1 5 9 (6 ) 7 0 (1 ) 4 3(1) 10(1) 6 .7(2) 0 .98(4) m v is = 35− 75 G eV 273 1 0 7 (1 ) 9 5 (4 ) 1 9 .2 (7 ) 1 2.8(7) 3 .7(7) 1.7(1) 0 .32(2) N trk (τ h ) = 1 o r 3 ,|Q (τ h )| = 1 180 9 8 .5 (1 ) 5 3 (4 ) 1 1 .0 (5 ) 6.7(5) 1 .8(5) 1.13(9) 0 .21(2) o p p o site sig n 151 9 8 (1 ) 2 5 (3 ) 6 .9 (5 ) 4.8(4) 1 .5(4) 1.02(8) 0 .18(1) 5.5 observation of z → ττ → `τh 133 Figure 5.22: An event display of a candidate Z → ττ → μτh event with a 3-prong hadronic tau decay, in the 2010 dataset [188]. ) [GeV]hτ, μ(vism 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / 5 G eV 0 2 4 6 8 10 12 Ev en ts / 5 G eV Data 2010 τ τ →Z Multijet ν μ →W ν τ →W μ μ →Z tt -1dt L = 8.5 pb∫ = 7 TeVsPreliminary ATLAS (a) muon channel ) [GeV]hτ(e, vism 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / 5 G eV 0 2 4 6 8 10 12 Ev en ts / 5 G eV Data 2010 τ τ →Z Multijet ν e →W ν τ →W e e→Z tt -1dt L = 8.3 pb∫ = 7 TeVsPreliminary ATLAS (b) electron channel Figure 6: The distributions of the visible mass of the combination of the chosen ! candidate and lepton. The distributions are shown after the full event selection, except for the visible mass window which is illustrated by the vertical red lines. ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 2 4 6 8 10 12 14 16 Ev en ts / 5 G eV Data 2010 τ τ →Z Multijet ν μ →W ν τ →W μ μ →Z tt -1dt L = 8.5 pb∫ = 7 TeVsPreliminary ATLAS (a) muon channel ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 2 4 6 8 10 Ev en ts / 5 G eV Data 2010 τ τ →Z Multijet ν e →W ν τ →W e e→Z tt -1dt L = 8.3 pb∫ = 7 TeVsPreliminary ATLAS (b) electron channel Figure 7: Distributions of the selected ! candidate ET, for events passing all signal selection requirements. ) [GeV]μ( T p 0 10 20 30 40 50 60 70 80 90 100 Ev en ts / 5 G eV 0 5 10 15 20 25 30 35 Ev en ts / 5 G eV Data 2010 τ τ →Z Multijet ν μ →W ν τ →W μ μ →Z tt -1dt L = 8.5 pb∫ = 7 TeVsPreliminary ATLAS (a) muon channel (e) [GeV] T p 0 10 20 30 40 50 60 70 80 90 100 Ev en ts / 5 G eV 0 2 4 6 8 10 12 14 16 Ev en ts / 5 G eV Data 2010 τ τ →Z Multijet ν e →W ν τ →W e e→Z tt -1dt L = 8.3 pb∫ = 7 TeVsPreliminary ATLAS (b) electron channel Figure 8: Distributions of the selected lepton pT, for events passing all signal selection requirements. 15 Figure 5.23: The μτh visible mass of events passing the full selection for the ATLAS Z → ττ observation. The red vertical lines indicate the 35–75 GeV mass window used as the final cut [146]. 134 5. measurement of the z → ττ cross section 5.6 Kinematics of selected Z → ττ → `τh events Using the entire 2010 dataset of approximately 36 pb−1, the observed events, estimated backgrounds, and SM signal expectation for both channels are summarized in Table 5.8. The number of observed events in the data after subtracting the estimated background is 164± 16 (stat.)± 4 (syst.) events (μτh channel) 114± 14 (stat.)± 3 (syst.) events (eτh channel) which is compatible with the Standard Model signal expectation of 186.2± 2.1 (stat.)± 25.7 (syst.) events (μτh channel) 97.8± 1.4 (stat.)± 16.2 (syst.) events (eτh channel) . Figure 5.24 shows distributions of the pT and η of the selected leptons and tau candidates for events passing all signal selection [181]. Distributions of EmissT and the ∆φ between the selected tau candidate and lepton, in events passing all selections are shown in Figure 5.25. Distributions of the number of tracks associated to the selected tau candidate are shown in Figure 5.26, for events passing all selections except the cut on the number of tracks or the magnitude of the charge for the tau candidate, showing the characteristic 1/3-prong peak for hadronic tau decays. 5.7 Background estimation 5.7.1 Overview The estimated number of background events from electroweak processes (W → `ν, W → τν, Z → ``, diboson) and tt was taken from Monte Carlo, provided that these backgrounds were small and the Monte Carlo prediction agreed well with the observed data in regions that are electroweak rich. To Table 5.8: Summary of the number of selected Z → ττ candidate events and the expected backgrounds, comparing the two methods for estimating the multijet background described in Section 5.7. μτh channel (35.5 pb −1) eτh channel (35.7 pb −1) data (after all selections) 213 151 estimated multijet bkg. OS/SS 24 ± 6 (stat.) ± 3 (syst.) 23 ± 6 (stat.) ± 3 (syst.) estimated multijet bkg. isol. lep. 23 ± 3 (stat.) ± 4 (syst.) 25 ± 3 (stat.) ± 3 (syst.) estimated W,Z, tt , diboson background 25 ± 1 (stat.) ± 5 (syst.) 14 ± 1 (stat.) ± 3 (syst.) data (after bkg. subtraction OS/SS) 164± 16(stat.)±4(syst.) 114± 14(stat.)±3(syst.) data (after bkg. subtraction isol. lep.) 164± 13(stat.)± 5(syst.) 111± 11(stat.)± 4(syst.) SM Z → ττ expectation 186.2± 2.1(stat.)± 25.7(syst.) 97.8± 1.4(stat.)± 16.2(syst.) 5.7 background estimation 135 ) [GeV]μ( T p 0 10 20 30 40 50 60 70 80 M uo ns / 5 G eV 0 20 40 60 80 100 120 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (a) muon channel (e) [GeV] T p 0 10 20 30 40 50 60 70 80 El ec tro ns / 5 G eV 0 10 20 30 40 50 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (b) electron channel )μ(η -3 -2 -1 0 1 2 3 M uo ns / 0. 5 0 10 20 30 40 50 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (c) muon channel (e)η -3 -2 -1 0 1 2 3 El ec tro ns / 0. 5 0 10 20 30 40 50 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (d) electron channel Figure 10: Distributions of the selected lepton pT and !, for events passing all signal selection. 29 ) [GeV]hτ(Tp 0 10 20 30 40 50 60 70 80 Ta u C an di da te s / 5 G eV 0 20 40 60 80 100 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (a) muon channel ) [GeV]hτ(Tp 0 10 20 30 40 50 60 70 80 Ta u C an di da te s / 5 G eV 0 10 20 30 40 50 60 70 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (b) electron channel ) h τ(η -3 -2 -1 0 1 2 3 Ta u C an di da te s / 0 .5 0 10 20 30 40 50 60 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (c) muon channel ) h τ(η -3 -2 -1 0 1 2 3 Ta u C an di da te s / 0 .5 0 5 10 15 20 25 30 35 40 45 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (d) electron channel Figure 9: Distributions of the selected ! candidate ET and ", for events passing all signal selection. 28 Figure 5.24: Distributions of t pT and η of the selected lepto and tau ca didates for events passing all signal selection [181]. 136 5. measurement of the z → ττ cross section [GeV]missTE 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 10 20 30 40 50 60 70 80 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.5 pb∫ = 7 TeVs (a) muon channel [GeV]missTE 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 10 20 30 40 50 60 70 80 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.7 pb∫ = 7 TeVs (b) electron channel )μ, h τ(φΔ 0 0.5 1 1.5 2 2.5 3 /1 5) π Ev en ts / ( 0 20 40 60 80 100 120 140 160 180 dataττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.5 pb∫ = 7 TeVs (c) muon channel , e) h τ(φΔ 0 0.5 1 1.5 2 2.5 3 /1 5) π Ev en ts / ( 0 20 40 60 80 100 120 data ττ→Z QCD est νl→W ll→*γZ/ ντ→W tt -1 dt L = 35.7 pb∫ = 7 TeVs (d) electron channel Figure 11: The distributions of the EmissT and !! between the selected " candidate and lepton, in the final visible mass window for the muon (a),(c) and electron (b),(d) channels. 30 Figure 5.25: The distributions of the EmissT and ∆φ between the selected tau candidate and lepton, in the final visible mass window for the muon (a),(c) and electron (b),(d) channels [181]. ) [GeV] h τ, μ(Tm 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 2 40 60 80 100 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (a) muon channel ) [GeV]hτ(e, Tm 0 20 40 60 80 100 120 140 Ev en ts / 5 G eV 0 10 20 30 40 50 60 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (b) electron channel φΔcos∑ -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Ev en ts / 0. 05 0 10 2 3 4 5 60 70 80 90 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (c) muon channel φΔcos∑ -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Ev en ts / 0. 05 0 10 20 30 40 50 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (d) electron channel Figure 12: W suppression cuts, ! cos!! and mT , after all other cuts applied. The standard mT cut is applied when plotting the ! cos!!, while the ! cos!! cut is applied when plotting the mT. )hτ(tracksN 0 2 4 6 8 10 Ev en ts 0 50 100 150 200 250 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (a) muon channel )hτ(tracksN 0 2 4 6 8 10 Ev en ts 0 20 40 60 80 100 120 140 160 180 data ττ→Z QCD est νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.7 pb∫ = 7 TeVs Preliminary ATLAS (b) electron channel Figure 13: The final track distribution after all cuts in opposite signed bin, except the requirement on the " track distribution itself and on the magnitude of the " charge. 31 Figure 5.26: The final track distribution after all cuts, except without the requirement of 1 or 3 tracks. The product of the reconstructed charges is required to be negative or zero (not same-sign) [181]. 5.7 background estimation 137 account for the mis-modeling of the tau identification fake rate for jets56, the combined W + jets Monte Carlo samples were normalized with a scale factor derived in a W + jets-rich control region of the data. Rates of real and fake leptons as well as fake tau candidates produced in multijet events are also not expected to be modeled well with Monte Carlo, as discussed in Section 5.2.1. The estimated number of multijet background events was determined with a data-driven technique, extrapolating from the number of events in the data with a same-sign lepton and tau candidate. with a lepton and tau candidate with the same sign reconstructed charges. It was cross-checked with a second data-driven method, extrapolating from the number of events observed in data with non-isolated leptons. 5.7.2 W Monte Carlo scale factor A very W + jets rich data sample can be selected using the same object selection but varying the event selection, making it possible to check the agreement between the W Monte Carlo and data in normalization and shape of kinematic distributions. This W control region (WCR) was constructed to contain events passing the dilepton veto, the cuts on the number of tracks associated to the tau candidate, the charge of the τ candidate, and the charge product (opposite or same sign) but failing both W suppression cuts (see Figure 5.20). The Monte Carlo agreed with the data reasonably well before imposing the tau identification requirements described in Section 5.4.4. Following tight tau identification, the Monte Carlo was found to overestimate the data. This is illustrated in Fig. 5.27. The W Monte Carlo was therefore corrected by normalizing it to the number of events observed in the data in the W control region, corrected for the contamination from the other electroweak processes predicted from Monte Carlo. That is, the nominal W Monte Carlo samples, both W → `ν and W → τν, were scaled by a factor kW , such that the predicted number of W events in the W control region was equal to the number of events observed in the data, subtracted for the small contamination from Z → ``, tt, and diboson: NWCRW → kWNWCRW = NWCRdata −NWCRZ→``,tt,diboson . Due to the high transverse mass requirement, the multijet contamination was found to be negligible in the W control region. This procedure was used to determine kW scale factors for the signal region with a tau candidate passing tight tau identification and an opposite-sign lepton, and also for other control regions. These control regions require individual kW scale factors to correct the fake rate for tau identification since 56 Due to the mis-modeling of the jet-width, the tau identification fake rate for jets is not reliable in Monte Carlo. Jets are slightly more wide in data than in MC, as discussed in Section 4.4.1. 138 5. measurement of the z → ττ cross section ) [GeV]μ( T p 0 20 40 60 80 100 120 140 M uo ns / 5 G eV 0 500 1000 1500 2000 2500 3000 3500 data ττ→Z νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (a) no ! identification ) [GeV]μ( T p 0 20 40 60 80 100 120 140 M uo ns / 5 G eV 0 20 40 60 80 100 120 data ττ→Z νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs Preliminary ATLAS (b) tight ! candidate ) [GeV]τ( T p 0 20 40 60 80 100 120 140 Ta us / 5 G eV 0 1000 2000 3000 4000 5000 6000 7000 data ττ→Z νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs (c) no ! identification ) [GeV]τ( T p 0 20 40 60 80 100 120 140 Ta us / 5 G eV 0 50 100 150 200 250 300 data ττ→Z νl→W ντ→W ll→*γZ/ tt -1 dt L = 35.5 pb∫ = 7 TeVs (d) tight ! candidate Figure 14: Muon and tau pT distributions in the W control region, following no ! identification (a)/(c) and tight (b)/(d) ! identification. Following tight ! identification, the Monte Carlo overestimates the W contribution. A similar e!ect is seen in the electron channel. 33 Figure 5.27: Muon and tau pT distributions in the W control region, following no tau identification (a)/(c) and tight (b)/(d) τ identification. Following tight tau identification, the Monte Carlo overestimates the W contribution. A similar effect is seen in the eτh channel [181]. the tau fake rate depends on the quark/gluon fraction, which varies among the W + jets samples57. The measured kW scale factors are: kW =    0.93± 0.04 (stat.) μτh channel, loose + not tight tau, opposite sign 0.73± 0.06 (stat.) μτh channel, tight tau, opposite sign 0.94± 0.13 (stat.) μτh channel, tight tau, same sign 0.97± 0.04 (stat.) eτh channel, loose + not tight tau, opposite sign 0.63± 0.07 (stat.) eτh channel, tight tau, opposite sign 0.83± 0.15 (stat.) eτh channel, tight tau, same sign . As a cross-check to the kW scale factors being consistent with correcting the tau mis-identification rate, instead of applying kW , a scale factor for the jet to tau fake rate was applied, measured in a 57 See the discussion of the variation of jet fake rates with composition in Section 4.4.8. 5.7 background estimation 139 data sample of Z + jets events [158] (see Figure 5.9). The estimated W + jets background after all cuts is listed in Table 5.10, comparing the estimates using the kW and tau-by-tau scale factor methods and showing them to be in agreement. The simplest method using the kW scale factors was chosen as the primary W + jets estimate. Investigations in methods of using scale factors to correct the rate for jets to fake tau identification later led to the development of the data-driven method for modeling fake backgrounds by applying fake factors to events in the data that fail tau identification, developed for the Z ′ → ττ search, which will be discussed in Section 6.4.4. 5.7.3 Multijet background estimation from the same-sign sample The multijet background was not simulated with Monte Carlo but instead estimated from control regions in the data. A common method for constructing a data-driven background model is to scale the data in a control region (or side band) by an appropriate weight, measured from the ratios of events in another pair of control regions. It is often called the "ABCD method", named for the labels for the four control regions used in the estimate. Essentially, it is the method of applying a single-bin scale factor to a data sample one expects to look like the background to model. It is important that the variables used to select the control regions be largely uncorrelated to give an unbiased model of the background58. Examples of uses of the ABCD method are plentiful in ATLAS, especially in 58 The variables used to define the ABCD regions need to be uncorrelated for the background sample to be modeled, but contaminations in the control regions that are not the background of interest can have correlations so long as Table 5.9: Scale factors for the jet to tau fake rate obtained in Z + jets events. The fake rate was about 3–7% in the 1-prong case and about 2–3% in the 3-prong case [181]. number of vertices 1-prong medium tau 3-prong tight tau 1, 2 0.949± 0.220 0.855± 0.280 > 2 0.626± 0.240 1.151± 0.436 Table 5.10: The predicted number of W + jets events in the signal region after all cuts, comparing estimates from the tau-by-tau scale factor and kW methods [181]. sample μτh channel tau fake rate scale factors kW W → `ν 10.8± 0.8 (stat.)± 2.6 (syst.) 9.3± 0.7 (stat.)± 2.0 (syst.) W → τν 4.1± 1.0 (stat.)± 1.1 (syst.) 3.6± 0.8 (stat.)± 0.8 (syst.) sample eτh channel tau fake rate scale factor kW W → `ν 6.6± 0.6 (stat.)± 1.6 (syst.) 4.8± 0.4 (stat.)± 1.2 (syst.) W → τν 2.0± 0.6 (stat.)± 0.5 (syst.) 1.5± 0.4 (stat.)± 0.4 (syst.) 140 5. measurement of the z → ττ cross section Sample muon channel ! fake rate scale factors kW W ! "# 10.8 ± 0.8 (stat.) ± 2.6 (syst.) 9.3 ± 0.7 (stat.) ± 2.0 (syst.) W ! !# 4.1 ± 1.0 (stat.) ± 1.1 (syst.) 3.6 ± 0.8 (stat.) ± 0.8 (syst.) Sample electron channel ! fake rate scale factor kW W ! "# 6.6 ± 0.6 (stat.) ± 1.6 (syst.) 4.8 ± 0.4 (stat.) ± 1.2 (syst.) W ! !# 2.0 ± 0.6 (stat.) ± 0.5 (syst.) 1.5 ± 0.4 (stat.) ± 0.4 (syst.) Table 16: Numbers of events in the signal region after all cuts and after application of ! fake rate scale factor or kW factor. Opposite Sign Same Sign Isolated Nonisolated A B C D Figure 15: Schematic diagram of the control regions for the main multijet background estimation method. • A: signal region with isolated lepton and the opposite sign requirement591 • B: control region with isolated lepton and the opposite sign requirement reversed592 • C: control region with inverted lepton isolation requirement and the opposite sign requirement593 • D: control region with the opposite sign and isolation requirements inverted.594 The four regions are illustrated schematically in Figure 15 This method takes advantage of the fact595 that the signal was composed of almost exclusively isolated leptons whose charges were opposite the !596 candidates' charges, and therefore signal contributions could e!ectively be excluded in all control regions597 B, C and D.598 All four regions had all the same cuts applied except for the opposite sign and isolation requirements,599 keeping this method simple and reducing the number of systematic uncertainties. In each of the control600 regions an estimate for the number of QCD events was obtained by correcting for the Z ! "", t t and601 diboson contributions as predicted from MC and for the W ! "# andW ! !# contributions by correcting602 the MC predictions using the kW normalisation factors discussed in Section 8.1:603 NiQCD = N i Data " NiZ!!! " NiZ!"" " Nit t,diboson " kW(NiW!"# + NiW!!#), for i = B,C,D (10) The leptons from the backgrounds W ! "#, W ! !# and Z ! "" were typically very isolated, like604 the signal, as discussed in Section 6.4. From Monte Carlo estimates this left regions C and D #99%605 QCD pure. These QCD rich regions were used to measure the OS/SS ratio ROSS S for QCD, expected to606 be very close to untity:607 35 Figure 4: Schematic diagram of the control regions for the main multijet background estimation method. control region is defined, passing all cuts but requiring a lepton and a ! candidate of the same sign. The ratio of opposite-sign to same-sign events, ROS/SS, is calculated in separate control regions of inverted isolation, after subtracting all non-multijet backgrounds. It was found to be 1.1 ± 0.2(stat.) ± 0.1(syst.) for the muon and 1.2 ± 0.2(stat.) ± 0.2(syst.) for the electron channel. The estimate for the opposite-sign multijet background in the signal region is obtained by scaling the observed number of events in the primary control region with this ratio, after non-multijet background subtraction. This method is limited by the poor statistics in the primary control region. In the electron channel, the multijet estimate is 2.7± 2.4(stat.)± 0.7(syst.) events, while for the muon channel is 2.1± 2.4(stat.)± 0.4(syst.) events are obtained. Thus the number of the estimated multijet events is in statistical agreement with the estimation obtained from the main method. 6 Systematic uncertainties Several possible sources of systematic uncertainties on the background estimation have been studied. The systematic un ertainties can broadly be divided into two categories – those a!ecting the Monte Carlo predictions due to the imperfect modelling of the data by the simulations, and those arising from the methods used to perform the data-driven multijet background estimation. For the first category the ! candidate fake rate is the most important, followed by the energy scale uncertainty. For the multijet bac ground estimation the statistical uncertainty on the number of events in the control regions turns out to give a larger contribution to the total uncertainty than the systematic uncertainties on the method itself. All of the systematic uncertainties are summariz in Tables 4 and 5. 6.1 Systematic Uncertainties on Monte Carlo Predictions The systematic uncertainties considered for the Monte Carlo predictions are described in the following. All of these uncertainties are applied to the Z and t t samples, while only the energy scale uncertainty is applied on the W samples, as these have been rescaled as described in Section 5.1 and thus are not susceptible to the other systematic uncertainties. Lepton trigger e!ciency A systematic uncertainty of 2% is assigned to the muon trigger e"ciency in the Monte Carlo predictions for the Z and t t backgrounds to the muon channel, by taking the di!erence 9 Figure 5.28: Diagrams of the c ntrol regions for two ABCD methods for estimating the multijet background. The figure on the left shows the regions for the primary estimate. The figure on the right shows regions for the cross-check method [181]. first observations and measurements because it can be implemented simply and performs well in low count scenarios by grouping the counts into only four bins to determine the normalization59. Two complementary ABCD methods, using different control regions, were used to estimate the multijet background. The first method took advantage of the fact that the multijet background is effectively symmetric between the samples with opposite sign (OS) and same sign (SS) charges for e lepton a d tau candidate. This propert is observ in dijet Monte Carlo samples60 as well as the data. Then these samples were divided into those that pass or fail lepton isolation requirements, giving the four combinations of regions: {A, B, C, D}, shown in Figure 5.28. A multijet-rich control region is defined to contain t e events that fail th lepton isolation requirements, den ted by th union of regions CD. The OS/SS ratio, ROS/SS, is measured in this control region and applied as a weight to the SS sample that passes lepton isolation (B), to predict the multijet background normalization in the signal region (A). Stated more explicitly, the method relies on the assumption that the OS/SS ratio is the same among multijet events with isolated and non-isolated lepton candidates: NAmultijet NBmultijet = NCmultijet NDmultijet . where N is the number of multijet events in four statistically independent regions, denoted {A, B, C, D} and defined as follows: • A: signal region with isolated lepton and opposite-sign tau candidate they can be modeled and are preferably small so they can be subtracted. For example, the Z → `` background is obviously OS biased, as is the W + jets. 59 An other example use of the ABCD method can be found in the first ATLAS W → τν cross section measurement [190], as discussed briefly in Section 4.4.2. 60 Like the dijet samples used in the Monte Carlo studies discussed in Section 5.2.1. 5.7 background estimation 141 • B: control region with isolated lepton and same-sign tau candidate • C: control region with non-isolated lepton and opposite-sign tau candidate • D: control region with non-isolated lepton and same-sign tau candidate. Regions B, C, and D are nearly signal free, and the regions C and D are very multijet pure. The contamination from other electroweak processes is estimated with Monte Carlo and subtracted in each control region: N imultijet = N i data −N iZ→ττ −N iZ→``,tt,diboson − kW (N iW→`ν +N iW→τν), for i = B,C,D . In each of the control regions an estimate for the number of multijet events was obtained by correcting for the Z → ``, tt and diboson contributions as predicted from MC, and for W + jets W → τν contributions by correcting the MC predictions using the kW normalisation factors discussed previously. The leptons from the backgrounds W → `ν, W → τν and Z → `` are typically very well isolated, like Z → ττ . From Monte Carlo, it is estimated that regions C and D are ≈99% multijet pure. These multijet rich regions were used to measure the OS/SS ratio, ROS/SS, for multijet events: ROS/SS = NCmultijet NDmultijet =    1.07± 0.04 (stat.)± 0.04 (syst.) μτh channel 1.07± 0.07 (stat.)± 0.07 (syst.) eτh channel . As expected it is consistent with 1. This measured ROS/SS was then used to scale the multijet estimate from region B to give the prediction in region A: NAmultijet = NCmultijet NDmultijet NBmultijet = ROS/SS N B multijet . This yielded the numbers for each region shown in Table 5.11. The expected number of multijet events in the signal region A is NAmultijet =    24± 6 (stat.)± 3 (syst.) μτh channel 23± 6 (stat.)± 3 (syst.) eτh channel . This gave the normalization of the multijet background estimate in the signal region. The shapes of kinematic distributions for the multijet background were modeled with the SS events in data (region B if following the isolation requirement), corrected for contamination with MC and scaled to this normalization. This model was used as the primary estimate of the multijet background. 142 5. measurement of the z → ττ cross section 5.7.4 Multijet background estimation from non-isolated leptons As a cross-check, a second method for estimating the multijet background selected a multijet rich control region by inverting the lepton isolation requirements. Then the number of multijet events in the isolated lepton signal region was estimated by scaling the number observed in the non-isolated region by the expected ratio of isolated to non-isolated leptons. This isolation ratio was measured in an independent pair of multijet rich control regions defined by changing the tau selection to choose the leading loose tau candidate and require that it fails medium (tight) tau identification for 1 prong (3 prong) candidates (electron veto is still applied however). This tau candidate selection will be referred to as "loose but not tight". The combinations of requiring an isolated or non-isolated lepton, and a tight or a loose but not tight tau candidate results in four statistically independent regions: • A: signal region with isolated lepton and tight tau candidate • B: control region with non-isolated lepton and tight tau candidate • C: control region with isolated lepton and loose but not tight tau candidate • D: control region with non-isolated lepton and loose but not tight tau candidate. Regions B, C, and D are multijet-rich, with some contamination from electroweak processes and tt. According to Monte Carlo predictions, in region C approximately 50% of this electroweak contamination consists of signal events, constituting about 30% of all events in region C. Since this background estimation method is only a cross-check of the primary method, the theoretical signal cross-section for Z → ττ was assumed and used to normalize the Z → ττ contamination in control regions (with its uncertainty propagated as a systematic uncertainty). A summary of the estimates in each control region are shown in Table 5.12. The key assumption of this method is that for the multijet background, the probability for a jet to fake tau identification should be largely independent of the probability for the fake or true lepton on the other side of the event to be isolated, and therefore the isolation ratio in multijet events is independent of the tau identification requirement: NAmultijet NBmultijet = NCmultijet NDmultijet The validity of this assumption and the possibility of correlations between the lepton isolation and tau identification are considered in Section 5.9.3. Given these assumptions, the number of multijet events in the signal region A can be estimated by NAmultijet = NCmultijet NDmultijet NBmultijet = Riso N B multijet , 5.7 background estimation 143 where Riso is the isolation ratio measured in regions C and D (Riso ∼ 1%). Since regions B, C, and D are not completely multijet pure, we correct for the expected electroweak contamination from Monte Carlo in each region: N imultijet = N i data −N iZ→ττ −N iZ→``,tt,diboson − kW (N iW→`ν +N iW→τν), for i = B,C,D . The expected number of multijet events in the signal region A is NAmultijet =    23± 3 (stat.)± 4 (syst.) μτh channel 25± 3 (stat.)± 3 (syst.) eτh channel , in good agreement with the estimate based on the same-sign sample, presented in the previous section. The shapes of the multijet background were modeled with the data in region B, corrected with MC for the small amount of contamination. 144 5. measurement of the z → ττ cross section Table 5.11: Numbers of events in the control regions discussed in Section 5.7.3. The numbers in parenthesis are the statistical errors in the least significant digits. The multijet expectations are determined by the data-driven method discussed in that section. The other processes are estimated with Monte Carlo [181]. μτh channel eτh channel isolated non-isolated isolated non-isolated lepton lepton lepton lepton region A region C region A region C data 213(15) 1521(39) 151(12) 398(20) Z → ττ 185(2) 8.4(4) 97(1) 3.2(2) γ → ττ 0.7(3) 0.05(5) 0.3(2) 0(0) multijet 24(6) 1511(39) 23(6) 394(20) OS events W → `ν 9.3(7) 0.3(1) 4.8(4) 0.2(1) W → τν 3.6(8) 0.08(8) 1.5(4) 0.04(4) Z → `` 8.7(3) 0.33(6) 4.9(2) 0.12(3) γ → `` 2.4(4) 0.16(8) 2.0(3) 0.03(3) tt 1.3(1) 0.99(8) 1.02(8) 0.11(3) diboson 0.28(2) 0.052(8) 0.18(1) 0.009(3) region B region D region B region D data 34(6) 1415(38) 29(5) 367(19) Z → ττ 1.3(2) 0.3(8) 1.0(1) 0.23(7) γ → ττ 0.06(6) 0.09(9) 0.2(1) 0(0) multijet 22(6) 1413(38) 21(5) 367(19) SS events W → `ν 3.7(5) 0.09(6) 2.3(3) 0(0) W → τν 2.1(7) 0.2(2) 0.3(3) 0(0) Z → `` 1.9(1) 0.11(3) 2.7(3) 0.05(2) γ → `` 2.5(4) 0.11(8) 1.3(3) 0.13(11) tt 0.21(4) 0.61(6) 0.1(3) 0.06(18) diboson 0.044(7) 0.021(4) 0.029(5) 0.005(3) 5.7 background estimation 145 Table 5.12: Numbers of events in the control regions discussed in Section 5.7.4. The numbers in parenthesis are the statistical errors in the least significant digits. The multijet expectations are determined by the data-driven method using non-isolated leptons, discussed in that section. The other processes are estimated with Monte Carlo [181]. μτh channel eτh channel isolated non-isolated isolated non-isolated lepton lepton lepton lepton region A region B region A region B data 213(15) 1521(39) 151(12) 398(20) Z → ττ 185(2) 8.4(4) 97(1) 3.2(2) γ → ττ 0.7(3) 0.05(5) 0.3(2) 0(0) multijet 23(3) 1510(39) 25(3) 394(20) tight tau candidate W → `ν 9.3(7) 0.31(12) 4.8(4) 0.2(1) W → τν 3.6(8) 0.08(8) 1.5(4) 0.04(4) Z → `` 8.7(3) 0.33(6) 4.9(2) 0.12(3) γ → `` 2.4(4) 0.16(8) 2.0(3) 0.03(3) tt 1.3(1) 0.99(8) 1.02(8) 0.11(3) diboson 0.28(2) 0.052(8) 0.18(1) 0.009(3) region C region D region C region D data 283(17) 9696(98) 225(15) 2159(46) Z → ττ 72(1) 4.2(3) 39.5(8) 1.4(2) γ∗ → ττ 3(1) 0.3(2) 0 0.03(3) multijet 144(17) 9688(98) 139(15) 2156(46) loose not tight W → `ν 35(2) 1.8(3) 22(1) 0.6(2) tau candidate W → τν 11(2) 0.5(3) 7.6(1) 0 Z → `` 6.3(2) 0.28(5) 9.6(3) 0.20(4) γ∗ → `` 7.5(7) 0.3(1) 5.2(5) 0.2(1) tt 2.3(1) 1.07(8) 1.4(1) 0.22(4) diboson 0.31(3) 0.09(1) 0.22(2) 0.019(4) 146 5. measurement of the z → ττ cross section 5.7.5 Summary of backgrounds The measurements of Z → ττ → `τh channels were combined with measurements of the Z → ττ → eμ and Z → ττ → μμ final states. A summary of the background and Z → ττ signal expectations for each channel is shown in Table 5.13. 5.8 Method for calculating the cross section As shown in Appendix A.1.5 when discussing scattering theory, the expected number of observed events from a particular scattering process at a collider can be calculated from the product of the integrated luminosity, the cross section, and correction factors for the acceptance and efficiency. This relation can be used to calculate the measured cross section for a process, given the number of observed events, subtracting the estimated backgrounds. The cross section may be calculated with σ(Z → ττ)× BR(τ → `νν, τ → τhν) = Nobs −Nbkg AZ CZ L , where: • Nobs is the number of observed events in data. • Nbkg is the number of estimated background events. • AZ denotes the kinematic and geometric acceptance for the signal process. It is determined from generator level Monte Carlo as AZ = Nfid,dressed Ngen whereNgen denotes the number of events generated with LO ττ invariant mass within 66–116 GeV. Nfid,dressed is the number of generated events that result in decay products that fall within the Table 5.13: A summary of the estimated backgrounds, number of Z → ττ signal events from Monte Carlo, and the number of observed events for analyses of Z → ττ in four final states: μτh, eτh, eμ, and μμ [113]. 9 TABLE I. Expected number of events per process and number of events observed in data for an integrated luminosity of 36 pb!1, after the full selection. The background estimates have been obtained as described in Section V. The quoted uncertainties are statistical only. !μ!h !e!h !e!μ !μ!μ ""/Z ! ## 11.1 ± 0.5 6.9 ± 0.4 1.9 ± 0.1 36 ± 1 W ! #$ 9.3 ± 0.7 4.8 ± 0.4 0.7 ± 0.2 0.2 ± 0.1 W ! !$ 3.6 ± 0.8 1.5 ± 0.4 < 0.2 < 0.2 tt 1.3 ± 0.1 1.02 ± 0.08 0.15 ± 0.03 0.8 ± 0.1 Diboson 0.28 ± 0.02 0.18 ± 0.01 0.48 ± 0.03 0.13 ± 0.01 Multijet 24 ± 6 23 ± 6 6 ± 4 10 ± 2 ""/Z ! !! 186 ± 2 98 ± 1 73 ± 1 44 ± 1 Total expected events 235 ± 6 135 ± 6 82 ± 4 91 ± 3 Nobs 213 151 85 90 φΔcos∑ -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Ev en ts / 0. 1 0 10 20 30 40 50 -1 Ldt = 36 pb∫ = 7 TeVs Data ττ→*/Zγ Multijet ν l→W ll→*/Z γ tt ATLAS Ev en ts / 0. 1 (a)!e!μ final state [GeV]missT + ET E∑ 0 50 100 150 200 250 300 350 400 450 500 Ev en ts / 10 G eV 0 5 10 15 20 25 -1 Ldt = 36 pb∫ = 7 TeVs Data ττ→*/Zγ Multijet ν l→W ll→*/Z γ tt ATLAS Ev en ts / 10 G eV (b)!e!μ final state FIG. 6. Distributions of the variables (a) ! cos!%, after the lepton isolation selection, and (b) ! ET + E miss T after the ! cos!% selection, for the !e!μ final state. The multijet background is estimated from data according to the method described in Section V; all other processes are estimated using MC simulations. The e!ciency of the remaining selection criteria is obtained from the same-sign non-isolated control region. This method assumes that the ROS/SS ratio is the same for non-isolated and isolated leptons. The measured variation of this ratio as a function of the isolation requirements is taken as a systematic uncertainty. The multijet background to the !μ!μ final state is estimated in a control region defined as applying the full selection, but requiring the subleading muon candidate to fail the isolation selection criteria. A scaling factor is then calculated in a separate pair of control regions, obtained by requiring that the leading muon candidate fails the isolation selection and that the subleading muon candidate either fails or passes it. This scaling factor is further corrected for the correlation between the isolation variables for the two muon candidates. The multijet background in the signal region is finally obtained from the number of events in the primary control region scaled by the corrected scaling factor. D. Summary Table I shows the estimated number of background events per process for all channels. The full selection described in Section IV has been applied. Also shown are the expected number of signal events, as well as the total number of events observed in data in each channel after the full selection. VI. CROSS SECTION CALCULATION The measurement of the cross sections is obtained using the formula "(Z ! !!) " B = Nobs # Nbkg AZ * CZ * L (4) where Nobs is the number of observed events in data, Nbkg is the number of estimated background events, B 5.9 systematic uncertainties 147 fiducial kinematic region defined in Table 5.14. The generator-level tau lepton decay products in the Nfid,dressed term were further "dressed" by combining their four-vectors with any photons radiated, either from the original tau or from its subsequent decay products simulated with TAUOLA [127], in order to correct for the final state radiation generated with PHOTOS [126]. The central values for the AZ factor were determined using a default PYTHIA Monte Carlo sample generated with the modified LO MRSTLO* parton distribution function [191] and the corresponding ATLAS MC10 tune [129]. The obtained central values are reported in Table 5.14. The difference in AZ values between muon and electron channel is essentially due to the exclusion of the calorimeter crack region from the fiducial region for the selection of electrons. The statistical uncertainty on the AZ correction factors is at the 0.2% level for both channels. • CZ is the correction factor that accounts for the efficiency of triggering, reconstructing and identifying decays within the geometrical acceptance. It is defined as CZ = Nreco,pass Nfid,dressed where Nreco,pass is the number of reconstructed MC signal events that pass the entire analysis selection. The statistical uncertainty on the CZ correction factors is 1.5% for the electron channel and 1.2% for the muon channel. • L denotes the integrated luminosity for the channel of interest: L = ∫ dt L . The cross section as calculated above gives the total inclusive cross section. The fiducial cross section is independent of the extrapolation to the full phase space with AZ , and therefore is less affected by theoretical uncertainties in the model. The fiducial cross section is calculated as σfid(Z → ττ)× BR(τ → `νν, τ → τhν) = Nobs −Nbkg CZ L . Table 5.15 summarizes the quantities used to calculate the cross sections in each channel. 5.9 Systematic uncertainties Experimental and theoretical systematic uncertainties are propagated to the final expected yields for signal and background. Object-level systematic uncertainties (like the energy scales and resolutions for leptons, hadronic tau decays, and jets) are evaluated by shifting the observables in Monte Carlo 148 5. measurement of the z → ττ cross section Table 5.14: Central values for the AZ acceptance factor determined with ATLAS MC10 Monte Carlo generated with PYTHIA and MRSTLO* PDFs, and for the CZ efficiency factor determined using the same generated sample after full detector simulation and selection [181]. μτh channel eτh channel AZ 0.11691± 0.00023 (stat.) 0.10073± 0.00021 (stat.) CZ 0.2045± 0.0024 (stat.) 0.1197± 0.0017 (stat.) fiducial region lepton pT > 15 GeV, |η| < 2.4 pT > 16 GeV, |η| < 2.47, excluding 1.37 < |η| < 1.52 hadronic tau decay pvisT > 20 GeV, |η| < 2.47, pvisT > 20 GeV, |η| < 2.47, excluding 1.37 < |η| < 1.52 excluding 1.37 < |η| < 1.52 event Σ cos ∆φ > −0.15, Σ cos ∆φ > −0.15, mT < 50 GeV, mT < 50 GeV, mvis = 35–75 GeV mvis = 35–75 GeV Table 5.15: A summary of the measured quantities used to calculate the Z → ττ cross section in four final states: μτh, eτh, eμ, and μμ [113]. 15 VIII. CROSS SECTION MEASUREMENT A. Results by final state The determination of the cross sections in each final state is performed by using the numbers from the previous sections, provided for reference in Table III, following the method described in Section VI. Table IV shows the cross sections measured individually in each of the four final states. Both the fiducial cross sections and the total cross sections for an invariant mass window of [66, 116] GeV are shown. TABLE III. The components of the Z ! !! cross section calculations for each final state. For Nobs " Nbkg the first uncertainty is statistical and the second systematic. For all other values the total error is given. !μ!h !e!h Nobs 213 151 Nobs " Nbkg 164 ± 16 ± 4 114 ± 14 ± 3 AZ 0.117 ± 0.004 0.101 ± 0.003 CZ 0.20 ± 0.03 0.12 ± 0.02 B 0.2250 ± 0.0009 0.2313 ± 0.0009 L 35.5 ± 1.2 pb!1 35.7 ± 1.2 pb!1 !e!μ !μ!μ Nobs 85 90 Nobs " Nbkg 76 ± 10 ± 1 43 ± 10 ± 3 AZ 0.114 ± 0.003 0.156 ± 0.006 CZ 0.29 ± 0.02 0.27 ± 0.02 B 0.0620 ± 0.0002 0.0301 ± 0.0001 L 35.5 ± 1.2 pb!1 35.5 ± 1.2 pb!1 B. Combination The combination of the cross section measurements from the four final states is obtained by using the Best Linear Unbiased Estimate (BLUE) method, described in [28, 29]. The BLUE method determines the best estimate of the combined total cross section using a linear combination built from the individual measurements, with an estimate of ! that is unbiased and has the smallest possible variance. This is achieved by constructing a covariance matrix from the statistical and systematic uncertainties for each individual cross section measurement, while accounting for correlations between the uncertainties from each channel. The systematic uncertainties on the individual cross sections due to di!erent sources are assumed to either be fully correlated or fully uncorrelated. All systematic uncertainties pertaining to the e"ciency and resolution of the various physics objects used in the four analyses TABLE IV. The production cross section times branching fraction for the Z ! !! process as measured in each of the four final states, and the combined result. For the fiducial cross sections the measurements include also the branching fraction of the ! to its decay products. The first error is statistical, the second systematic and the third comes from the luminosity. Final State Fiducial cross section (pb) !μ!h 23 ± 2 ± 3 ± 1 !e!h 27 ± 3 ± 5 ± 1 !e!μ 7.5 ± 1.0 ± 0.5 ± 0.3 !μ!μ 4.5 ± 1.1 ± 0.6 ± 0.2 Final State Total cross section ([66, 116] GeV) (nb) !μ!h 0.86 ± 0.08 ± 0.12 ± 0.03 !e!h 1.14 ± 0.14 ± 0.20 ± 0.04 !e!μ 1.06 ± 0.14 ± 0.08 ± 0.04 !μ!μ 0.96 ± 0.22 ± 0.12 ± 0.03 Z ! !! 0.97 ± 0.07 ± 0.06 ± 0.03 reconstructed electron, muon, and hadronically decaying tau candidates are assumed to be fully correlated between final states that make use of these objects. No correlation is assumed to exist between the systematic uncertainties relating to di!erent physics objects. Similarly, the systematic uncertainties relating to the triggers used by the analyses are taken as fully correlated for the final states using the same triggers and fully uncorrelated otherwise. The systematic uncertainty on the energy scale is conservatively taken to be fully correlated between the final states. As the multijet background is estimated using the same method in the "e"μ, "μ"h, and "e"h final states, the systematic uncertainty on the method is conservatively treated as fully correlated. Finally, the systematic uncertainties on the acceptance are assumed to be completely correlated, as are the uncertainties on the luminosity and those on the theoretical cross sections used for the normalization of the Monte Carlo samples used to estimate the electroweak and tt backgrounds. This discussion is summarized in Table II where the last column indicates whether a given source of systematic uncertainty has been treated as correlated or uncorrelated amongst the relevant channels when calculating the combined result. Individual cross sections and their total uncertainties for the BLUE combination, as well as the weights for each of the final states in the combined cross section, together with their pulls, are also shown in Table V. Under these assumptions, a total combined cross section of 5.9 systematic uncertainties 149 up and down within their uncertainties. Other uncertainties (like the uncertainty in the integrated luminosity or theoretical cross sections) are applied directly to the normalization of the expectation. The total systematic uncertainties were estimated to be 15%/17% and the statistical uncertainties were 9.8%/12% in the μτh/eτh channels. Table 5.16 summarizes the systematic uncertainties assumed for each channel. The leading systematic uncertainties were the tau identification efficiency and the tau energy scale, which are discussed below with a few other example sources of systematic error. The systematic uncertainties are discussed in detail in Ref. [181]. 5.9.1 Cross sections and integrated luminosity An uncertainty of 5% on the NNLO cross section for Z and +7%/−9.5% for tt was assumed [192, 193]. The uncertainty on the luminosity was taken to be 3.4% [194]. These uncertainties were not applied to the multijet or W + jets backgrounds since their estimates were data-driven as described in Section 5.7. 5.9.2 Tau energy scale and efficiency This analysis used the first ATLAS recommended systematic uncertainties on the tau energy scale and identification efficiency for true hadronic tau decays that were estimated with dedicated Monte Table 5.16: A summary of the systematic uncertainties of the measurement of the Z → ττ cross section in four final states: μτh, eτh, eμ, and μμ [113]. 14 TABLE II. Relative statistical and systematic uncertainties in % on the total cross section m asurement. The electron and muon e!ciency terms include the lepton trigger, reconstruction, identification and isolation uncertainties, as described in the text. The last column indicates whether a given systematic uncertainty is treated as correlated (!) or uncorrelated (X) among the relevant channels when combining the results, as described in Section VIIIB. For the multijet background estimation method, the uncertainties in the !μ!h, !e!h, and !e!μ channels are treated as correlated while the !μ!μ uncertainty is treated as uncorrelated, since a di"erent method is used, as described in Section V. Systematic uncertainty !μ!h !e!h !e!μ !μ!μ Correlation Muon e!ciency 3.8% – 2.2% 8.6% ! Muon d0 (shape and scale) – – – 6.2% X Muon resolution & energy scale 0.2% – 0.1% 1.0% ! Electron e!ciency, resolution & Charge misidentification – 9.6% 5.9% – ! !h identification e!ciency 8.6% 8.6% – – ! !h misidentification 1.1% 0.7% – – ! Energy scale (e/!/jets/EmissT ) 10% 11% 1.7% 0.1% ! Multijet estimate method 0.8% 2% 1.0% 1.7% (!) W normalization factor 0.1% 0.2% – – X Object quality selection criteria 1.9% 1.9% 0.4% 0.4% ! pile-up description in simulation 0.4% 0.4% 0.5% 0.1% ! Theoretical cross section 0.2% 0.1% 0.3% 4.3% ! AZ systematics 3% 3% 3% 4% ! Total Systematic uncertainty 15% 17% 7.3% 14% Statistical uncertainty 9.8% 12% 13% 23% X Luminosity 3.4% 3.4% 3.4% 3.4% ! imal deviation between the acceptance obtained using the default sample and the values obtained by reweighting this sample to the CTEQ6.6 and HERAPDF1.0 [25] PDF sets. The uncertainties within the PDF set are determined by using the 44 PDF error eigenvectors available [26] for the CTEQ6.6 NLO PDF set. The variations are obtained by reweighting the default sample to the relevant CTEQ6.6 error eigenvector. The uncertainties due to the modeling of W and Z production are estimated using mc@nlo interfaced with herwig for parton showering, with the CTEQ6.6 PDF set and ATLAS MC10 tune and a lower bound on the invariant mass of 60 GeV. Since herwig in association with external generators does not handle ! polarizations correctly [27], the acceptance obtained from the mc@nlo sample is corrected for this e!ect, which is of order 2% for the !e!h and !μ!h channels, 8% for the !e!μ channel, and 3% for the !μ!μ channel. The deviation with respect to the AZ factor obtained using the default sample reweighted to the CTEQ6.6 PDF set central value and with an applied lower bound on the invariant mass of 60 GeV is taken as uncertainty. In the default sample the QED radiation is modeled by photos which has an accuracy of better than 0.2%, and therefore has a negligible uncertainty compared to uncertainties due to PDFs. Summing in quadrature the various contributions, total theoretical uncertainties of 3% are assigned to AZ for both of the semileptonic and the !e!μ final states and of 4% for the !μ!μ final state. C. Summary of systematics The uncertainty on the experimental acceptance CZ is given by the e!ect of the uncertainties described in Section VII A on the signal Monte Carlo, after correction factors have been applied. For the total background estimation uncertainties, the correlations between the electroweak and tt background uncertainties and the multijet background uncertainty, arising from the subtraction of the former in the control regions used for the latter, are taken into account. The largest uncertainty results from the ! identification and energy scale uncertainties for the !μ!h and !e!h final states. Additionally, in the !e!h final state, the uncertainty on the electron e"ciency has a large contribution. This is also the dominant uncertainty in the !e!μ final state. In the !μ!μ final state, the uncertainty due to the muon e"ciency is the dominant source, with the muon d0 contribution being important in the background estimate contributions for that channel. The correlation between the uncertainty on CZ and on (Nobs ! Nbkg) is accounted for in obtaining the final uncertainties on the cross section measurements, which are summarized in Table II. 150 5. measurement of the z → ττ cross section Carlo samples with with systematic shifts or changes of: the event generator, underlying event model, hadronic shower model, amount of detector material, and the topological clustering noise thresholds, as discussed briefly in Section 4.4.5. These studies constrained the energy scale for true hadronic tau decays to a few percent, resulting in a 10%/11% uncertainty on the yield in the μτh/eτh channels. The uncertainty on the efficiency scale factor was constrained to ≈ 10%, consistent with 1 [100]. This contributed a 8.6% uncertainty on the yield in both the μτh and eτh channels. 5.9.3 Multijet background estimation from the same-sign sample The key assumption of the multijet background estimate from the same-sign sample is that the ratio ROS/SS is independent of the lepton isolation. In order check the potential dependence on the isolation of the selected lepton the ROS/SS ratio was measured in bins of lepton isolation. In order to increase the statistics in each of the isolation bins and to suppress the signal at low lepton isolation, the identification on the hadronic tau candidate was reversed. To ensure that there was not an additional dependence on the ratio as a function of hadronic tau identification, ROS/SS was also measured in bins of hadronic tau identification in the anti-isolated lepton region. Figure 5.29 summarizes the results. A conservative systematic uncertainty was derived by measuring the maximum deviation of ROS/SS as a function of isolation and combining this error in quadrature with the statistical error of the nominally measured value. An error of 5%/10% was measured for the μτh/eτh channels. The systematic error was dominated by the statistical uncertainty from the number of data events in the same-sign sample. This resulted in a net 0.8%/2% systematic error on the Z → ττ yield in the μτh/eτh channels [181]. 5.10 Results The Z → ττ cross section was measured independently in four channels: μτh, eτh, eμ, and μμ. The resulting fiducial and total cross sections, calculated as described in the previous section, are shown in Table 5.17. The cross section measurements were combined with the Best Linear Unbiased Estimate (BLUE) method [195, 196]. The BLUE method combines the results with a linear combination of the individual measurements, with an estimate of the total uncertainty that is unbiased and has the smallest possible variance. This is achieved by constructing the covariance matrix from the statistical and systematic uncertainties for each individual cross section measurement, while accounting for correlations between the uncertainties from each channel. Related systematic uncertainties among the channels such as reconstructed energy scales, identification efficiencies, and trigger efficiencies were 5.10 results 151 )μ(T / p 0.4 T EI 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 O S/ SS 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Data EW Subtracted Data EW Contamination Nominal Ratio Statistical Error Preliminary ATLAS -1 dt L = 35 pb∫ = 7 TeVs (a) (e)T / p 0.3 T EI 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 O S/ SS 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Data EW Subtracted Data EW Contamination Nominal Ratio Statistical Error Preliminary ATLAS -1 dt L = 35 pb∫ = 7 TeVs (b) idτ Loose Medium Tight O S/ SS 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Data EW Subtracted Data EW Contamination Nominal Ratio Statistical Error Preliminary ATLAS -1 dt L = 35 pb∫ = 7 TeVs (c) idτ Loose Medium Tight O S/ SS 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Data EW Subtracted Data EW Contamination Nominal Ratio Statistical Error Preliminary ATLAS -1 dt L = 35 pb∫ = 7 TeVs (d) Figure 22: Stability of the OS vs SS ratio as a function of calorimeter isolation (! identification) on top (bottom) for muons (electrons) on left (right) in data. The nominal ratio is shown with the solid line where the dashed lines represent the statistical error on the nominal ratio. The expected electroweak impurity from Monte Carlo is shown with the shaded box at each bin. The first bin from the left on the isolation plots represents data with isolated muons passing the calorimeter isolation requirements, while the last bin from the left on the ! identification plots represents the nominal measured ROSS S value. 54 Figure 5.29: Plots demonstrating the stability of ROS/SS as a function of calorimeters isolation (top) and tau identification requirements (bottom), for the μτh (left) and eτh (right) channels [181]. treated as fully correlated. Statistical uncertainties from the MC or data samples are treated as uncorrelated [197]. The combined measured cross section published61 by ATLAS [113] is σ(Z → ττ , 66 < mττ < 116 GeV) = 0.97± 0.07 (stat.)± 0.06 (syst.)± 0.03 (lumi) nb . A comparison of the individual cross sections with the combined result is shown in Figure 5.30, along with the combined Z → `` cross section measured in the Z → ee and Z → μμ final states by ATLAS [108]. The measurement is compatible with the NNLO SM theoretical expectation of 0.96 ± 0.05 nb for ττ invariant mass within 66–116 GeV. The result is also comparable with the Z → ττ cross section measurement published by CMS [199] of62 σ(Z → ττ , 60 < mττ < 120 GeV) = 1.00± 0.05 (stat.)± 0.08 (syst.)± 0.04 (lumi) nb . 61 The author presented this result at the 2011 International Europhysics Conference on High Energy Physics (EPS) in Grenoble, France [198]. 62 The primary references discussing the topics of this chapter in more detail are • A selection strategy for Z → ττ → μτh with the first 100 inverse picobarns from ATLAS 152 5. measurement of the z → ττ cross section 16 !(Z ! "", 66 < minv < 116 GeV) = 0.97 ± 0.07 (stat) ± 0.06 (syst) ± 0.03 (lumi) nb (6) is obtained from the four final states, "μ"h, "e"h, "e"μ, and "μ"μ. <116 GeV) [nb]inv ll, 66<m→(Z σ 0.6 0.8 1 1.2 1.4 1.6 -136pb combinedττ →Z -10.3pb μμ ee/→Z hτ μτ hτ eτ μτ eτ μτ μτ Stat Stat ⊕Syst Lumi⊕ Stat ⊕Syst Theory (NNLO) ATLAS FIG. 12. The individual cross section measurements by final state, and the combined result. The Z ! !! combined cross section measured by ATLAS in the Z ! μμ and Z ! ee final states is also shown for comparison. The gray band indicates the uncertainty on the NNLO cross section prediction. A comparison of the individual cross sections with the combined result is shown in Figure 12, along with the combined Z ! ## cross section measured in the Z ! μμ and Z ! ee final states by ATLAS [15]. The theoretical expectation of 0.96 ± 0.05 nb for an invariant mass window of [66, 116] GeV is also shown. The obtained result is compatible with the Z ! "" cross section in four final states published recently by the CMS Collaboration [5], 1.00±0.05 (stat)±0.08 (syst)±0.04 (lumi) nb, in a mass window of [60, 120] GeV. TABLE V. Individual cross sections and their total uncertainties used in the BLUE combination, the weights for each of the final states in the combined cross section, and their pulls. The pull here is defined as the di!erence between the individual and combined cross sections divided by the uncertainty on this di!erence. The uncertainty on the di!erence between the measured and combined cross section values includes the uncertainties on the cross section both before and after the combination, taking all correlations into account. "μ"h "e"h "e"μ "μ"μ #Z!!! (nb) 0.86 1.14 1.06 0.96 Total unc. (nb) 0.15 0.24 0.17 0.25 Weight 39.4% 7.9% 39.0% 13.7% Pull 1.02 -0.76 -0.68 0.06 IX. SUMMARY A measurement of the Z ! "" cross section in protonproton collisions at " s = 7 TeV using the ATLAS detector is presented. Cross sections are measured in four final states, "μ"h, "e"h, "e"μ, and "μ"μ within the invariant mass range [66, 116] GeV. The combined measurement is also reported. A total combined cross section of ! = 0.97 ± 0.07 (stat) ± 0.06 (syst) ± 0.03 (lumi) nb is measured, which is in good agreement with the theoretical expectation and with other measurements. ACKNOWLEDGMENTS We thank CERN for the very successful operation of the LHC, as well as the support sta! from our institutions without whom ATLAS could not be operated e"ciently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Denmark; ARTEMIS, European Union; IN2P3-CNRS, CEA-DSM/IRFU, France; GNAS, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation, Germany; GSRT, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS (MECTS), Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia; DST/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of America. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CCIN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide. Figure 5.30: The combined measurement of the Z → ττ cross section in four final states: μτh, eτh, eμ, and μμ [113]. The combination of the ATLAS measurements of the Z → ee/μμ cross sections is shown for comparison [108]. ATL-PHYS-INT-2009-044 [177], • Benchmark analysis for Z → ττ → `τh with the first 100 pb−1 ATL-PHYS-INT-2010-075 [174], • Observation of Z → ττ decays with the ATLAS detector support note for the `τh channel ATL-COM-PHYS-2010-1033 [189], – support note for ATLAS-CONF-2011-010, • Observation of Z → τhτl decays with the ATLAS detector ATLAS-CONF-2011-010 [146], • Measurement of Z → ττ production cross section in proton-proton collisions at √s = 7 TeV with the ATLAS detector Support Note for lep-had channels ATL-COM-PHYS-2011-416 [181], • Measurement of the Z → ττ cross section in pp collisions at √s = 7 TeV with the ATLAS detector arxiv:1108.2016 [hep-ex] [113]. Table 5.17: A summary of the results of measuring the total and fiducial cross sections for Z → ττ in four final states: μτh, eτh, eμ, and μμ [113]. 15 VIII. CROSS SECTION MEASUREMENT A. Results by final state The determination of the cross sections in each final state is performed by using the numbers from the previous sections, provided for reference in Table III, following the method described in Section VI. Table IV shows the cross sections measured individually in each of the four final states. Both the fiducial cross sections and the total cross sections for an invariant mass window of [66, 116] GeV are shown. TABLE III. The components of the Z ! !! cross section calculations for each final state. For Nobs " Nbkg the first uncertainty is statistical and the second systematic. For all other values the total error is given. !μ!h !e!h Nobs 213 151 Nobs " Nbkg 164 ± 16 ± 4 114 ± 14 ± 3 AZ 0.117 ± 0.004 0.101 ± 0.003 CZ 0.20 ± 0.03 0.12 ± 0.02 B 0.2250 ± 0.0009 0.2313 ± 0.0009 L 35.5 ± 1.2 pb!1 35.7 ± 1.2 pb!1 !e!μ !μ!μ Nobs 85 90 Nobs " Nbkg 76 ± 10 ± 1 43 ± 10 ± 3 AZ 0.114 ± 0.003 0.156 ± 0.006 CZ 0.29 ± 0.02 0.27 ± 0.02 B 0.0620 ± 0.0002 0.0301 ± 0.0001 L 35.5 ± 1.2 pb!1 35.5 ± 1.2 pb!1 B. Combination The combination of the cross section measurements from the four final states is obtained by using the Best Linear Unbiased Estimate (BLUE) method, described in [28, 29]. The BLUE method determines the best estimate of the combined total cross section using a linear combination built from the individual measurements, with an estimate of ! that is unbiased and has the smallest possible variance. This is achieved by constructing a covariance matrix from the statistical and systematic uncertainties for each individual cross section measurement, while accounting for correlations between the uncertainties from each channel. The systematic uncertainties on the individual cross sections due to di!erent sources are assumed to either be fully correlated or fully uncorrelated. All systematic uncertainties pertaining to the e"ciency and resolution of th various physics objects used in the four analyses TABLE IV. The production cross section times branching fraction for the Z ! !! process as measured in each of the four final states, and the combined result. F r the fid cial cross sections the measurements include also the branching fraction of the ! to its decay products. The first error is statistical, the second systematic and the third comes from the luminosity. Final State Fiducial cross section (pb) !μ!h 23 ± 2 ± 3 ± 1 !e!h 27 ± 3 ± 5 ± 1 !e!μ 7.5 ± 1.0 ± 0.5 ± 0.3 !μ!μ 4.5 ± 1.1 ± 0.6 ± 0.2 Final State Total cross section ([66, 116] GeV) (nb) !μ!h 0.86 ± 0.08 ± 0.12 ± 0.03 !e!h 1.14 ± 0.14 ± 0.20 ± 0.04 !e!μ 1.06 ± 0.14 ± 0.08 ± 0.04 !μ!μ 0.96 ± 0.22 ± 0.12 ± 0.03 Z ! !! 0.97 ± 0.07 ± 0.06 ± 0.03 reconstructed electron, muon, and hadronically decaying tau candidates are assumed to be fully correlated between final states that make use of these objects. No correlation is assumed to exist between the systematic uncertainties relating to di!erent physics objects. Similarly, the systematic uncertainties relating to the triggers used by the analyses are taken as fully correlated for the final states using the same triggers and fully uncorrelated otherwise. The systematic uncertainty on the energy scale is conservatively taken to be fully correlated between the final states. As the multijet background is estimated using the same method in the "e"μ, "μ"h, and "e"h final states, the systematic uncertainty on the method is conservatively treated as fully correlated. Finally, the systematic uncertainties on the acceptance are assumed to be completely correlated, as are the uncertainties on the luminosity and those on the theoretical cross sections used for the normalization of the Monte Carlo samples used to estimate the electroweak and tt backgrounds. This discussion is summarized in Table II where the last column indicates whether a given source of systematic uncertainty has been treated as correlated or uncorrelated amongst the relevant channels when calculating the combined result. Individual cross sections and their total uncertainties for the BLUE combination, as well as the weights for each of the final states in the combined cross section, together with their pulls, are also shown in Table V. Under these assumptions, a total combined cross section of Chapter 6 Search for high-mass resonances decaying to τ+τ− This chapter describes the first search for new physics in very high-mass ditau events at ATLAS with the 2011 dataset. No significant excess above the SM expectation is observed. The result is interpreted as an upper limit on the cross section times branching fraction to τ+τ− vs mass for a high-mass resonance. A lower limit is set on the mass of a Sequential Standard Model Z ′ boson decaying to τ+τ−. The model dependence of these results is discussed. 6.1 Introduction Many extensions of the Standard Model (SM), motivated by grand unification, predict additional U(1) gauge symmetries which result in new heavy gauge bosons, often denoted Z ′ [200, 52, 201, 202, 203, 204, 205, 206, 207, 208]. As lepton universality is not necessarily a requirement for these new gauge bosons, it is essential to search in all decay modes. In particular, some models with extended gauge groups that offer an explanation for the high mass of the top quark predict that such bosons preferentially couple to third-generation fermions [205, 209]. The Sequential Standard Model (SSM) is a benchmark model that contains a heavy neutral gauge boson, Z ′SSM, with the same couplings to fermions as the Z boson of the SM but with a larger mass. Limits on the cross section times τ+τ− branching fraction for the Z ′SSM are reported as an example of a generic high-mass neutral resonance63. Direct searches for high-mass ditau resonances have been performed previously by the CDF [210] and CMS [211] collaborations, excluding a Z ′SSM with a mass less than 399 GeV and 468 GeV, at 63 The model dependence of the limit is discussed in Section 6.7.4. 153 154 6. search for high-mass resonances decaying to τ+τ− the 95% Confidence Level (CL)64, respectively. With the 5 fb−1 of integrated luminosity at √ s = 7 TeV collected by the ATLAS and CMS expriments in 2011, both [212, 213] collaborations exclude a Z ′SSM with a mass less than 1.4 TeV, the ATLAS result being the the subject of this chapter. For comparison, the limits on Z ′SSM with the 2011 data from combined searches in the dielectron and dimuon decay channels combined is 2.2 TeV from ATLAS [214] and 2.3 TeV from CMS [215]. Z ′ → `` searches (` = e or μ) with 8 TeV data collected in 2012 extended these exclusions to 2.86 TeV from ATLAS [216] and 2.96 TeV from CMS [217], which are currently the most stringent limits on Z ′ bosons. Indirect limits on Z ′ bosons with non-universal flavour couplings have been set using measurements from LEP and LEP II [218] and translate to a lower bound on the Z ′SSM mass of 1.09 TeV. This chapter presents the first search for high-mass resonances decaying into τ+τ− pairs using the ATLAS detector. The analysis combines searches for Z ′ → ττ , where both taus decay hadronically (τhτh), one tau decays leptonically and the other hadronically (`τh), and where both taus decay leptonically to the eμ final state. The τhτh channel, having a large branching fraction of 42% of ττ decays, is the most sensitive. The eτh and μτh channels, with a branching fraction of 22% each for ττ decays, are generally more competitive in new physics searches at lower mass scales, such as for the H → ττ search [29]. But since the SM backgrounds fall rapidly in reconstructed variables that measures of the mass of a resonance, the τhτh channel contributes more in searches for high-mass new physics. The search gains sensitivity from combining the τhτh and `τh channels. The eμ channel has the weakest sensitivity for a Z ′ → ττ because it only gets 2.9% of the branching fraction, but is a comparatively clean channel since the SM background does not involve fake hadronic tau decays. First, the searches for Z ′ → ττ in the `τh channels are the focus of this chapter. Then the search in the τhτh channel will be quickly reviewed 65. 6.2 Data samples 6.2.1 Data In the year 2011, ATLAS recorded over 5 fb−1 of integrated luminosity66, extending the potential for many searches for new physics. The instantaneous luminosity of the LHC climbed from 1 × 1030 to 3.7 × 1033 cm−2 s−1, with the average number of interactions per bunch crossing typically ranging from 2 to 20 [114]. The searches for Z ′ discussed in this chapter use 4.6 fb−1 of data after 64 The limit-setting procedure will be discussed briefly in Section 6.7.3. 65 See Ref. [97] for more details on the τhτh and eμ channels. 66 See the discussion of the ATLAS running periods and datasets in Section 3.5. 6.3 object preselection 155 making suitable data quality requirements67 for the operation of the tracking, calorimetry, and muon spectrometer subsystems. Table 6.1 shows the data periods used in the analysis, the triggers used, and the corresponding integrated luminosity. The data were reconstructed with the ATLAS Athena framework [82] release 17, part of the prod10 reprocessing. The data format used are D3PDs from the Tau Performance group with production tag p851. 6.2.2 Simulation Monte Carlo samples used in this analysis were produced with the ATLAS simulation infrastructure [118] as part of the ATLAS mc11c production campaign. The Monte Carlo events were reweighted to match the distribution of the number of reconstructed primary vertices per bunch crossing in data, same as described in Section 5.3.2. Corrections applied to data or Monte Carlo for object reconstruction or trigger modelling are described in Ref. [97]. 6.3 Object preselection All channels use a common preselection of objects from the output of common ATLAS reconstruction, which is outlined here. Pre-selected objects are used for overlap removal, carried out in the order of muons, electrons, taus and jets, as described below. 67 More details on the event-cleaning cuts are given in Ref. [97]. Table 6.1: Data periods, triggers, and the integrated luminosity for the four analysis channels. The eμ channel uses the same triggers as the μτh channel [97]. Periods Run numbers EF Trigger [pb−1] τhτh B-E 178109-180776 EF_tau29_medium1_tau20_medium1 (loose) 215 F-K 182013-187815 EF_tau29_medium1_tau20_medium1 (default) 2021 L-M 188921-191933 EF_tau29T_medium1_tau20T_medium1 2363 All 178109-191933 EF_tau125_medium1 4600 μτh and eμ D-I 179725-186493 EF_mu18_MG or EF_mu40_MSonly_barrel 1451 J-M 186516-191933 EF_mu18_MG_medium or EF_mu40_MSonly_barrel_medium 3142 eτh D-J 179725-186755 EF_e20_medium 1675 K 186873-187815 EF_e22_medium 555 L-M 188921-191933 EF_e22vh_medium1 2363 156 6. search for high-mass resonances decaying to τ+τ− Table 6.2: Summary of object preselection [97]. Muons StoreGate key: StacoMuonCollection Tau D3PD prefix: mu staco * pT > 4 GeV |η| < 2.5 mu staco loose == 1 Require a B-layer hit if expected (expectBLayerHit == 0 or nBLHits > 0) N(pixel hits) +N(pixel dead) ≥ 2 N(SCT hits) +N(SCT dead) ≥ 6 N(pixel holes) +N(SCT holes) ≤ 2 TRT quality cuts: if abs(eta) < 1.9: if not ( (nTRTHits + nTRTOutliers > 5) and \ (nTRTOutliers < 0.9*(nTRTHits + nTRTOutliers))): return False elif (nTRTHits + nTRTOutliers > 5): if not (nTRTOutliers < 0.9*(nTRTHits + nTRTOutliers)): return False return True Electrons StoreGate key: ElectronAODCollection Tau D3PD prefix: el * pT > 15 GeV |η| < 2.47 and not in 1.37 < |η| < 1.52 el author is 1 or 3 el mediumPP == 1 Require a B-layer hit if expected (expectBLayerHit == 0 or nBLHits > 0) Hadronic tau decays StoreGate key: TauRecContainer Tau D3PD prefix: tau * pT > 25 GeV |η| < 2.47 and not in 1.37 < |η| < 1.52 lead track |η| > 0.05 tau author is 1 or 3 tau numTrack > 0 Remove candidates overlapping with preselected electrons or muons within ∆R < 0.2 Jets StoreGate key: AntiKt4LCTopoJets Tau D3PD prefix: jet * pT > 25 GeV |η| < 4.5 |JVF| > 0.75 for jets with |η| < 2.4 Remove candidates overlapping with preselected electrons or selected taus within ∆R < 0.2 6.3 object preselection 157 6.3.1 Muons Muon candidates considered were reconstructed with the Staco algorithm68, which matches tracks reconstructed in the muon spectrometer to tracks found in the inner detector [69]. Muons with |η| < 2.5, pT > 10 GeV, and passing cuts according to the ATLAS Muon Performance Group recommendations [219] summarized in Table 6.2 were preselected. 6.3.2 Electrons Electrons are reconstructed69 in ATLAS by matching inner detector tracks to calorimeter clusters in the EM calorimeter [69]. Electron candidates are preselected if they have pT > 15 GeV, |η| < 2.47 and are not in the barrel-end-cap transition region region where 1.37 < |η| < 1.52 (also called the "crack" region). The preselection also requires medium++ electron identification [88, 89], which has an electron efficiency of approximately 90% and a pion fake rate of 1-3% [90]. 6.3.3 Hadronic tau decays The reconstruction of hadronic tau decays at ATLAS was discussed in detail in Chapter 4. Tau candidates are preselected if they have pT > 25 GeV, |η| < 2.47 and not in the crack region where 1.37 < |η| < 1.52, and have 1 or 3 core tracks. Core tracks are the tracks associated to the tau candidate, selected to be consistent with the vertex associated with the tau candidate, and within ∆R < 0.2 of the tau axis, defined with respect to the η, φ of the calorimeter jet that seeded the tau candidate [101]. Tau candidates are removed from consideration if they overlap with preselected electron or muon candidates within ∆R < 0.2. The final selections for jet rejection using the BDT, the allowed number of tracks, and the minimum pT differ among channels, and are discussed in later sections. 6.3.4 Jets Jets are reconstructed70 with the anti-kt algorithm [94], with distance parameter R = 0.4, and with three-dimensional topological energy clusters in the calorimeter [91] as input. The energy scale is calibrated with the local hadron calibration scheme (LC) [95], where the energy is split and corrected for each cluster in a jet [93]. Jets are preselected if they have pT > 25 GeV and |η| < 4.5. Especially for the highest luminosity runs in the later part of 2011, it is not rare for secondary pile-up interactions to produce jets. For jets within the tracking acceptance, one can select jets with 68 Muon reconstruction is introduced briefly in Section 3.3.3. 69 Electron reconstruction is introduced briefly in Section 3.3.4. 70 Jet reconstruction is introduced briefly in Section 3.3.6. 158 6. search for high-mass resonances decaying to τ+τ− energy deposits consistent with coming from the primary reconstructed vertex by requiring a high JVF, discussed in Section 3.3.6. Jets within |η| < 2.4 are required to have |JVF| > 0.75. Finally, in each channel jet candidates are removed that overlap with preselected electron or selected hadronic tau candidates within ∆R < 0.2, where the final tau selection depends on the channel71 6.3.5 Missing transverse energy The signal events are characterized by true missing transverse momentum (EmissT ) due to the presence of neutrinos. This analysis uses the ATLAS refined EmissT reconstruction (MET_RefFinal_BDTMedium), where the EmissT is calculated from the vector sum of the transverse momentum of all the high-pT objects reconstructed in the event, as well as a term for the remaining soft activity in the calorimeter. In the refined calculation scheme [105], each type of object is calibrated independently (electrons, muons, taus, etc.), with tau candidates calibrated at the tau energy scale if they pass the JetBDTSigMedium identification criteria. 6.4 Search in the `τh channels 6.4.1 Triggering For the search in the `τh channels, events passing single-lepton triggers were selected. The analysis of the μτh channel required events to pass the following unprescaled single muon triggers: • EF mu18 MG or EF mu40 MSonly barrel for data in periods D-I, • EF mu18 MG medium or EF mu40 MSonly barrel medium for data in periods J-M. The first trigger requires a combined muon with pT & 20 GeV, while the second trigger only requires a candidate in the muon spectrometer and has slower turn-on with pT. Together, the trigger requirements have approximately 80% efficiency in the barrel and 90% efficiency in the end-caps, limited mainly by geometric acceptance [220]. The search in the eτh channel required events to pass the following unprescaled single electron triggers for a loosely identified electron with pT & 20 GeV: • EF e20 medium for data in periods D-J, • EF e22 medium for data in period K, • EF e22vh medium1 for data in periods L-M, 71 Selected jets are only used in this analysis directly in the jet-veto of the eμ channel, however, tau candidates failing identification, which essentially define the selected jet candidates not overlapping with taus, are considered in the data-driven background estimations used in these analyses. 6.4 search in the `τh channels 159 which have efficiencies [221] between 94–98% for electrons passing el tightPP. 6.4.2 Object selection Objects are preselected as discussed in Section 6.3. Before exploring the event selection, requirements are further made of the lepton and hadronic tau candidates, defining selected leptons and taus. Preselected leptons are used in the overlap removal done for tau preselection, and they are used later in the event selection to veto on the presence of additional leptons. Muon selection For the μτh channel, selected muons are defined as those with • pT > 25 GeV, • having a combined muon spectrometer and inner detector offline candidate (mu staco isCombinedMuon == 1), • etcone20/pT < 4%. To suppress the presence of leptons produced in jets, the calorimeter isolation requirement listed above is required, where etcone20 denotes the sum of the transverse energy of the calorimeter cells within ∆R < 0.2 of the muon track. Electron selection For the eτh channel, selected electrons are defined as those with • pT > 30 GeV, • passing tight electron identification (el tightPP == 1). To suppress real or fake electrons produced in jets, the following calorimeter and tracking isolation cuts are applied to selected electrons: •    corrected etcone20/pT < 5% if pT < 100 GeV corrected etcone20 < 5 GeV if pT ≥ 100 GeV , • ptcone40/pT < 5%, where etcone20 denotes the sum of the transverse energy of the calorimeter cells within ∆R < 0.2 of the electron track, corrected for leakage with a pT-dependent correction and for pile-up with an N(vertex)-dependent correction [222]. The variable ptcone40 denotes the sum of the pT of tracks 160 6. search for high-mass resonances decaying to τ+τ− with pT > 1 GeV, within ∆R < 0.4 of the electron track, and associated to the same vertex as the electron candidate. The vertex requirement makes the track-based isolation inherently more robust against pile-up than the calorimeter-based isolation, and can therefore utilize a larger ∆R-cone. Beginning for electrons with pT > 100 GeV, the pT-dependent calorimeter isolation requirement becomes a constant cut on the magnitude of the isolation measures. Hadronic tau selection The `τh channels use only 1-prong hadronic tau candidates which comprise 50% of the tau decay branching fraction (80% of the hadronic tau decay branching fraction) and better signal purity than 3-prong decays. 3-prong tau decays also have poor reconstruction efficiency that is falling with pT as it becomes harder to reconstruct each of the 3 collimated tracks, as discussed in Section 4.4.7. Tau candidates are required to have pT > 35 GeV and pass a BDT selection optimized for rejecting jets (the medium working point). In addition to not overlapping with preselected muons, tau candidates must pass the ATLAS cut-based muon veto, which requires a loose matching between the track momentum and calorimeter energy by having a low ftrack, but only for candidates that have EM fraction, fEM, near 0 or 1 [102]. The fEM must also be greater than 0.1 if the visible mass of the lepton and tau candidate are near the Z peak [97]. For the eτh channel, to suppress the rate of electrons faking taus, we use the medium ATLAS BDT-based electron veto discussed in Section 4.3.5. Since the dominant background source of true electrons, Z → ee, falls quickly with pT, the loose veto is used for tau candidates with pT > 100 GeV. A final cleaning cut removes tau candidates from consideration that are very near η ≈ 0, where there is a small crack dividing the A and C sides of the inner detector and calorimeter barrels. A large fraction of reconstructed hadronic tau candidates in this region are faked by electrons that are not removed by overlap removal due to poor electron identification in this region and poor efficiency for high-threshold hits in the TRT. Tau candidates with leading tracks within |η| < 0.05 are vetoed. The hadronic tau selection can be summarized as • pT > 35 GeV. • 1 core-track, • tau JetBDTSigMedium == 1, • tau muonVeto == 0, • fEM > 0.1 if 80 GeV < m(μ, τh) < 100 GeV, (only for the μτh channel) 6.4 search in the `τh channels 161 •    tau EleBDTMedium == 0 if pT < 100 GeV tau EleBDTLoose == 0 if pT ≥ 100 GeV , (only for the eτh channel) • lead track |η| > 0.05. 6.4.3 Event selection The event preselection defining the kinematic region explored is: events with exactly one selected electron or muon, no additional preselected electrons or muons (see Section 6.3), and having exactly one selected 1-prong hadronic tau decay. Distributions of kinematic variables for the μτh channel are shown in Figures 6.1 and 6.2. Distributions for the eτh channel are shown in Figures 6.3 and 6.4. The plots in this section show the estimated background composition, using data-driven methods for the multijet and W/Z + jets backgrounds, and Monte Carlo simulation to predict the remaining backgrounds. The plots of the ratio of the observed over the expected counts contain bands meant to help visualize the dominant systematic uncertainties, as discussed in Section 6.6. Hypothetical Z ′ → ττ events produce high-pT tau decay products that are back-to-back in the transverse plane. Figure 6.1 (top) shows the distribution of the absolute difference in φ between the selected muon and hadronic tau. Events with back-to-back candidates are selected by requiring |∆φ(μ, τh)| > 2.7. Next, the hadronic tau and the muon are required to have opposite sign charges. Figure 6.1(middle) shows the distribution of the product of the charges of the selected muon and hadronic tau. Because the sample of electrons is less pure than muons, and because electrons fake tau candidates more readily than muons, the eτh channel has more significant fake backgrounds than μτh. Additional event-level cuts were chosen for the eτh channel 72. The Z → ee and multijet contributions are reduced to a negligible level by requiring EmissT > 30 GeV. The W + jets background is suppressed by requiring mT < 50 GeV, where mT is the transverse mass of the electron-E miss T system, defined as mT(e, E miss T ) = √ 2 pT(e) pT(τh)(1− cos ∆φ) , where ∆φ is the angle between the electron and EmissT in the transverse plane. This summarizes our baseline event selection. It provides a region dominated by Z → ττ and W/Z + jets, without yet focusing on high-mass events. The total transverse mass of the four-vector sum of the muon, the hadronic tau decay, and the missing transverse momentum, mtotT (`, τh, E miss T ), is calculated. 72 An updated result with the 2012 analysis will proabably harmonize the `τh event selection. Part of the reason the μτh and eτh channels have different selections, is that they were approved in succession and not together. 162 6. search for high-mass resonances decaying to τ+τ− The data were blinded in the regions where, • pT(τh) > 140 GeV, • or pT(`) > 140 GeV, • or EmissT > 140 GeV, • or mtotT (`, τh, EmissT ) > 300 GeV, to verify that the background modeling is well controlled outside of a high-mass signal region, and then the selections were frozen. After the baseline event selection, a cut on mtotT was optimized to give the best expected upper limit, as described later in Section 6.7, on the strength parameter of a SSM Z ′ in bins of its mass. The primary signal region which excludes the highest Z ′SSM mass at the 95% confidence level requires mtotT > 600 GeV for the μτh channel and m tot T > 500 GeV for the eτh channel, with cuts stepping down to 400 GeV to exclude lower masses most effectively, as shown in Table 6.6. The event selection can be summarized as 1. exactly one selected muon 2. no additional preselected electrons or muons 3. exactly one selected 1-prong hadronic tau decay 4. |∆φ(`, τh)| > 2.7 5. opposite sign charges for the ` and τh 6. EmissT > 30 GeV (only for the eτh channel) 7. mT(e, E miss T ) < 50 GeV (only for the eτh channel) 8. mtotT (`, τh, E miss T ) > 400–600 GeV (depending on the signal mass) Table 6.3 shows the number of events passing each step in the event selection with the predictions for each background. Table 6.4 shows the signal expectations passing high-mass thresholds on mtotT . 6.4.4 Background estimation Overview The dominant backgrounds involving fake hadronic tau decays from multijet and W+jets events are modeled in data-driven ways. Data-driven estimates are required because the rate for jets to pass tau identification is mis-modeled by the ATLAS full simulation, as discussed briefly in Section 4.4.1. 6.4 search in the `τh channels 163 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 24 /3 0) π Ev en ts / ( 0 1000 2000 3000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ )μ, h τ(φΔ 0 0.5 1 1.5 2 2.5 3o bs . / e xp . 0 1 2 /3 0) π Ev en ts / ( -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ )μ, h τ(φΔ 0 0.5 1 1.5 2 2.5 3o bs . / e xp . 0 1 2 Figure 7: The distribution of the absolute di!erence in ! between the selected muon and hadronic tau. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau. Ev en ts 0 2000 4000 6000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) h τ charge(×) μcharge( -4 -2 0 2 4o bs . / e xp . 0 1 2 Ev en ts -110 1 10 210 310 410 510 data 2011τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) h τ charge(×) μcharge( -4 -2 0 2 4o bs . / e xp . 0 1 2 Figure 8: The distribution of the product of the charges of the selected muon and hadronic tau. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, and |"!(μ, "h)| > 2.7, N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 24 /3 0) π Ev en ts / ( 0 1000 2000 3000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ )μ, h τ(φΔ 0 0.5 1 1.5 2 2.5 3o bs . / e xp . 0 1 2 /3 0) π Ev en ts / ( -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ )μ, h τ(φΔ 0 0.5 1 1.5 2 2.5 3o bs . / e xp . 0 1 2 Figure 7: The distribution of the absolute di!erence in ! between the selected muon and hadronic tau. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau. Ev en ts 0 2000 4000 6000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) h τ charge(×) μcharge( -4 -2 0 2 4o bs . / e xp . 0 1 2 Ev en ts -110 1 10 210 310 410 510 data 2011τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) h τ charge(×) μcharge( -4 -2 0 2 4o bs . / e xp . 0 1 2 Figure 8: The distribution of the product of the charges of the selected muon and hadronic tau. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, and |"!(μ, "h)| > 2.7, N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 26 Ta u C an di da te s / ( 5 G eV ) 0 1000 2000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 1 2 Figure 10: The distribution of the transverse momentum of the selected hadronic tau. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(μ, "h)| > 2.7, and opposite sign μ and "h. Ev en ts / (5 G eV ) 0 500 1000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 50 100 150 200 250 300350 400 450 500o bs . / e xp . 0 1 2 Figure 11: The distribution of the missing transverse momentum. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(μ, "h)| > 2.7, and opposite sign μ and "h. Figure 6.1: Kinematic distributions for the μτh channel. (top) The distribution of the absolute difference in φ between the selected muon and tau candidate in events with exactly one selected muon, o dditional preselected electrons or muons, and exactly one selected 1-prong tau. (middle) The distribution of the product of the reconstructed charges of the selected electron and tau candidate in events with the event preselection listed above, and requiring ∆φ(μ, τh) > 2.7. (bottom) The distribution of the E miss T in events with the above selection, and requiring opposite-sign charges for the μ and τh (the μτh baseline event selection) [97]. 164 6. search for high-mass resonances decaying to τ+τ− N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 25 The plots in this section show the estimated background composition, using data-driven methods610 for the multijet and W/Z+jet backgrounds, and Monte Carlo simulation to predict the remaining back-611 grounds. The plots of the ratio of the observed over the expected counts contain bands meant to help612 visualize the dominant systematic uncertanties, as discussed in Appendix G.1.613 Hypothetical Z! " !! events produce high-pT tau decay products that are back-to-back in the trans-614 verse plane. Figure 7 shows the distribution of the absolute di!erence in " between the selected muon615 and hadronic tau. We select events with back-to-back candidates by requiring |""(μ, !h)| > 2.7. Next,616 we require the hadronic tau and the muon to have opposite sign charges. Figure 8 shows the distribution617 of the product of the charges of the selected muon and hadronic tau. This summarizes our baseline event618 selection. It provides a region dominated by Z " !! and W+jet, without yet focusing on high mass619 events.620 The total transverse mass of the four-vector sum of the muon, the hadronic tau decay, and the missing621 transverse momentum, MT(μ, !h, EmissT ), is calculated. Then, we blinded the data in the region where,622 • pT(!h) > 140 GeV,623 • or pT(μ) > 140 GeV,624 • or EmissT > 140 GeV,625 • or MT(μ, !h, EmissT ) > 300 GeV,626 to verify that the background modeling is well controlled outside of a high mass signal region. Figures 9,627 10, and 11 show the distributions of the transverse momentum of the muon, transverse momentum of628 the hadronic tau and missing transverse momentum, respectively. Figure 12 shows the distributions of629 MT(μ, !h, EmissT ).630 M uo ns / (5 G eV ) 0 500 1000 1500 2000 data 2011τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]μ( T p 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 M uo ns / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]μ( T p 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 9: The distribution of the transverse momentum of the selected muon. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |""(μ, !h)| > 2.7, and opposite sign μ and !h. After the baseline event selection, a cut on MT was optimized to give the best expected upper limit,631 as described later in Section 9, on the strength parameter of a SSM Z! in bins of its mass. The primary632 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 26 Ta u C an di da te s / ( 5 G eV ) 0 1000 2000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 10: The distribution of the transverse momentum of the selected hadronic tau. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(μ, "h)| > 2.7, and opposite sign μ and "h. Ev en ts / (5 G eV ) 0 500 1000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 50 100 150 200 250 300350 400 450 500o bs . / e xp . 0 1 2 Figure 11: The distribution of the missing transverse momentum. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(μ, "h)| > 2.7, and opposite sign μ and "h. 6. Search for high-mass resonances decaying to ⌧+⌧  178 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 25 The plots in this section show the estimated background co position, using data-driven methods610 for the multijet and W Z+jet backgrounds, and Monte Carlo simulation to predict the remaining back-611 grounds. The plots of the ratio of the observed over the expected counts contain bands meant to help612 visualize the dominant systematic uncertanties, as discussed in Appendix G.1.613 Hypothetical Z       events produce high-pT tau decay products that are back-to-back in the trans-614 verse plane. Figure 7 shows the distribution of the absolute di erence in   between the selected muon615 and hadronic tau. We select events with back-to-back candidates by requiring |  (  h)| 2 7. Next,616 we require the hadronic tau and the muon to have opposite sign charges. Figure 8 shows the distribution617 of the product of the charges of the selected muon and hadronic tau. This summarizes our baseline event618 selection. It provides a region dominated by Z      and W+jet, without yet focusing on high mass619 events.620 The total transverse mass of the four-vector sum of the muon, the hadronic tau decay, and the missing621 transverse momentum, MT(  h EmissT ), is calculated. Then, we blinded the data in the region where,622 • pT( h) 140 GeV,623 • or pT( ) 140 GeV,624 • or EmissT 140 GeV,625 • or MT(  h EmissT ) 300 GeV,626 to verify that the background modeling is well controlled outside of a high mass signal region. Figures 9,627 10, and 11 show the distributions of the transverse momentum of the muon, transverse momentum of628 the hadronic tau and missing transverse momentum, respectively. Figure 12 shows the distributions of629 MT(  h EmissT ).630 M uo ns / (5 G eV ) 0 500 1000 1500 2000 data 2011τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]μ( T p 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 M uo ns / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]μ( T p 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 9: The distribution of the transverse momentum of the selected muon. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (  h)| 2 7, and opposite sign and  h. After the baseline event selection, a cut on MT was optimized to give the best expected upper limit,631 as described later in Section 9, on the strength parameter of a SSM Z  in bins of its mass. The primary632 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 26 Ta u C an di da te s / ( 5 G eV ) 0 1000 2000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 10: The distribution of the transverse momentum of the selected hadronic tau. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (μ,  h)| > 2.7, and opposite sign μ and  h. Ev en ts / (5 G eV ) 0 500 1000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 50 100 150 200 250 300350 400 450 500o bs . / e xp . 0 1 2 Figure 11: The distribution of the missing transverse momentum. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (μ,  h)| > 2.7, and opposite sign μ and  h. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 27 Ev en ts / (1 0 G eV ) 0 500 1000 1500 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ, μ(TM 0 50 100 150 200 250 300 350 400o bs . / e xp . 0 1 2 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ, μ(TM 0 200 400 600 800 1000 1200 1400o bs . / e xp . 0 1 2 Figure 12: The distribution of the total transverse mass of the four-vector sum of the selected muon, selected hadronic tau, and the missing transverse momentum. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (μ,  h)| > 2.7, and opposite sign μ and  h. signal region which excludes the highest mass at the 95% confidence level requires MT > 600 GeV, with633 cuts stepping down to 500 and 400 GeV to exclude lower masses most e ectively, as shown in Table 7.634 SSM Z  mass [GeV] 500, 625 750, 875  1000 MT [GeV] >400 >500 >600 Table 7: Mass dependent cuts on MT. The event selection can be summarized as635 1. exactly one selected muon636 2. no additional preselected electrons or muons637 3. exactly one selected 1-prong hadronic tau decay638 4. |  (μ,  h)| > 2.7639 5. opposite sign charges for the μ and  h640 6. MT(μ,  h, EmissT ) > 600 GeV641 Table 8 shows the number of events passing each step in the event selection with the predictions for each642 background. Table 9 shows the signal expectations passing high mass thresholds on MT.643 Figure 6.2: The distribution of the transverse momentum of the selected muon. These plots include the requirements of: exactly one selected muon, no additional pre-selected electrons or muons, exactly one selected 1-prong tau, |  (μ, ⌧h)| > 2.7, and opposite sign μ and ⌧h. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 150 /3 0) π Ev en ts / ( 0 500 1000 1500 2000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ φΔ∑ 0 1 2 3 4 5 6o bs . / e xp . 0 1 2 /3 0) π Ev en ts / ( -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ φΔ∑ 0 1 2 3 4 5 6o bs . / e xp . 1 2 Figure 101: The distribution of the sum of the magnitudes of the di!erences in ! of between the m on and the EmissT , and the hadronic tau candidate and the E miss T , ! "! = "!(μ, EmissT ) + "!("h, EmissT ). These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau. Events with the EmissT between the lepton and hadronic tau candidate in the transverse plane have ! "! < #, while W+jet events have the jet and lepton ballancing the EmissT and large values of ! "!. Ev en ts -110 1 10 210 310 410 510 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ, μ(TM 210 310o bs . / e xp . 0 1 2 Figure 102: The distribution of the total transverse ass of the four-vector sum of the selected muon, selected hadronic tau, and the transverse missing energy. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, exactly one selected 1-prong tau, |"!(μ, "h)| > 2.7, and opposite sign μ and "h. Figure 6.2: Kinematic distributions for the μτh channel. (top) The distribution of pT(μ), (middle) the distribution of pT(τh), and (bottom) the distribution of m tot T (μ, τh, E miss T ) in events passing the μτh baseline event selection (MT ≡ totT ) [97]. 6.4 search in the `τh channels 165 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 40 Finally, we use an additional cleaning cut, recommended from the conclusions of the recent ATLAS860 TauWorkshop in Oxford [53], which removes tau candidates from consideration that are very near ! ! 0,861 where there is a small crack dividing the A and C sides of the inner detector and calorimeter barrels. A862 large fraction of reconstructed hadronic tau candidates in this region are faked by electrons that are not863 removed by overlap removal due to poor electron identification in this region and poor e!ciency for864 high-threshold hits in the TRT. We veto tau candidates with leading tracks within |!| < 0.05.865 The hadronic tau selection can be summarized as866 • pT > 35 GeV ,867 • 1 core-track,868 • tau JetBDTSigMedium == 1 ,869 • !""#""$ tau EleBDTMedium == 0 if pT < 100 GeV tau EleBDTLoose == 0 if pT " 100 GeV ,870 • lead track |!| > 0.05 .871 6.4 Event selection872 The event selection for the e"h channel begins analogous to that used for the μ"h channel (see Section873 5.4). The event preselection defining the kinematic region we explore is: events with exactly one selected874 electron, no additional preselected electrons or muons (see Section 3), and having exactly one selected875 1-prong hadronic tau decay.876 The plots in this section show the estimated background composition, using data-driven methods877 for the multijet and W/Z+jet backgrounds, and Monte Carlo simulation to predict the remaining back-878 grounds. The plots of the ratio of the observed over the expected counts contain bands meant to help879 visualize the dominant systematic uncertanties, as discussed in Appendix G.1.880 /3 0) π Ev en ts / ( 0 500 1000 1500 2000 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ , e) h τ(φΔ 0 0.5 1 1.5 2 2.5 3o bs . / e xp . 0 1 2 /3 0) π Ev en ts / ( -110 1 10 210 310 410 510 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ , e) h τ(φΔ 0 0.5 1 1.5 2 2.5 3o bs . / e xp . 0 1 2 Figure 19: The distribution of the absolute di"erence in # between the selected electron and hadronic tau. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, and exactly one selected 1-prong tau. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 41 Ev en ts 0 1000 2000 3000 4000 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) h τ charge(×charge(e) -4 -2 0 2 4o bs . / e xp . 0 1 2 Ev en ts -110 1 10 210 310 410 510 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) h τ charge(×charge(e) -4 -2 0 2 4o bs . / e xp . 0 1 2 Figure 20: The distribution of the product of the charges of the selected electron and hadronic tau. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, and |!!(e, "h)| > 2.7, Figure 19 shows the distribution of the absolute di"erence in ! between the selected electron and881 hadronic tau. We select events with back-to-back candidates by requiring |!!(e, "h)| > 2.7. Next, we882 require the hadronic tau and the electron to have opposite sign charges. Figure 20 shows the distribution883 of the product of the charges of the selected electron and hadronic tau.884 Thus far, the event selection of the e"h channel has been the same as for the μ"h channel. Because885 the e"h channel has a more significant contamination by multijet events in the control sample failing tau886 identification but passing lepton isolation (the control region used to estimate the W/Z+jets background887 as discussed later in Section 6.5.3), two additional event selection cuts are made to simplify the back-888 ground composition. Requiring EmissT > 30 GeV significantly suppresses multijet and Z ! ee events.889 The distribution of the EmissT prior to making this cut is shown in Figure 21.890 The transverse mass between the electron and the EmissT is shown in Figure 22. Events are selected891 if mT(e, EmissT ) < 50 GeV, a common cut used by H ! "" and Z ! "" analyses [47, 48] to reject W+jet892 events, where the neutrino in the event tends to recoil hard against jets in the event.893 This summarizes our baseline event selection for the e"h channel. It provides a region dominated by894 Z ! "" and W+jet, without yet focusing on high-mass events. The total transverse mass of the four-895 vector sum of the electron, the hadronic tau decay, and the missing transverse energy, MT(e, "h, EmissT ), is896 calculated. Then, we blinded the data in the region where,897 • pT("h) > 200 GeV,898 • or pT(e) > 160 GeV,899 • or EmissT > 160 GeV,900 • or MT(e, "h, EmissT ) > 400 GeV,901 to verify that the background modeling is well controlled outside of a high mass signal region. Figures 23,902 24, and 25 show the distributions of the transverse momentum of the electron, transverse momentum903 of the hadronic tau and transverse missing energy, respectively. Figure 26 shows the distributions of904 MT(e, "h, EmissT ).905 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 3, 2012 – 15 : 44 DRAFT 42 Ev en ts / (5 G eV ) 0 200 400 600 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 510 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 50 100 150 200 250 300350 400 450 500o bs . / e xp . 0 1 2 Figur 21: Th distribution of transverse missing energy. These plots i clude the requirements of: exactly one s lected electron, no ad itional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, and opposite sign e and "h. Ev en ts / (1 0 G eV ) 0 50 100 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T (e, ETm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T (e, ETm 0 100200 300 400 500 600700 800 9001000o bs . / e xp . 0 1 2 Figure 22: The distribution of transverse missing energy. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, and EmissT > 30 GeV. Figure 6.3: Kinematic distributions for the eτh channel. (top) The distribution of the absolute difference in φ between the selected electron and tau candidate in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one selected 1-prong tau. (middle) The distribution of the product of the reconstructed charges of the selected electron and tau candidate in events with the event preselection listed above, and requiring ∆φ(e, τh) > 2.7. (bottom) The distribution of the E miss T in events with the above selection, and requiring opposite-sign charges for the e and τh [97]. 166 6. search for high-mass resonances decaying to τ+τ− N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 43 El ec tro ns / (5 G eV ) 0 50 100 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [GeV] T p 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [GeV] T p 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 23: The distribution of the transverse momentum of the selected electron. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. Ta u C an di da te s / ( 5 G eV ) 0 20 40 60 80 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 24: The distribution of the transverse momentum of the selected hadronic tau. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, EmissT > 30 GeV, and mT(e, E miss T ) < 50 GeV. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 43 El ec tro ns / (5 G eV ) 0 50 100 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [GeV] T p 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [GeV] T p 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 23: The distribution of the transverse momentum of the selected electron. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. Ta u C an di da te s / ( 5 G eV ) 0 20 40 60 80 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 24: The distribution of the transverse momentum of the selected hadronic tau. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, EmissT > 30 GeV, and mT(e, E miss T ) < 50 GeV. 6. Search for high-mass resonances decaying to ⌧+⌧  180 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 43 El ec tro ns / (5 G eV ) 0 50 100 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [GeV] T p 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [GeV] T p 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 23: The distribution of the transverse momentum of the selected electron. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. Ta u C an di da te s / ( 5 G eV ) 0 20 40 60 80 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 24: The distribution of the transverse momentum of the selected hadronic tau. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, E miss T ) < 50 GeV. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 43 El ec tro ns / (5 G eV ) 0 50 100 data 2011 τ τ →Z W/ +jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [GeV] T p 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ (e) [G V] T p 0 100 200 300 400 500 600o bs . / e xp . 1 2 Figure 23: The distribution of the transverse momentum f the selected electron. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. Ta u C an di da te s / ( 5 G eV ) 0 20 40 60 80 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 24: The distribution of the transverse momentum of the selected hadronic tau. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, E miss T ) < 50 GeV. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 44 Ev en ts / (5 G eV ) 0 50 100 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ [GeV]missTE 0 50 100 150 200 250 300350 400 450 500o bs . / e xp . 0 1 2 Figure 5: The distribution of transverse missing energy. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. Ev en ts / (1 0 G eV ) 0 20 40 6 d ta 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ(e, TM 0 50 100 150 200 250 300 350 400o bs . / e xp . 0 1 2 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400o bs . / e xp . 0 1 2 Figure 26: The distribution of the total transverse mass of the four-vector sum of the selected electron, selected hadronic tau, and the transverse missing energy. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. Figure 6.4: ODO. The distribution of the transverse momentum of the selected muon. These plots include the requirements of: exactly one selected muon, no additional pre-selected electrons or muons, exactly one selected 1-prong tau, |  (μ, ⌧h)| > 2.7, and opposite sign μ and ⌧h. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 164 Ev en ts -11 1 10 20 310 410 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ(e, TM 210 310o bs . / e xp . 0 1 2 Figure 120: The distribution of the total transverse mass of th four-vect r sum of the selected electron, selected hadronic tau, a d the transverse missing energy. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. Figure 6.4: Kinematic distributions for the eτh channel. (top) The distribution of pT(e), (middle) the distribution of p (τh), and (bottom) the distribution of m tot T (e, τh, E miss T ) in events passing the eτh baseline event selection (MT ≡ mtotT ) [97]. 6.4 search in the `τh channels 167 T ab le 6. 3: T h e n u m b er of ev en ts p as si n g ea ch st ep in th e ev en t se le ct io n o f th e `τ h ch a n n el s. T h e n u m b er s in p a re n th es es d en o te th e st a ti st ic a l u n ce rt ai n ty in th e le as t si gn ifi ca n t d ig it s [9 7 ]. μ τ h ch a n n e l d a ta to ta l S M Z → τ τ W + je ts m u lt ij e t Z → μ μ tt d ib o so n si n g le to p Z ′ ( 1 0 0 0 ) o n e μ , o n e τ h 1 1 6 0 5 1 1 6 5 3 (4 7 ) 3 8 6 7 (3 5 ) 4 9 1 3 (2 1 ) 5 8 3 (5 ) 8 9 7 (2 1 ) 9 6 3 (7 ) 3 2 3 (4 ) 1 0 8 (3 ) 1 8 .7 (2 ) |∆ φ (μ , τ h )| > 2 .7 6 0 6 1 5 9 4 1 (3 8 ) 2 8 2 9 (3 1 ) 1 8 1 1 (1 4 ) 4 0 3 (4 ) 5 3 3 (1 7 ) 2 2 1 (3 ) 1 1 7 (2 ) 2 7 (1 ) 1 7 .9 (2 ) o p p o si te si g n μ a n d τ h 5 3 2 0 5 2 4 2 (3 7 ) 2 7 9 1 (3 1 ) 1 4 4 6 (1 3 ) 2 1 3 (3 ) 4 5 2 (1 6 ) 2 0 8 (3 ) 1 0 7 (2 ) 2 4 (1 ) 1 7 .6 (2 ) m t o t T > 2 0 0 G eV 2 2 9 2 6 3 (5 ) 3 0 .0 (5 ) 1 1 4 (4 ) 5 .5 (4 ) 5 (1 ) 7 6 (2 ) 2 2 .3 (8 ) 9 .4 (9 ) 1 6 .5 (2 ) m t o t T > 3 0 0 G eV 3 1 5 3 (2 ) 7 .3 (2 ) 1 8 (2 ) 0 .6 (1 ) 0 .3 (2 ) 1 7 .6 (9 ) 6 .7 (6 ) 3 .0 (5 ) 1 4 .1 (2 ) m t o t T > 4 0 0 G eV 1 3 1 5 (1 ) 2 .3 1 (5 ) 5 .0 (8 ) 0 .1 5 (7 ) 0 .1 (1 ) 4 .5 (4 ) 1 .7 (2 ) 0 .9 (3 ) 1 1 .0 (2 ) m t o t T > 5 0 0 G eV 1 4 .5 (5 ) 0 .8 2 (3 ) 1 .6 (5 ) 0 .0 2 (2 ) < 0 .1 1 .2 (2 ) 0 .6 (1 ) 0 .3 (2 ) 8 .0 (1 ) m t o t T > 6 0 0 G eV 1 1 .4 (3 ) 0 .3 6 (2 ) 0 .3 (2 ) < 0 .0 1 0 .3 (1 ) 0 .2 3 (7 ) 0 .2 (1 ) 5 .5 (1 ) m t o t T > 7 0 0 G eV 1 0 .5 (1 ) 0 .1 7 (1 ) 0 .0 7 (7 ) 0 .0 3 (3 ) 0 .1 3 (5 ) 0 .1 (1 ) 3 .3 8 (9 ) e τ h ch a n n e l d a ta to ta l S M Z → τ τ W / Z + je ts m u lt ij e t Z → e e tt W γ d ib o so n si n g le to p Z ′ ( 1 0 0 0 ) o n e e , o n e τ h 7 2 9 5 7 2 7 0 (5 1 ) 1 3 4 0 (2 0 ) 3 2 5 1 (2 1 ) 7 6 6 (2 2 ) 1 2 8 0 (3 5 ) 4 0 2 (4 ) 6 8 (6 ) 1 1 5 (2 ) 4 9 (2 ) 1 5 .6 (2 ) |∆ φ (e , τ h )| > 2 .7 3 9 2 9 3 9 3 3 (4 3 ) 9 1 8 (1 7 ) 1 2 4 2 (1 5 ) 5 5 6 (1 8 ) 1 0 2 0 (3 2 ) 1 0 6 (2 ) 2 8 (4 ) 4 8 (1 ) 1 5 (1 ) 1 4 .9 (2 ) o p p o si te si g n e a n d τ h 3 1 8 3 3 3 2 2 (4 0 ) 9 0 2 (1 7 ) 1 0 0 4 (1 4 ) 2 7 9 (1 3 ) 9 5 8 (3 1 ) 9 9 .9 (2 ) 2 2 (4 ) 4 4 (1 ) 1 3 .3 (9 ) 1 4 .6 (2 ) E m is s T > 3 0 G eV 8 3 2 8 1 7 (1 5 ) 1 5 8 (6 ) 3 8 8 (8 ) 3 9 (6 ) 1 0 1 (1 0 ) 8 5 (2 ) 9 (2 ) 2 6 .8 (9 ) 1 0 .7 (9 ) 1 2 .8 (2 ) m T (e , E m is s T ) < 5 0 G eV 2 6 3 2 9 8 (1 0 ) 1 1 3 (5 ) 1 0 1 (5 ) 2 2 (4 ) 4 1 (6 ) 1 5 .1 (7 ) 1 .3 (9 ) 3 .1 (2 ) 1 .9 (3 ) 8 .7 (1 ) m t o t T > 2 0 0 G eV 4 6 5 9 (4 ) 1 5 .6 (7 ) 3 1 (2 ) 4 (2 ) 0 .0 3 (2 ) 5 .7 (5 ) 0 .6 (6 ) 1 .1 (1 ) 0 .8 (2 ) 8 .5 (1 ) m t o t T > 3 0 0 G eV 1 4 1 4 (2 ) 4 .4 (3 ) 6 (1 ) 2 (1 ) 0 .0 2 (2 ) 1 .4 (2 ) < 0 .1 0 .2 9 (7 ) 0 .1 1 (8 ) 7 .7 (1 ) m t o t T > 4 0 0 G eV 4 3 .0 (8 ) 1 .4 2 (4 ) 0 .8 (6 ) 0 .3 (3 ) < 0 .0 1 0 .4 (1 ) 0 .1 4 (5 ) < 0 .1 6 .5 (1 ) m t o t T > 5 0 0 G eV 0 1 .6 (4 ) 0 .5 7 (2 ) 0 .8 (4 ) < 0 .1 0 .1 3 (7 ) 0 .0 6 (3 ) 5 .0 (1 ) m t o t T > 6 0 0 G eV 0 0 .5 (2 ) 0 .2 3 (2 ) 0 .2 (2 ) 0 .0 4 (4 ) 0 .0 2 (2 ) 3 .6 7 (9 ) 168 6. search for high-mass resonances decaying to τ+τ− T ab le 6.4: T h e n u m b er o f ex p ected S M an d sig n a l even ts p a ssin g p o ssib le m to t T cu ts in th e `τ h ch an n els. T h e n u m b ers in p aren th eses d en ote th e sta tistica l u n certa in ty in th e least sig n ifi ca n t d ig its. T h e b o ld n u m b ers d en o te th e ex p ected sign al for th e ch osen m ass cu ts sh ow n in T a b le 6.6 [97]. μ τ h ch a n n e l to ta l S M Z ′(5 0 0 ) Z ′(6 2 5 ) Z ′(7 5 0 ) Z ′(8 7 5 ) Z ′(1 0 0 0 ) Z ′(1 1 2 5 ) Z ′(1 2 5 0 ) Z ′(1 3 7 5 ) Z ′(1 5 0 0 ) Z ′(1 6 2 5 ) Z ′(1 7 5 0 ) m t o t T > 4 0 0 G eV 1 5 (1 ) 4 2 ( 1 ) 4 4 ( 1 ) 2 9 .1 (5 ) 1 7 .4 (4 ) 1 1 .0 (2 ) 6 .1 (1 ) 3 .9 4 (5 ) 2 .3 5 (4 ) 1 .3 9 (3 ) 0 .8 5 (2 ) 0 .5 2 (1 ) m t o t T > 5 0 0 G eV 4 .5 (5 ) 5 .8 (5 ) 1 8 .1 (9 ) 1 7 .0 ( 4 ) 1 1 .5 ( 3 ) 8 .0 (1 ) 4 .7 (1 ) 3 .1 4 (5 ) 1 .9 4 (4 ) 1 .1 7 (2 ) 0 .7 3 (1 ) 0 .4 5 0 (9 ) m t o t T > 6 0 0 G eV 1 .4 (3 ) 1 .0 (2 ) 3 .9 (4 ) 8 .3 (3 ) 6 .9 (2 ) 5 .5 ( 1 ) 3 .3 8 ( 9 ) 2 .3 6 ( 4 ) 1 .5 5 ( 4 ) 0 .9 6 ( 2 ) 0 .6 0 ( 1 ) 0 .3 7 4 ( 8 ) m t o t T > 7 0 0 G eV 0 .5 (1 ) 0 .3 (1 ) 1 .0 (2 ) 2 .3 (1 ) 3 .4 (2 ) 3 .3 8 (9 ) 2 .3 8 (8 ) 1 .7 8 (4 ) 1 .1 9 (3 ) 0 .7 6 (2 ) 0 .4 8 (1 ) 0 .3 1 4 (7 ) e τ h ch a n n e l to ta l S M Z ′(5 0 0 ) Z ′(6 2 5 ) Z ′(7 5 0 ) Z ′(8 7 5 ) Z ′(1 0 0 0 ) Z ′(1 1 2 5 ) Z ′(1 2 5 0 ) Z ′(1 3 7 5 ) Z ′(1 5 0 0 ) Z ′(1 6 2 5 ) Z ′(1 7 5 0 ) m t o t T > 4 0 0 G eV 3 .0 (8 ) 3 2 ( 1 ) 2 8 ( 1 ) 1 7 .7 ( 4 ) 1 0 .5 (3 ) 6 .5 (1 ) 3 .6 (1 ) 2 .1 5 (4 ) 1 .2 4 (3 ) 0 .7 5 (2 ) 0 .4 6 (1 ) 0 .2 8 3 (7 ) m t o t T > 5 0 0 G eV 1 .6 (4 ) 5 .0 (5 ) 1 2 .3 (7 ) 1 1 .1 (3 ) 7 .9 ( 3 ) 5 .0 ( 1 ) 2 .8 8 ( 9 ) 1 .8 2 ( 4 ) 1 .0 7 ( 3 ) 0 .6 5 ( 2 ) 0 .4 1 ( 1 ) 0 .2 5 8 ( 7 ) m t o t T > 6 0 0 G eV 0 .5 (2 ) 0 .7 (2 ) 3 .7 (4 ) 5 .5 (2 ) 5 .2 (2 ) 3 .6 7 (9 ) 2 .2 5 (8 ) 1 .4 5 (3 ) 0 .9 0 (3 ) 0 .5 5 (2 ) 0 .3 5 (1 ) 0 .2 2 3 (6 ) 6.4 search in the `τh channels 169 The multijet and W/Z + jets backgrounds are estimated with data-driven techniques involving fake factors parameterizing the rate for jets to fake lepton isolation and tau identification. The fake-factor method populates the tail of the background model with high-mass events from data, that typically outnumber the contribution of that background to the signal region because more events fail the tau identification or lepton isolation than pass. Fake factor methods have precedence in other ATLAS analyses, including using fake factors for muon isolation and electron identification to predict the W+jets background to WW → `` [223, 224]. A fake-factor method is also used in the ATLAS search for exotic excesses in same-sign dileptons [225]. The remaining backgrounds considered (Z → ττ , Z → μμ, tt, single top, and diboson) are modeled with ATLAS fully simulated Monte Carlo samples. Multijet background The background from multijet events is demonstrated to be negligible at high mtotT , but it is also important to model its contribution at lower mass for modeling control regions. Multijet events are unique among our backgrounds because the leptons produced in jets are often not isolated in the calorimeter. The ratio of the number of isolated leptons to the number of non-isolated leptons in a multijet-rich region of data (multijet control region or multijet–CR) is measured, and used to predict the number of leptons from multijet events passing isolation requirements. The multijet–CR is defined as • exactly one selected lepton ignoring the isolation requirements, • no additional preselected electrons or muons • at least one preselected hadronic tau candidate, • zero selected 1-prong hadronic tau candidates, • EmissT < 30 GeV, • mT(`, EmissT ) < 30 GeV, • |d0(μ)| > 0.08 mm (only in the μτh channel). The selected leptons in this control sample are then divided into two categories: those that pass and those that fail the lepton isolation requirements discussed in Section 6.4.2. These are used to define a fake factor, f`–iso, for lepton isolation as the number of isolated leptons in the data, divided by the number of non-isolated leptons, binned in pT and η: f`–iso(pT, η) ≡ Npass `–iso(pT, η) N fail `–iso(pT, η) ∣∣∣∣ multijet–CR . 170 6. search for high-mass resonances decaying to τ+τ− 6. Search for high-mass resonances decaying to ⌧+⌧  185 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 31 The muon isolation fake factor is shown in Figure 13. Then, in the event selection, we predict the number678 of multijet events passing muon isolation by multiplying the number of events that fail isolation by their679 fake factor:680 Nmultijet(pT,  , x) = fμ–iso(pT,  ) * Nfail μ–isomultijet (pT,  , x) . (3) This assumes that the ratio of the number of isolated muons to the number of non-isolated muons in681 multijet events is not strongly correlated with the cuts used to enrich the multijet control sample. This682 assumption was verified with studies that are discussed in Appendix G.4.1, but we allow for a conser-683 vative 100% systematic on the isolation fake factor method, which has negligible e ect on the final684 limit because the multijet background is less than a hundredth of an event. We correct the sample of685 non-isolated muons in the data by subtracting the expected contamination of electroweak processes in686 Monte Carlo. This correction is approximately 5% of the number of isolated muons and negligible for687 the number of non-isolated muons.688 Nmultijet(pT,  , x) = fμ–iso(pT,  ) *   Nfail μ–isodata (pT,  , x)   N fail μ–iso MC (pT,  , x)   . (4) The shape of the multijet background in any kinematic variable, x   {  ,MT, . . .}, is modeled from689 the events in the data with non-isolated muons, with Monte Carlo modeling the other contamination690 subtracted.691 ) [GeV]μ( T p 0 20 40 60 80 100 120 140 : m ul tij et -is o μf 0 0.02 0.04 0.06 0.08 0.1 Inclusive Barrel Crack Endcap ATLAS Internal T etcone20 / p -0.1 0 0.1 0.2 0.3 0.4 0.5 M uo ns / 0. 01 0 200 400 600 800 1000 1200 data 2011 τ τ →Z ν μ →W ν τ →W μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 13: (left) Muon isolation fake factors derived in the multijet control region. (right) The distribution of the muon calorimeter isolation variable etcone20/pT in the multijet control region. Figure 13(left) shows how muon isolation fake factors depend on the pT of the muon. Figure 14692 shows the multijet estimate in the distributions of mT(μ, EmissT ) and d0(μ), after the event preselection,693 where it is 583 ± 5 (stat.) events, or 5% of the expected background. The expected multijet background694 falls to less than 0.02 of an event for events with MT   500 GeV, and it is therefore considered negligible695 in the signal region with MT(μ,  h, EmissT ) > 600 GeV, as is also clearly shown in Figure 15.696 As a cross-check, the normalization of the multijet background was also predicted by fitting the697 muon calorimeter isolation distribution with data-driven templates for isolated and non-isolated muons,698 to extract the multijet normalization. The estimates were found to be consistent and are discussed more699 in Appendix G.4.700 5.5.3 W+jets background701 The dominant background throughout most of the high-MT tail comes fromW+jets events. It is estimated702 with a data-driven technique using fake factors parameterizing the rate for jets to fake tau identification.703 We select a W(  μ )-rich region of data (which we call the W+jets control region or W–CR) by704 selecting events which have705 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 49 (e) [GeV] T p 0 50 100 150 200 250 300 350 400 : m ul tij et eis o f 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Inclusive Barrel Endcap ATLAS Internal ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 JetBDTSigMedium JetBDTSigLoose Inclusive SM background multijetATLAS Internal -1dt L = 4.6 fb∫ Figure 27: (left) Electron isolation fake factors derived in the multijet control region. (right) The MT distribution of the expected multijet background, with predictions for medium (used in the nominal selection), loose, and no jet-tau discrimination, in events with exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. The loosened MT distributi ns are scaled to the integral predicted by the nominal selection, JetBDTSigMedium. Ev en ts / (1 0 G eV ) 0 500 1000 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T (e, ETm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 0 1 2 El ec tro ns / (0 .0 2 m m ) -110 10 310 510 710 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ (e) [mm]0d -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1o bs . / e xp . 0 1 2 Figure 28: (left) The distribution of the transverse mass of the combination of the selected electron and the EmissT , mT(e, E miss T ). in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one selected 1-prong tau. (right) The distribution of the electron impact parameter, d0, in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one 1-prong tau candidate (without ID). igure 6.5: (left) Muon isolation fake factors eri e i the multijet control region. (right) The i tion f muon calorimeter isolati n variable etcone20/pT in the multijet control regio . processes in Monte Carlo. This correction is approximately 5% of the number of isolated muons and2949 n gligible for he number of non-isolated muons.2950 Nmultijet(pT, ⌘, x) = fμ–iso(pT, ⌘) * ⇣ N fail μ–isodata (pT, ⌘, x)   N fail μ–iso MC (pT, ⌘, x) ⌘ . The shape of the multijet background in any kinematic variable, x 2 {  , mtotT , . . .}, is modeled from2951 the events in the data with non-isolated muons, with Monte Carlo modeling the other contamination2952 subtracted.2953 Figure ??(left) shows how muon isolation fake factors depend on the pT of the muon. Figure ??2954 shows the multijet estimate in the distributions of mT(μ, E miss T ) and d0(μ), after the event pre-2955 selection, where it is 583± 5 (stat.) events, or 5% of the expected background. The expected multijet2956 background falls to less than 0.02 of an event for events with MT & 500 GeV, and it is therefore2957 considered negligible in the signal region with MT(μ, ⌧h, E miss T ) > 600 GeV, as is also clearly shown2958 in Figure ??.2959 6. Search for high-mass resonances decaying to ⌧+⌧  185 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 31 The muon isolation fake factor is shown in Figure 13. Then, in the event selection, we predict the number678 of multijet events passing muon isolation by multiplying the number of events that fail isolation by their679 fake factor:680 Nmultijet(pT,  , x) = fμ–iso(pT,  ) * Nfail μ–isomultijet (pT,  , x) . (3) This assumes that the ratio of the number of isolated muons to the number of non-isolated muons in681 multijet events is not strongly correlated with the cuts used to enrich the multijet control sample. This682 assumption was verified with studies that are discussed in Appendix G.4.1, but we allow for a conser-683 vative 100% systematic on the isolation fake factor method, which has negligible e ect on the final684 limit because the multijet background is less than a hundredth of an event. We correct the sample of685 non-isolated muons in the data by subtracting the expected contamination of electroweak processes in686 Monte Carlo. This correction is approximately 5% of the number of isolated muons and negligible for687 the number of non-isolated muons.688 Nmultijet(pT,  , x) = fμ–iso(pT,  ) *   Nfail μ–isodata (pT,  , x)   N fail μ–iso MC (pT,  , x)   . (4) The shape of the multijet background in any kinematic variable, x   {  ,MT, . . .}, is modeled from689 the events in the data with non-isolated muons, with Monte Carlo modeling the other contamination690 subtracted.691 ) [GeV]μ( T p 0 20 40 60 80 100 120 140 : m ul tij et -is o μf 0 0.02 0.04 0.06 0.08 0.1 Inclusive Barrel Crack Endcap ATLAS Internal T etcone20 / p -0.1 0 0.1 0.2 0.3 0.4 0.5 M uo ns / 0. 01 0 200 400 600 800 1000 1200 data 2011 τ τ →Z ν μ →W ν τ →W μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 13: (left) Muon isolation fake factors derived in the multijet control region. (right) The distribution of the muon calorimeter isolation variable etcone20/pT in the multijet control region. Figure 13(left) shows how muon isolation fake factors depend on the pT of the muon. Figure 14692 shows the multijet estimate in the distributions of mT(μ, EmissT ) and d0(μ), after the event preselection,693 where it is 583 ± 5 (stat.) events, or 5% of the expected background. The expected multijet background694 falls to less than 0.02 of an event for events with MT   500 GeV, and it is therefore considered negligible695 in the signal region with MT(μ,  h, EmissT ) > 600 GeV, as is also clearly shown in Figure 15.696 As a cross-check, the normalization of the multijet background was also predicted by fitting the697 muon calorimeter isolation distribution with data-driven templates for isolated and non-isolated muons,698 to extract the multijet normalization. The estimates were found to be consistent and are discussed more699 in Appendix G.4.700 5.5.3 W+jets background701 The dominant background throughout ost of the high-MT tail comes fromW+jets events. It is estimated702 with a data-drive technique using fake factors parameterizing the rate for jets to fake tau identification.703 We select a W(  μ )-rich region of dat (which we call the W+jets control region or W–CR) by704 selecting ev nts which have705 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 49 (e) [GeV] T p 0 50 100 150 200 250 00 350 40 : m ul tij et eis o f 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Inclusive Barrel Endcap ATLAS Internal ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 JetBDTSigMedium JetBDTSigLoose Inclusive SM background multijetATLAS Internal -1dt L = 4.6 fb∫ Figur 27: (left) Electron isolation fake factors derived in the multijet control region. (right) The MT distribution of t expect d multijet background, with predictions for medium (used in the nominal selection), loose, and no jet-tau discrimination, in events with exactly one selected electron, no additi nal preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposit sign e and  h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. The loosen d MT distributi ns are scaled to the integral predicted by the nominal selection, JetBDTSigMedium. Ev en ts / (1 0 G eV ) 0 500 1000 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T (e, ETm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 1 2 El ec tro ns / (0 .0 2 m m ) -110 10 310 510 710 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ (e) [mm]0d -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1o bs . / e xp . 0 1 2 Figure 28: (left) The distribution of the transverse mass of the combination of the selected electron and the EmissT , mT(e, E miss T ). in events with exactly one selected electron, no additional preselected lectrons or m ons, and actly one selected 1-prong tau. (right) The distribution of the electron impact parameter, d0, in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one 1-prong tau candidate (without ID). igure 6.5: (left) Muon isolation ake factors eri e i the multijet control region. (right) The i tion f on calorimete isolati n variable etcone20/pT in the multijet control regio . processes in Monte Carlo. This correction is approximately 5% of the number of isolated muons and2949 n gligible for he number of non-is lated muons.2950 Nmultijet(pT, ⌘, x) = fμ–iso(pT, ⌘) * ⇣ N fail μ–isodata (pT, ⌘, x)   N fail μ–iso MC (pT, ⌘, x) ⌘ . The shape of the multijet background in any kinematic variable, x 2 {  , mtotT , . . .}, is modeled from2951 the events in the data with n-isolated muons, with Monte Carlo modeling the other contamination2952 subtracted.2953 Figure ??(left) shows how muon isolation fake factors depend on the pT of the muon. Figure ??2954 shows the multijet estim te in the distributions of mT(μ, E miss T ) and d0(μ), after the event pre-2955 selection, where it is 583± 5 (stat.) events, or 5% of the expected background. The expected multijet2956 background falls to less than 0.02 of an event for events with MT & 500 GeV, and it is therefore2957 considered negligible in the signal region with MT(μ, ⌧h, E miss T ) > 600 GeV, as is also clearly shown2958 in Figure ??.2959 ig 6.5: Lepton isolation fake factors derived in the ultij t l regi for the μτh channel (left) and the eτh channel (right)[97]. The lepton isolation fake factors are shown in Figure 6.5. The number of multijet events passing l pton isol tion nd event sel ions is predicted by multiplying the number of events that fail isolation but pass all other selection criteria by fake factors binned in pT and η: Nmultijet(pT, η, x) = f`–iso(pT, η) *N fail `–isomultijet (pT, η, x) . The sample of non-isolated leptons in the data is corrected by subtracting the expected contamination of electroweak processes in Monte Carlo: Nmultijet(pT, η, x) = f`–iso(pT, η) * ( N fail `–isodata (pT, η, x)−N fail `–isoMC (pT, η, x) ) . This correction is approximately 3% of the number of isolated muons, 25% of the number of isolated electrons, and negligi le for the number of non-isolated leptons. Since this relation is true, binby-bin, the shape of the multijet background in any kinematic variable, x ∈ {∆φ,mtotT , . . .}, is modeled from the events in the data with non-isolated leptons, with Monte Carlo modeling the other contamination subtracted. Figure 6.6 shows the multijet estimate in the distributions of mT(`, E miss T ) and d0(`), after the event preselection, where it is 583 ± 5 (stat.) events, or 5% of the expected background in the μτh channel, and 766± 22 (stat.) events, or 10% of the expected background in the eτh channel. In Figure 6.6 (bottom-right), tau identification and electron veto requirements are also loosened. After baseline event selection in the μτh channel, the expected multijet background falls to less than 0.02 of an event for events with mtotT & 500 GeV, and it is therefore considered negligibl in the signal region with mtotT (μ, τh, E miss T ) > 600 GeV, as is also shown in Figure 6.7 (left). This method assumes that the ratio of the number of isolated leptons to the number of nonisolated leptons in multijet events is not strongly correlated with the cuts used to enrich the multijet 6.4 search in the `τh channels 171 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 32 Ev en ts / (1 0 G eV ) 0 500 1000 1500 2000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T , Eμ(Tm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 0 1 2 M uo ns / (0 .0 2 m m ) -110 1 10 210 310 410 510 data 2011τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ ) [mm]μ(0d -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1o bs . / e xp . 0 1 2 Figure 14: (left) The distribution of the transverse mass of the combination of the selected muon and the EmissT , mT(μ, E miss T ). (right) The distribution of the muon impact parameter, d0. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau. ) [GeV]missT, Ehτ, μ(TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 510 multijet syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ, μ(TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 510 μ μ →Z syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 15: Plots demonstrating that the multijet and Z ! μμ backgrounds are negligible at high mass. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 49 (e) [GeV] T p 0 50 100 150 200 250 300 35 400 : m ul tij et eis o f 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Inclusive Barrel Endcap ATLAS Internal ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 JetBDTSigMedium JetBDTSigLoose Inclusive SM background multijetATLAS Internal -1dt L = 4.6 fb∫ Figure 27: (left) Electron isolation fake factors derived in the multijet control region. (right) The MT distribution of the expected multijet background, with predictions for medium (used in the nominal selection), loose, and no jet-tau discrimination, in events with exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. The loosened MT distributions are scaled to the integral predicted by the nominal selection, JetBDTSigMedium. Ev en ts / (1 0 G eV ) 0 500 1000 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T (e, ETm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 0 1 2 El ec tro ns / (0 .0 2 m m ) -110 10 310 510 710 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ (e) [mm]0d -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1o bs . / e xp . 0 1 2 Figure 28: (left) The distribution of the transverse mass of the combination of the selected electron and the EmissT , mT(e, E miss T ). in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one selected 1-prong tau. (right) The distribution of the electron impact parameter, d0, in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one 1-prong tau candidate (without ID). Figure 6.6: (left) The distribution of the transverse mass of the combination of the selected lepton and the EmissT , mT(`, E miss T ). (right) The distribution of the impact parameter, d0 of the selected lepton. hese plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau, except the (bottom-right) has the tau id ntification completely remov includi g the elect veto [97]. 172 6. search for high-mass resonances decaying to τ+τ−6. Search for high-mass resonances decaying to ⌧+⌧  187 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 32 Ev en ts / (1 0 G eV ) 0 500 1000 1500 2000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T , Eμ(Tm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 0 1 2 M uo ns / (0 .0 2 m m ) -110 1 10 210 310 410 510 data 2011τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ ) [mm]μ(0d -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1o bs . / e xp . 0 1 2 Figure 14: (left) The distribution of the transverse mass of the combination of the selected muon and the EmissT , mT(μ, E miss T ). (right) The distribution of the muon impact parameter, d0. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau. ) [GeV]missT, Ehτ, μ(TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 510 multijet syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ, μ(TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 510 μ μ →Z syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 15: Plots demonstrating that the multijet and Z   μμ backgrounds are negligible at high mass. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 52 ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (2 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 e e-fake→Z e e + jet-fake→Z SM background e e→Z ATLAS Int rnal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (2 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 EleBDTMedium EleBDTLoose BDTEleScore > 0.3 SM background e e→Z ATLAS Inter al -1dt L = 4.6 fb∫ Figure 30: (left) The MT distribution of the Z   ee modeled with Alpgen Monte Carlo, divided into cases where the reconstructed tau candidate matched a true electron or a jet. (right) The MT distribution of the expected Z   ee background, with predictions for medium (used in the nominal selection), loose, and no electron-veto applied to the hadronic tau candidate. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, E miss T ) < 50 GeV. For the (right), the reconstructed tau candidate is required to match a true Monte Carlo electron. accounts for both W and Z+jets events, since the jet to tau fake rates are consistent within the 20% fake1036 factor systematic uncertainty assumed, as described in Appendix G.5.3.1037 The prediction for the Z   ee background, where an electron fakes the reconstructed hadronic1038 tau, was cross-checked by enriching the statistics in the high-mass tail by relaxing the electron veto in1039 the Monte Carlo. Figure 30(right) shows the distributions of MT in events with the nominal medium1040 electron veto, the loose veto, and with an even looser requirement of BDTEleScore > 0.3, each scaled1041 to the expectation passing medium. The shapes of the loosened distributions are statistically consistent1042 and show that the Z   ee background continues to fall to less than 0.02 events with MT   300 GeV, and1043 is therefore considered negligible in the signal region with MT(e,  h, EmissT ) > 500 GeV and an expected1044 SM background of 1.6 events.1045 6.5.5 Other backgrounds1046 The remaining backgrounds to this channel are estimated with ATLAS full simulation Monte Carlo1047 samples (see Appendix A.2).1048 • Z/  (    ) + jets This process is the largest irreducible background and of the same order as1049 the background from fakes in W/Z+jets events. We estimate it using fully simulated Monte Carlo1050 generated with Alpgen. The Z     Monte Carlo is of su cient size to give only a 4% statistical1051 uncertainty. The dominant systematic uncertainties are 6% on the tau identification e ciency, 14%1052 on the energy scale, and 11% on the generator production cross section, including the uncertainties1053 on both the EW and QCD k-factors discussed in Appendix A.2.3. A more careful discussion of1054 the uncertainty on the tau identification e ciency at high-pT is given in Section 8.3.1055 • t t The background from t t events is sub-dominant throughout the event selection, and is esti-1056 mated with Monte Carlo generated with MC@NLO. The background is well controlled in regions1057 where t t dominates the sample, including at high values of EmissT , and N(jets) (shown in Figures 25,1058 and 118 respectively).1059 i re 6.7: Plots d monstrating that the multijet and Z ! μμ backgrounds ar negligible at high mass. As a cross-check, the normalization of the multijet background was also predicted by fitting2960 the muon calorimeter isolation distribution with data-driven templates for isolated and non-isolated2961 muons, to extract the multijet normalization. The estimates were found to be consistent and are2962 discussed more in Appendix ??.2963 W+jets background2964 The dominant background throughout most of the igh-mtotT tail comes from W + jets events. It is2965 estimated with a data-driven technique using fake factors parameterizing the rate for jets to fake tau2966 identification.2967 We select a W (! μ⌫)-rich region of data (which we call the W+jets control region or W–CR) by2968 selecting events which have2969 • exactly one selected muon,2970 • no additional pre-selected muons or electrons,2971 6. Search for high-mass resonances decaying to ⌧+⌧  185 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 31 The muon isolation fake factor is shown in Figure 13. Then, in the event selection, we predict the number678 of multijet events passing muon isolation by multiplying the number of events that fail isolation by their679 fake factor:680 Nmultijet(pT,  , x) = fμ–iso(pT,  ) * Nfail μ–isomultijet (pT,  , x) . (3) This assumes that the ratio of the number of isolated muons to he number of non-isolated muons in681 multijet events is not strongly correlated with the cuts used to enrich the multijet control sample. This682 assumption was verified with studies that are discussed in Appendix G.4.1, but we allow for a conser-683 vative 100% systematic on the isolation fake factor method, which has negligible e ect on the final684 limit because the multijet background is less than a hundredth of an event. We correct the sample of685 non-isolated muons in the data by subtracting the expected contamination of electroweak processes in686 Monte Carlo. This correction is approximately 5% of the number of isolated muons and negligible for687 the number of non-isolated muons.688 Nmultijet(pT,  , x) = fμ–iso(pT,  ) *   Nfail μ–isodata (pT,  , x)   N fail μ–iso MC (pT,  , x)   . (4) The shape of the multijet background in any kinematic variable, x   {  ,MT, . . .}, is modeled from689 the events in the data with non-isolated muons, with Monte Carlo modeling the other contamination690 subtracted.691 ) [GeV]μ( T p 0 20 40 60 80 100 120 140 : m ul tij et -is o μf 0 0.02 0.04 0.06 0.08 0.1 Inclusive Barrel Crack Endcap ATLAS Internal T etcone20 / p -0.1 0 0.1 0.2 0.3 0.4 0.5 M uo ns / 0. 01 0 200 400 600 800 1000 1200 data 2011 τ τ →Z ν μ →W ν τ →W μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 13: (left) Muo isolation fake actors derived in the multijet control region. (right) The distribution of the muon calorimeter isolation variable etcone20/pT in the multijet control region. Figure 13(left) shows how muon isolation fake factors depend on the pT of the muon. Figure 14692 shows the multijet estimate in the distributions of mT(μ, EmissT ) and d0(μ), after the event preselection,693 where it is 583 ± 5 (stat.) events, or 5% of the expected background. The expected multijet background694 falls to less than 0.02 of an event for events with MT   500 GeV, and it is therefore considered negligible695 in the signal region with MT(μ,  h, EmissT ) > 600 GeV, as is also clearly shown in Figure 15.696 As a cross-check, the normalization of the multijet background was also predicted by fitting the697 muon calorimeter isolation distribution with data-driven templates for isolated and non-isolated muons,698 to extract the multijet normalization. The estimates were found to be consistent and are discussed more699 in Appendix G.4.700 5.5.3 W+jets background701 The dominant background throughout most of the high-MT tail comes fromW+jets events. It is estimated702 with a data-driven technique using fake factors parameterizing the rate for jets to fake tau identification.703 We select a W(  μ )-rich region of data (which we call the W+jets control region or W–CR) by704 selecting events which have705 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 49 (e) [ ]p 5 10 15 200 25 300 350 400 : m ul tij et eis o f 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Inclusive Barrel Endcap ATLAS Internal ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 140 Ev en ts / (5 0 G eV ) -310 -210 -10 1 10 210 310 410 510 610 JetBDTSigMedium JetBDTSigLoose Inclusive SM background multijetATLAS Internal -1dt L = 4.6 fb∫ Figure 27: (left) Electron isolation fake factors derived in the multijet control region. (right) The MT distribution of the expected multijet background, with predictions for medium (used in the nominal selection), loose, and no jet-tau discrimination, in events with exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, EmissT ) < 50 GeV. The loosened MT distributi ns are scaled to the integral predicted by the nominal selection, JetBDTSigMedium. Ev en ts / (1 0 G eV ) 0 500 1000 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T (e, ETm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 0 1 2 El ec tro ns / (0 .0 2 m m ) -110 10 310 510 710 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ (e) [mm]0d -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1o bs . / e xp . 0 1 2 Figure 28: (left) The distribution of the transverse mass of the combination of the selected electron and the EmissT , mT(e, E miss T ). in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one selected 1-prong tau. (right) The distribution of the electron impact parameter, d0, in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one 1-prong tau candidate (without ID). igure 6. : (lef ) Mu isolation fake factors eri e i the multij t control region. (right) The i tion f muon calorimeter isolati n variable etcone20/pT in the multijet control regio . processes in Monte Carlo. This correction is approximately 5% of the number of isolated muons and2949 n gligible for he number of non-isolated muons.2950 Nmultijet(pT, ⌘, x) = fμ–iso(pT, ⌘) * ⇣ N fail μ–isodata (pT, ⌘, x)   N fail μ–iso MC (pT, ⌘, x) ⌘ . The shape of the multijet background in any kinematic variable, x 2 {  , mtotT , . . .}, is modeled from2951 the events in the data with non-isolated muons, with Monte Carlo modeling the other contamination2952 subtracted.2953 Figure ??(left) shows h w mu n isolati n fake factors de en on the pT f the muo . Figure ??2954 shows the multijet estimate in the distributions of mT(μ, E miss T ) and d0(μ), after the event pre-2955 selection, where it is 583± 5 (stat.) events, or 5% of the expected background. The expected multijet2956 background falls to less th n 0.02 of an event for events with MT & 500 GeV, and it is therefore2957 considered negligible in the signal region with MT(μ, ⌧h, E miss T ) > 600 GeV, as is also clearly shown2958 in Figure ??.2959 Figur 6.7: Plots dem strating th t the multijet backgrounds are negligible at high mass for ev nts passing the baseline event selections. (left) The mtotT distribution of the ultijet estimate in μτh channel, showing that the multijet background falls to O(10−2) events for mtotT & 400 GeV. (right) The mtotT distribution of the multijet estimate in eτh channel, with predictions for medium (used in the nominal selection), loose, and no jet-tau discrimination, The loosened mt tT distributions are scaled to the integral predicted by the nominal selection, JetBDTSigMedium. (MT ≡ mtotT ) [97]. control sample. This assumption was justified by studies showing no significant dependence of the isolation fake factors on the thresholds of the mT and d0 cuts [97]. However, the analysis allows for a conservative 100% systematic on the isolation fake-factor method, which has negligible effect on the final limit because t multijet backgro nd is less th n a hund edth of an event (see Table 6.3). In the eτh channel, the multijet background is less clearly neglible than in the μτh channel, but it is still dominated by the Z → ττ and W/Z + jets background and falling quickly to O(0.1) events with mtotT & 500 GeV. The multijet background prediction was cross-checked by enriching the statistics in the high-mass tail by relaxing the tau identification from requiring the medium BDT jet-discriminant used in the selection, to loose, and to the inclusive reconstructed 1-prong taus. The loosened mtotT distributions, shown in Figure 6.7 (right), are scaled to the integral predic ed by the nominal selection, and are consistent in shape as could be expected because the tau identification efficiency and rejection are reasonably flat vs pT for 1-prong candidates 73. The loosened distributions indicate that the multijet mtotT distribution continues to fall to less than 0.1 ev nts with m tot T & 500 GeV, and is therefore considered negligible in the primary signal region with an expected SM background of 1.6 events. The multijet estimate of 0.3±0.3 events from the nominal selection (medium BDT, which turned ut t be th most cons rva ive) is used for the secondary signal region of mtotT > 400 GeV. The multije background w s also cross-checked with a combined e timate of the W/Z + jets and the multijet backgrounds, using a single fake factor for tau identification, discussed in the following 73 See Figure 4.27 in Section 4.4.7. 6.4 search in the `τh channels 173 sub-section. W+jets background The dominant background throughout most of the high-mtotT tail comes from W + jets events. It is estimated with a data-driven technique using fake factors parameterizing the rate for jets to fake tau identification, similar to the lepton-isolation fake-factor method used to estimate the multijet background. Fundamentally, using a data-driven method to predict the rate of fake hadronic tau decays is necessary for the same reason the kW scale factor was needed to correct normalization of the W + jets MC in the Z → ττ cross section measurement discussed in Section 5.7.2, because the rate of jets faking tau identification is mis-modeled in Monte Carlo74 The larger dataset in 2011 allows one to make a tau-by-tau correction, binned in pT and η. Moreover, building the model from the events failing identification populates the tail of the background model with high-mass events from data, that typically outnumber the contribution of that background to the signal region because more events fail the tau identification or lepton isolation than pass. A W + jets rich region of data can be selected by requiring high mT for the lepton-E miss T combination75 The W+jets control region (or W–CR) is defined by selecting events which have • exactly one selected muon, • no additional preselected muons or electrons, • at least one preselected hadronic tau candidate, • mT(`, EmissT ) = 70–200 GeV, The preselected tau candidates in this region are divided into two categories: those that pass the medium BDT tau identification, and those that fail. A fake factor fτ for hadronic tau identification is defined as the number of tau candidates that pass divided by the number that fail identification, binned in pT and η: fτ (pT, η) ≡ Npass τ−ID(pT, η) N fail τ−ID(pT, η) ∣∣∣∣ W–CR . The tau identification fake factors are shown in Figure 6.8. To predict the number of W+jet events passing tau identification and event selection, the W+jet events that fail tau identification are weighted by their fake factor: NW+jet(pT, η, x) = fτ (pT, η) *N fail τ−IDW+jet (pT, η, x) , 74 The tau identification fake rate for jets is mis-modeled, ultimately because jets are slightly more wide in data than in the simulation. See the discussion in Section 4.4.1. 75 As shown in Figure 6.7, which shows the W + jets peak at high mT in the sample passing tau identification. It is O(10) times larger in the sample failing tau identification. 174 6. search for high-mass resonances decaying to τ+τ− N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 34 !"#$%& !"#$%&#'()*+( ,-.#&%$.&#$-. !"#$%&#' /01'#" ,-.#&%2 $.&#$-. !"#$%&#'()*+( ,-.#&%$.&#$-. '(#&"#")&(*+,-(./*01$.%2"$%."1$ '(#&"#")&(*+,-(./*01$.%2"$%."1$'1$3$(#&"#")&(*456*01$.%2"$%."1$ 7%//*.%8*96 7%//*&(:.1$*"/1 !"#$%&"'%() 7%//*&(:.1$*"/1 7%//*.%8*96 !"#$%$*+&,-%#., !"#$%&"'%() !"#$%$*+&,-%#., Figure 16: A diagram illustrating the combined use of the two data-driven methods to predict the multijet and W+jets backgrounds. First, the multijet contamination is estimated from the rate of non-isolated leptons in both the signal sample that passes tau identification, and the sample that fails. Then, the corrected number of tau candidates failing identification is weighted to predict the W+jets background. ) [GeV]hτ(Tp 0 50 100 150 200 250 ) hτ, μ )+ je ts , O S( ν μ → : W ( τ f 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Inclusive Barrel (inner) Barrel (outer) Endcap ATLAS Internal Figure 17: Tau identification fake factors derived in the W(! μ!) control region. The binning in " is defined as inner barrel: |"| < 0.8, outer barrel: 0.8 < |"| < 1.37, crack: 1.37 < |"| < 1.52, and end-cap: 1.52 < |"| < 2.47. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 51 Figure 16 in Section 5.5.3 summarizes the procedure for the data-driven background estimates. First,1007 the multijet contamination is estimated from the rate of anti-isolated electrons in both the sample that1008 passes tau identification, and the sample that fails tau identification, using the method described in Sec-1009 tion 6.5.2. Then, the corrected number of tau candidates failing identification is weighted to predict the1010 W/Z+jets background. Figure 29 shows how the tau fake factors depend on pT and !.1011 ) [GeV]hτ(Tp 0 50 100 150 200 250 ) hτ )+ je ts , O S( e, ν e → : W ( τ f 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Inclusive Barrel (inner) Barrel (outer) Endcap ATLAS Internal Figure 29: Tau identificat fake factors derived in the W(! e") control region. The binning in ! is defined as inner barrel: |!| < 0.8, outer barrel: 0.8 < |!| < 1.37, crack: 1.37 < |!| < 1.52, and end-cap: 1.52 < |!| < 2.47. Figure 28 shows the normalization of the W/Z+jets estimate in the distribution of mT(e, EmissT ) after1012 event preselection, showing a modeling that is consistent with the estimates of multijet, Z ! ##, and1013 other backgrounds. An advantage of the fake factor method is that there is typically a larger sample1014 of tau candidates that fail tau identification than those that pass, however, the statistical uncertainty1015 (43%) from the count of candidates failing tau identification in the data in the signal region, remains1016 the dominant uncertainty for this background. The W/Z+jets background has a 30% total systematic1017 uncertainty coming from the sum in quadrature of a 20% systematic uncertainty on the consistency of1018 the fake factor between the signal region and theW+jet control region where it was measured (discussed1019 in Appendix H.4), and a 22% statistical uncertainty on the count of high-pT events in the W+jet control1020 region.1021 The W/Z+jets background was also cross-checked with a combined estimate of the W/Z+jets and1022 multijet backgrounds, discussed in Appendix H.5.1023 6.5.4 Z ! ee background1024 Figure 30(left) shows that the Z ! ee background where an electron fakes the tau candidate peaks at1025 the Drell-Yan distribution and falls quickly at high mass. The case where a jet fakes the tau candidate1026 has a longer tail in MT, but is sub-dominant to the case of electrons faking the hadronic tau candidate.1027 Throughout Section 6 discussing the e#h channel, plots illustrating the Z ! ee background are showing1028 the distributions for events with tau candidates matched to true Monte Carlo electrons, unless otherwise1029 noted.1030 The small contribution of Z ! ee+jets events where a jet fakes the hadronic tau candidate are mod-1031 eled with tau fake factors with the same method used to predict the W+jets background, as discussed1032 in the previous section. When deriving the W/Z+jets estimate, the subtraction of other contaminating1033 processes discussed in Section 6.5.3, includes only the Z ! ee events where the reconstructed tau candi-1034 date is matched to a true Monte Carlo electron. The resulting data-driven estimate with tau fake-factors1035 Figure 6.8: Tau identifica ion fake factors derived in the W + jets control region. The binning in η is defined as inner barrel: |η| 0.8, outer barrel: 0.8 < |η| < 1.37, crack: 1.37 < |η| < 1.52, and end-cap: 1.52 < |η| < 2.47 [97]. where x is any kinematic variable (∆φ,mtotT , . . .). The sample of failing tau candidates in the data w s c rrected for conta ination from other electroweak processes as well as from multijet events: NW+jet(pT, η, x) = fτ (pT, η) * ( N fail τ−IDdata (pT, η, x)−N fail τ−IDmultijet (pT, η, x)−N fail τ−IDMC (pT, η, x) ) . The multijet contamination is estimated using the lepton-isolation fake-factor method described in the previous sub-section. The shape of the W + jets background in any kinematic variable, x, is modeled from the events in the data tha failed ta identification, wit the multijet estimat and Monte Carlo modeling of the other contamination subtracted. Figure 6.9 illustrates the procedure for the data-driven background estimates. First the multijet contamination is estimated from the rate of non-isolated muons in both the sample that passes tau identification, and the sample that fails tau identification. Then the corrected number of tau candidates failing identification is weighted to predict the W + jets background. This method assumes the tau identification fake factor is not strongly correlated with the cuts used to enrich the W + jets control sample where they were measured. This assumption was justified by studies showing no significant dependence of the fake factors on the thresholds of the mT cuts (see Figure 6.10). Also, the Alpgen W + jets Monte Carlo does not show a strong dependence of the generator-level quark-gluon fraction that would cause a sampl dependence of th fake factor, as shown in the plots of the true quark-gluon fraction in MC in Figure 4.36. Figure 6.6 shows the normalization of the W + jets estimate in the distribution of mT(μ,E miss T ) after event preselection, showing a modeling that is consistent with the estimates of multijet, Z → ττ , and other backgrounds. An advantage of the fake-factor method is the larger sample of tau candidates that fail tau identification than those that pass, however, the statistical uncertainty (71%) 6.4 search in the `τh channels 175 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 34 !"#$%& !"#$%&#'()*+( ,-.#&%$.&#$-. !"#$%&#' /01'#" ,-.#&%2 $.&#$-. !"#$%&#'()*+( ,-.#&%$.&#$-. '(#&"#")&(*+,-(./*01$.%2"$%."1$ '(#&"#")&(*+,-(./*01$.%2"$%."1$'1$3$(#&"#")&(*456*01$.%2"$%."1$ 7%//*.%8*96 7%//*&(:.1$*"/1 !"#$%&"'%() 7%//*&(:.1$*"/1 7%//*.%8*96 !"#$%$*+&,-%#., !"#$%&"'%() !"#$%$*+&,-%#., Figure 16: A diagram illustrating the combined use of the two data-driven methods to predict the multijet and W+jets backgrounds. First, the multijet contamination is estimated from the rate of non-isolated leptons in both the signal sample that passes tau identification, and the sample that fails. Then, the corrected number of tau candidates failing identification is weighted to predict the W+jets background. ) [GeV]hτ(Tp 0 50 100 150 200 250 ) hτ, μ )+ je ts , O S( ν μ → : W ( τ f 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Inclusive Barrel (inner) Barrel (outer) Endcap ATLAS Internal Figure 17: Tau identification fake factors derived in the W(! μ!) control region. The binning in " is defined as inner barrel: |"| < 0.8, outer barrel: 0.8 < |"| < 1.37, crack: 1.37 < |"| < 1.52, and end-cap: 1.52 < |"| < 2.47. Figure 6.9: A diagram illustrating the combined use of the two data-driven methods to predict the multijet and W + jets backgrounds. First, the multijet contamination is estimated from the rate of non-isolated leptons in both the signal sample that passes tau identification, and the sample that fails. Then, the corrected number of tau candidates failing identification is weighted to predict the W + jets background. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 143 ) [GeV]miss T , Eμ(Tm 0 20 40 60 80 100 120 140 160 180 200 Ev en ts / (1 0 G eV ) 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 data 2011 τ τ →Z multijet μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 50 100 150 200 250 ) hτ )+ je t, O S( l, ν l → : W ( τ f 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 ) > 50 GeVmiss T (l, ETm ) > 60 GeVmiss T (l, ETm ) > 70 GeVmiss T (l, ETm ) > 80 GeVmiss T (l, ETm ) > 90 GeVmiss T (l, ETm Figure 89: (left) The distribution of mT(μ, EmissT ) near the W+jets control region, before applying a cut of mT(μ, EmissT ) > 70 GeV. (right) Tau identification fake factors with various mT(!, E miss T ) cuts applied in the W(! !")+jets control region. A cut of mT(!, EmissT ) > 70 GeV defines the W(! !")+jets control region. Within statistical error, the fake factor does not vary significantly as the cut on mT(!, EmissT ) is varied. ) [GeV]missT, Ehτ, μ(TM 0 50 100 150 200 250 300 350 400 Ev en ts / (1 0 G eV ) 0 200 400 600 800 1000 data 2011 τ τ →Z multijet μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140 Ta u Ca nd id at es / (5 G eV ) 0 500 1000 1500 2000 2500 3000 data 2011 τ τ →Z multijet μ μ →Z tt diboson single top syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 90: (left) The distribution of MT(μ, #h, EmissT ) after event preselection, with tau identification inverted and fake factor weighting applied. (right) The distribution of the transverse momentum of the selected hadronic tau after event preselection, with tau identification inverted and fake factor weighting applied. i re 6.10: (left) The distribution of m (μ,EmissT ) near the W + jets c trol region, before applying a cut of mT(μ,E miss T ) > 70 GeV. (right) T u iden ificat on f ke factors derived from mo ified control regions with various mT(μ,E miss T ) cuts applied, showing that the fake factors d not have a strong dependenc on mT(μ,E miss T ) [97]. 176 6. search for high-mass resonances decaying to τ+τ− from the count of candidates failing tau identification in the data in the high-mass signal region, remains the dominant uncertainty for this background. The W + jets background has a 30% total systematic uncertainty coming from the sum in quadrature of a 20% systematic uncertainty on the consistency of the fake factors measured in the W + jets control region and a control region Z + jets events, added with a 20% statistical uncertainty on the count of high-pT events in the W+jet control region [97]. Single-fake-factor method The W/Z + jets background was also cross-checked with a combined estimate of the W/Z + jets and the multijet backgrounds, using a single fake factor for tau identification. One might have estimated the background from all fake hadronic tau candidates, from both multijet and W/Z + jets events, with a fake factor applied to tau candidates, without estimating the multijet background independently and subtracting it. If one estimates the combined fake backgrounds with a single76 set of tau identification fake factors from the W + jets control region, this should over-predict the background in regions where the multijet contamination is significant, since multijet events have a higher gluon-fraction which lowers the tau identification fake rate. This single-fake-factor method77 should improve at higher-pT(τh), where the quark-fraction increases, and the fake factors forW + jets and multijet events become more similar78. Figures 6.11 (top) show that as expected, the low-mtotT and low-pT(τh) part of the distribution is over-estimated, due to the significant multijet contribution, and the estimate improves at higher mass. Figure 6.11 (bottom) compares the high-mass parts of the mtotT distributions using the nominal ("double fake factor") estimate described above, and using the single-fake-factor estimate. The single-fake-factor method provides a cross-check for the eτh channel, that avoids the coupling of the estimates of the multijet and W/Z + jets backgrounds in the contamination subtraction that is done. The predictions are consistent and are summarized in Table 6.5. Z/γ∗(→ ``) + jets background In the μτh channel, the Z + jets background is steeply falling in m tot T and negligible at high-m tot T in either case where a jet or a lepton fakes the tau candidate as estimated with Monte Carlo generated with Alpgen (see Figure 6.12). 76 As opposed to using both W + jets tau fake factors and multijet isolation fake factors (or another multijet estimate). This effectively means that the right-side of the diagram in Figure 6.9 is ignored, and that the multijet contamination is not separately corrected for, but instead is covered with tau identification fake factors. 77 A recent ATLAS Higgs search with taus does a similar estimate of the backgrounds with fake hadoric tau candidates [226]. In that method, fake factors appropriate for multijet and W/Z + jets are mixed to give a single set of fake factors. For this method, only the W/Z + jets fake factor is used. 78 Recall from Figures 4.31 and 4.36, that the tau identification fake factors derived in W + jets and multijet control regions become more similar, ultimately because they get more quark-enriched. 6.4 search in the `τh channels 177 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 158 pT part of the distribution is over-estimated, due to the significant multijet contribution, and the estimate2401 improves at higher mass. Figure 113 compares the high-mass parts of the MT distributions of the nominal2402 ("double fake factor") estimate and the single fake factor estimate.2403 Ev en ts / (1 0 G eV ) 0 20 40 60 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ Bl in de d ) [GeV]missT, Ehτ(e, TM 0 50 100 150 200 250 300 350 400o bs . / e xp . 0 1 2 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ Bl in de d ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400o bs . / e xp . 0 1 2 Figure 111: The distribution of MT(e, !h, EmissT ) for the single fake factor estimate, in events with: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!"(e, !h)| > 2.7, opposite sign e and !h, and EmissT > 30 GeV. Ta u C an di da te s / ( 5 G eV ) 0 20 40 60 80 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ Bl in de d ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 112: The distribution of pT(!h) for the single fake factor estimate, in events with: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1prong tau, |!"(e, !h)| > 2.7, opposite sign e and !h, and EmissT > 30 GeV. The single fake factor method provides a cross-check that avoids the coupling of the estimates of the2404 multijet and W/Z+jets backgrounds in the contamination subtraction that is done. The predictions are2405 consistent and are summarized in Table 45.2406 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 158 pT part of the distribution is over-estimated, due to the significant multijet contribution, and the estimate2401 improves at higher mass. Figure 113 compares the high-mass parts of the MT distributions of the nominal2402 ("double fake factor") estimate and the single fake factor estimate.2403 Ev en ts / (1 0 G eV ) 0 20 40 60 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ Bl in de d ) [GeV]missT, Ehτ(e, TM 0 50 100 150 200 250 300 350 400o bs . / e xp . 0 1 2 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ Bl in de d ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400o bs . / e xp . 0 1 2 Figure 111: The distribution of MT(e, !h, EmissT ) for the single fake factor estimate, in events with: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!"(e, !h)| > 2.7, opposite sign e and !h, and EmissT > 30 GeV. Ta u C an di da te s / ( 5 G eV ) 0 20 40 60 80 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]hτ(Tp 0 20 40 60 80 100 120 140o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) -110 1 10 210 310 410 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ Bl in de d ) [GeV]hτ(Tp 0 100 200 300 400 500 600o bs . / e xp . 0 1 2 Figure 112: The distribution of pT(!h) for the single fake factor estimate, in events with: exactly one s ed electron, no additional pr selected electrons or muons, exactly one selected 1prong tau, |!"(e, !h)| > 2.7, opposite sign e and !h, and EmissT > 30 GeV. The single fake factor method provides a cross-check that avoids the coupling of the estimates of the2404 multijet and W/Z+jets backgrounds in the contamination subtraction that is done. The predictions are2405 consistent and are summarized in Table 45.2406 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 159 Ev en ts / (2 0 G eV ) 0 5 10 15 data 2011 τ τ →Z W/Z+jets multijet e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ(e, TM 200 250 300 350 400 450 500 550 600o bs . / e xp . 0 1 2 Ev en ts / (2 0 G eV ) 0 5 10 15 data 2011 τ τ →Z hτfake e e→Z tt γW diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ Bl in de d ) [GeV]missT, Ehτ(e, TM 200 250 300 350 400 450 500 550 600o bs . / e xp . 0 1 2 Figure 113: MTdistributions for the nominal "double fake factor" estimate (left), and the single fake factor estimate (right), in events with: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |!!(e, "h)| > 2.7, opposite sign e and "h, and EmissT > 30 GeV. H.6 Sources of fake hadronic taus for systematics2407 Table 46 shows the fraction of tau candidates coming from true jets, electrons, and hadronic tau decays2408 in the SM background modeled with Monte Carlo. The systematic uncertainti s on the hadronic tau2409 e"ciency, jet to tau fake rate, and electron to tau fake rate (discussed in Section 8) are applied on the2410 correspo ding fraction that is truth-matched in the Monte Carlo.2411 double fake factor single fake factor W/Z+jets multijet total fake "h MT > 400 GeV 0.8(6) 0.3(3) 1.1(4) 1.3(4) MT > 500 GeV 0.8(4) < 0.1 0.8(4) 0.9(4) Table 45: Comparison of estimates of the fake hadronic tau background. Figure 6.11: Kinematic distributions for events passing the eτh baseline event selection, comparing estimates of the fake backgrounds with the nominal double-fake-factor method and the single-fake-factor method. The distribution of m otT (e, τh, E miss T ) (top-left) and pT(τh) (top-right) using the single-fake-factor method. The high-mass tail of the m tot T distribution using the nominal double-fake-factor method (bottom-left) and the singlefake-factor method (bottom-right) (MT ≡ mtotT ) [97]. The "Fake τh" estimate is meant to cover fake hadronic tau decays from W + jets and multijet events. Because it uses a tau fake factor derived in a W + jets sample, which is rich in quark-initiated jets, the fake estimate should over estimate the multijet contribution, which is more gluon-rich. Table 6.5: Comparison of estimates of the fake hadronic tau background for the eτh channel, showing the nominal fake background estimate (double fake factor) and the single-fake-factor method [97]. double fake factor single fake factor W/Z + jets multijet total fake τh mtotT > 400 GeV 0.8(6) 0.3(3) 1.1(4) 1.3(4) mtotT > 500 GeV 0.8(4) < 0.1 0.8(4) 0.9(4) 178 6. search for high-mass resonances decaying to τ+τ−6. Search for high-mass resonances decaying to ⌧+⌧  187 N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 32 Ev en ts / (1 0 G eV ) 0 500 1000 1500 2000 data 2011 τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]miss T , Eμ(Tm 0 20 40 60 80 100 120140 160 180 200o bs . / e xp . 0 1 2 M uo ns / (0 .0 2 m m ) -110 1 10 210 310 410 510 data 2011τ τ →Z W+jets multijet μ μ →Z tt diboson single top syst.⊕stat. Z'(750) Z'(1000) Z'(1250) ATLAS Internal-1dt L = 4.6 fb∫ ) [mm]μ(0d -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1o bs . / e xp . 0 1 2 Figure 14: (left) The distribution of the transverse mass of the combination of the selected muon and the EmissT , mT(μ, E miss T ). (right) The distribution of the muon impact parameter, d0. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau. ) [GeV]missT, Ehτ, μ(TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 510 multijet syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ, μ(TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (5 0 G eV ) -110 1 10 210 310 410 510 μ μ →Z syst.⊕stat. ATLAS Internal -1dt L = 4.6 fb∫ Figure 15: Plots demonstrating that the multijet and Z   μμ backgrounds are negligible at high mass. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 52 ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (2 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 e e-fake→Z e e + jet-fake→Z SM background e e→Z ATLAS Int rnal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (2 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 EleBDTMedium EleBDTLoose BDTEleScore > 0.3 SM background e e→Z ATLAS Inter al -1dt L = 4.6 fb∫ Figure 30: (left) The MT distribution of the Z   ee modeled with Alpgen Monte Carlo, divided into cases where the reconstructed tau candidate matched a true electron or a jet. (right) The MT distribution of the expected Z   ee background, with predictions for medium (used in the nominal selection), loose, and no electron-veto applied to the hadronic tau candidate. These plots include the requirements of: exactly one selected electron, no additional preselected electrons or muons, exactly one selected 1-prong tau, |  (e,  h)| > 2.7, opposite sign e and  h, EmissT > 30 GeV, and mT(e, E miss T ) < 50 GeV. For the (right), the reconstructed tau candidate is required to match a true Monte Carlo electron. accounts for both W and Z+jets events, since the jet to tau fake rates are consistent within the 20% fake1036 factor systematic uncertainty assumed, as described in Appendix G.5.3.1037 The prediction for the Z   ee background, where an electron fakes the reconstructed hadronic1038 tau, was cross-checked by enriching the statistics in the high-mass tail by relaxing the electron veto in1039 the Monte Carlo. Figure 30(right) shows the distributions of MT in events with the nominal medium1040 electron veto, the loose veto, and with an even looser requirement of BDTEleScore > 0.3, each scaled1041 to the expectation passing medium. The shapes of the loosened distributions are statistically consistent1042 and show that the Z   ee background continues to fall to less than 0.02 events with MT   300 GeV, and1043 is therefore considered negligible in the signal region with MT(e,  h, EmissT ) > 500 GeV and an expected1044 SM background of 1.6 events.1045 6.5.5 Other backgrounds1046 The remaining backgrounds to this channel are estimated with ATLAS full simulation Monte Carlo1047 samples (see Appendix A.2).1048 • Z/  (    ) + jets This process is the largest irreducible background and of the same order as1049 the background from fakes in W/Z+jets events. We estimate it using fully simulated Monte Carlo1050 generated with Alpgen. The Z     Monte Carlo is of su cient size to give only a 4% statistical1051 uncertainty. The dominant systematic uncertainties are 6% on the tau identification e ciency, 14%1052 on the energy scale, and 11% on the generator production cross section, including the uncertainties1053 on both the EW and QCD k-factors discussed in Appendix A.2.3. A more careful discussion of1054 the uncertainty on the tau identification e ciency at high-pT is given in Section 8.3.1055 • t t The background from t t events is sub-dominant throughout the event selection, and is esti-1056 mated with Monte Carlo generated with MC@NLO. The background is well controlled in regions1057 where t t dominates the sample, including at high values of EmissT , and N(jets) (shown in Figures 25,1058 and 118 respectively).1059 i re 6.7: Plots d monstrating that the multijet and Z ! μμ backgrounds ar negligible at high mass. As a cross-check, the normalization of the multijet background was also predicted by fitting2960 the muon calorimeter isolation distribution with data-driven templates for isolated and non-isolated2961 muons, to extract the multijet normalization. The estimates were found to be consistent and are2962 discussed more in Appendix ??.2963 W+jets background2964 The dominant background throughout most of the igh-mtotT tail comes from W + jets events. It is2965 estimated with a data-driven technique using fake factors parameterizing the rate for jets to fake tau2966 identification.2967 We select a W (! μ⌫)-rich region of data (which we call the W+jets control region or W–CR) by2968 selecting events which have2969 • exactly one selected muon,2970 • no additional pre-selected muons or electrons,2971 Figure 6.12: The distribution of mtotT (μ, τh, E miss T ) for the Z → μμ background of the μτh channel. The Z → μμ background is negligible at high mtotT , falling to 0.1 events with mtotT & 400 GeV compared to a total expected SM background of 15± 1 events. (MT ≡ mtotT ) [97]. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 52 ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (2 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 e e-fake→Z e e + jet-fake→Z SM background e e→Z ATLAS Internal -1dt L = 4.6 fb∫ ) [GeV]missT, Ehτ(e, TM 0 200 400 600 800 1000 1200 1400 Ev en ts / (2 0 G eV ) -310 -210 -110 1 10 210 310 410 510 610 EleBDTMedium EleBDTLoose BDTEleScore > 0.3 SM background e e→Z ATLAS Internal -1dt L = 4.6 fb∫ Figure 30: (left) The MT distribution of the Z ! ee modeled with Alpgen Monte Carlo, divided into cases where the reconstructed tau candidate matched a true electron or a jet. (right) The MT distribution of the expected Z ! ee background, with predictions for medium (used in the nominal selection), loose, and no electron-veto applied to the hadronic tau candidate. These plots include the requirements of: exactly one selected electron, no additional preselected ele trons or muons, exactly one sele ted 1-prong tau, |!!( , "h)| > 2.7, opposite sign e and "h, EmissT > 30 GeV, and mT(e, E miss T ) < 50 GeV. For the (right), the reconstructed tau candidate is req ired to match a true M te Carlo electron. accounts for both W and Z+jets events, si c the jet to tau fake rates re consistent within the 20% fake1036 f ctor systematic uncertainty assumed, as described in App ndix G.5.3.1037 The pr diction f r t e Z ! ee backgro nd, where an electron fakes the reconstructed hadronic1038 tau, was cross-checked by enriching the statistics in the high-mass tail by relaxing the electron veto in1039 the Monte Carlo. Figure 30(right) shows the distributions of MT in events with the nominal medium1040 electron veto, the loose veto, and with an even looser requirement of BDTEleScore > 0.3, each scaled1041 to the expectation passing medium. The shapes of the loosened distributions are statistically consistent1042 and show that the Z ! ee background continues to fall to less than 0.02 events with MT ! 300 GeV, and1043 is therefore considered negligible in the signal region with MT(e, "h, EmissT ) > 500 GeV and an expected1044 SM background of 1.6 events.1045 6.5.5 Other backgrounds1046 The remaining backgrounds to this channel are estimated with ATLAS full simulation Monte Carlo1047 samples (see Appendix A.2).1048 • Z/!!(" "") + jets This process is the largest irreducible background and of the same order as1049 the background from fakes in W/Z+jets events. We estimate it using fully simulated Monte Carlo1050 generated with Alpgen. The Z ! ""Monte Carlo is of su"cient size to give only a 4% statistical1051 uncertainty. The dominant systematic uncertainties are 6% on the tau identification e"ciency, 14%1052 on the energy scale, and 11% on the generator production cross section, including the uncertainties1053 on both the EW and QCD k-factors discussed in Appendix A.2.3. A more careful discussion of1054 the uncertainty on the tau identification e"ciency at high-pT is given in Section 8.3.1055 • t t The background from t t events is sub-dominant throughout the event selection, and is esti-1056 mated with Monte Carlo generated with MC@NLO. The background is well controlled in regions1057 where t t dominates the sample, including at high values of EmissT , and N(jets) (shown in Figures 25,1058 and 118 respectively).1059 i 6.13: Plots demonstrating that the Z → e backgrou is egli ibl at high mass for events passing the eτh baseline event selection. (left) The m tot T distribution of the Z → ee modeled with Alpgen Monte Carlo, divided into cases where the reconstructed tau candidate matched a true electron or a jet. (right) The mtotT distribution of the expected Z → ee background, with predictions for medium (used in the nominal selection), loose, and no electron-veto applied to the hadronic tau candidate. For the (right), the reconstructed tau candidate is required to match a true Monte Carlo electron [97]. In the eτh channel, it was recognized that the Z + jets background is dominated by events where one of the elec ro s fr m Z → ee fak s the tau candidate, and results in a background with low mtotT near the Z m ss. The ontribution from Z + jets with a jet faking the tau candidate is small, being O(1%) of the Z + jets background (see Figure 6.13 (left)). The Monte Carlo estimate was filtered for eve ts wher the tau candi ate is matched to a true lectron, so that jet fake contribution is covered by the data-driven W + jets tau fake factor estimate. 6.4 search in the `τh channels 179 The prediction for the Z → ee background, where an electron fakes the reconstructed hadronic tau decay, was cross-checked by enriching the statistics in the high-mass tail by relaxing the electron veto in the Monte Carlo. Figure 6.13 (right) shows the distributions of mtotT in events with the nominal medium electron veto, the loose veto, and with an even looser requirement of BDTEleScore > 0.3, each scaled to the expectation passing medium. The shapes of the loosened distributions are statistically consistent and show that the Z → ee background continues to fall to less than 0.02 events with mtotT & 300 GeV, and is therefore considered negligible in the signal region with mtotT (e, τh, E miss T ) > 500 GeV and an expected SM background of 1.6 events. Other backgrounds The remaining backgrounds to this channel are estimated with ATLAS full simulation Monte Carlo samples. • Z/γ∗(→ ττ ) + jets This process surpasses W+jets as the largest background for events with mtotT & 600 GeV. We estimate it using fully simulated Monte Carlo generated with Alpgen. The samples are binned in the number of additional hard final-state partons (NpX), and binned in the true ditau mass. The available statistics in low-mass, low-NpX samples are up to 10M events, decreasing to 20k events in the high-mass, high-NpX samples, sufficient to give only a 5% statistical uncertainty on this background. While data-driven methods are used to estimate some of the other backgrounds with fake hadronic taus, the Monte Carlo scale factor for tau identification of real taus is consistent with 1.0 (see Section 4.4.6), which justifies using a Monte Carlo based estimate without additional corrections. • tt and single top While subdominant throughout the cutflow, the background from topquark events is of the same order as the W+jets and Z/γ∗(→ ττ) backgrounds in the high mtotT (`, τh, E miss T ) signal region, and is estimated with Monte Carlo generated with MC@NLO for tt and AcerMC for single top events. The background is well normalized in control regions in regions where tt dominates the sample, including at high values of EmissT , mT(μ,E miss T ), and N(jets)79. • Diboson This background is small compared to the total background and is estimated with Monte Carlo generated with MC@NLO. 79 See in EmissT plots in Figures 6.1 and 6.3 and the additional plots in Ref. [97]. 180 6. search for high-mass resonances decaying to τ+τ− 6.5 Search in the τhτh channel 6.5.1 Triggering In the τhτh channel, events are triggered by either a ditau trigger with pT thresholds of 20 and 29 GeV, or a single-tau trigger with pT > 125 GeV. 6.5.2 Object selection Selected tau candidates in the τhτh channel must have pT > 50 GeV, pass the loose BDT identification, have one or three tracks and a charge magnitude of one. At least two selected taus are required in the event. If more than two are found, the two leading pT selected taus are chosen to be used in the analysis. 6.5.3 Event selection Events are selected which have two loosely identified hadronic tau decays with pT > 50 GeV that have opposite-signed charges, and ∆φ > 2.7, where ∆φ is the angle between the reconstructed tau decays in the transverse plane. Events are vetoed that have any preselected electrons or muons, as described in Section 6.3. The total transverse mass of the combination of the two tau decays and the EmissT , m tot T , is calculated, and shown in Figure 6.14. High-m tot T signal regions are optimized as a function of the mass of the Z ′ signal, shown in Table 6.6. 6.5.4 Background estimation The two main backgrounds are multijet and Z → ττ . The contribution from Z → ττ is irreducible and taken directly from simulation, as the tau identification efficiency is well-modeled with Monte Carlo. The multijet background shape is estimated from a fit to data in the high purity same-sign control region, and normalized in a side band of mtotT . The other backgrounds make very minor contributions and are estimated directly from simulation. Table 6.6: Mass-dependent cuts on mtotT for different Z ′ signal masses [97]. SSM Z ′ mass [GeV] 500 625 750 875 1000 1125 1250 τhτh channel 350 400 500 500 625 625 700 μτh channel 400 400 500 500 600 600 600 eτh channel 400 400 400 500 500 500 500 eμ channel 300 350 350 350 500 500 500 6.6 systematic uncertainties 181 ) [GeV]missTE, had-visτ, had-visτ(totTm 0 500 1000 1500 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs (a) Data 2011 Multijet ττ→*γ/Z ντ→W Others ττ→(1250)Z' ) [GeV]missTE, had-visτ, μ(totTm 0 500 1000 1500 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs (b) Data 2011 ττ→*γ/Z +jetsW Multijet μμ→Z tt Diboson Single top ττ→(1000)Z' ) [GeV]missTE, had-visτ, e(totTm 0 500 1000 1500 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs (c) Data 2011 ττ→*γ/Z +jetsZ/W Multijet ee→Z tt Diboson Single top ττ→(1000)Z' ) [GeV]missTE, μ, e(totTm 0 500 1000 1500 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs (d) Data 2011 ττ→*γ/Z Diboson μμ→Z tt +jetsW ττ→(750)Z' Figure 1: The mtotT distribution after event selection in each channel: (a) !had!had, (b) !μ!had, (c) !e!had and (d) !e!μ. The estimated contributions from SM processes are stacked and appear in the same order as in the legend. A Z!SSM signal and the events observed in data are overlaid. The signal mass point closest to the Z!SSM exclusion limit in each channel is chosen and is indicated in parentheses in the legend in units of GeV. The uncertainty on the total estimated background (hatched) includes only the statistical uncertainty from the simulated samples. The visible decay products of hadronically decaying taus are denoted by !had-vis. mZ! 500 625 750 875 1000 1125 !1250 !had!had 350 400 500 500 625 625 700 !μ!had 400 400 500 500 600 600 600 !e!had 400 400 400 500 500 500 500 !e!μ 300 350 350 350 500 500 500 Table 1: Thresholds on mtotT used for each signal mass point in each channel. All values are given in GeV. contribution comes from W (! !")+jets. Contributions from Z(! ##)+jets (# = e or μ), W (! #")+jets, tt, single top-quark and diboson production are collectively referred to as others. The shape of the multijet mass distribution is estimated from data that pass the full event selection but have two tau candidates of the same electric charge. The contribution is normalised to events that pass the full event selection but have low mtotT . All other background contributions are estimated from simulation. The main background contributions in the !lep!had channels come from Z/$! ! !! , W+jets, tt and diboson production, with minor contributions from Z(! ##)+jets, multijet and single top-quark events. The contributions involving fake hadronic tau decays from multijet and W+jets events are modelled with data-driven techniques involving fake factors, which parameterise the rate for lepton candidates in jets to pass lepton isolation or jets to pass tau identification, respectively. The remaining background is estimated using simulation. The dominant background processes in the !e!μ channel are tt, Z/$! ! !! and diboson production. Contributions from processes such as Z(! μμ)+jets, W+jets and W$+jets, where a jet or photon is misidentified as 4 Figure 6.14: The mtotT (τh, τh, E miss T ) distribution for the τhτh channel after the full selection (excluding the final mtotT window). The estimated contributions from SM processes and Z ′SSM signal are stacked and theobserved events in data are overlayed. The uncertainty on the data/MC ratio includes only the statistical uncertainty from the data and the MC simulated samples, while the uncertainty on the multijet contribution is not included [212]. 6.6 Systematic uncertainties Experimental and theoretical systematic uncertainties are propagated to the final expected yields for signal and background, some object-by-object, in a similar way as discussed for the Z → ττ cross section measurement in Section 5.9. The systematic uncertainties on the background processes have little effect on the final mass limit, due to the very low number of expected events. The uncertainties on the signal, however, have a significant impact on the signal sensitivity. The experimental systematic uncertainties can be split into efficiency uncertainties, which primarily result in scaling of the samples and have little impact on variable distributions, and energy scale uncertainties, which can impact the shape of key variables and cause changes in efficiency through cut acceptance. The dominant uncertainty on the signal is the uncertainty on the tau identification efficiency, which increases with the Z ′ mass (due to the inflation with pT, see Section 4.4.7) and contributes 15% in the τhτh channel and 8–10% in the `τh channel for a Z ′ SSMwith a mass of 1250 GeV. The dominant systematic uncertainties on the irreducible Z → ττ background (with little effect on the expected Z ′SSM mass limit) are 14–20% (τhτh channel) and 11–14% (`τh channels) on the energy scale, 14% (τhτh channel) and 6% (`τh channels) on the tau identification efficiency 80, and 11% on 80 A more de ailed discussion of the uncertainty th tau identification efficiency at high-pT is given in Section 4.4.7. 182 6. search for high-mass resonances decaying to τ+τ− the NNLO production cross section for high-mass Z → ττ including the uncertainties on both the EW and QCD k-factors [97]. A summary of the effects of systematic uncertainties on the Z ′ signal and background predictions in all channels is shown in Table 6.7. A more detailed breakdown of how each uncertainty effects each background for the `τh channels is shown in Tables 6.8 and 6.9. Table 6.7: Uncertainties on the estimated signal and total background contributions in percent for each channel. The following signal masses, chosen to be close to the region where the limits are set, are used: 1250 GeV for τhτh (hh); 1000 GeV for `τh (μh) and eτh (eh); and 750 GeV for eμ. A dash denotes that the uncertainty is not applicable. The statistical uncertainty corresponds to the uncertainty due to limited sample size in the MC and control regions [212]. uncertainties are treated as fully correlated. Energy scale and resolution uncertainties on all objects are propagated to the EmissT calculation. The uncertainty on the E miss T due to clusters that do not belong to any reconstructed object is negligible in all channels. Table 2 summarises the systematic uncertainties in each channel. The dominant uncertainties on the background come from the multijet shape estimation and the tau energy scale uncertainty for Z/!! ! "" events in the "had"had channel, from the limited sample size and the fake factor estimate of the W+jets background in the "lep"had hannels and fr m the statistical uncertainty of the MC samples in the "e"μ channel. The dominant uncertainty on the signal for the "had"had and "lep"had channels come fr m the tau id ntification e!ciency and for the "e"μ channel, from the statistical uncertainty on the MC samples. Uncertainty [%] Signal Background hh μh eh eμ hh μh eh eμ Stat. uncertainty 1 2 2 3 5 20 23 7 E!. and fake rate 16 10 8 1 12 16 4 3 Energy scale and res. 5 7 6 2 +22!11 3 8 5 Theory cross section 8 6 6 5 9 4 4 5 Luminosity 4 4 4 4 2 2 2 4 Data-driven methods – – – – +21!11 6 16 – Table 2: Uncertainties on the estimated signal and total background contributions in percent for each channel. The following signal masses, chosen to be close to the region where the limits are set, are used: 1250 GeV for !had!had (hh); 1000 GeV for !μ!had (μh) and !e!had (eh); and 750 GeV for !e!μ (eμ). A dash denotes that the uncertainty is not applicable. The statistical uncertainty corresponds to the uncertainty due to limited sample size in the MC and control regions. 7. Results and discussion The numbers of observed and expected events including their total uncertainties, after the full selection in all channels, are summarised in Table 3. In all cases, the number of observed events is consistent with the expected Standard Model background. Therefore, upper limits are set on the production of a high-mass resonance decaying to "+"" pairs. The statistical combination of the channels employs a likelihood function constructed as the product of Poisson probability terms describing the total number of events observed in each channel. The Poisson probability in each channel is evaluated for the observed number of data events given the signal plus background expectation. Systematic uncertainties on the expected number of events are incorporated into the likelihood via Gaussian-distributed nuisance parameters. Correlations across channels are taken into account. A signal strength parameter multiplies the expected signal in each channel, for which a positive uniform prior probability distribution is assumed. Theoretical uncertainties on the signal cross section are not included in the calculation of the experimental limit as they are model-dependent. Bayesian 95% credibility upper limits are set on the cross section times branching fraction for a high-mass resonance decaying into a "+"" pair as a function of the resonance mass, using the Bayesian Analysis Toolkit [61]. Figs. 2(a) and 2(b) show the limits for the individual channels and for the combination, respectively. The resulting 95% credibility lower limit on the mass of a Z #SSM decaying to "+"" pairs is 1.40 TeV, with an expected limit of 1.42 TeV. The observed and expected limits in the individual c annels are, respectively: 1.26 and 1.35 TeV ("ha "had); 1.07 and 1.06 TeV ("μ"had); 1.10 and 1.03 TeV ("e"had); and 0.72 and 0.82 TeV ("e"μ). The impact of the choice of the prior on the signal strength parameter has been evaluated by also considering the reference prior [62]. Use of the reference prior improves the mass limits by approximately 50 GeV. The impact of the vector and axial coupling strengths of the Z # has been investigated, as these can alter the fraction of the tau momentum carried by the visible decay products. For purely V "A couplings, the limit on the cross section times "+"" branching fraction is improved by #10% over the mass range. For purely V + A couplings, there is a massdependent degradation, from #15% at high mass to #40% at low mass. All variations lie within the 1# band of the expected exclusion limit. 8. Conclusion A search for high-mass ditau resonances has been performed using 4.6 fb"1 of data collected with the ATLAS detector in pp collisions at $ s = 7 TeV at the LHC. The "had"had, "μ"had, "e"had and "e"μ channels are analysed. The observed number of events in the high-transverse-mass region is consistent with the SM expectation. Limits are set on the cross section times branching fraction for such resonances. The resulting lower limit on the mass of a Z # decaying to "+"" in the Sequential Standard Model is 1.40 TeV at 95% credibility, in agreement with the expected limit of 1.42 TeV in the absence of a signal. 9. Acknowledgements We thank CERN for the very successful operation of the LHC, as well as the support sta" from our institutions without whom ATLAS could not be operated e!ciently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWF and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET and ERC, European Union; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation, 7 6.6 systematic uncertainties 183 Table 6.8: The final predicted event yields for the μτh channel and their systematic uncertainties, for the primary signal region with mtotT > 600 GeV. The first line of numbers reports the number of expected events. The uncertainties are reported as percent of that background. The syst. uncert. denotes the total systematic uncertainty on the estimate of each background, calculated from the sum in quadrature of the individual systematic uncertainties, listed below that. The stat. uncert. denotes the statistical uncertainty either from the number of Monte Carlo events, or the events used in a data-driven model. The total uncert. denotes the total uncertainty on the estimate of each background, calculated from the sum in quadrature of the statistical and the total systematic uncertainty [97]. W+jets Z → ττ tt diboson single top Z ′(1000) expected events 0.3 0.4 0.3 0.2 0.2 5.5 total. uncert. 77 18 46 33 95 13 stat. uncert. 71 5 35 29 74 2 syst. uncert. 30 17 30 15 59 12 μ efficiency 0 0 0 0 2 μ pT resolution ID 0 0 2 0 2 μ pT resolution MS 0 0 1 0 2 τh efficiency 6 5 5 0 10 jet→ τh fake rate 0 11 0 0 0 e→ τh fake rate 0 25 11 58 0 jet energy scale 11 2 2 0 6 jet energy resolution 1 0 2 0 2 cluster energy scale 0 1 2 0 2 luminosity 2 2 2 2 2 theo. cross section 11 10 7 13 τh fake factor 30 - - - - 184 6. search for high-mass resonances decaying to τ+τ− Table 6.9: The final predicted event yields for the eτh channel and their systematic uncertainties, for the primary signal region with mtotT > 500 GeV. The first line of numbers reports the number of expected events. The uncertainties are reported as percent of that background. The syst. uncert. denotes the total systematic uncertainty on the estimate of each background, calculated from the sum in quadrature of the individual systematic uncertainties, listed below that. The stat. uncert. denotes the statistical uncertainty either from the number of Monte Carlo events, or the events used in a data-driven model. The total uncert. denotes the total uncertainty on the estimate of each background, calculated from the sum in quadrature of the statistical and the total systematic uncertainty [97]. W/Z+jets Z → ττ tt diboson Z ′(1000) expected events 0.8 0.6 0.1 0.1 5.0 total. uncert. 52 19 72 55 10 stat. uncert. 43 4 54 50 2 syst. uncert. 30 19 48 23 10 e efficiency 1 1 1 1 e energy scale 0 0 0 0 e energy resolution 0 0 0 0 τh efficiency 6 5 6 8 jet→ τh fake rate 0 21 0 0 e→ τh fake rate 0 23 17 0 jet energy scale 14 24 11 6 jet energy resolution 1 25 6 0 cluster energy scale 0 5 0 1 luminosity 2 2 2 2 theo. cross section 11 10 7 τh fake factor 30 - - - 6.7 results 185 6.7 Results 6.7.1 Observed events Table 6.10 shows a summary of the number of observed events in each channel, in the primary signal regions optimized for the highest Z ′SSM mass that can be excluded independently in that channel. In the τhτh channel 0.97± 0.27 events are expected and 2 events are observed. In the μτh and eτh channels, 1.4± 0.4 and 1.6± 0.5 events are expected, with 1 and 0 events observed, respectively. In all cases, the number of observed events is consistent with the expected Standard Model backgrounds. Therefore, upper limits are set on the production of a high-mass resonance decaying to τ+τ− pairs. 6.7.2 Likelihood model The statistical combination of the channels employs a likelihood function constructed as the product of Poisson probability terms describing the total number of events observed in each channel. The Poisson probability in each channel is evaluated for the observed number of data events given the signal plus background expectation. Systematic uncertainties on the expected number of events are incorporated into the likelihood via Gaussian-distributed nuisance parameters. The combined Likelihood is parameterized as L(μ, αi;nc) = ∏ c Poisson ( nc;μ (sc + ∆sc) + bc + ∆bc ) ∏ i Gaussian(αi; 0, 1) , Table 6.10: A summary of the number of events observed and the number of background events expected in the primary signal regions optimized for the highest Z ′SSM mass that can be excluded independently in each channel. The total uncertainties on each estimated contribution are shown. The signal efficiency denotes the expected number of signal events divided by the product of the production cross section, the ditau branching fraction and the integrated luminosity: σ(pp→ Z ′SSM)×BR(Z ′SSM → ττ)× ∫ Ldt [212]. !had!had !μ!had !e!had !e!μ mZ! [GeV] 1250 1000 1000 750 mtotT threshold [GeV] 700 600 500 350 Z/"! ! !! 0.73±0.23 0.36±0.06 0.57±0.11 0.55±0.07 W+jets < 0.03 0.28±0.22 0.8 ±0.4 0.33±0.10 Z(! ##)+jets < 0.01 < 0.1 < 0.01 0.06±0.02 tt < 0.02 0.33±0.15 0.13±0.09 0.97±0.22 Diboson < 0.01 0.23±0.07 0.06±0.03 1.69±0.24 Single top < 0.01 0.19±0.18 < 0.1 < 0.1 Multijet 0.24±0.15 < 0.01 < 0.1 < 0.01 Total expected background 0.97±0.27 1.4 ±0.4 1.6 ±0.5 3.6 ±0.4 Events observed 2 1 0 5 Expected signal events 6.3 ±1.1 5.5 ±0.7 5.0 ±0.5 6.72±0.26 Signal e!ciency (%) 4.3 1.1 1.0 0.4 Table 3: Number of expected and observed events in selected signal regions for each analysis channel. The expected contribution from the signal and background in each channel is calculated for the signal mass point closest to the Z!SSM exclusion limit. The total uncertainties on each estimated contribution are shown. The signal e!ciency denotes the expected number of signal events divided by the product of the production cross section, the ditau branching fraction and the integrated luminosity, !(pp ! Z!SSM) " BR(Z!SSM ! "") " ! Ldt. [GeV]Z'm 500 1000 1500 ) [ pb ] ττ → Z'( BR ×) Z' → pp( σ -310 -210 -110 1 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs (a) μτeτ hadτeτ / hadτμτ hadτhadτ comb.Observed limits Expected limits SSMZ' th. uncert.SSMZ' [GeV]Z'm 500 1000 1500 ) [ pb ] ττ → Z'( BR ×) Z' → pp( σ -310 -210 -110 1 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs Channels combined (b) Expected limit σ 1±Expected σ 2±Expected Observed limit SSMZ' th. uncert.SSMZ' Figure 2: (a) The expected (dashed) and observed (solid) 95% credibility upper limits on the cross section times "+"" branching fraction, in the "had"had, "μ"had, "e"had and "e"μ channels and for the combination. The expected Z ! SSM production cross section and its corresponding theoretical uncertainty (dotted) are also included. (b) The expected and observed limits for the combination including 1! and 2! uncertainty bands. Z!SSM masses up to 1.40 TeV are excluded, in agreement with the expected limit of 1.42 TeV in the absence of a signal. Germany; GSRT, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; BRF and RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS (MECTS), Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia; DST/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of America. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide. 8 186 6. search for high-mass resonances decaying to τ+τ− where c is summed over the channels, i is summed over the systematic uncertainties, nc is the number of events observed in a channel, sc and bc are the expected number of signal and background events, and ∆sc and ∆bc are linear functions of nuisance parameters, αi: ∆sc = ∑ i αi δsci and ∆bc = ∑ i αi δbci . Here δsci and δbci denote the change in normalization of the signal and background models, respectively, when the nuisance parameter αi = ±1, corresponding to a shift of one standard deviation under the Gaussian constraints81. Correlations across channels are taken into account by using common nuisance parameters among the channels. A signal-strength parameter, μ, multiplies the expected signal for all channels. Theoretical uncertainties on the signal cross section are not included in the calculation of the experimental limit as they are model-dependent. 6.7.3 Limit-setting procedure Bayesian82 credibility intervals are determined leading to 95% CL upper limits on the cross section times branching fraction for a high-mass resonance decaying into a τ+τ− pair as a function of the resonance mass. The upper limit of the Bayesian credibility interval for the signal strength with 95% confidence, μup, is determined by 0.95 = ∫ μup 0 dμ p(μ;nc) where the posterior probability distribution for the signal-strength parameter given the observed data, p(μ;nc), is determined by marginalizing the nuisance parameters [136]: p(μ;nc) ∝ ∫ dαi L(μ, αi;nc) π(μ) for which a positive uniform prior probability distribution is assumed for π(μ)83. The Bayesian Analysis Toolkit (BAT) [231] was used to implement the sampling of the posterior using the method of Markov Chain Monte Carlo (MCMC) [232, 233]. Figure 6.15 (left) shows limits derived independently in each channel and their improvement in combination. Figure 6.15 (right) shows the combined expected limit and a band showing its esti81 The example model is somewhat simplified because the actual model can be bifurcated to have a different variations depending on if α is positive or negative. This only concerns systematic uncertainties that have significantly different up and down variations, and was only used for the jet energy scale and multijet shape uncertainties in the τhτh channel. The HistFactory tool of the RooStats framework to was used to configure and build the model described for calculating CLs limits. See the HistFactory manual [227] for a detailed description of the parametrizations of the likelihood. The same configuration but an independent implementation using bifurcated Gaussians with two width parameters was used to calculate the Bayesian limits. 82 As a cross-check, frequentist upper limits were also evaluated using the CLs technique [228, 229] as described in Ref. [97], giving similar results also excluding a Z′SSM with a mass up to 1.4 TeV. 83 The impact of the choice of the prior on the signal-strength parameter has been evaluated by also considering the reference prior [230] which prior improves the combined mass limit by approximately 50 GeV or 3.6%. 6.7 results 187 !had!had !μ!had !e!had !e!μ mZ! [GeV] 1250 1000 1000 750 mtotT threshold [GeV] 700 600 500 350 Z/"! ! !! 0.73±0.23 0.36±0.06 0.57±0.11 0.55±0.07 W+jets < 0.03 0.28±0.22 0.8 ±0.4 0.33±0.10 Z(! ##)+jets < 0.01 < 0.1 < 0.01 0.06±0.02 tt < 0.02 0.33±0.15 0.13±0.09 0.97±0.22 Diboson < 0.01 0.23±0.07 0.06±0.03 1.69±0.24 Single top < 0.01 0.19±0.18 < 0.1 < 0.1 Multijet 0.24±0.15 < 0.01 < 0.1 < 0.01 Total expected background 0.97±0.27 1.4 ±0.4 1.6 ±0.5 3.6 ±0.4 Events observed 2 1 0 5 Expected signal events 6.3 ±1.1 5.5 ±0.7 5.0 ±0.5 6.72±0.26 Signal e!ciency (%) 4.3 1.1 1.0 0.4 Table 3: Number of expected and observed events in selected signal regions for each analysis channel. The expected contribution from the signal and background in each channel is calculated for the signal mass point closest to the Z!SSM exclusion limit. The total uncertainties on each estimated contribution are shown. The signal e!ciency denotes the expected number of signal events divided by the product of the production cross section, the ditau branching fraction and the integrated luminosity, !(pp ! Z!SSM) " BR(Z!SSM ! "") " ! Ldt. [GeV]Z'm 500 1000 1500 ) [ pb ] ττ → Z'( BR ×) Z' → pp( σ -310 -210 -110 1 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs (a) μτeτ hadτeτ / hadτμτ hadτhadτ comb.Observed limits Expected limits SSMZ' th. uncert.SSMZ' [GeV]Z'm 500 1000 1500 ) [ pb ] ττ → Z'( BR ×) Z' → pp( σ -310 -210 -110 1 ATLAS -1L dt = 4.6 fb∫ = 7 TeVs Channels combined (b) Expected limit σ 1±Expected σ 2±Expected Observed limit SSMZ' th. uncert.SSMZ' Figure 2: (a) The expected (dashed) and observed (solid) 95% credibility upper limits on the cross section times "+"" branching fraction, in the "had"had, "μ"had, "e"had and "e"μ channels and for the combination. The expected Z ! SSM production cross section and its corresponding theoretical uncertainty (dotted) are also included. (b) The expected and observed limits for the combination including 1! and 2! uncertainty bands. Z!SSM masses up to 1.40 TeV are excluded, in agreement with the expected limit of 1.42 TeV in the absence of a signal. Germany; GSRT, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; BRF and RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS (MECTS), Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia; DST/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of America. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide. 8 i ure 6.15: (left) The xpected (dashe ) and o served (solid) 95% credibility upper limits on the cross section times τ+τ− branching fraction, in the τhτh, μτh, eτh, and eμ channels, and for their combination. The expected Z ′SSM production cross section a d its corresponding theoretical uncertainty (dotted) are also included. (right) The expected and observed upper limits for the combination including 1σ and 2σ uncertainty bands. Z ′SSM masses up to 1.40 TeV are excluded, in agreement with the expected limit in the absence f a signal of 1.42 TeV [212]. mated stat stical variance, evaluate by generating Monte Carlo ps udo-experiments. As a result84, SSM Z ′ bosons are excluded with masses less than 1.4 TeV at 95% CL. CMS performed a similar search, also excluding SSM Z ′ bosons decaying to τ+τ− with masses less than 1.4 TeV [213]. 6.7.4 Model dependence The exclusion is nearly model-independent such that theorists with a model for a high-mass τ+τ− resonance should be able to calculate the cross section as a function of mass of their model and compare it to the excluded cross section. Using the predicted cross section of Z ′SSM at NNLO as a function of mass, the upper limit on the signal-strength parameter was converted to the cross section times τ+τ− branching fraction excluded at 95% CL shown in Figures 6.15. The exclusion is model-independent insofar as it applies to models predicting a high-mass τ+τ− resonances with a width small compared to its mass85, modulo the effects of the polarization of the out-going tau leptons. Any such model will result in back-to-back tau decays that can only vary in the initial polarization of the tau leptons depending on the type of coupling the signal has to taus. 84 The author presented this result at the Tau2012 International Workshop on Tau Lepton Physics in Nagoya, Japan [234]. 85 The mass has to be small enough to be produced on-resonance at the LHC (m . √ ŝ) and not in the higher-mass, contact interaction regime [235]. 188 6. search for high-mass resonances decaying to τ+τ− The polarization of the out-going tau leptons can have a significant effect on the fraction of the momentum carried by the visible decay products because the tau lepton decays through a lefthanded coupling to the W boson [236]. Hence changing the polarization of the tau leptons in this analysis would affect the signal acceptance, mainly through the thresholds applied to the transverse momentum of the visible tau decay products and on mtotT . For Z → ττ decays, the tau polarization is determined by the relative strengths of the vector and axial couplings, CV and CA, parameterized by the Weinberg angle. For charged leptons these are defined as [237, 136] CV = −1 + 4 sin2 θW ≈ −0.08 and CA = −1 . In the SSM, the Z ′ has the same vector and axial coupling strengths as the Z of the SM. However, for a generic Z ′ with chiral couplings, CV and CA can have other values. To determine the extent of the effect of tau polarization on signal acceptance, the two extreme cases for chiral couplings are considered: • CV = +1 and CA = −1, purely left-handed coupling (V −A), • CV = +1 and CA = +1, purely right-handed coupling (V + A). Monte Carlo Z ′ → ττ samples were generated using PYTHIA 6.4 for each signal mass point with SSM (nominal), V −A, and V + A couplings. For hadronic tau decays, the visible fraction of momentum (the part not carried by neutrinos) is slightly larger for V −A than for V + A. (see Figure 6.16 (top-left)). For leptonic decays, the opposite is true but to a lesser degree (see Figure 6.16 (top-right)). The net impact of the tau polarizations on the final mtotT distribution for a 1250 GeV Z ′ is shown in Figure 6.16 for the τhτh channel (bottom-left) and the `τh channels (bottom-right). The acceptance varies by ±10–20% as a result of the change in couplings, as shown in Figure 6.17. The impact of the different chiral couplings on the excluded cross section times τ+τ− branching fraction is shown in Figure 6.18, with dashed lines indicating the spread in expected limits in the case of V −A or V + A couplings. The mass limit is improved by ≈ 30 GeV or 2.1% for V −A couplings, since the observable fraction momentum is larger, and degraded by ≈ 50 GeV or 3.6% for V + A couplings86. 86 The primary references discussing the topics of this chapter in more detail are • A search for high-mass resonances decaying to τ+τ− in pp collisions at √s = 7 TeV with the ATLAS detector ATL-COM-PHYS-2012-394 [97] – support note for the Z′ → ττ search with 2011 data, • A search for high-mass resonances decaying to τ+τ− in the ATLAS detector ATLAS-CONF-2012-067 [238] – conference note. • A search for high-mass resonances decaying to τ+τ− in pp collisions at √s = 7 TeV with the ATLAS detector arxiv:1210.6604 [hep-ex] [212] – publication. 6.7 results 189 0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 Nominal V-A V+A 0 100 200 300 400 500 600 700 800 900 10000 200 400 600 800 1000 1200 Nominal V-A V+A 0 200 400 600 800 1000 1200 1400 1600 1800 20000 50 100 150 200 250 300 Nominal V-A V+A 0 200 400 600 800 1000 1200 1400 1600 1800 20000 50 100 150 200 250 300 Nominal V-A V+A pT(!h) [GeV] pT(") [GeV] mtotT [GeV] m tot T [GeV] "!h channel "!h channel "!h channel!h!h channel Figure 6.16: Generator-level kinematic distributions for a Z ′SSM with a mass of 1250 GeV, after the baseline event selection, with SSM (nominal), V −A, and V + A couplings. (top-left) and (top-right) show the visible pT of hadronic tau decay and lepton, respectively, in the `τh channel. (bottom-left) and (and bottom-right) compare the m tot T distributions in the τhτh and `τh channels, respectively. [97]. N ot re vi ew ed ,f or in te rn al ci rc ul at io n on ly October 23, 2012 – 15 : 44 DRAFT 201 [GeV]Z'm 600 800 1000 1200 1400 1600 1800 (a cc ep t.) [% ] Δ -30 -20 -10 0 10 20 30 V-A V+A hadhad [GeV]Z'm 600 800 1000 1200 1400 1600 1800 (a cc ep t.) [% ] Δ -30 -20 -10 0 10 20 30 V-A V+A lephad [GeV]Z'm 600 800 1000 1200 1400 1600 1800 (a cc ep t.) [% ] Δ -30 -20 -10 0 10 20 30 V-A V+A leplep Figure 156: The relative change in signal acceptance for the V ! A and V + A samples with respect to the nominal sample vs. mZ" for the !h!h (top), "!h (middle) and eμ (bottom) channels. Figure 157 shows the combined limit including the maximal e!ects of tau polarisation. The max-2564 imum e!ect on the signal acceptance due to the tau polarisation is included in the experimental limit2565 (shown by the dashed blue and red lines). For V ! A couplings, the limit on the cross section times2566 ditau branching fraction is improved by #10% over the mass range. For V + A couplings there is a2567 mass-dependent degradation, from #15% at high-mass to #40% at low-mass. Both variations lie within2568 the 1# band of the expected exclusion limit. A summary of the limits on the cross section times ditau2569 branching fraction are given in Table 54. Please note that the limits for the V ! A and V + A couplings2570 were inferred from generator-level information, and do not include a full simulation of the response of2571 the ATLAS detector.2572 If the altered limits on the cross section times branching fraction are compared directly to the SSM2573 production cross section, the e!ect is to improve the mass limit by #30 GeV for V ! A couplings and to2574 degrade the mass limit by #50 GeV for V + A couplings. However, for both V ! A and V + A couplings,2575 the signal cross section is largely enhanced with respect to the SSM, which more than compensates for2576 the small degradation due to acceptance for the V + A case. Taking into account the e!ects on both the2577 signal acceptance and the cross section, the corresponding expected limits on the mass of Z" bosons with2578 either V ! A or V + A couplings are 1.6 TeV (in each case).2579 L.4 Study reweighting full simulation2580 This section presents a cross-check of the results from the previous section in which only generator-2581 level information was used. To better incorporate the response of the ATLAS detector, the standard full2582 simulated signal samples are reweighted so that the pT spectra of the visible decay products of both taus2583 Figure 6.17: The relative change in signal acceptance for the V −A and V + A samples (in % of the nominal SSM signal) vs. the Z ′ mass for the τhτh channel (left) and the `τh channel (right) [97]. 190 6. search for high-mass resonances decaying to τ+τ− [GeV]Z'm 500 1000 1500 ) [p b] ττ → Z ' ( B R ×) Z ' → pp( σ -210 -110 1 ATLAS Internal -1dt L =4.6 fb∫ =7TeVs Channels combined Expected limit σ1±Expected σ2±Expected Expected (V-A) Expected (V+A) Observed limit √ _ Z'SSM Figure 6.18: The expected and observed upper limits for the combination, showing the change in expected limit for V −A and V + A couplings [97]. Chapter 7 Conclusion The start-up and last few years of running of the LHC have been a huge success for particle physics. Many properties of the SM have been measured and validated at a new energy scale. Figure 7.1 shows a summary of many of the SM cross section measurements made at ATLAS in the 2011 and 2012 data. A new particle has been observed, and so far, it looks consistent with the SM Higgs boson. This thesis has presented a summary of many of the aspects of tau performance at ATLAS, a Z → ττ cross section measurement with the 2010 ATLAS dataset, and an upper limit on the cross section times branching ratio for a hypothetical high-mass resonance (Z ′) decaying to τ+τ−. The Z ′ → ττ result is one of several searches for exotic phenomena at ATLAS, many of which are summarized in Figure 7.2. It is the first search for exotic phenomena at ATLAS with reconstructed hadronic tau decays in the final state. There has not yet been any evidence for new physics beyond the SM among the searches for supersymmetry or other exotic phenomena at the LHC, but exclusions in the TeV scale are just beginning. The LHC is scheduled to begin a new run in 2015 with a target energy of √ s = 13 TeV. The experiments are busily preparing updgrades to the experiments, updates to the trigger system, and getting ready for new analyses. 191 192 7. conclusion W Z WW Wt [p b] to ta l σ 1 10 210 310 410 510 -120 fb -113 fb -15.8 fb -15.8 fb -14.6 fb -12.1 fb -14.6 fb -14.6 fb -11.0 fb -11.0 fb -135 pb -135 pb tt t WZ ZZ = 7 TeVsLHC pp Theory )-1Data (L = 0.035 4.6 fb = 8 TeVsLHC pp Theory )-1Data (L = 5.8 20 fb ATLAS Preliminary Figure 7.1: Summary of several Standard Model total production cross section measurements, correcting for leptonic branching fractions, compared to the corresponding theoretical expectations. The W and Z vector-boson inclusive cross sections were measured with 35 pb−1 of integrated luminosity from the 2010 dataset. All other measurements were performed using the 2011 dataset or the 2012 dataset. The luminosity used for each measurement is indicated close to the data point [239]. 193 Mass scale [TeV] -110 1 10 210 O th er E xc it. fe rm . N ew qu ar ks LQ V ' C I E xt ra d im en si on s Magnetic monopoles (DY prod.) : highly ionizing tracks Multi-charged particles (DY prod.) : highly ionizing tracks jjmColor octet scalar : dijet resonance, ll m), μμll)=1) : SS ee (→ L ±± (DY prod., BR(HL ±±H Zlm (type III seesaw) : Z-l resonance, ±Heavy lepton N Major. neutr. (LRSM, no mixing) : 2-lep + jets WZ mll), νTechni-hadrons (LSTC) : WZ resonance (l μμee/mTechni-hadrons (LSTC) : dilepton, γl m resonance, γExcited leptons : lWtmExcited b quark : W-t resonance, jjmExcited quarks : dijet resonance, jetγ m-jet resonance, γExcited quarks : qνlmVector-like quark : CC, Ht+X→Vector-like quark : TT ,missT E SS dilepton + jets + →4th generation : b'b' WbWb→ generation : t't'th4 jjντjj, ττ=1) : kin. vars. in βScalar LQ pair ( jjνμjj, μμ=1) : kin. vars. in βScalar LQ pair ( jjν=1) : kin. vars. in eejj, eβScalar LQ pair ( tb m tb, LRSM) : → (RW' tqm=1) : R tq, g→W' ( μT,e/mW' (SSM) : tt m l+jets, → tZ' (leptophobic topcolor) : t ττmZ' (SSM) : μμee/mZ' (SSM) : ,missTEuutt CI : SS dilepton + jets + ll m, μμqqll CI : ee & ) jj m(χqqqq contact interaction : )jjm(χQuantum black hole : dijet, F T pΣ=3) : leptons + jets, DM /THMADD BH ( ch. part.N=3) : SS dimuon, DM /THMADD BH ( tt m l+jets, → t (BR=0.925) : tt t→ KK RS g lljjmBulk RS : ZZ resonance, νlν,lTmRS1 : WW resonance, llmRS1 : dilepton, llm ED : dilepton, 2/Z 1S ,missTEUED : diphoton + / llγγmLarge ED (ADD) : diphoton & dilepton, ,missTELarge ED (ADD) : monophoton + ,missTELarge ED (ADD) : monojet + mass862 GeV , 7 TeV [1207.6411]-1=2.0 fbL mass (|q| = 4e)490 GeV , 7 TeV [1301.5272]-1=4.4 fbL Scalar resonance mass1.86 TeV , 7 TeV [1210.1718]-1=4.8 fbL )μμ mass (limit at 398 GeV for L ±±H409 GeV , 7 TeV [1210.5070]-1=4.7 fbL | = 0)τ| = 0.063, |Vμ| = 0.055, |Ve mass (|V ±N245 GeV , 8 TeV [ATLAS-CONF-2013-019]-1=5.8 fbL ) = 2 TeV) R (WmN mass (1.5 TeV , 7 TeV [1203.5420]-1=2.1 fbL )) T ρ(m) = 1.1 T (am, Wm) + Tπ(m) = Tρ(m mass (Tρ920 GeV , 8 TeV [ATLAS-CONF-2013-015] -1=13.0 fbL ) W ) = MTπ(m) Tω/Tρ(m mass (Tω/Tρ850 GeV , 7 TeV [1209.2535] -1=5.0 fbL = m(l*))Λl* mass (2.2 TeV , 8 TeV [ATLAS-CONF-2012-146]-1=13.0 fbL b* mass (left-handed coupling)870 GeV , 7 TeV [1301.1583]-1=4.7 fbL q* mass3.84 TeV , 8 TeV [ATLAS-CONF-2012-148]-1=13.0 fbL q* mass2.46 TeV , 7 TeV [1112.3580]-1=2.1 fbL )Q/mν = qQκVLQ mass (charge -1/3, coupling 1.12 TeV , 7 TeV [ATLAS-CONF-2012-137] -1=4.6 fbL T mass (isospin doublet)790 GeV , 8 TeV [ATLAS-CONF-2013-018]-1=14.3 fbL b' mass720 GeV , 8 TeV [ATLAS-CONF-2013-051]-1=14.3 fbL t' mass656 GeV , 7 TeV [1210.5468]-1=4.7 fbL gen. LQ massrd3534 GeV , 7 TeV [1303.0526]-1=4.7 fbL gen. LQ massnd2685 GeV , 7 TeV [1203.3172]-1=1.0 fbL gen. LQ massst1660 GeV , 7 TeV [1112.4828]-1=1.0 fbL W' mass1.84 TeV , 8 TeV [ATLAS-CONF-2013-050]-1=14.3 fbL W' mass430 GeV , 7 TeV [1209.6593]-1=4.7 fbL W' mass2.55 TeV , 7 TeV [1209.4446]-1=4.7 fbL Z' mass1.8 TeV , 8 TeV [ATLAS-CONF-2013-052]-1=14.3 fbL Z' mass1.4 TeV , 7 TeV [1210.6604]-1=4.7 fbL Z' mass2.86 TeV , 8 TeV [ATLAS-CONF-2013-017]-1=20 fbL (C=1)Λ3.3 TeV , 8 TeV [ATLAS-CONF-2013-051]-1=14.3 fbL (constructive int.)Λ13.9 TeV , 7 TeV [1211.1150]-1=5.0 fbL Λ7.6 TeV , 7 TeV [1210.1718]-1=4.8 fbL =6)δ (DM4.11 TeV , 7 TeV [1210.1718] -1=4.7 fbL =6)δ (DM1.5 TeV , 7 TeV [1204.4646]-1=1.0 fbL =6)δ (DM1.25 TeV , 7 TeV [1111.0080]-1=1.3 fbL mass KK g2.07 TeV , 7 TeV [1305.2756]-1=4.7 fbL = 1.0)PlM/kGraviton mass (850 GeV , 8 TeV [ATLAS-CONF-2012-150] -1=7.2 fbL = 0.1)PlM/kGraviton mass (1.23 TeV , 7 TeV [1208.2880] -1=4.7 fbL = 0.1)PlM/kGraviton mass (2.47 TeV , 8 TeV [ATLAS-CONF-2013-017] -1=20 fbL -1 ~ RKKM4.71 TeV , 7 TeV [1209.2535] -1=5.0 fbL -1Compact. scale R1.40 TeV , 7 TeV [1209.0753]-1=4.8 fbL =3, NLO)δ (HLZ SM4.18 TeV , 7 TeV [1211.1150]-1=4.7 fbL =2)δ (DM1.93 TeV , 7 TeV [1209.4625]-1=4.6 fbL =2)δ (DM4.37 TeV , 7 TeV [1210.4491]-1=4.7 fbL Only a selection of the available mass limits on new states or phenomena shown* -1 = ( 1 20) fbLdt∫ = 7, 8 TeVs ATLAS Preliminary ATLAS Exotics Searches* 95% CL Lower Limits (Status: May 2013) Figure 7.2: Mass reach of several ATLAS searches for new phenomena other than Supersymmetry. Dark blue lines indicate 8 TeV data results with the 2012 data [239]. Appendix A A review of the Standard Model Here, I outline my understanding of the highlights in the recent history of rational discourse and scientific experiment that have led physicists to the current, concise, yet often precise, but mysterious model we have for the dynamics of nature's most elementary constituents. I discuss the questions: What is quantum mechanics? And, how did we arrive at the Standard Model? The Standard Model (SM) is the culmination of several incremental breakthroughs in particle physics, many of which will be noted in what follows, but quickly. I begin the discussion with quantum mechanics, because it marks such a huge shift from the classical paradigm, and it's a good story87. A.1 Quantum mechanics A.1.1 A brief history Quantum mechanics has its roots in the first investigations of the particulate nature of matter and energy at the end of the 19th century, including: Boltzmann's development of statistical mechanics, J.J. Thomson's discovery that cathode rays are composed of electrons in 1897 [246], and Planck's studies of thermal radiation. In 1900, in order to explain anomalous measurements of the spectrum of thermal radiation of hot objects (so called "black-body radiation"), Planck predicted that the energy from thermal radiation is quantized in discrete units, hν, where ν is the frequency of the electromagnetic radiation and h was a new constant (now called "Planck's constant") representing the quantum unit of action [247, 248]. Einstein later used Planck's hypothesis of the quantization of the energy of radiation to explain the photoelectric-effect [249], drawing into question whether light should fundamentally be described by a wave as in classical electrodynamics. 87 Some especially useful references in writing this summary have been Refs. [240, 241, 242, 237, 243, 244, 245, 33, 136]. 194 A.1 quantum mechanics 195 Rutherford's scattering experiments of 1911 [250] led Bohr to develop a model of the atom in 1913 that resembles a tiny solar system, with nuclei confined to the center and electrons traveling in bound orbitals [251, 252, 253]. While the Bohr model correctly predicted the Rydberg formula for the atomic spectrum of hydrogen [254], a more satisfactory motivation of its energy levels and a description of its fine-structure would have to wait. Louis de Broglie's discovery of electron diffraction in 1925 brought the notion of wave-particle duality to matter consisting of fermions [255], in comparison to photons whose wave-particle nature was already known from classical electrodynamics and the discoveries of Planck and Einstein. These observations were first consistently formalized that year in the matrix mechanics of Heisenberg, Born, and Jordan [256, 257, 258], marking the birth of modern quantum mechanics. Their formalism allows for the wave-like interference effects observable in phenomena consisting of quantum particles because, according to the Born rule [259], the probability to observe a system in a specific state is given by the square of a quantum amplitude, which can in general be the sum of complex numbers giving the square of the amplitude negative terms. Pauli then used this formalism in 1926 to predict the atomic spectrum of hydrogen, including the first-order perturbative corrections to the energy due to external electric and magnetic fields [260]. Independently in 1926, Schrödinger developed his theory of wave mechanics and used it to describe the orbital structure of hydrogen [261, 262]. That same year, Schrödinger proved that his wave mechanics and Heisenberg's matrix mechanics were equivalent formulations of the modern theory of quantum mechanics [263]. In 1927, Heisenberg published his uncertainty principle that highlights an important consequence of quantum mechanics: that not all observables are compatible, meaning that some observables, like momentum and position in the same direction, cannot be predicted simultaneously to arbitrary precision, but must always have the product of their quantum mechanical uncertainties be of the order of Planck's constant or greater [264]. Dirac developed the first relativistic quantum theory of electrons when he introduced the Dirac equation in 1928 and used it to predict the existence of antimatter [265, 266]. This laid much of the groundwork for what would later become the modern theory of Quantum Electrodynamics (QED). Two early seminal textbooks attempt to clarify the principles underlying quantum mechanics. The first is Dirac's The Principles of Quantum Mechanics (published in 1930) [267], which pedagogically motivates the necessity of quantum mechanics to describe superpositions of states. The second is John von Neumann's The Mathematical Foundations of Quantum Mechanics (published in 1932) [268], written during his time as a founding member of the Institute for Advanced Studies. In his book, von Neumann axiomatized quantum mechanics as fundamentally describing the linear algebra of state vectors in a Hilbert space (or a direct product of them in multi-particle systems). 196 A. a review of the standard model Observables are represented by Hermitian operators with possible outcomes corresponding to their eigenvalues: Ĥ |n〉 = En |n〉 , and the probability of observing an outcome is given by the Born rule: P (n) = | 〈n|ψ〉 |2 . In the book's introduction, von Neumann comments on the success quantum theory had already had in predicting experiments throughout the 1920s, but he also noted the conceptual revolution the theory was bringing [268]: And, what was fundamentally of greater significance, was that the general opinion in theoretical physics had accepted the idea that the principle of continuity ("natura non facit saltus"), prevailing in the perceived macrocosmic world, is merely simulated by an averaging process in a world which in truth is discontinuous by its very nature. With these stable foundations, the known consequences of quantum theory continued to build. In 1940, Pauli discovered the spin-statistics theorem88 which fundamentally constrains the statistics obeyed by identical particles: whether their state is even (bosons) or odd (fermions) under exchange, depends directly on the spin of the particles. Integer-spin particles must be bosons, and half-integerspin particles must be fermions [269]. This single fact has the dramatic observable consequence that the spin12 fermions of the SM form stable matter by stacking their states in bound systems like nuclei, atoms, and molecules, while the spin-1, force-carrying bosons are free to fill the same state. This and other developments have led to rapid progress in the last century in the understanding and applications of quantum theory. Some of the applications of quantum mechanics include: forming the framework for understanding chemical bonding in the field of computational chemistry, describing many of the electrical properties of semiconductors underlying the current technology of electrical transistors and memory devices, the development of lasers, and of course, successfully modeling the outcomes of generations of scientific experiments studying a range of phenomena from cold ion traps to high-energy particle colliders. A.1.2 The measurement problem Since quantum mechanics fundamentally involves some notion of probability and introduces some strange concepts (e.g. superpositions), there has been a lot of trouble over how to interpret the theory. Problems like-what do the elements of randomness in the theory say about reality? and 88The source and consequences of the spin-statistics theorem are discussed in more detail in Appendix A.1.4. A.1 quantum mechanics 197 specifically, how is the outcome of a measurement determined?-are still debated among physicists today. The Copenhagen interpretation of quantum mechanics grew out of discussions between Bohr, Heisenberg, and others in the years 1924–1927. It postulates that isolated quantum systems evolve under unitary evolution according to the Schödinger equation, but that when a system is measured by an outside agent, the wave function (read state vector) instantly collapses into a single eigenstate of the observable, a non-unitary operation. A particularly bizarre consequence of this is highlighted by the Einstein-Podolsky-Rosen (EPR) thought experiment published in 1935 [270], where an isolated quantum system of two bodies is in a coherent quantum state, i.e. the two bodies are entangled. Then, the two bodies are brought sufficiently far apart that they are causally separated. One is then asked what the outcome will be of measurements of two non-commuting observables, if one observable is measured from one body and the second simultaneously from the other (i.e. outside the light cone of the first measurement). A common hypothetical implementation of the experiment is to measure orthogonal components of the spins of a spin-0 system that decays into two spin12 particles 89 or decays into two photons which are correlated to have opposite polarizations. EPR point out that assuming that: (1) the laws of physics are only allowed to act locally, meaning the measurement of one decay product cannot have an immediate effect on the other, and that (2) the physical observables in question are real or have counterfactual definiteness in the sense that it is meaningful to talk about the status of observables independent of a particular measurement, is in direct contradiction with the entangled observables being non-commuting. Because according to quantum mechanics, non-commuting observables will satisfy an uncertainty relationship. The authors were so repulsed by the idea of two observables not having simultaneous reality that they were "thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete" [270]. Years later, in 1964, John S. Bell followed the reasoning of the EPR thought experiment, and proved his now famous Bell's theorem [271] which shows that any theory with observables that have local elements of reality, or that depend on other so called "local hidden variables", will not predict the correlations required by quantum mechanics. This is quantified in the relationships called the "Bell's inequalities" for simultaneous measurements of non-commuting observables. And so while quantum mechanics served as a very predictive framework, it remained controversial whether the theory is complete if one wants to retain the common notions of locality and counterfactual definiteness. Remarkably, the experiments of John Clauser and Stuart Freedman in 1972 [272] and Alain Aspect in 1982 [273, 274] definitively showed that Bell's inequalities are violated in actual 89 This means the system is in the singlet state: 1√ 2 (↑↓ − ↓↑). 198 A. a review of the standard model implementations of EPR-like experiments, using laser-excited cascade sources of two photons with correlated polarizations. After which, it became clear that nature does not respect together the concepts of locality and counterfactual definiteness, and that therefore a theory relying on local hidden variables cannot describe quantum phenomena. In the Copenhagen interpretation of quantum mechanics, this paradox is avoided by not claiming that quantum mechanics describes reality, that it only describes the probabilities of measurements, and therefore does not have counterfactual definiteness. Further, it rejects locality90 by allowing for instantaneous wave function collapse to describe measurements of entangled states, what Einstein called "spooky action at a distance". While still controversial, the Copenhagen interpretation of quantum mechanics has been regarded as the standard interpretation among physicists since its inception. Some of the mystery of apparent wave function collapse has been resolved by the modern theory of decoherence, which explains why superpositions of eigenstates of position or charge91 (or other macroscopic observables) are never observed, due to the interactions of a quantum system and the many more degrees of freedom in its environment (including the measuring device). H. Dieter Zeh was one of the first to suggest the plausibility of this mechanism in his paper published in 1970, where he says [276]: Superpositions of states with different charge therefore cannot be observed for similar reasons as those valid for superpositions of macroscopically different states: They cannot be dynamically stable because of the significantly different interaction of their components with their environment. In the 1980s, the theory of decoherence was worked out in more detail in the work of Zurek [277, 278] and Joos and Zeh [279], and is summarized in a textbook by Giulini, Joos, Kiefer, Kupsch, Stamatescu, and Zeh [280]. Essentially, because measurement inherently involves breaking the isolation of a quantum system, the process of decoherence rapidly takes a system in a pure quantum state to being an incoherent mixture of states, where each state is weighted by the squares of the amplitudes for each possible measurement. In the modern version of the Copenhagen interpretation, the process leading to wave function collapse is recognized as an emergent phenomena from the dephasing effects of decoherence, but which of the possible eigenstates is actually observed in any given measurement is still inherently 90 Although accepting the Copenhagen interpretation requires a strict loss of locality, it preserves causality because the results of the entangled measurements, while correlated, are inherently random and therefore cannot be used to send signals faster than light. 91 The basis of states that are eigenstates of position and charge are selected out of any other arbitrary basis, fundamentally because the Lagrangian describing the interactions of a system has terms that are local in that basis [275]. A.1 quantum mechanics 199 indeterministic. The Copenhagen interpretation still views that during a measurement, the terms in a state vector representing the other possibilities not observed in a measurement are dropped, and the state is immediately re-normalized in the observed eigenstate (including any required non-local collapse for entangled systems). One of the alternative interpretations of quantum mechanics, the many-worlds interpretation, first developed by Hugh Everett in 1957 [281] and popularized Bryce DeWitt in the 1970s [282], removes the non-unitary operation of wave function collapse entirely from the theory. It postulates that since any isolated quantum system evolves unitarily under the Schrödinger equation, the state of universe itself being a closed system, evolves unitarily under the Schrödinger equation, continuously. The many worlds interpretation has influenced and been heavily influenced by the development of the theory of decoherence. Decoherence explains why superpositions of observable eigenstates decouple in the presence of an environment with many more degrees of freedom, although the state of the total system, including the environment, remains a pure quantum state evolving under the Schrödinger equation. According to the many worlds interpretation, these decoupled mixtures of states are each independently real although they are effectively disconnected observationally. This leads to the fantastic claim that all possibilities from all possible interactions have a corresponding branch in the immensely fragmented universal state vector of the multiverse, but it remains a controversial proposal among physicists92. The many worlds interpretation succeeds in removing the ad hoc wave collapse from quantum mechanics; the multiverse continues to evolve unitarily. It also succeeds in preserving locality because interference and the coordinated acts of entangled systems happen naturally when different terms in the universal state vector are coherent. There are also other interpretations of quantum mechanics including de Broglie-Bohm theory, the theory of consistent histories, and others that generally try to straddle some labored construction to preserve locality or a notion of realism or both, but people are thinking93. And so it remains that while quantum mechanics has formed a highly predictive framework for predicting experiments, the metaphysical implications of the theory and what a state vector actually corresponds to in reality are not understood. 92 As I heard one put it once during lunch in the Penn faculty lounge: "Are we supposed to believe that there is a universe where I am throwing my food at you?" 93 There has even been a recent claim that quantum mechanics cannot be interpreted statistically [283]. 200 A. a review of the standard model A.1.3 Fields In physics, a field94 generally means a mathematical structure which has a tensor (scalar, vector, or higher rank) defined at every point on a manifold. Most often, the manifold is space-time. A field being a concept used throughout classical physics, examples of scalar fields include the temperature of some body or the Newtonian gravitational potential in some space. Examples of vector fields include the velocity of wind or electric and magnetic fields. In Quantum Field Theory (QFT), the field itself plays the leading role as the dynamical variable. Naively, one may have thought to start with the position and momentum of particles as the fundamental dynamical variables, but instead particles emerge from the theory, and can be thought of as the minimum quanta of excitation in a given field, localized in space-time and momentum-space in wave packets. According to the process of canonical quantization95 the dynamical variables of a quantum theory are operators in a Hilbert space. From this, one can calculate decay rates and scattering cross sections of relativistic quantum systems, as will be discussed in Appendix A.1.5. QFTs can be made compatible with Einstein's special theory of relativity [285], describing relativistic dynamics, by requiring that the operators defining the four-momentum of the system satisfy the Poincaré algebra, the implications of which will be discussed in the following section. It is still an open question: what is the unique96 quantum theory that in the classical limit reduces to Einstein's general theory of relativity [286], the modern classical field theory of gravity. General relativity is particular as a field theory in that it relates the stress-energy tensor field to the metric of space-time. A resolution of this issue of how to quantize gravity has been a primary pursuit in research in theoretical physics since the developments of relativity and quantum theory. As we will discuss in Appendix A.1.6, in particle physics, it is useful to use QFTs with a particular type of symmetry among the internal degrees of freedom of the field (components of the tensor) called a "gauge symmetry". The U(1) gauge invariance of the classical electromagnetic potential has been know since the 19th century, but some thought the electromagnetic force fields ( ~E and ~B, or Fμν covariantly) were fundamental and the potential fields (Aμ), used to derive them, were just a mathematical tool. This issue was shown to be testable in principle when Werner Ehrenberg and Raymond E. Siday first predicted the Aharonov-Bohm effect in 1949 [287], which was was later 94 Not to be confused with the more basic concept of a field from abstract algebra, which defines a field as "a ring whose nonzero elements form an abelian group under multiplication", or equivalently as "a mathematical set on which the usual operations addition, subtraction, and multiplication are defined for all elements, and division for non-zero elements" (paraphrasing Wikipedia [284]). Tensors themselves are formally constructed as being linear functions of vectors, which rely on the mathematical concepts of vectors spaces, which in turn depend on the definition of a vector sum and scalar product, which depend on the concept of an algebraic field. 95 Canonical quantization is discussed briefly in Appendix A.1.4. 96 String theory is considered by many as a candidate for the quantum theory of gravity, but it is still being understood and is only defined perturbatively. Most agree that a quantum theory of gravity will require new frameworks beyond QFT. A.1 quantum mechanics 201 independently predicted by Yakir Aharonov and David Bohm in 1959 [288]. The effect is predicted to occur in a thought experiment where an electron travels through a region where ~B = 0 effectively, but the vector potential ~A is not trivial, like near the outside of a long solenoid or through the hole along the axis of symmetry of a toroid. Due to traveling through such a region, quantum mechanics predicts that an electron should take on a phase-shift. In an electron interference experiment, like a Young's double-slit, arranged with such a vector potential, the phase-shift should be observable. The effect was first experimentally verified by Robert G. Chambers in 1960 [289], and confirmed later by Peshkin et al. [290] and Osakabe et al. [291]. Physicists now view the gauge fields as more fundamental and the effects of force fields as being a result of the constraints of the gauge symmetry. A.1.4 The importance of symmetry Complementary to the conceptual revolutions that were happening in modern physics during the late 19th and early 20th century due to the development of the theories of quantum mechanics and general relativity, several ideas in mathematics also advanced at that time and have forever changed how theories of physics are constructed. Most importantly were several developments that deepened the understanding of the implications of symmetry on physical systems, including a maturing of the fields of variational calculus, differential geometry, group theory, and algebraic geometry. Noether's theorem Foremost is Noether's theorem of differential symmetries, proved by Emmy Noether in 1915 and published in 1918 [292], which explained that physical quantities that are conserved in time, like energy or momentum, are fundamentally a consequence of the symmetries of the theory. It says that any differentiable symmetry of the action of a physical system has a corresponding conservation law. It generalizes the constants of motion observed in Lagrangian and Hamiltonian mechanics. For example, energy conservation is a consequence of time-translation invariance; angular momentum conservation is a consequence of rotation invariance, etc. (see Table A.1). This revolutionized how physicists describe their theories in the most fundamental and compact form: by specifying the symmetries obeyed by a system. The study of differential and continuous symmetries is the study of Lie groups97, a field founded by the work of Sophus Lie and Friedrich Engel, and extended by Élie Cartan, who succeeded in classifying all the simple Lie groups, which can each be thought of as a differentiable manifold that is simply connected, and where each point on the manifold represents an 97 Many Lie groups are especially useful in physics, for example to describe gauge invariance, as discussed in Appendix A.1.6. Examples of Lie groups include the special orthogonal and special unitary groups, SO(n)/SU(n), which are the set of all n× n orthogonal/unitary matrices with determinate 1, which describe the group of rotations in the space Rn/Cn, respectively. 202 A. a review of the standard model element of a non-abelian group98. Much of the mathematical properties of Lie groups were proved or conjectured independently by Wilhelm Killing. Poincaré invariance ⇒ representations Many important constraints on the types of models that are capable of describing fundamental physics are a result of requring the theory be covariant with respect to the Poincaré group, the group of isometries of Minkowski spacetime, and therefore consistently describe relativistic dynamics. In 1939, Eugene Wigner classified the irreducible unitary representations of the Poincaré group [294]. Under the constraint that the states are eigenstates of mass, the valid representations are the familiar scalars, spinors, vectors, and 2-forms. Combined with consequences of the spin-statistics theorem, this fundamentally limits the types of fields and spins allowed in a relativistic QFT (see Table A.2). Poincaré invariance ⇒ canonical commutation relations Another essential implication of the requirements of Poincaré invariance is evident in the practice of canonical quantization. A quantum field, φ, and its conjugate momentum, π, become operators in a Hilbert space: φ, π; consequently, the classical expressions for the four-momentum of the field, Pμ, and its Lorentz charges, Mμν , can be derived as operators. Requiring that Pμ and Mμν satisfy the Poincaré Lie algebra as generators enforces a set of commutation relations from which one can 98 It is remarkable that the study and classification of Lie groups effectively unified concepts in differential geometry and abstract algebra, and eventually led to Felix Klein's proposal of his influential Erlangen program [293], where he proposed that geometries be classified by their associated symmetries. Table A.1: Conserved Noether currents in the Standard Model. symmetry Lie group Noether charge space-time translations R1,3 ⇐⇒ four-momentum spacial rotations SO(3) ⇐⇒ angular momentum gauge U(1)EM ⇐⇒ EM charge gauge U(1)Y ⇐⇒ weak hypercharge gauge SU(2)L ⇐⇒ weak isospin gauge SU(3)C ⇐⇒ color Table A.2: A modern summary of Wigner's classification of the irreducible unitary representations of the Poincaré group. representation spin statistics typical field example scalar 0 boson φ Higgs spinor 1/2 fermion ψa quarks, leptons vector 1 boson Aμ vector bosons vector× spinor 3/2 fermion ψμα gravitino vector× vector 2 boson gμν graviton A.1 quantum mechanics 203 derive the equal time commutation relations that are often assumed in QFT textbooks: [ φ(t, ~x), φ(t, ~y) ] = [ π(t, ~x), π(t, ~y) ] = 0 , [ φ(t, ~x), π(t, ~y) ] = i ~ δ3(~x− ~y) , for a scalar boson field, φ, for example. This is also how one can motivate the constraints of the spin-statistics theorem. For spinor representations, one is forced to satisfy anti-commutation relations instead of commutation relations for the field and its conjugate momentum, ultimately due to sign constraints in the forms of the single-particle plane-wave solutions of the Dirac equation. Consequently anti-commutation relations also have to be satisfied by creation and anihilation opperators for single particles excitations of a spinor field: { b(~k, s), b(~k′, s′) } = { b†(~k, s), b†(~k′, s′) } = 0 , { b(~k, s), b†(~k′, s′) } = δ3(~k − ~k′) δss′ . From the first line with creation opperators, b†, { b†(~k, s), b†(~k′, s′) } = b†(~k, s) b†(~k′, s′) + b†(~k′, s′) b†(~k, s) = 0 ⇒ b†(~k, s) b†(~k′, s′) = −b†(~k′, s′) b†(~k, s) one can see the interesting consequence that a state created with two spinors is anti-symmetric under exchange, and is said to obey "fermion statistics". Boson fields, on the other hand, satisfy (normal) commutation relations, and are symmetric under exchange. Another point to note is that if a state has two identical fermion creation operators applied: b†2 = 1 2 { b†, b† } = 0 , the amplitude is destroyed. Therefore no two identical fermions (spinors) can be in the same state. Coleman-Mandula theorem The Coleman-Mandula theorem [295] prohibits types of symmetries for a relativistic QFT that are not a simple direct product of the Poincaré group and internal symmetries. Therefore, the ColemanMandula theorem limits the symmetry groups of relativistic QFTs to direct products of the form: (Poincaré group)× ∏ (internal symmetry groups) . Internal symmetries are often described by gauge symmetries, as discussed in Appendix A.1.6, and are represented by unitary Lie groups such as U(1), SU(2), etc. In the case of the SM, the total 204 A. a review of the standard model symmetry group of the field theory is 99 (Poincaré group)× SU(3)C × SU(2)L ×U(1)Y , which will be discussed in more detail in Appendix A.2. According to the assumptions of the Coleman-Mandula theorem, a QFT cannot have symmetries that mix the internal degrees of symmetry and Poincaré symmetry, which is satisfied by the fields being Wigner representations: scalars, vectors, and spinors. The Haag-Lopuszanski-Sohnius theorem (HLS) [38], generalizes the assumptions of the ColemanMandula theorem to not only consider symmetries that have a Lie algebra, but to also consider symmetries that have a Lie superalgebra, which in general can have anti-commutation relations among the generators. The HLS theorem demonstrates that the only consistent combination of Poincaré and internal symmetries that is not a simple direct product is the supersymmetry algebra. This is one of the motivations for considering supersymmetry as a natural extension of the SM, discussed briefly in Section 2.5.1. A.1.5 Scattering theory QED and renormalization Having discussed how naturally constrained the framework of QFT is, let us survey how it developed and discuss an important way it is predictive. The first successful relativistic QFT to be developed was Quantum Electrodynamics (QED), which has its roots in the formulations of Dirac. QED initially seemed to not be a predictive theory because perturbation series describing any interactions appeared to be divergent. These so-called "ultraviolet" divergences are a symptom of the fact that QFT describes interactions as ideal points in space-time and describes space-time as an ideal continuum. An example of the problem is evident even in the classical EM self-energy of a point charge. Certain statistical and quantum mechanical constructions are ill defined in the smalldistance/high-energy continuum limit, unless the limit is taken very carefully. The problem deals directly with the fact that to evaluate the quantum mechanical amplitude for a particle to propagate from a point A to a point B involves an infinite sum of amplitudes of the possible intermediate processes. Analogously the amplitude for the fundamental QED interaction, the photon-electron vertex, involves an infinite sum of processes within an effective vertex (see the illustrations in Figure A.1). In the latter half of the 1940s, a series of developments by Julian Schwinger [298, 299, 300] and independently by Sin-Itiro Tomonaga [301, 302, 303, 304, 305], using the canonical operator formalism, and also independently by Richard Feynman [306, 307], using his path integral formulation 99 The Poincaré group itself is often written as R1,3 ×O(1, 3), the direct product of space-time translations and Lorentz boosts/rotations. A.1 quantum mechanics 205 D B A C Figure A.1: Diagrams illustrating that the QED fermion propagator (left) and the QED vertex (right) are inherently an infinite sum of indistinguisable quantum amplitudes that result in an effective mass and coupling, respectively, when renormalized [296, 297]. of quantum mechanics [308], showed that the divergent terms could be renormalized to give finite predictions. In 1949, Freeman Dyson proved the equivalence of the operator and path integral formulations of QED [309], and he formalized perturbative problems in QED as depending on the Dyson series for the expansion of the S-matrix [310]: Ŝ = T [ exp ( −i ∫ d4x′ ĤI(x′) )] = ∞∑ n=0 (−i)n n! ∫ . . . ∫ d4x1 . . . d 4xn T [ ĤI(x′1) . . . ĤI(x′n) ] , to which we will return. Renormalization involves rescaling the field strengths, masses, and couplings that are the input parameters in the Lagrangian of a theory to account for the finite shifts in the effective mass or coupling due to the infinite sum of quantum corrections. Not only does renormalization succeed in producing finite results in QED, it additionally predicts that the effective coupling should scale with the energy exchanged in an interaction. Essentially, an electron has a cloud of radiated photons and e+e− pairs from quantum corrections that effectively screens part of the EM coupling. A higherenergy interaction probes deeper into this virtual cloud, resulting in an effective coupling that rises with the energy exchanged. The scaling of couplings with energy is described by the renormalization group. Initially physicists were generally skeptical about the mathematical soundness of renormalization as a way to remove infinities in the theory. Beginning in the 1970s, however, physicists began to better appreciate the role of the renormalization group and its applications in effective field theories. Kenneth G. Wilson [311, 312, 313] and others demonstrated the usefulness of the renormalization group in statistical field theories applied to the physics of condensed matter, where it provides 206 A. a review of the standard model important insights into the behavior of phase transitions. Green's functions It turns out that many calculations in QFT reduce to calculating Green's functions, also called "npoint correlation functions", which are defined as the vacuum expectation value of n field operators. The 2-point function is simply the Feynman propagator: G(2)(x, y) = x y , which can be interpreted as the quantum amplitude for a particle created at a space-time position x to propagate to a position y. The blob in the middle of the propagator indicates a sum over all possible intermediate quantum processes that result in the same final state. A rather beautiful calculation, shown in detail in many QFT textbooks100, proves that the n-point correlation function, being the vacuum expectation value of the product of n Heisenberg101 field operators, in the vacuum of the interacting Hamiltonian, |Ω〉, can be expanded and factored as follows: G(n)(x1, . . . , xn) = 〈Ω|T [ φH(x1) . . . φH(xn) ] |Ω〉 = 〈0|T [ φI(x1) . . . φI(xn) Ŝ ] |0〉 〈0|Ŝ|0〉 = ∑ (external diagrams) * (((( (((( ((( ( exp (∑ (vacuum bubbles) ) (((( (((( (((( exp (∑ (vacuum bubbles) ) = ∑ (external diagrams) , where in the above, we have expanded the in-coming and out-going states as momentum eigenstates in the interaction picture102, with plane-wave solutions of the free Hamiltonian. The Dyson series for the S-matrix defined above gives the perturbative expansion for small coupling, where each term results in diagrams with more interaction vertices suppressed by more factors of the coupling constant. When expanded, the series results in diagrams with products of so called "vacuum bubbles" that are not connected to the external part of the diagram like× , 100 See, for example, Peskin and Schroeder [314] or David Tong's lecture notes [315]. 101 In the Heisenberg picture the operators carry the time dependence in the Hilbert space and state vectors are stationary. 102 In the interaction picture the operators carry the time dependence only due to the interaction terms in the Hamiltonian, and are stationary in the free theory. The state vector carries the time-dependence due to the free Hamiltonian. A.1 quantum mechanics 207 but these vacuum bubbles factor into exponentials and cancel in the numerator and denominator. Therefore in the sum over all diagrams, one only has to consider diagrams with parts that are externally connected. Further, due to the cluster decomposition theorem [316, 317], diagrams that do not connect all points, but instead have two or more disconnected parts, contribute only a part of measure zero to the total amplitude, because the amplitude vanishes for diagrams with space-like separated parts, ultimately a consequence of locality in QFT. For example, G(2) for QED is given by: G(2) = = + + + + . . . G(4), describing 2→ 2 interactions, is given by G(4) = = × 4∏i,f ( ) = ( + + + + + . . .) × 4∏i,f () The reduction formula Again assuming that in the problems of interest, the in-coming and out-going states will be in a narrow wave-packet superposition of momentum eigenstates, one can show that the matrix elements of the S-matrix that give the quantum amplitude for some scattering process can be expressed 208 A. a review of the standard model according to the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula [318] as Sfi = 〈f |Ŝ|i〉 = G(n)(−pf , . . . , pi) ∏ f ( G(2)(pf ) )−1 ∏ i ( G(2)(pi) )−1 = × n∏ i,f ()−1 =−iM = −iM (2 π)4 δ4 (∑ pi − ∑ pf ) , where G(n) denotes the momentum-space Fourier transform of the space-time n-point correlation function: G(n)(p1, . . . , pn) ≡ n∏ i [∫ d4pi (2 π)4 e−i pi*xi ] G(n)(x1, . . . , xn) . The expansion of the in-coming and out-going states as momentum eigenstates introduces inverse factors of the propagators that cancel the factors of propagators appearing in G(n). The irreducible matrix element, M, is defined as the remaining part of the diagram, with the external lines held on mass-shell, but summing over all connected intermediate possible diagrams, and integrating over all possible virtual momenta. An overall momentum-conserving δ-function will always result, and a factor of −i is often factored out by convention. Scattering cross sections The scattering theory developed from QFT is especially useful for describing the event rates in experiments at particle colliders. At particle colliders like the LHC, two anti-parallel beams of particles of known energies are squeezed to cross in a small cross-sectional area of the order of a few hundred square microns. In such a scenario one can show that the differential collision rate for some process, dN/dt, factors into the luminosity, L, that characterizes the flux of particles in the beam per area per time, and the differential cross section, dσ, an area proportional to the rate for that process: dN = ε L dt dσ . A.1 quantum mechanics 209 The factor, ε, is a dimensionless variable to account for experimental inefficiencies in reconstructing/identifying/selecting the process. The differential scattering cross section of 2→ n process can be calculated from the n+ 2-point function, which can be expressed in terms of its irreducible matrix element as dσ = ∏ f ( d3pf (2 π)3 2 Ef ) |M|2 4 E1 E2 |v1 − v2| (2 π)4 δ4 ( p1 + p2 − ∑ f pf ) . In the case of 2→ 2 scattering with energies high enough to neglect the masses of the in-coming or out-going particles, one can further simplfy dσ to dσ dΩ ∣∣∣∣ CM = 1 64 π2 E2CM |M|2 , where CM denotes that the dσ is valid in the center-of-momentum reference frame, and ECM is the center-of-momentum energy of the incoming two particles. Integrating dN over some running time for the experiment and over the kinematic phase-space of the process in question gives the theoretical prediction for the expected number of events observed: N = ∫ dt L ∫ dσ ε = (∫ dt L ) A C σ , where A is a dimensionless variable to account for the acceptance, the fraction of events produced in the instrumented fiducial volume selected in the experiment: A = ∫ dt L ∫ fiducial dσ∫ dt L ∫ dσ = ∫ dt L ∫ fiducial dΩ dσdΩ σ ∫ dt L , and C is a dimensionless variable to account for the overall experimental efficiency to reconstruct and identify events from the process: C = ∫ dt L ∫ fiducial dσ ε∫ dt L ∫ fiducial dσ = ∫ dt L ∫ fiducial dΩ dσdΩ ε(Ω)∫ dt L ∫ fiducial dσ . In practice, high-energy physics experiments generally estimate these integrals numerically with Monte Carlo methods, using matrix-element event generators and often very detailed simulations103 of the geometry, material, and instrumentation of the experiments. The integrated luminosity, ∫ dt L, is measured independently [180, 319]. A.1.6 Gauge invariance U(1)EM local gauge invariance As discussed previously, gauge invariance plays an important role in constructing the SM. As an example, consider the U(1)EM gauge invariance of electrodynamics. The fundamental representation 103 See the brief discussion of ATLAS simulation in Section 3.6. 210 A. a review of the standard model of U(1) is a complex number with unit modulus, which can be written ei θ, where θ is a real number. So U(1) gauge invariance demands that the action be unchanged by a transformation that shifts the phase of the fermion fields: ψ(x)→ ψ′(x) = ei θ(x) ψ(x) . Note that we are additionally requiring that the gauge invariance be local, since θ(x) being an arbitrary function implies that the phase can be transformed independently at every point in spacetime. Consider the impact this has on the Lagrangian for a free Dirac fermion: L = i ψ γμ ∂μ ψ −m ψ ψ . The conjugate field, ψ, transforms as ψ(x)→ e−i θ(x) ψ(x) . and the phase shift is just right to cancel in the m ψ ψ term. But in the kinetic term, one needs to consider the transformation of ∂μ ψ, which accumulates an additional term because we allowed the phase to be local: ∂μ ψ(x)→ ei θ ∂μ ψ + i ei θ ψ ∂μ θ . This second term breaks the gauge invariance of the Lagrangian. Posit that one can introduce an additional four-vector field, Aμ, to cancel this second term, making the derivative gauge invariant. The covariant derivative is defined: Dμ ψ ≡ (∂μ − i q Aμ) ψ , where Aμ is referred to as the "connection" in the covariant derivative. Let us express the U(1) transformation of Aμ as Aμ → Aμ + δAμ Consider how Dμ ψ transforms under U(1): Dμ ψ ′ = ∂μ ψ ′ − i q A′μ ψ′ = ei θ ∂μ ψ + i e i θ ψ ∂μ θ − i q Aμ ei θ ψ − i q δAμ ei θ ψ = ei θ (∂μ − iq Aμ)} {{ } Dμ ψ ψ + i ei θ ψ (∂μ θ − q δAμ)} {{ } 0 = ei θ Dμ ψ . Note that now the phase will cancel with the ψ only if we require the term on the right to be zero, and this constrains how Aμ can transform: ⇒ δAμ = 1 q ∂μ θ A.1 quantum mechanics 211 ⇒ Aμ → Aμ + 1 q ∂μ θ . Now if we replace the derivative in the Lagrangian for the Dirac field with the covariant derivative under U(1), then the entire Lagrangian will be gauge invariant: L = i ψ γμ Dμ ψ −m ψ ψ − 1 4 Fμν F μν = i ψ γμ ∂μ ψ + q ψ γ μ ψ Aμ −m ψ ψ − 1 4 Fμν F μν = LQED . Note that this results in a Lagrangian that no longer describes a free Dirac fermion, but has an additional interaction term between the fermion, ψ, and the gauge boson field, Aμ, describing the photon. The term with Fμν ≡ ∂μ Aν − ∂ν Aμ is included to account for the kinematic energy of the gauge field (which will be generalized in the following section). The Lagrangian for QED can be derived by requiring local U(1)EM gauge invariance. This is an example of the general fact that demanding local gauge invariance under some gauge group requires the introduction of gauge boson fields to serve as the connections in the corresponding covariant derivatives. Yang-Mills gauge theories While the importance of the U(1)EM gauge invariance of electrodynamics is something that has been recognized since the development of classical electrodynamics, considering gauge invariance under general SU(n) transformations as the guiding principle in constructing theories of elementary interactions was first proposed in 1954 by Yang and Mills, in an attempt to describe the isospin invariance observed among the spectrum of hadrons [1]. Any unitary transformation among the internal degrees of freedom of a field, ψi, can be written as ψi → exp ( i θa T aij ) ψj , where T aij are the generators of the gauge symmetry group, and θ a are dimensionless real parameters. For infinitesimal transformations, one can expand the exponential: ψi → ( 1 + i θa T aij ) ψj . One can define a covariant derivative: Dμ ψi ≡ ∂μ ψi + i g Aaμ T aij ψj . where gauge boson fields, Aaμ, serve as connections and g is a free dimensionless coupling parameter. Then one can show104 that the covariant derivate Dμ ψi will transform with the same phase factor 104 See, for example, Peskin chapter 15 [314], and Martin chapter 10 [244]. 212 A. a review of the standard model as the fermion field it acts on, provided that the gauge fields transform as Aaμ → Aaμ − 1 g ∂μ θ a − fabc θb Acμ , where fabc are the structure constants of the Lie algebra of the gauge group. Note that for abelian groups, the structure constants are zero, which is why there was not a third term in the example for U(1)EM discussed above. It follows that one can construct Lagrangian terms that are both Lorentz and gauge invariant with space-time tensors constructed from Aaμ, called the "field strength tensors": F aμν ≡ ∂μ Aaν − ∂ν Aaμ − g fabc Abμ Acν which transform as F aμν → F aμν − fabc θb F cμν . The kinetic energy term of the Lagrangian for the gauge fields can be expressed as Lgauge = − 1 4 F aμν F aμν . and is Lorentz and gauge invariant. Specifying the gauge symmetry, and the field content of the fermions fully determines a YangMills theory: LYang-Mills = Lgauge + Lfermions = −1 4 F aμν F aμν + i ψi γ μ Dμ ψi +m ψi ψi . The gauge symmetry determines the gauge boson fields of the theory. Combining this with a set of given Dirac fields describing the fermions determines the allowed interaction terms of the Lagrangian, by using gauge-covariant derivatives. In this way, the structure of the gauge symmetry of a theory specifies the structure of its interactions. A.2 The Standard Model A.2.1 Quarks, leptons, and gauge bosons In the SM, the fermions are described by spinor representations of the Poincaré group. The boson force carriers are described by gauge fields that are a result of requiring invariance of the action under a specific gauge group, which specifies a particular symmetry among the internal degrees of freedom of the spinor fields: SU(3)C × SU(2)L ×U(1)Y . Gauge invariance requires the introduction of gauge boson fields Gαμ , W a μ , and Bμ, which serve as the connections in the covariant derivatives needed in the terms for the fermion kinetic energies105. 105 See the discussion of gauge invariance and covariant derivatives in Appendix A.1.6. A.2 the standard model 213 SU(3)C × SU(2)L × U(1)Y ⇓ ⇓ ⇓ Gαμ : ( 8,1, 0 ) W a μ : ( 1,3, 0 ) Bμ : ( 1,1, 0 ) α ∈ { 1, 2, . . . , 8 } a ∈ { 1, 2, 3 } The gauge-covariant derivative is Dμ ψ ≡ ( ∂μ + i g1 Bμ Yl/r + [ i g2 W a μ T a ] l + [ i g3 G a μ τ a ] c ) ψ . Besides this particular gauge invariance, another peculiar feature of the SM is the structure of the representations of the fermions. The bracketed terms only appear for interaction terms with fermions that have the relevant Noether charges for that gauge symmetry. Some fermions transform as singlets under part of the SM gauge symmetries, and therefore not all fermions participate in all the gauge interactions. The types of fermions happen to divide evenly between quarks, which carry red, green, and blue color charges in a triplet representation of SU(3)C, and leptons which transform as color singlets. Table A.3 shows the gauge-group representations of the SM fermions. Another important feature is that only the left-chiral part of the fermions (as denoted by the l) form doublet representations of SU(2), while the right-chiral part of the fields are singlets. Finally, Y denotes the hypercharge quantum number carried by all fermions as a consequence of their U(1)Y invariance, but note that the leftand right-chiral parts of the fields form separate singlets. These chiral ingredients of the SM are what allow for parity and CP violation in the weak interactions. Table A.3: Gauge-group representations of the SM fermions. The rows are components of weak iso-spin, and the columns are components of color. The sets of three numbers on right denote if the fields have a singlet or triplet representation of SU(3)C, doublet or singlet representation of SU(2)L, and their weak hypercharge quantum number respectively. Left-handed quarks: ( url u g l u b l drl d g l d b l ) , ( crl c g l c b l srl s g l s b l ) , ( trl t g l t b l brl b g l b b l ) : ( 3,2, 16 ) Right-handed quarks: ( urr u g r u b r ) , ( crr c g r c b r ) , ( trr t g r t b r ) : ( 3,1, 23 ) ( drr d g r d b r ) , ( srr s g r s b r ) , ( brr b g r b b r ) : ( 3,1,− 13 ) Left-handed leptons: ( νel el ) , ( νμl μl ) , ( ντl τl ) : ( 1,2,− 12 ) Right-handed leptons: er, μr, τr : ( 1,1,−1 ) 214 A. a review of the standard model A.2.2 The Standard Model Lagrangian The SM is a Yang-Mills theory with the gauge group: SU(3)C × SU(2)L ×U(1)Y, and with the particular combination of triplet/doublet/singlet representations of fermions discussed in the previous section. Additionally, an SU(2) doublet of complex scalar Higgs fields is coupled to the electroweak gauge bosons and to the fermions following the Higgs mechanism discussed in the following section. The full Lagrangian density is kinetic energies and self-interactions of the gauge bosons LSM = − 1 4 Bμν B μν − 1 4 W aμν W aμν − 1 4 Gαμν G αμν kinetic energies and electroweak interactions of the left-handed fermions + Li γ μ ( i ∂μ − 1 2 g1 Yil Bμ − 1 2 g2 σ aW aμ ) Li kinetic energies and electroweak interactions of the right-handed fermions + Ri γ μ ( i ∂μ − 1 2 g1 Yir Bμ ) Ri strong interactions between quarks and gluons + i g3 2 Qj γ μ λα Gαμ Qj electroweak boson masses and Higgs couplings + 1 2 ∣∣∣∣ ( i ∂μ − 1 2 g1 Bμ − 1 2 g2 σ aW aμ ) Φ ∣∣∣∣ 2 − V (Φ) fermion masses and Higgs couplings − ( ydk` Lk ΦR` + y u k` Rk Φ L` + h.c. ) . It is important to note that there are several types of spaces being indexed above. Some remarks about notation: • Bμν , W aμν , and Gαμν are the field strength tensors defined for the gauge field of U(1)Y: Bμν ≡ ∂μ Bν − ∂ν Bμ , for the 3 gauge fields of SU(2)L: W aμν ≡ ∂μW aν − ∂ν W aμ − g2 εabcW bμW cν for a ∈ { 1, 2, 3 } , and for the 8 gauge fields of SU(3)C: Gαμν ≡ ∂μ Gαν − ∂ν Gαμ + g3 fαβγ Gβμ Gγν for α ∈ { 1, 2, . . . , 8 } , with fαβγ being the structure constants of SU(3). A.2 the standard model 215 • L and R denote the left and right projections of the Dirac fermion fields, including quarks and leptons. Q denote the Dirac fermion fields for the quarks, which have leftand right-chiral parts: Q = L + R. But note that the strong interactions are not chiral. • μ and ν are four-vector indices, which result from the fact that the gauge fields transform as four-vector representations of the gauge symmetries of the Standard Model (SU(3)C × SU(2)L ×U(1)Y). • a, b, c index the 3 generators of SU(2), expanded in terms of the Pauli matrices: T a = 1 2 σa for a ∈ { 1, 2, 3 } . • α, β, γ index the 8 generators of SU(3), expanded in terms of the Gell-Mann matrices: τα = 1 2 λα for α ∈ { 1, 2, . . . , 8 } . • i, j, k, ` sum over the generations of the Standard Model. In the chiral terms related to the electroweak and Higgs interactions, coupling to the leftand right-handed spinors: L and R, the sums over generations include both leptons and quarks. In the strong interaction term, j only indexes generations of the quarks, since the leptons do not interact strongly. • There are 3 types of indexes left implied (i.e. being contracted but not written explicitly): 1. the 4 components of the spinors of the fermion fields: L, R, Q, and their corresponding Dirac matrices: γμ, 2. the 2 components of the SU(2)L doublets: L, R, Φ, and their corresponding Pauli matrices: σa, 3. the 3 components of the SU(3)C triplets: Qj , and their corresponding Gell-Mann matrices: λα. • Φ is the SM Higgs doublet: Φ ≡  φ + φ0   : ( 1,2, 1 2 ) , and it is conventional to define Φ ≡   0 1 −1 0  Φ∗ =   φ 0∗ −φ+∗   . • h.c. denotes the Hermitian conjugate of the previous terms in the parenthesis. Expanding this Lagrangian in the Dyson series for the S-matrix gives the interaction vertices shown in Figure A.2. 216 A. a review of the standard model Figure A.2: The interactions of the Standard Model [320]. A.2.3 The Higgs mechanism Motivation Terms in the Lagrangian that would represent Lorentz invariant masses for the gauge bosons would look like 1 2 m2A A μ Aμ . But because the gauge bosons have non-trivial gauge transformations: Aμ → Aμ + 1 e ∂μ θ , such terms are not gauge invariant. It seemed that requiring gauge invariance excludes the theory from describing massive gauge bosons, but gauge invariance is seen as the motivating principle behind the existence of boson fields in Yang-Mills theories. The mystery of how to incorporate massive boson fields into gauge invariant theories was solved by the Higgs mechanism. A.2 the standard model 217 Also note that in the SM, Dirac fermion mass terms are no longer gauge invariant106 because they are not gauge singlets: m ψ ψ = m (ψl ψr + ψr ψl) The left-handed fermions form SU(2)L doublets, while the right-handed are SU(2)L singlets, so their products do not close. Goldstone's theorem and the Higgs mechanism In 1960, spontaneous symmetry breaking (discussed more bellow) was described by Yoichiro Nambu [321] to explain the apparent breakdown of EM gauge invariance in the BCS theory of superconductivity [322, 323]. Further, he suggested that an analogus mechanism could used in particle physics to explain the approximate but broken symmetries among the spectrum of hadrons, and suggested the lightest meson, the pion was a boson predicted to exist as a consequence chiral symmetry breaking of the strong interactions [324, 325]. In 1961, Jeffery Goldstone [326] generalized Nambu's ideas to any spontaneously broken symmetry of relativistic QFT. He motivated that spontaneous breaking of a symmetry in a relativistic field theory always results in massless spin-zero bosons, called "Goldstone bosons", and proved the conclusion was a theorem of QFT the following year with Abdus Salam and Steven Weinberg [327]. In 1964, three groups: Robert Brout and Francois Englert [2]; Peter Higgs [3, 4]; and Gerald Guralnik, Carl R. Hagen, and Tom Kibble [5], independently demonstrated an exception to Goldstone's theorem, showing that Goldstone bosons do not occur when a spontaneously broken symmetry is local. Instead, the Goldstone mode provides the third polarization of a massive vector field, resulting in massive gauge bosons. The other mode of the original scalar doublet remains as a massive spinzero particle, the Higgs boson. This is the Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism, or Higgs mechanism. In the SM, the Higgs boson also couples to the fermions, generating their bare masses, as discussed briefly later in Appendix A.2.6 and A.2.7. Electroweak symmetry breaking in the SM The Higgs mechanism is utilized in the unified model of the electroweak interactions of Sheldon Glashow [6], Steven Weinberg [7], and Abdus Salam [8, 9, 10], that forms the modern basis of the Standard Model. As implemented in the SM, the Higgs mechanism couples the SU(2)L and the U(1)Y parts of the gauge symmetry through a Higgs field that is a complex scalar invariant under 106 A fermion mass term, m ψ ψ, is gauge invariant in QED, see Appendix A.1.6, but is not gauge invariant in the SM. 218 A. a review of the standard model | [GeV]\| 0 50 100 150 200 250 4 V / ( 10 0 G eV ) -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Figure A.3: Illustration of the Higgs potential, V (Φ). (left) The shape of the potential in any two components of: Re(φ+), Im(φ+), Re(φ0), Im(φ0). (right) A plot of the Higgs potential assuming mH = 126 GeV, as shown in Table A.5 [328]. U(1)Y and an SU(2)L doublet: Φ ≡  φ + φ0   : ( 1,2, 1 2 ) , where both φ+ and φ0 are complex numbers. The potential of the Higgs field is expanded as V (Φ) = μ2 Φ† Φ + λ ∣∣Φ† Φ ∣∣2 . To spontaneously break the symmetry, the potential V (Φ) is chosen to have an unstable maximum at Φ = 0 by requiring that μ2 < 0 (see Figure A.3). Finding the minimum of the potential: μ2 + 2 λ Φ†Φ ∣∣ min = 0 gives degenerate minima with Φ† Φ = |Φ|2 = |φ+|2 + |φ0|2 = −μ 2 2 λ . At energies low compared to the local maximum in the potential, the vacuum settles into the degenerate minima, a process called "spontaneous symmetry breaking". The freedom in phase of the minimum results in the U(1)EM symmetry after electroweak symmetry breaking: SU(2)L ×U(1)Y → U(1)EM . For purposes of notation, one can choose all of the vacuum expectation value to be real and in one component of the Higgs doublet: 〈Φ〉 =   0 v/ √ 2   , A.2 the standard model 219 The vacuum expectation value can be expressed in terms of the parameters in the Higgs potential: 〈Φ† Φ〉 = v 2 2 = −μ2 2 λ ⇒ v ≡ √ −μ2 λ . Now, one can expand Φ around this new vacuum, to find the spectrum of excitations in the lowenergy theory: Φ(x) = 1√ 2   0 v + h(x)   . Massive gauge bosons To see the effect the non-zero Higgs vacuum has on the gauge bosons, one can expand the appropriate term in the Lagrangian: ∣∣∣∣ ( −1 2 g1 Bμ − 1 2 g2 σ aW aμ ) Φ ∣∣∣∣ 2 = 1 8 ∣∣∣∣∣∣  g1 Bμ + g2 W 3 μ g2 (W 1 μ − iW 2μ) g2 (W 1 μ + iW 2 μ) g1 Bμ − g2 W 3μ    0 v   ∣∣∣∣∣∣ 2 = 1 8 g22 v 2 (W 1μ − iW 2μ)(W 1μ + iW 2μ) + 1 8 v2 (g2 W 3 μ − g1 Bμ)(g2 W 3μ − g1 Bμ) . Let W±μ ≡ 1√ 2 (W 1μ ∓ i W 2μ) , and Zμ ≡ 1√ g21 + g 2 2 (g2 W 2 μ − g1 Bμ) . Then the above Lagrangian terms become 1 4 v2 g22 } {{ } 1 2 m 2 W W+μ W −μ + 1 4 v2 (g21 + g 2 2) 2 } {{ } 1 2 m 2 Z Zμ Z μ . Here we recognize the appropriate terms for generating the tree-level masses for the W± and Z bosons: ⇒ mW = v g2√ 2 and mZ = v√ 2 √ g21 + g 2 2 . 220 A. a review of the standard model The Higgs boson Plugging the vacuum expectation into V (Φ) and finding the coefficient for the h2 term reveals that a tree-level mass is also generated for the boson associated with the Higgs field: V = μ2 2 (v + h)2 + λ 4 (v + h)4 ∼ μ 2 2 h2 + λ 4 6 v2 h2 , to order h2 = μ2 2 h2 + 3 2 (−μ2 v2 ) v2 h2 = −μ2 h2 = 1 2 m2H h 2 ⇒ mH = √ −2 μ2 = √ 2 λ v2 . A.2.4 Electroweak theory A unified theory of the electroweak interactions, the cornerstone of the SM, was the culmination of several incremental developments including Fermi's four-fermion interaction model for β-decay in 1934 [329] and the first direct detection of neutrinos in 1956 at the Cowan-Reines nuclear reactor experiment [330]. Tsung Dao Lee and Chen Ning Yang published a systematic review of parity conservation in 1956 [331], noting that parity conservation could be verified and constrained by atomic electromagnetic interactions, but it had not been tested for weak interactions. They further suggested experiments that could probe for parity conservation in β-decays and meson or hyperon decays. The following year, teams led by Chien-Shiung Wu [332] and Leon Lederman [333] discovered the parity violation of the weak interactions in β-decays of cobalt-60 and muon decays, respectively. One of the most important features of the unified theory of the electroweak interactions is that the gauge group is chiral; the left-chiral part of the fermion fields forms SU(2) doublets, allowing the theory to have parity-violating and CP-violating interactions. E. C. George Sudarshan and Robert Marshak were first to propose a vector–axial-vector (V-A) chiral couplings for the weak interaction in 1958 [334], followed by similar theories by Murray Gell-Mann and Feynman [335] and by Nambu [336]. In 1961, Glashow [6] was the first to suggest the SU(2)×U(1) gauge structure to unify the electromagnetic and weak interactions. Weinberg [7] and Salam [10] incorporated the Higgs mechanism into Glashow's electroweak theory in 1967, formulating the modern basis of the SM. Bejamin Lee demonstrated the first renormalizable theory with a spontaneously broken global symmetry in 1969 [337]. In 1972, during his doctoral studies advised by Martinus Veltman, Gerardus 't Hooft proved that all Yang-Mills theories with massive gauge bosons produced via the Higgs A.2 the standard model 221 mechanism, including the SM, are renormalizable [338, 339]. Then, 't Hooft and Veltman introduced dimensional regularization as a new general method for regularizing gauge theories [340]. By the early 1970s, these theoretical developments formed the consensus that the weak interactions should be mediated by gauge bosons in analogy with the photon from QED, but that the bosons needed to be sufficiently massive to limit the range of weak interactions to nuclear scales. While charged-current interactions were known to exist from neutrino-production processes like β-decay, neutral currents had not been observed until 1973, when the Gargamelle experiment first observed neutral currents exchanged in a bubble chamber exposed to a beam of neutrinos [341, 342]. Measuring the ratio of charged and neutral currents at Gargamelle resulted in the first measurement of the Weinberg angle that parametrizes the mixing of the W 3μ and Bμ bosons in the Glashow-Weinberg-Salam model:  Zμ Aμ   =  cos θW − sin θW sin θW cos θW    W 3 μ Bμ   where the Weinberg angle is determined by the ratios of the weak couplings and boson masses by the following relationships: ⇒ sin θW = g1√ g21 + g 2 2 cos θW = g2√ g21 + g 2 2 = mW mZ tan θW = g1 g2 . The coupling of the resulting electromagnetic interaction, mediated by the Aμ boson, is related to the fundamental couplings by e ≡ √ 4 π α ≡ g1 cos θW ≡ g2 sin θW , where α ≈ 1/137 is the traditional EM fine-structure constant. The fundamental coupling g2 is related to Fermi's effective coupling constant for charged-current interactions by GF√ 2 ≡ g 2 2 8m2W . Knowing these couplings and the newly measured Weinberg angle allowed for the first quantitative prediction of W± and Z boson masses: m2W = √ 2 GF g22 8 = √ 2 GF e2 8 sin2 θW = π α√ 2GF 1 sin2 θW ⇒ mW = √ π α√ 2GF 1 sin θW ≈ (37 GeV) 1 0.48 ≈ 80 GeV 222 A. a review of the standard model and mZ = mW cos θW ≈ 80 GeV 0.88 ≈ 90 GeV . In 1976, this led to Carlo Rubbia to suggest converting the CERN SPS pp-collider to the first pp-collider to directly produce the W± and Z gauge bosons. In 1983, after the construction of the first anti-proton factory and the commissioning of the accelerator complex at CERN, the UA1 [343, 344, 345, 346] and UA2 [347, 348] collaborations discovered the W± and Z bosons in high-pT lepton events, with masses clearly consistent with the Glashow-Weinberg-Salam prediction, firmly establishing the SM [349]. A.2.5 Strong interactions The quark model and confinement Meanwhile, physicists studying hadrons in the 1950s and 1960s were beginning to suspect more and more that hadrons are composite from studying the spectrum of hadrons and their decays, but theorists were still struggling to find a theory of the strong interactions that bind hadrons. In 1957, Murray Gell-Mann and Arthur Rosenfeld published the first review review of particle physics, cataloging the particle spectrums and decay rates observed [350]. In 1964, Gell-Mann [351] and George Zweig [352, 353] independently proposed the quark model which classified hadrons as composite states of 3-quark baryons or quark-antiquark mesons. Inelastic electron-proton collision experiments at the Stanford Linear Accelerator Center (SLAC)107 in 1969 verified the composite structure of the proton [354, 355]. One of the most important implications of identifying the symmetries of a system is that one can then predict its degenerate states. Even when a symmetry is approximate, the spectrum of possible 107 Now: SLAC National Accelerator Laboratory. Table A.4: Approximate values of the electroweak parameters. Only three of the dimensionless and one of the ∼ GeV parameters are fundamental, and the remaining can be derived [136]. g1 ≈ 0.36 mW ≈ 80.4 GeV g2 ≈ 0.65 mZ ≈ 91.2 GeV e ≈ 0.31 v ≈ 246 GeV sin2 θW ≈ 0.23 √ 2GF ≈ (246 GeV)−2 Table A.5: The SM parameters of the Higgs vacuum potential, assuming the Higgs-like particle observed at the LHC, as discussed in Section 2.3.2, is the SM Higgs boson. Two of the three parameters: μ, λ, and mH are fundamental and one can be derived. mH ≈ 126 GeV −μ2 ≈ (126 GeV)2/2 λ ≈ 0.13 A.2 the standard model 223 e μ τ u d c s b t T e V G e V M e V k e V e V m e V neutrinos Figure A.4: Mass range of the SM fermions [356]. For approximate values of the masses, see Table A.6. states of a system will cluster into approximate representations of the symmetries of the system. In the 1960s, the known hadrons consisted of combinations of u, d, and s quarks, which each have relatively small masses (1–100 MeV, see Table A.6). An effective way to predict the spectrum of hadrons is to consider SU(3) transformations of the u, d, s flavors (ignoring color for the moment). This SU(3)flavor symmetry is approximate because of the differences in the masses and charges of the quarks breaks the symmetry (see Figure A.6). When a quark and anti-quark combine to form a meson, they transform as an octet and a singlet of states under SU(3)flavor rotations: 3 ⊗ 3 = 8 ⊕ 1 (see Figure A.5). The two neutral s = 0 octet states and the singlet mix in general, as is the case for the η/η′ and φ/ω mesons. When three quarks combine to form a baryon, they transform as a fully symmetric108 decuplet, two octets that 108 Symmetry under exchange is not an issue for mesons because quarks and anti-quarks are distinguishable, but combinations of quarks in a baryon are not in general. Table A.6: Masses and electroweak charges of the SM fermions [136]. For a visualization of the range of masses, see Figure A.4. name approx. bare mass T 3l Yl Yr Q quarks up (u) 1–3 MeV +1/2 +1/6 +2/3 +2/3 down (d) 4–6 MeV -1/2 +1/6 -1/3 -1/3 charm (c) 1,300 MeV +1/2 +1/6 +2/3 +2/3 strange (s) 100 MeV -1/2 +1/6 -1/3 -1/3 top (t) 173,000 MeV +1/2 +1/6 +2/3 +2/3 bottom (b) 4,200 MeV -1/2 +1/6 -1/3 -1/3 leptons νe . 1 eV +1/2 -1/2 0 0 e 0.5 MeV -1/2 -1/2 -1 -1 νμ . 1 eV +1/2 -1/2 0 0 μ 106 MeV -1/2 -1/2 -1 -1 ντ . 1 eV +1/2 -1/2 0 0 τ 1,776 MeV -1/2 -1/2 -1 -1 224 A. a review of the standard model Figure A.5: (left) Pseudoscalar mesons (JPC = 0−+). (right) Pseudovector mesons (JPC = 1−−) [358]. Figure A.6: (left) Spin-3/2 baryon decuplet. (right) Spin-1/2 baryon octet [358]. are symmetric under exchange of the first two or the last two quarks, and a fully antisymmetric singlet: 3 ⊗ 3 ⊗ 3 = 10S ⊕ 8M ⊕ 8M ⊕ 1A (see Figure A.6). When the Ω− baryon (consisting of a sss combination of quarks) was discovered at Brookhaven National Laboratory (BNL) in 1964 [357], it completed the symmetric decuplet predicted by the quark model and established the model's success. In 1964, Oscar Greenberg noted that the antisymmetry under exchange required of fermions by the spin-statistics theorem could not be accounted for in states that appeared fully symmetric like the ∆++ ( = |uuu, ↑↑↑〉 ) baryon [359]. The next year, Moo-Young Han and Nambu proposed a new conserved current called "color" to solve this symmetry problem for baryons [360]. The red/green/blue color charges form a triplet representation of an independent SU(3) symmetry. Baryons are always in the fully antisymmetric color singlet of 3⊗3⊗3, and therefore the remaining spin and flavor parts of the state-vector must be a fully symmetric combination like for the ∆++. For the baryon octet, the mixed symmetry octets of spin and flavor are combined to give a fully symmetric combination. A.2 the standard model 225 Further, Han and Nambu suggested that the strong force was mediated by the eight SU(3) gauge bosons that later became known as "gluons". These developments marked the beginning of the formation of the theory of Quantum Chromodynmaics (QCD), and by 1973 it was seen as integrated into the SM [15]. In 1979, the TASSO Collaboration discovered evidence for the gluon in events with a 3-jet signature [361, 362]. The strong force is sufficiently strong compared to the masses of the lightest quarks that when quarks in a hadron are given enough energy to overcome the binding energy of the hadron, they also have sufficient energy to pair-produce other quarks until the color charge is neutralized and all quarks are bound into color singlets. This feature of the strong interactions is called "confinement"-that all quarks are bound in color-singlet combinations and never bare. The process of an energetic colored state fragmenting into additional hadrons is called "hadronization". A "jet" refers to the collection of nearby hadrons, which will be relatively colinear due to the boost of the outgoing high-pT quark or gluon that hadronized to produce them109. In high-energy collisions producing strongly interacting particles, the cross section is dominated by dijet production, as predicted by Sterman and Weinberg in 1977 [363]. High-pT dijet production was first observed at UA2 [364] in 1982 and UA1 [365] in 1983. The parton picture and asymptotic freedom The organization of hadrons into multiplets, discussed previously, concerned the valence quark content of hadrons. But the proton, for example, also derives much of its physical properties from a cloud of virtual particles it carries with it from quantum corrections. Back in 1969, Bjorken [366] and Feynman [367] both argued that high-energy experiments demonstrated that quarks were real particles because at high enough collision energies, quarks should not care that they are in a bound system and the physics should be described by collisions between free quarks or gluons within hadrons, which Feynman collectively called "partons". Eventually this asymptotic freedom was explained by Politzer [11] and Gross and Wilczek [12, 13, 14] as being a consequence of the strong interaction having a negative β-function, which characterizes the renormalization group equation that governs the scaling of the coupling constant with energy. Strong interactions get weaker at higher energies. According to the factorization theorem [368, 369], asymptotic freedom allows one to factor the amplitude of high-energy hadron collisions into the cross section for the parton-level interaction, convolved with Parton Distribution Functions (PDFs), fi(x), which describe the probability for a parton of flavor i to carry fraction x of the total momentum of the hadron. Below the factorization 109 Jet reconstruction at ATLAS will be discussed briefly in Section 3.3.6. 226 A. a review of the standard model x -410 -310 -210 -110 1 )2 xf (x ,Q 0 0.2 0.4 0.6 0.8 1 1.2 g/10 d d u uss, cc, 2 = 10 GeV2Q )2 xf (x ,Q x -410 -310 -210 -110 1 )2 xf (x ,Q 0 0.2 0.4 0.6 0.8 1 1.2 g/10 d d u u ss, cc, bb, 2 GeV4 = 102Q )2 xf (x ,Q MSTW 2008 NLO PDFs (68% C.L.) Figure 1: MSTW 2008 NLO PDFs at Q2 = 10 GeV2 and Q2 = 104 GeV2. with broader grid coverage in x and Q2 than in previous sets. In this paper we present the new MSTW 2008 PDFs at LO, NLO and NNLO. These sets are a major update to the currently available MRST 2001 LO [15], MRST 2004 NLO [18] and MRST 2006 NNLO [21] PDFs. The "end products" of the present paper are grids and interpolation code for the PDFs, which can be found at Ref. [27]. An example is given in Fig. 1, which shows the NLO PDFs at scales of Q2 = 10 GeV2 and Q2 = 104 GeV2, including the associated one-sigma (68%) confidence level (C.L.) uncertainty bands. The contents of this paper are as follows. The new experimental information is summarised in Section 2. An overview of the theoretical framework is presented in Section 3 and the treatment of heavy flavours is explained in Section 4. In Section 5 we present the results of the global fits and in Section 6 we explain the improvements made in the error propagation of the experimental data to the PDF uncertainties, and their consequences. Then we present a more detailed discussion of the description of di!erent data sets included in the global fit: inclusive DIS structure functions (Section 7), dimuon cross sections from neutrino–nucleon scattering (Section 8), heavy flavour DIS structure functions (Section 9), low-energy Drell–Yan production (Section 10), W and Z production at the Tevatron (Section 11), and inclusive jet production at the Tevatron and at HERA (Section 12). In Section 13 we discuss the low-x gluon and the description of the longitudinal structure function, in Section 14 we compare our PDFs with other recent sets, and in Section 15 we present predictions for W and Z total cross sections at the Tevatron and LHC. Finally, we conclude in Section 16. Throughout the text we will highlight the numerous refinements and improvements made to the previous MRST analyses. 5 Figure A.7: NLO PDFs for the proton at Q2 = 10 GeV2 (left) and Q2 = 104 GeV2 (right) [54]. scale, the QCD behavior is non-perturbative, but at high-Q2 (the scale of the momentum-transfer squared), the amplitud can be factored as: σ(pp→ X) = ∑ ij ∫ dx1 dx2 fi(x) fj(x) σ(ij → X) , where the PDFs depend on the Q2 scale of the factorization. PDFs can be evolved to different Q2 scales using the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) [370, 371, 372] and the Balitsky-Fadin-Kuraev-Lipatov (BFKL) [373, 374] equations. Examples of proton PDFs for the collisions at the LHC are shown in Figure A.7. Proton PDFs are best c nstrained at el ctronproton colliders like HERA. Because PDFs are necessary to calculate cross sections for collisions with hadrons, the measurement of PDFs and the estimation of their uncertainties is an active area research r leva t for searches for new physics at the LHC [54]. A.2.6 Quark flavor mixing The Cabibbo angle Excited mesons and baryons have preferences for certain weak decays. In 1963, Nicola Cabibbo proposed a way to preserve a universal coupling for the charged-current weak interaction, if the quark eigenstates of the charged-current weak interaction are mixtures of the mass eigenstates of A.2 the standard model 227 the total Hamiltonian:  d ′ s′   =   cos θC sin θC − sin θC cos θC    d s   . By comparing the relative branching fractions of certain leptonic decay modes, such as K+ → μ+ ν and π+ → μ+ ν, Cabibbo was able to single-out charged-current weak interactions to estimate the Cabibbo mixing angle: θC ≈ 0.23 [375]. Three generations of quarks In 1970, Glashow, Iliopoulos, and Maiani proposed that a fourth quark: charm, completing the second weak-isospin doublet with the strange quark, was necesary to cancel box diagrams contributing to neutral kaon decays to suppress unobserved flavor-changing neutral currents [376]. In 1974, the charm quark was discovered by two independent teams led by Burton Richter at SLAC [377] and Samuel Ting at BNL [378]. Both laboratories produced J/ψ mesons110 (cc) on resonance in e+e− collisions. The b-quark of the third quark doublet was discovered in 1977 by a team led by Lederman when the Υ meson (bb) was first produced at Fermilab [379]. Complementary discoveries about the three generations of leptons were also made, as discussed briefly in the following section. It has come to seem that nature has three generations of fermions (as shown Figure 2.1 and Table A.3), three doublets that each have the same quantum numbers but higher masses for each successive generation. The completion of the three doublets with the discovery of the top quark had to wait until 1995 for the operation of the world's first superconducting proton-antiproton collider, the Tevatron, where the top quark was discovered by the CDF [380] and DØ [381] collaborations. Note that high-energy experiments had to climb orders of magnitude in collision energy to discover all the known flavors of quarks because their mass hierarchy spans 5 orders of magnitude, with the most massive quark being the top quark with a mass of about 173 GeV (see Figure A.4). The CKM matrix In 1973, Kobayashi and Maskawa generalized the quark-flavor-mixing formalism of Cabibbo to include three generations, defining the Cabibbo-Kobayashi-Maskawa (CKM) matrix [382]:   d′ s′ b′   = VCKM   d s b   =   Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb     d s b   . The primed states on the left are the eigenstates of the charged-current weak interaction and the states on the right are mass eigenstates that are slightly mixed among the weak eigenstates. While 110 Now dubbed "J/ψ", the cc meson was first called "J" by the BNL team and "ψ" by the team at SLAC. 228 A. a review of the standard model 3 ! ! " " dm# K$ K$ sm# & dm# SLub V % &ub V 'sin 2 (excl. at CL > 0.95) < 0'sol. w/ cos 2 e xc lu d e d a t C L > 0 .9 5 " '! ( -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 ) -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 excluded area has CL > 0.95 Winter 11 CKM f i t t e r FIG. 1. Constraints on the CKM (⇢, ⌘) coordinates from the global SM CKM-fit. Regions outside the coloured areas have CL > 95.45 %. For the combined fit the yellow area inscribed by the contour line represents points with CL < 95.45 %. The shaded area inside this region represents points with CL < 68.3 %. has passed the statistical test of the global consistency of all observables embodied in the fit, although some discrepancies are detailed in the following sections. We are therefore allowed to perform the metrology of the CKM parameters and to give predictions for any CKM-related observable within the SM. Let us add that the existence of a CL < 95.45 % region in the (⇢, ⌘) plane is not equivalent to the statement that each individual constraint lies in the global range of CL < 95.45 %. One of the interest of SM predictions is that each comparison between the prediction issued from the fit and the corresponding measurement constitutes a null-test of the SM hypothesis. Indeed, we will see that discrepancies actually do exist among the present set of observables considered in this letter (the corresponding pulls are reported in Table II). We predict observables that were not used as input constraints, either because they are not measured with a su cient accuracy yet, e.g., B(Bs ! `+` ), or because the control on the theoretical uncertainties remains controversial, e.g.,   s/ s. The corresponding predictions can then be directly compared with their experimental measurements (when they are available). We also consider some particularly interesting observables used as an input of the fit, e.g., B(B ! ⌧⌫). In this last case, we must compare the measurement of the observable with the outcome of the fit without including the observable among the inputs, so that the experimental information is used only once. Following this procedure, we do not take the following quantities as inputs, but we predict their values: the semileptonic asymmetries asSL and a d SL, the weak phase in the B0s mixing  s, the branching ratios of the dileptonic decays of neutral B mesons B(Bd,s ! `+` ), the branching ratio of (exclusive and inclusive) radiative b ! s transitions, and rare K ! ⇡⌫⌫ decays. The first three observables have all in common to provide only loose constraints on the CKM parameters, while the two latter, though fulfilling the requirement of a good control of their related theoretical uncertainties, are so far out of reach of the current experiments. The LHCb experiment should bring a breakthrough in that respect very soon and these quantities will be included in the global fit once the required measurement accuracy is achieved [13]. The experimental situation is pretty similar for the semileptonic asymmetries related to neutral-meson mixing, with the additional drawback that these observables su↵er from large theoretical uncertainties. The exclusive radiative b ! s transitions su↵er from significant uncertainties and are thus only consider for predictions. On the contrary, the inclusive B ! Xs , which have been measured and are well controlled theoretically, will be added as input of the global fit [12], but are kept for the present letter among the predictions. Finally, rare kaon decays have not been measured yet or provide only loose constraints on the CKM matrix elements. In the following sections, we first discuss the main sources of theoretical uncertainty, before spelling out some of the fundamental formulae used for our predictions within the SM. We then collect the results obtained and compare them with their measurements (when available). II. STRONG INTERACTION PARAMETERS The first category of theoretical uncertainties in flavour analyses arise from matrix elements that encode the effects of strong interaction in the non-perturbative regime. These matrix elements boil down to decay constants, form factors and bag parameters for most of the observables under scrutiny in the present note, and all our predictions are subjected to and limited by the uncertainties in the determination of these observables. These uncertainties must be controlled with care since their misassessment or underestimation would a↵ect the statements that we will make on flavour observables. Among the di↵erent methods used to estimate nonperturbative QCD parameters, quark models, sum rules, and lattice QCD (LQCD) simulations are tools of choice. We opt for the latter whenever possible, as they provide well-established methods to compute these observables not only with a good accuracy at the present time, but also with a theoretical framework allowing for a systematic improvement on the theoretical control of the uncertainties. Over the last few years, many new estimates Figure A.8: Constraints on the CKM (ρ, η) coordinates from the global SM CKM-fit. Regions outside the colored areas have been excluded at 95%. For the combined fit the yellow area inscribed by the contour line represents points with CL ≤ 95%. The shaded area inside this region represents points with CL ≤ 68.3% [383]. the elements of the CKM matrix are in general complex numbers, considering their magnitudes demonstrates that the matrix is approximately diagonal:   |Vud| |Vus| |Vub| |Vcd| |Vcs| |Vcb| |Vtd| |Vts| |Vtb|   ≈   0.97 0.23 0.003 0.23 0.97 0.040 0.01 0.04 0.999   . This means that when the quark doublets are considered in terms of their mass eigenstates, exchanges of W± bosons prefer to flip the flavor of quarks within their doublets (like c↔ s) but CKM-suppressed transitions (like c↔ d) do occur. The Wolfenstein parametrization [384, 385] is a common parametrization of the CKM matrix A.2 the standard model 229 using four real parameters: ρ, η, A, and λ that are conveniently each O(1): ρ+ i η ≡ − Vud V ∗ ub Vcd V ∗cb , λ2 ≡ |Vus| 2 |Vud|2 + |Vus|2 , A2 λ4 ≡ |Vcb| 2 |Vud|2 + |Vus|2 . The ρ and η determine the position of the free third point of the relevant unitary triangle that can be derived from the constraint that the CKM matrix is unitary (see Figure A.8). The CKM matrix is now reasonably well constrained by several heavy-flavor measurements from the Belle and BaBar experiments at B-factories, as well as the Tevatron experiments, which are combined by the CKMFitter Group [383]. Relation to the Yukawa couplings In the SM, the Higgs mechanism not only gives rise to the gauge boson masses, it also generates masses for the fermions. The flavor mixing descrbribed by the CKM matrix is actually a result of the Yukawa couplings of the Higgs to the fermions fields not being diagonal. After EW symmetry breaking, the fermion-mass matrix can be calculated in terms of the Higgs vacuum expectation value and the Yukawa couplings: Mxij = v√ 2 yxij , where x ∈ {u,d, e} give three matrices for the up-type quarks, down-type quarks, and charged leptons. The indices i, j run over the three generations, allowing them to mix. By the diagonalization theorem, the mass matrix can be put in diagonal-form with unitary transformation matrices: U†l M Ur = Md . In this notation the CKM matrix is given by VCKM = U u† l U d l . A.2.7 Neutrino flavor mixing Three generations of leptons In 1962, Leon Lederman, Melvin Schwartz, and Jack Steinberger showed that neutrinos come in more than one flavor [386] by demonstrating that neutrinos from charged-pion decays to muons always created muons when they are detected (never electrons or taus111). In 1975, the τ lepton 111 The experiment was at the AGS accelerator at BNL and over laboratory distances where neutrino oscillation was neglible. 230 A. a review of the standard model was discovered by Martin Perl and collaborators at SLAC [387, 388, 389]. In 1990, after performing precision measurements of the width of Z boson at LEP, the ALEPH Collaboration constrained the number of neutrino generations to which the Z can decay to 3 [390]. The updated result in 2006 combining all four LEP experiments is consistent with the number of neutrino types with masses less than half the Z mass being 2.984± 0.008 [236]. The ντ was not observed directly until it was discovered by the DONUT Collaboration at Fermilab in 2001 [391]. Completing the third generation, it is the last lepton to be discovered. Together, these results conclude that like the quark sector, the leptons seem to come in three generations. Neutrino oscillation In the 1950s, it was realized that the rate of neutrino production from fusion processes in the Sun was large and that the neutrino flux may be detectable on Earth. The Solar Standard Model, describing the fusion rates in the sun, was worked out in more detail, and John Bahcall predicted the flux of solar electron neutrinos on Earth with energies of a few 100 keV to be ∼ 8× 1010 cm−2 s−1 [392, 393]. The first experiment sensitive to this flux was the Homestake Mine experiment by Ray Davis Jr. In 1968, Davis measured the solar neutrino flux on Earth to be ∼ 2.5× 1010 cm−2 s−1 [394, 395], roughly a third of Bahcall's predicted value. This issue remained unresolved for over 30 years, known as the solar neutrino problem [396]. In analogy with the CKM matrix for the quark sector, if the neutrino flavor eigenstates are a mixture of mass eigenstates, and if those mass eigenstates have different masses, then the mass eigenstates will drift in and out of phase as they propagate through free space, modulating the probability to observe a given flavor. This phenomena is called "neutrino oscillation", and was first proposed by Bruno Pontecorvo in 1957 [397]. A hypothetical explanation of the solar neutrino problem was that solar neutrinos were oscillating to other flavors in-flight to Earth. Solar neutrinos (100 keV to 20 MeV) are not energetic enough for the νμ and ντ flavors to participate in chargecurrent interactions, because it requires the production of heavy charged leptons. The existing solar neutrino experiments like Davis' were only sensitive to the νe-flux, and therefore observed a deficit112. In 1998, Super-Kamiokande observed another deficit in the expected flux of several GeV atmospheric neutrinos produced in cosmic ray showers, hypothetically due to νμ-disappearance by oscillating to other flavors [31]. The Sudbury Neutrino Observatory (SNO) put an end to the mystery by being the first solar neutrino experiment sensitive to both chargedand neutral-current 112 Solar neutrino oscillations are additionally complicated by the high-density environment of the sun, which due to the MSW effect on neutrinos traveling through matter [398, 399], adiabatically rotates the electron neutrinos created in fusion processes in the sun into nearly pure ν2 mass eigenstates by the time they exit the sun. Therefore, solar neutrino experiments are really measuring the flavor fractions of the ν2 mass eigenstate. A.2 the standard model 231 interactions, and therefore could measure the total solar ν-flux and the νe-flux independently. In 2001, SNO reported its first measurements of the solar neutrino flux, consistent with the neutrino oscillation hypothesis [32]. Therefore, the weak eigenstates of neutrinos must be a mix of mass eigenstates with differing masses. This was the first conclusive evidence that (at least some of) the neutrino masses are non-zero, which is technically beyond the Standard Model physics, since the SM does not have any righthanded neutrinos. Extending the SM to include massive neutrinos is reasonably straight-forward and allows for a flavor-mixing matrix like CKM for the quark sector. However, there are two types of massive fermions: Dirac or Majorana, with different mass terms for the Lagrangian. While it is now well known to physicsts that neutrinos have mass, measuring the related parameters and constraining the neutrino sector is still an active area of research [33, 400]. The PMNS matrix The mixing of the neutrino flavor and mass eigenstates is described by the Pontecorvo-MakiNakagawa-Sakata (PMNS) matrix [397, 401, 402]:   νe νμ ντ   = UPMNS   ν1 ν2 ν3   =   Ue1 Ue2 Ue3 Uμ1 Uμ2 Uμ3 Uτ1 Uτ2 Uτ3     ν1 ν2 ν3   The standard parametrization of the PMNS matrix has 3 Eulerian angles for the mixing between mass states: θ12, θ23, θ13, which have been experimentally measured (see Table A.7), and 3 unknown phase factors: α1, α2, δ. The α1 and α2 parameters are physically meaningful only if neutrinos are Majorana particles (if the neutrino is identical to its antiparticle), which is currently unknown, and do not enter into oscillation phenomena regardless. If neutrinos are Majorana, then these factors influence the rate of neutrinoless double-beta decay. The phase factor δ is non-zero only if neutrino oscillation violates CP symmetry. Neutrino oscillation is best observable at various distances depending on the energies and mixing parameters of the neutrinos. The parameters θ12 and ∆m 2 21 dominate the effects of solar neutrino oscillation and have been measured most precisely by the SNO [32, 403] and KamLAND [404] collaborations. Atmospheric neutrino oscillations are the result of θ23 and |∆m232|, measured by the Super-K [31, 405], K2K, and MINOS experiments, among others. In 2011, T2K reported an indication that the last unobserved neutrino parameter θ13 was non-zero [406]. The following year (in April of 2012), the Daya Bay Reactor Neutrino Experiment measured θ13, with 5σ evidence of it being non-zero [407]. Recently, the result from Daya Bay has been combined with measurements from RENO, T2K, MINOS, and Double Chooz [408]. Approximate values of the measured neutrino 232 A. a review of the standard model m2 0 solar~7.6×10–5eV2 atmospheric ~2.5×10–3eV2 atmospheric ~2.5×10–3eV2 m1 2 m2 2 m3 2 m2 0 m2 2 m1 2 m3 2 ν e ν μ ν τ ? ? solar~7.6×10–5eV2 Figure A.9: An illustration of the two possible neutrino mass hierarchies: normal (left) with m1 < m2 < m3 and inverted (right) with m3 < m1 < m2 [356]. parameters are summarized in Table A.7. Approximate values of the magnitudes of the elements of the PMNS matrix are [136]   |Ue1| |Ue2| |Ue3| |Uμ1| |Uμ2| |Uμ3| |Uτ1| |Uτ2| |Uτ3|   ≈   0.8 0.5 0.15 0.4 0.6 0.7 0.4 0.6 0.7   . Note that unlike the CKM matrix, the PMNS matrix is far from being diagonal, and instead appears to be maximally mixed. The ν1 mass eigenstate is mostly the νe flavor. ν2 is almost evenly divided between all three flavors. Lastly, ν3 has barely any νe and is approximately evenly shared between the other two flavors. The magnitude of |∆m232| is ∼ 30 times larger than ∆m221, and its sign is not known, allowing for the two possible mass hierarchies shown in Figure A.9. Table A.7: Approximate values of the measured neutrino mixing parameters. The remaining unknown parameters are α1, α2, δ, and the sign of ∆m 2 32 [136]. mixing angles mass differences sin2(2 θ12) ≡ sin2(2 θsol) ≈ 0.86 ∆m221 ≡ ∆m2sol ≈ 7.6× 10−5 eV2 sin2(2 θ23) ≡ sin2(2 θatm) > 0.92 |∆m232| ≡ |∆m2atm| ≈ 2.5× 10−3 eV2 sin2(2 θ13) ≈ 0.09 |∆m231| ≈ |∆m232| Appendix B Tau identification variables This appendix defines all identification variables used by the jet and electron discriminants.The variables are: Electromagnetic radius (REM): the transverse energy weighted shower width in the electromagnetic (EM) calorimeter: REM = ∑∆Ri<0.4 i∈{EM 0−2} ET,i ∆Ri∑∆Ri<0.4 i∈{EM 0−2} ET,i , (B.1) where i runs over cells in the first three layers of the EM calorimeter (pre-sampler, layer 1, and layer 2), associated to the tau candidate. Track radius (Rtrack): the pT weighted track width: Rtrack = ∑∆Ri<0.4 i pT,i ∆Ri∑∆Ri<0.4 i pT,i , (B.2) where i runs over all core and isolation tracks of the tau candidate, and pT,i is the track transverse momentum. Note that for candidates with only one track, Rtrack simplifies to the ∆R between the track and the tau candidate axis. Leading track momentum fraction (ftrack): ftrack = ptrackT,1 pτT , (B.3) where ptrackT,1 is the transverse momentum of the leading pT core track and p τ T is the transverse momentum of the tau candidate, calibrated at the EM energy scale. Note that for candidates with one track, ftrack is the fraction of the candidate's momentum attributed to the track, compared to the total momentum of the candidate, which can have contributions from the calorimeter deposits from π0s and other neutrals. 233 234 B. tau identification variables Core energy fraction (fcore): the fraction of transverse energy within (∆R < 0.1) of the tau candidate: fcore = ∑∆Ri<0.1 i∈{all} ET,i∑∆Rj<0.4 j∈{all} ET,j , (B.4) where i runs over all cells associated to the tau candidate within ∆R < 0.1 and j runs over all cells in the wide cone. The calorimeter cells associated to a tau candidate are those which are clustered in the topological clusters that are constituents of the jet that seeded tau reconstruction. ∆Ri is defined between a calorimeter cell and the tau candidate axis. ET,i is the cell transverse energy, calibrated at the EM scale. Note that an unconventional definition of the core cone is used for fcore, as it provides better discrimination. Electromagnetic fraction (fEM): the fraction of transverse energy of the tau candidate deposited in the EM calorimeter: fEM = ∑∆Ri<0.4 i∈{EM 0−2} ET,i∑∆Rj<0.4 j∈{all} ET,j , (B.5) where ET,i (ET,j) is the transverse energy deposited in cell i (j), and i runs over the cells in the first three layers of the EM calorimeter, while j runs over the cells in all layers of the calorimeter. Cluster mass (meff. clusters): the invariant mass computed from the constituent clusters of the seed jet, calibrated at the LC energy scale. To minimise the effect of pileup, only the first N leading ET clusters (effective clusters) are used in the calculation, defined as N = ( ∑ iETi) 2 ∑ iET 2 i , (B.6) where i runs over all clusters associated to the tau candidate, and N is rounded up to the nearest integer. Track mass (mtracks): the invariant mass of the track system, where the tracks used for the invariant mass calculation use both core and isolation tracks. Transverse flight path significance (SflightT ): the decay length significance of the secondary vertex for multi-prong tau candidates in the transverse plane: SflightT = LflightT δLflightT , (B.7) where LflightT is the reconstructed signed decay length, and δL flight T is its estimated uncertainty. Only core tracks are used for the secondary vertex fit. 235 TRT HT fraction (fHT): the ratio of high-threshold to low-threshold hits (including outlier hits), in the Transition Radiation Tracker (TRT), for the leading pT core track. fHT = High-threshold TRT hits Low-threshold TRT hits (B.8) Since electrons are lighter than pions, and therefore have higher Lorentz γ factors, they are more likely to produce the transition radiation that causes high-threshold hits in the TRT [76]. This variable can be used to discriminate hadronic 1-prong tau candidates from electrons. Number of isolation tracks (N isotrack): the number of tracks in the isolation annulus. Hadronic radius (RHad): the transverse energy weighted shower width in the hadronic calorimeter RHad = ∑∆Ri<0.4 i∈{Had,EM3} ET,i ∆Ri∑∆Ri<0.4 i∈{Had,EM3} ET,i , (B.9) where i runs over cells associated to the tau candidate in the hadronic calorimeter and also layer 3 of the EM calorimeter. Only cells in the wide cone, defined as ∆R < 0.4 from the tau candidate axis, are considered. Calorimetric radius (RCal): the shower width in the electromagnetic and hadronic calorimeter weighted by the transverse energy of each calorimeter part. RCal = ∑∆Ri<0.4 i∈{all} ET,i ∆Ri∑∆Ri<0.4 i∈{all} ET,i , (B.10) where i runs over cells in all layers of the EM and hadronic calorimeters. Only cells in the wide cone are considered. Leading track IP significance (Slead track): the impact parameter significance of the leading track of the tau candidate: Slead track = d0 δd0 , (B.11) where d0 is the distance of closest approach of the track to the reconstructed primary vertex in the transverse plane, and δd0 is its estimated uncertainty. First 2(3) leading clusters energy ratio (f2 lead clusters(f3 lead clusters)): the ratio of the energy of the first two (three) leading clusters (highest energy first) over the total energy of all clusters associated to the tau candidate. Maximum ∆R (∆Rmax): the maximal ∆R between a core track and the tau candidate axis. 236 B. tau identification variables Hadronic track fraction (f trackHad ): the ratio of the hadronic transverse energy over the transverse momentum of the leading track: f trackHad = ∑∆Ri<0.4 i∈{Had} ET,i ptrackT,1 , (B.12) where i runs over all cells in the hadronic calorimeter within the wide cone. Maximum strip ET (E strip T,max): the maximum transverse energy deposited in a cell in the presampler layer of the electromagnetic calorimeter, which is not associated with that of the leading track. Electromagnetic track fraction (f trackEM ): the ratio of the transverse energy deposited in the electromagnetic calorimeter over the transverse momentum of the leading track: f trackEM = ∑∆Ri<0.4 i∈{EM} ET,i ptrackT,1 , (B.13) where i runs over all cells in the EM calorimeter within the wide cone. Ring isolation (fiso): fiso = ∑0.1<∆R<0.2 i∈{EM 0−2}ET,i∑∆R<0.4 j∈{EM 0−2}ET,j , (B.14) where i runs over cells in the first three layers of the EM calorimeter in the annulus 0.1 < ∆R < 0.2 around the tau candidate axis and j runs over EM cells in the wide cone. Corrected cluster isolation energy (EisoT,corr): the transverse energy of isolated clusters: EisoT,corr = E iso T − δEisoT = 0.2<∆Ri<0.4∑ i ET,i − δEisoT (B.15) where i runs over all clusters associated to the tau candidate. ∆Ri is defined between the cluster and the tau candidate axis. The pileup correction term is defined as δEisoT = (1−JVF)× ∑ pT,trk, where JVF is the jet vertex fraction of the jet seed of the tau candidate, calculated with respect to the primary vertex and ∑ pT,trk the sum of the transverse momentum of the tracks associated to that jet. List of Tables 2.1 The approximate branching ratios for the decays of the SM Higgs boson withmH = 125GeV [27]. 8 3.1 Some notable facts about the LHC. The LHC beam parameters are shown in more detail in Table 3.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Some of the key differences in the designs of the ATLAS and CMS experiments [68, 71]. 23 3.3 Number of readout channels per sub-detector in ATLAS for the primary sub-detectors (ignoring the minbias trigger system, luminosity monitors, and DCS sensors) [68]. . . . 25 3.4 Milestones of some of important beam parameters of the LHC for 2009 to 2012 [66, 115]. 42 3.5 A summary of the size per event for various ATLAS data formats [135]. . . . . . . . . . 50 4.1 The values of the loose/medium/tight cuts for the working points of the 2010 simple cut-based ID [142]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2 Parametrized cut values for the updated 2010 working points. The formulas for the parametrized cuts use pT in units of GeV. Currently, 1/ftrack, and not its inverse, is the variable stored in the tau Event Data Model (EDM) [147]. . . . . . . . . . . . . . . . . 65 4.3 Comparison of variables used by each discriminant for the 2010 dataset [100]. . . . . . 66 4.4 The 2011 e-veto scale factors derived from the Z → ee tag-and-probe measurement [102]. 81 4.5 Data/MC tau ID efficiency ratio (SF) measured in bin of tau-pT in the Z → ττ tag and probe analysis. The individual contributions to the uncertainty are: the statistical uncertainty, ∆SFstat; the normalisation uncertainties on the W+jets and multijet backgrounds, ∆SFW+jets and ∆SFQCD; and the experimental uncertainties on the muon, tau and the integrated luminosity, ∆SFexp [97]. . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.6 An accounting of the pT and pile-up dependence of some of the key tau ID variables. A '+' indicates a positive correlation of that variable with pT or Nvertex. A '-' indicates a negative correlation. Tau++ refers to the experimental version of the cut-based ID discuss in Section 4.4.9 [170]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.7 Cut values for the working points for the experimental Tau++ ID, using the JVF-corrected EisoT,corr [117]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.1 The EF e15 medium trigger was required for the eτh channel, including a prescale in part of period E. In the μτh channel the trigger, EF mu10 MG was used for run period 160899– 165632, EF mu13 MG for the run period 165703–167576 and EF mu13 MG tight for run period 167607–167844, respectively to avoid the use of prescaled triggers. In period E, the eτh channel is using data from period E3 (160613) and above, while the μτh channel starts at period E4 (160899) [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 237 238 list of tables 5.2 Electron trigger efficiency measured with respect to offline selected electrons in three pT bins [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.3 Muon trigger efficiency measured with respect to offline selected muons with pT > 15GeV [181]. 122 5.4 Efficiency of isolation variables for electrons and muons in signal Monte Carlo and multijet background after object selection cuts. In brackets is given the statistical error of the last digit [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.5 Selection summary [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.6 Summary of the events passing object selection [181]. . . . . . . . . . . . . . . . . . . . 129 5.7 Numbers of events passing the cumulative event selections for the μτh and eτh channels. The statistical errors on the least significant digits are given in the parentheses. The predictions for individual processes were taken from Monte Carlo, except for multijet, which was estimated from the data with non-isolated leptons as described in Section 5.7.3 [181]. 132 5.8 Summary of the number of selected Z → ττ candidate events and the expected backgrounds, comparing the two methods for estimating the multijet background described in Section 5.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.9 Scale factors for the jet to tau fake rate obtained in Z + jets events. The fake rate was about 3–7% in the 1-prong case and about 2–3% in the 3-prong case [181]. . . . . . . . 139 5.10 The predicted number of W + jets events in the signal region after all cuts, comparing estimates from the tau-by-tau scale factor and kW methods [181]. . . . . . . . . . . . . 139 5.11 Numbers of events in the control regions discussed in Section 5.7.3. The numbers in parenthesis are the statistical errors in the least significant digits. The multijet expectations are determined by the data-driven method discussed in that section. The other processes are estimated with Monte Carlo [181]. . . . . . . . . . . . . . . . . . . . . . . 144 5.12 Numbers of events in the control regions discussed in Section 5.7.4. The numbers in parenthesis are the statistical errors in the least significant digits. The multijet expectations are determined by the data-driven method using non-isolated leptons, discussed in that section. The other processes are estimated with Monte Carlo [181]. . . . . . . . . 145 5.13 A summary of the estimated backgrounds, number of Z → ττ signal events from Monte Carlo, and the number of observed events for analyses of Z → ττ in four final states: μτh, eτh, eμ, and μμ [113]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.14 Central values for the AZ acceptance factor determined with ATLAS MC10 Monte Carlo generated with PYTHIA and MRSTLO* PDFs, and for the CZ efficiency factor determined using the same generated sample after full detector simulation and selection [181]. 148 5.15 A summary of the measured quantities used to calculate the Z → ττ cross section in four final states: μτh, eτh, eμ, and μμ [113]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 5.16 A summary of the systematic uncertainties of the measurement of the Z → ττ cross section in four final states: μτh, eτh, eμ, and μμ [113]. . . . . . . . . . . . . . . . . . . . 149 5.17 A summary of the results of measuring the total and fiducial cross sections for Z → ττ in four final states: μτh, eτh, eμ, and μμ [113]. . . . . . . . . . . . . . . . . . . . . . . . 152 6.1 Data periods, triggers, and the integrated luminosity for the four analysis channels. The eμ channel uses the same triggers as the μτh channel [97]. . . . . . . . . . . . . . . . . 155 6.2 Summary of object preselection [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 6.3 The number of events passing each step in the event selection of the `τh channels. The numbers in parentheses denote the statistical uncertainty in the least significant digits [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.4 The number of expected SM and signal events passing possible mtotT cuts in the `τh channels. The numbers in parentheses denote the statistical uncertainty in the least significant digits. The bold numbers denote the expected signal for the chosen mass cuts shown in Table 6.6 [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 list of tables 239 6.5 Comparison of estimates of the fake hadronic tau background for the eτh channel, showing the nominal fake background estimate (double fake factor) and the single-fake-factor method [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6.6 Mass-dependent cuts on mtotT for different Z ′ signal masses [97]. . . . . . . . . . . . . . 180 6.7 Uncertainties on the estimated signal and total background contributions in percent for each channel. The following signal masses, chosen to be close to the region where the limits are set, are used: 1250 GeV for τhτh (hh); 1000 GeV for `τh (μh) and eτh (eh); and 750 GeV for eμ. A dash denotes that the uncertainty is not applicable. The statistical uncertainty corresponds to the uncertainty due to limited sample size in the MC and control regions [212]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 6.8 The final predicted event yields for the μτh channel and their systematic uncertainties, for the primary signal region with mtotT > 600GeV. The first line of numbers reports the number of expected events. The uncertainties are reported as percent of that background. The syst. uncert. denotes the total systematic uncertainty on the estimate of each background, calculated from the sum in quadrature of the individual systematic uncertainties, listed below that. The stat. uncert. denotes the statistical uncertainty either from the number of Monte Carlo events, or the events used in a data-driven model. The total uncert. denotes the total uncertainty on the estimate of each background, calculated from the sum in quadrature of the statistical and the total systematic uncertainty [97]. 183 6.9 The final predicted event yields for the eτh channel and their systematic uncertainties, for the primary signal region with mtotT > 500GeV. The first line of numbers reports the number of expected events. The uncertainties are reported as percent of that background. The syst. uncert. denotes the total systematic uncertainty on the estimate of each background, calculated from the sum in quadrature of the individual systematic uncertainties, listed below that. The stat. uncert. denotes the statistical uncertainty either from the number of Monte Carlo events, or the events used in a data-driven model. The total uncert. denotes the total uncertainty on the estimate of each background, calculated from the sum in quadrature of the statistical and the total systematic uncertainty [97]. 184 6.10 A summary of the number of events observed and the number of background events expected in the primary signal regions optimized for the highest Z ′SSM mass that can be excluded independently in each channel. The total uncertainties on each estimated contribution are shown. The signal efficiency denotes the expected number of signal events divided by the product of the production cross section, the ditau branching fraction and the integrated luminosity: σ(pp→ Z ′SSM)× BR(Z ′SSM → ττ)× ∫ L dt [212]. . . . . 185 A.1 Conserved Noether currents in the Standard Model. . . . . . . . . . . . . . . . . . . . . 202 A.2 A modern summary of Wigner's classification of the irreducible unitary representations of the Poincaré group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 A.3 Gauge-group representations of the SM fermions. The rows are components of weak iso-spin, and the columns are components of color. The sets of three numbers on right denote if the fields have a singlet or triplet representation of SU(3)C, doublet or singlet representation of SU(2)L, and their weak hypercharge quantum number respectively. . 213 A.4 Approximate values of the electroweak parameters. Only three of the dimensionless and one of the ∼ GeV parameters are fundamental, and the remaining can be derived [136]. 222 A.5 The SM parameters of the Higgs vacuum potential, assuming the Higgs-like particle observed at the LHC, as discussed in Section 2.3.2, is the SM Higgs boson. Two of the three parameters: μ, λ, and mH are fundamental and one can be derived. . . . . . . . . 222 A.6 Masses and electroweak charges of the SM fermions [136]. For a visualization of the range of masses, see Figure A.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A.7 Approximate values of the measured neutrino mixing parameters. The remaining unknown parameters are α1, α2, δ, and the sign of ∆m 2 32 [136]. . . . . . . . . . . . . . . . 232 List of Figures 2.1 An illustration of the field content of the Standard Model. The numbers in parentheses denote the year the particle for that field was discovered. Note that the fermions are only grouped into doublets for their left-chiral parts. The right-chiral parts are SU(2)L singlets. The structure of the gauge group representations is shown in more detail in Figure A.3 in Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The "Livingston plot", showing the effective energy of collisions probed for various collider and fixed-target particle experiments as if they were each fixed-target experiments, as a function of the time the experiment began taking data [16]. . . . . . . . . . . . . . . . 6 2.3 (left) The 95% CL upper limit on the coupling for Higgs production at LEP, ξ2 = (gHZZ/g SM HZZ) 2, as a function of the Higgs mass [17]. (right) The 95% CL upper limit on the signal strength for the SM Higgs boson as a function of its mass [19]. . . . . . . . . 7 2.4 The distribution of the ∆χ2 = χ2−χ2min as a function of the SM Higgs mass, mH , for the combined LEP-Tevatron EW fit. The blue band illustrates the theoretical uncertainty due to missing higher order corrections. The yellow vertical bands show the mH regions excluded by LEP-II (up 114 GeV) and the Tevatron (160–170 GeV), as of August 2009. The best-fit result is mH = 87 +35 −26GeV, equivalent to an upper limit of mH < 157GeV at 95% CL [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 (left) The branching ratios the SM Higgs decays with estimated theoretically uncertainties shown by the bands [25, 26]. (right) Measurements of the signal strength parameter μ for mH = 126 GeV for the individual channel and their combinatio [23]. . . . . . . . . 9 2.6 The distributions of the reconstructed mH invariant mass of H → γγ [28] (left) and H → ZZ∗ → 4` [23] (right) candidates after all selections for the combined 7 TeV (2011) and 8 TeV (2012) data sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.7 (left) The distribution of the transverse mass of the dilepton system and the missing transverse momentum, mT, in the 0-jet and 1-jet channels of the H → WW ∗ → eμ search for events satisfying all selection criteria [23]. (right) Confidence intervals in the (μ, mH) plane for the H → γγ, H → ZZ∗ → 4`, and H → WW ∗ → `ν`ν channels, including all systematic uncertainties. The markers indicate the maximum likelihood estimates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.8 The triviality upper bound and vacuum stability lower bound on the SM Higgs boson mass vs the cut-off scale, Λ, where new physics is required to keep the theory consistent [34]. 12 2.9 Two-loop renormalization group evolution of the inverse gauge couplings α−1(Q) in the Standard Model (dashed lines) and the Minimal Supersymmetric Standard Model (MSSM, solid lines). In the MSSM case, the sparticle masses are treated as a common threshold varied between 500 GeV (blue) and 1.5 TeV (red) [39]. . . . . . . . . . . . . 14 240 list of figures 241 3.1 Production cross sections from proton-(anti)proton collisions for several processes of interest as a function of center-of-momentum energy, √ s. The discontinuity at ≈ 4 TeV is from the difference in pp cross sections on the left for the Tevatron, and pp cross sections on the right for the LHC. The vertical lines indicate the center-of-momentum energy for the Tevatron at 1.96 TeV (2001-2011), for the LHC at 7 TeV (2010-2011) and 8 TeV (2012) and 13 TeV (target for future 2015 run) [54, 55]. . . . . . . . . . . . . . . . . . . 18 3.2 An illustration of the location of the LHC, facing south between the Alps and Jura mountain chains on the left and right respectively. The vertical dimension is exaggerated since the LHC is about 100 m underground and 27 km in circumference or 9 km in diameter [58]. 19 3.3 The CERN accelerator complex for the LHC [62, 63]. . . . . . . . . . . . . . . . . . . . 20 3.4 An illustration of the relative sizes of the region enveloping the beam at the interaction point in ATLAS [64]. At the point of collisions the beams are squeezed in the transverse plane to be confined in an area of about 0.1 mm× 0.1 mm. . . . . . . . . . . . . . . . . 21 3.5 An illustration giving an overview of the ATLAS experiment [68]. . . . . . . . . . . . . 22 3.6 An illustration of the ATLAS magnet systems [70] . . . . . . . . . . . . . . . . . . . . . 23 3.7 An illustration of the ATLAS inner detector and its sub-systems [68, 72]. . . . . . . . . 24 3.8 (left) A plot of the TRT hit efficiency as a function of the distance of the track from the wire in the centre of the straw, for straws in the barrel of the TRT [75]. (right) A plot of the probability for a hit on a track to trigger the TRT high-threshold as a function of γ factor, for samples of pions and electrons in the TRT end-caps [68]. Both of these plots use the first collision data taken in 2009 at √ s = 0.9TeV and compare the corresponding distributions from Monte Carlo simulation. . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.9 An illustration of the ATLAS calorimeter and its sub-systems [68]. . . . . . . . . . . . 27 3.10 An illustration of the ATLAS barrel EM calorimeter and the granularity of its readout cells [68]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.11 An illustration of the ATLAS muon spectrometer and its sub-systems [68]. . . . . . . . 29 3.12 An illustration of the inputs and outputs of ATLAS reconstruction. Raw Data Object (RDO) files are typically the input to reconstruction (event size: 1–2 MB/event). Event Summary Data (ESD) files are produced, containing the hitand cell-level information as well as the reconstructed objects (1–2 MB/event). The reconstruction also produced Analysis Object Data (AOD) files, containing a sub-set of the information in the ESD intended for use in analyses (100–200 kB/event). . . . . . . . . . . . . . . . . . . . . . 31 3.13 (left) An illustration of a typical extrapolation process within a Kalman filter step. The track parameters on an active layer of the detector, Module 1, are propagated onto the next measurement surface, resulting in the track prediction on Module 2. The traversing of the material layer between the two modules is accounted for by inflating the uncertainties on the track parameters. The final resulting measurement of the track parameters (shown in red) is improved by combination of all the hits on track. (right) An illustration of the perigee parameters for a track: the longitudinal coordinate along the beamline, z0, and the impact parameter, d0, being the distance-of-closest-approach of a track to the beamline in the transverse plane [83]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.14 An event display of a eeμμ candidate event from a search for H → ZZ∗ → 4` with the 2011 dataset [85]. The masses of the lepton pairs are 76.8 GeV and 45.7 GeV, and the event has m4l = 124.3GeV. The tracks from the muon candidates are traced in blue. The electron candidates are absorbed in the calorimeter and traced in red [86]. . . . . . . . 33 242 list of figures 3.15 An event display of an e+ candidate in a W+ → e+ν candidate event in the ATLAS 2010 run. The positron track is traced in yellow and the energy deposit in the EM calorimeter is indicated in yellow as well. High-threshold hits in the TRT are indicated by the red dots. The positron has pT = 23GeV and η = 0.6. The missing transverse momentum, EmissT , was measured to be 31 GeV and its direction is indicated by the red line from the beam axis. The transverse mass of the combination of the positron and the EmissT is 55 GeV [86]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.16 Plots of the energy in MeV distributed in η×φ cells in each layer of the barrel calorimeter for a single topological cluster from a simulated charged pion. Each pane shows a different layer of the calorimeter but within the same η × φ range [92]. . . . . . . . . . . . . . . 35 3.17 (left) A diagram illustrating tracks from pile-up vertices (in red) falling on a tau candidate (in blue). Conceptually, JVF is the fraction of the scalar sum of the pT of the tracks pointing to the jet seeding the tau candidate that are associated with the chosen primary vertex (i.e. the fraction of the scalar some of the blue and red tracks that is blue). (right) The distribution of JVF from ATLAS simulation for jets truth-matched to the hard-scatter (in red) and jets from pile-up interactions (in blue) for events with L ≈ 1032 cm−2 s−1, corresponding to 〈Nvertex〉 ≈ 5 [99]. . . . . . . . . . . . . . . . . . . . . 37 3.18 An event display of a μτh + 2 jet candidate event from a search for tt events with hadronic tau decays in the 2011 dataset [104]. The muon track is shown in red, has positive reconstructed electric charge, and pT = 20GeV. The 3-track tau candidate is shown at the lower right, has negative charge, and pT = 53GeV [86]. . . . . . . . . . . . 39 3.19 The design of the ATLAS trigger and DAQ architecture, indicating the event rate passing the trigger levels on the left, and showing the flow of the data volume on the right. The numbers in black indicate the design specifications and the numbers in red indicate the peak running conditions in 2012 [106]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.20 The Event Filter (EF) bandwidth used by each trigger stream as function of time in the year 2011 [107]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.21 Distributions of the number of colliding bunches per beam, the peak instantaneous luminosity, and the peak mean number of interactions per bunch crossing, as a function of time for the years 2010–2012 [114]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.22 (left) The integrated luminosity delivered by the LHC as a function of time for the years 2010–2012. (right) The distribution of the mean number of interactions per bunch crossing, μ, for the √ s = 7 TeV run in 2011 and the √ s = 8 TeV run in 2012 [114]. . . 44 3.23 A close-up event display of the reconstructed primary vertices in a Z → μμ event in the 2012 dataset with 25 vertices. The tracks from the muons are highlighted with thick yellow lines [86]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.24 The flow of the ATLAS simulation software, from event generators (top-left) through to the reconstruction (bottom-left). Additional minimum bias pile-up events are generated and overlaid. Monte Carlo truth is saved in addition to energy depositions in the detector (hits). Digitization simulates the read-out electronics and RODs to give simulated raw data that is processed with the Athena reconstruction like the data from ATLAS [82]. . 46 3.25 The distributions of the dielectron invariant mass of Z → ee candidate events, before applying electron identification cuts on the probe electron, in the ET-range 20–25 GeV (left) and 35–40 GeV (right) [90]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.26 (left) Locations of the sites of WLCG computing centers with an orange spot indicating tier-0 at CERN, green spots indicating the 10 tier-1 centers, and blues spots indicating tier-2 centers [130]. (right) The amount of data available to ATLAS users on the WLCG grid, including replicas, as a function of time. By the end of 2012, the data volume exceeded 140 PB = 140 million GB [131]. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.27 An illustration of the tiered structure of the ATLAS computing infrastructure [132]. . . 49 list of figures 243 3.28 An illustration of the flow of ATLAS data as it is reconstructed and analyzed on the WLCG computing grid. The process of producing Monte Carlo simulation and pushing it through the same reconstruction and user analysis is also shown [134]. . . . . . . . . 49 4.1 The approximate branching ratios of the dominate decay modes of the tau lepton. For the decays within the hadronic mode, the branching ratios are shown as the fraction of the total hadronic mode and not the fraction of all decays. . . . . . . . . . . . . . . . . 52 4.2 The reconstruction efficiency of true hadronic decays of tau leptons as a function of EvisibleT and η visible from a sample of MC W → τν events (mc08) [140]. . . . . . . . . . 54 4.3 The overlap between track and calorimeter seeds as a function of ET in a Monte Carlo sample of true W → τhν decays (mc08) [140]. . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4 (left) A sketch illustrating things that can affect tau identification, and that the core tracks are counted in ∆R < 0.2, while many ID variables are calculated in ∆R < 0.4. (right) The Ntrack distribution for simulated hadronic decays of taus in MC W → τν and Z → ττ events, and the distribution for a selection of dijet background events from both the 2010 data and compared with PYTHIA dijet MC (mc09) [100]. . . . . . . . . . . . 56 4.5 (left) The reconstruction efficiency to correctly select the track from a 1-prong hadronic decay as a function of μ in MC Z → ττ events from mc11, using track selection with respect to the "Default" vertex with the highest ∑ p2T, or with respect to the vertex with the highest JVF, called "Tau Jet Vertex Association (TJVA)" in this figure. (right) The Ntrack distribution in ideal MC with no additional pile-up (μ = 0), compared to the distribution with significant pile-up (μ = 20), showing both the Default and TJVA vertex selection (mc11) [102]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.6 The distributions for the three tau identification variables used by the cut-based ID for 1-prong (left) and 3-prong (right) candidates. The signal sample is MC Z → ττ events (blue) and the background is dijet events from 2010 (red). The cuts for the working points are indicated by the dashed lines. The values of these cuts are shown in Table 4.1 (mc09) [143]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.7 The dependence of key tau identification variables as a function of the candidate pT, separately for 1-prong (left) and 3-prong (right) tau candidates. The points indicate the means in each bin. The colored bands indicate the standard deviation. The blue points correspond to tau candidates matched to hadronically decaying taus in simulatedW → τν and Z → ττ events. The red points are for the dijet sample from data (mc10) [117]. . . 61 4.8 Profile plots of 〈R × pT〉 vs the candidate pT, separately for 1-prong (left) and 3-prong (right) tau candidates, for REM (top) and Rtrack (bottom). The points indicate the means in each bin. The colored bands indicate the standard deviation. The blue points correspond to tau candidates matched to hadronically decaying taus in simulatedW → τν and Z → ττ events. The red points are for the dijet sample from data (mc09) [147]. . . 63 4.9 The cut values for the working points for the updated pT-parametrized cut-based ID with the 2010 dataset are shown by the dashed lines. Note that the piecewise parts with constant cut values for pT ≥ 80GeV are not shown, but would simply be a flat continuation of the curves shown, beginning at 80GeV. The same cut values are given in Table 4.2 (mc09) [147]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.10 The efficiency of the 2010 simple cut-based ID (top) and the pT-parametrized cuts (bottom), for both 1-prong (left) and 3-prong (right) true hadronic tau decays (mc09) [143]. 65 4.11 The fake rate of the 2010 simple cut-based ID (top) and the pT-parametrized cuts (bottom), for both 1-prong (left) and 3-prong (right) tau candidates in a dijet sample from the 2010 dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 244 list of figures 4.12 Distributions for REM, Rtrack, and ftrack, for 1-prong (left) and 3-prong (right) candidates. Note that the discontinuity in Rtrack for 1-prong candidates is due to the fact that they can optionally have additional tracks in the isolation annulus (see the definition of Rtrack in Section 4.3.1). The dashed lines indicate the cut boundaries for the tight pT-parameterized cut-based ID, discussed later in Section 4.3.3. Since the cuts on REM and Rtrack are parameterized in pT, the characteristic range of the cut values is demonstrated by showing lines for the cuts for candidates with pT = 20GeV, and then an arrow pointing to the cut for candidates with pT = 60GeV (mc09) [100]. . . . . . . . . . . . . 67 4.13 Distributions for fcore, fEM, and mclusters, for 1-prong (left) and 3-prong (right) candidates (mc09) [100]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.14 Distributions of mtracks (top-left) and S flight T (top-right) for 3-prong candidates, the loglikelihood-ratio for 1-prong (center-left) and 3-prong (center-right) tau candidates, and the jet BDT score for 1-prong (bottom-left) and 3-prong (bottom-right) tau candidates (mc09) [100]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.15 A simple example of a decision tree training process where there are two distributions labeled signal (S) and background (B) over two variables X and Y . The process begins at point 1, by determining the best value of the best variable to cut on, which in this case is Y at a. All objects with Y > a are passed to the right node and all objects with Y ≤ a are passed to the left. This process continues recursively until a stopping condition is satisfied, such as a minimum number of objects contained by a node [147]. . . . . . . . 71 4.16 (top-left) The efficiency for true hadronic tau decays to the identified with by an overlapping electron candidates with the 2010 ID. (top-right) The distributions of the TRT high-threshold-fraction for tau candidates in MC Z → ττ and Z → ee events, a variables used to discriminant electrons from hadronic decays of taus [101]. (bottom-left) The distribution of the BDT score for the e-veto used to veto real electrons faking tau candidates. (bottom-right) The inverse background efficiency vs signal efficiency for various cuts on the BDT score for the e-veto [102]. . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.17 First data-MC comparison of tau candidates in soft, non-diffractive events from 2009 collisions at √ s = 900GeV (left), and from dijet events from 2010 collisions at √ s = 7TeV (right) [154, 144]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.18 From theW → τhν observation, distributions of the the SEmissT with the full event selection except for the SEmissT cut (top-left), the mT distribution in the full event selection (topright), the Rtrack distribution in the full event selection except with tau ID relaxed to loose (bottom-right), and an illustration of the ABCD control regions (bottom-left) [145]. 76 4.19 The inverse background efficiency versus signal efficiency for the jet-tau discriminants for 1-prong (left) and 3-prong (right) candidates, with pT > 20GeV (top) and pT > 60GeV (bottom), used with the 2010 dataset [100]. . . . . . . . . . . . . . . . . . . . . . . . . 78 4.20 The background efficiency (left) and signal efficiency (right) vs pT for the loose/medium/tight working points (top/center/bottom) of the jet-tau discriminants for 1-prong candidates, used with the 2010 dataset [147]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.21 The background efficiency (left) and signal efficiency (right) vs pT for the loose/medium/tight working points (top/center/bottom) of the jet-tau discriminants for 3-prong candidates, used with the 2010 dataset [147]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.22 Visible mass distributions of eτh candidates from the Z → ee tag-and-probe measurement of e-veto efficiency, for the selection without (left) and with (right) the medium BDT e-veto applied, using the 2011 dataset [102]. . . . . . . . . . . . . . . . . . . . . . . . . 81 4.23 (left) Response functions for the 2011 TES. (right) The uncertainty on the 2011 TES as a function of pT derived with systematically shifted MC [101]. . . . . . . . . . . . . . . 82 list of figures 245 4.24 (left) The uncertainty on the updated 2011 TES as a function of pT derived with singleparticle-response uncertainties. (right) The visible mass of μτh candidates in a Z → ττ selection with the TES shifted by +10%, for example, which can be constrained by the poor agreement between data and MC in the Z → ττ peak [159]. . . . . . . . . . . . . 83 4.25 The tau identification efficiency uncertainty for the 2010 cut-based ID, using dedicated Monte Carlo samples with systematic shifts or changes of: the event generator, underlying event model, hadronic shower model, amount of detector material, and the topological clustering noise thresholds, [100]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.26 The visible mass of μτh candidates in the Z → ττ tag-and-probe selection without tau ID required (left-top), and after medium BDT ID (left-bottom). (right) The scale factors derived after subtracting background and dividing those selections [102]. . . . . . . . . 84 4.27 The efficiency for true 1-prong (left) and 3-prong (right) hadronic tau decays to be reconstructed with the correct number of tracks and pass the tau discriminants for rejecting jets, measured with Monte Carlo simulation for a SSM Z ′ with a mass of 1000GeV [97]. 86 4.28 The efficiency for true 3-prong hadronic tau decays to be reconstructed with 2, 3, or 4 tracks, measured with Monte Carlo simulation for a SSM Z ′ with a mass of 1000GeV [97]. 86 4.29 The efficiency true for 1-prong hadronic tau decays to be reconstructed and pass the tau discriminants for rejecting jets, in Monte Carlo simulation for a SSM Z ′ with a mass of 1000GeV, as a function of the true visible pT (left) and η of hadronic tau decays [97]. . 87 4.30 The efficiency true for 1-prong hadronic tau decays to be reconstructed with the corrected number of tracks and pass the tau discriminants for rejecting leptons, in Monte Carlo simulation for a SSM Z ′ with a mass of 1000GeV, as a function of the true visible pT (left) and η of hadronic tau decays [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.31 Fake factors derived for the medium BDT tau ID in a sample of events from the 2011 dataset rich in W → μν+jets events (left) and dijet events (right) with the 2011 data [97]. 89 4.32 Profile plots of the number of tracks associated to a jet (left) and the track width (defined the same as Rtrack) (right) vs pT of jets in ATLAS simulation. Note that gluon-initiated jets are systematically wider and have a higher track multiplicity than quark-initiated jets (mc11) [166]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.33 (left) A profile plot of 1−Ψ(0.3) vs pT using 2010 ATLAS data. Such a quantity is a measure of the jet width, quantifying the fraction of the jet energy not within ∆R < 0.3 [157]. (right) The generator-level distribution for Ψ(0.1) separately for quarkand gluon-initiated jets with pT = 200GeV [168]. Note that while both have significant tails with Ψ approaching 0, quark-initiated jets have Ψ peaked much closer to 1, meaning that quark-initiated jets are more likely to be tightly collimated. . . . . . . . . . . . . . 91 4.34 Leading order Feynman diagrams for production of W + jets at hadron-hadron colliders. Note that the ± simply denotes the sign of the electric charge, and that quarks have fractional magnitudes of charge. The diagrams with the quark current flipped also contribute, but diagrams with a q in the initial state will be suppressed by the proton PDFs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.35 Distributions of the predicted quark/gluon fraction of jets in W/Z + jets events (left) and dijet events (right) [169]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.36 The true leading quark/gluon fraction of a jet in Alpgen W + jets Monte Carlo events plotted as a function of the transverse mass, mT, of the selected muon and E miss T (left), and as a function of the pT of the tau candidate seeded by the jet (right) [97]. . . . . . 93 4.37 Distributions showing the pile-up dependence of the signal efficiency (top) and fake rate (bottom) of the 2010 pT-parametrized cut-based tau ID, using ATLAS simulation. There is a distribution for each loose/medium/tight working point, and binned in the number of reconstructed vertices, showing a dramatic drop in efficiency as the number of vertices increases (mc09) [147]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 246 list of figures 4.38 A sketch illustrating that fcore is calculated as the ratio of energies in ∆R < 0.1 to ∆R < 0.2, smaller than the REM size of 0.4, to be more pile-up robust. . . . . . . . . . 95 4.39 Distributions of JVF (left) and ppile-upT = (1− JVF) ∑ pT(track) (right), for true Monte Carlo hadronic tau decays (blue) and jets from a dijet sample of 2011 ATLAS data (red). 97 4.40 The dependence of key tau identification variables as a function of the number of reconstructed vertices, separately for 1-prong (left) and 3-prong (right) tau candidates. The points indicate the means in each bin. The coloured bands indicate the standard deviation. The blue (filled) points correspond to tau candidates matched to hadronically decaying taus in simulated W → τν and Z → ττ events. The red (open) points are for the dijet sample from data [101]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.41 The dependence of key tau identification variables as a function of (1−JVF)∑ pT(track), a local measure of the summed pT from pile-up tracks that contribute to the tau candidate, separately for 1-prong (left) and 3-prong (right) tau candidates. The points indicate the means in each bin. The coloured bands indicate the standard deviation. The blue (filled) points correspond to tau candidates matched to hadronically decaying taus in simulated W → τν and Z → ττ events. The red (open) points are for the dijet sample from data [101]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.42 Signal efficiency of the experimental Tau++ cut-based identification for 1-prong (left) and 3-prong (right) candidates using the chosen value of the parameter, α = 0.0/0.6/1.0 for (top/center/bottom) [117]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.43 Inverse background efficiency as a function of signal efficiency for 1-prong (left) and 3-prong (right) candidates, in low (top) and high (bottom) pT ranges, for the jet-tau discriminants re-optimized in the summer of 2011 [101]. . . . . . . . . . . . . . . . . . . 102 4.44 Profile plots of the cluster isolation, EisoT , without a pile-up correction (left), corrected with extrapolated pile-up tracks (center), and corrected with extrapolated pile-up tracks and a term linear in Nvertex (right) [171]. . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.45 (left) Profile plot of fcore vs Nvertex for the uncorrected (black) and pile-up corrected (red) versions. (right) The signal efficiency of the BDT working points vs Nvertex, using the pile-up corrected versions of fcore and ftrack, from 2012 ATLAS simulation [103]. . 104 5.1 Generator-level truth information for muons in the mc08 PYTHIA J2 dijet sample [177]. 108 5.2 The pT of reconstructed muon candidates, comparing dijet and Z → ττ MC (mc08, √ s = 10TeV) [177] J1, J2, and J3 denote simulated dijet samples with an out-going parton in the pT ranges 17–35, 35–70, and 70–140 GeV respectively. . . . . . . . . . . . . . . . . 108 5.3 The distribution of the reconstructed missing transverse momentum for the relevant MC samples with preselected μτh events [177]. . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.4 Distributions of trackingand calorimeter-based muon isolation variables for Z → ττ and dijet samples [177]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.5 Tau identification fake rates derived with dijet and bb Monte Carlo samples (mc08,√ s = 10TeV) [177]. The identification used is a preliminary version of the likelihood method [148]. The fake rate in the bb sample is enhanced compared to the inclusive sample of dijets, mainly due to the presence of real leptons from B decays, but the effect is not significant after removing pre-selected leptons. . . . . . . . . . . . . . . . . . . . 110 5.6 Distributions of the visible mass of the combination of a muon and a selected tau candidate. (left) A comparison of Monte Carlo bb events that pass tau identification with a distribution from scaling candidates by a fake rate (with no lepton isolation). (right) The combined SM background model for selected μτh events with tau identification and muon isolation requirements. A preliminary likelihood-based tau identification [148] was used by requiring that the likelihood score was greater than 4. The isolation requirements used were: N∆R<0.4tracks (μ) = 0 and E ∆R<0.4 T (μ) < 2GeV [177]. . . . . . . . . . . . . . . . . 111 5.7 The visible mass of μτh events with opposite-sign (left) and same-sign (right) reconstructed charges. Note that the W + jets background is OS-biased [177]. . . . . . . . . 112 list of figures 247 5.8 Diagrams illustrating representative transverse plane orientations of W and Z decay products and the EmissT . The shaded angles indicate the angle less than π between the lepton and the (fake) tau-jet. τh denotes the visible sum of the decay products of a hadronic decay of a tau lepton. In (a), the Z is depicted to have nonzero pT, which must be balanced on the left by some other activity omitted for clarity [177]. . . . . . . . . . 113 5.9 (left) In Z → ττ → `τh events, since there are two neutrinos on the side of the leptonic decay, the EmissT tends to point along the lepton in the transverse plane. (right) The transverse mass of the lepton and the EmissT in reconstructed μτh events for Z → ττ and W + jets Monte Carlo samples (mc08, √ s = 10TeV) [177]. . . . . . . . . . . . . . . . . 114 5.10 (left) A scatter plot of the cos ∆φ for the angles between each decay product and the EmissT for μτh events with Monte Carlo. (right) The distribution of ∑ cos ∆φ for the same events [177]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.11 (left) A scatter plot of the cos ∆φ for the angles between each decay product and the EmissT for μτh events from Monte Carlo. (right) The distribution of the transverse mass of the combination of the muon and the EmissT . Both of these plots are after requiring∑ cos ∆φ > −0.15 [177]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.12 The effective cross section passing successive event selections for a preliminary Z → ττ → μτh event selection (mc08, √ s = 10TeV) [177]. . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.13 The μτh visible mass of events passing the entire analysis selection except for a visibile mass window. The number of reconstructed tracks associated to the tau candidate in events passing the entire selection except relaxing the 1 or 3 and OS requirements [177]. Toy data drawn from a Poisson distribution for the expected value in each bin is shown to give a visualization of the expected statistics. . . . . . . . . . . . . . . . . . . . . . . 118 5.14 The efficiency for true reconstructed leptons in Monte Carlo to pass the trigger using fully simulated Monte Carlo. This efficiency was fit and the parametrtization used to weight fast simulation samples (ATLFAST-II) that did not have a simulated trigger decision (mc08) [174]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.15 The μτh visible mass of events passing the entire analysis selection except for a visibile mass window as predicted with the full simulation dijet samples, weighted by fake rates (left), and as predicted with ATLFAST-II dijet Monte Carlo (right) [174]. . . . . . . . 119 5.16 Comparison, for data and Monte Carlo, of the distributions of the number of reconstructed vertices in each event before (left) and after (right) vertex re-weighting [181]. . 120 5.17 Distributions of the isolation variables used after selecting one tau candidate and an opposite-sign lepton. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. 125 5.18 Kinematic distributions of the selected leptons and tau candidates following all object selections. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. . . 128 5.19 Distributions of the number of preselected leptons, counted for the dilepton veto, following all object selections. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.20 The distributions of ∑ cos ∆φ are shown for the muon (a) and electron (b) channels. The distributions of transverse mass, mT, of the combination of the lepton and the E miss T are shown for the muon (c) and electron (d) channels. All of these distributions are shown following the full object selections, the dilepton veto, and requiring opposite sign. The electroweak background is estimated with Monte Carlo. The multijet background is modeled with the same-sign data, corrected with Monte Carlo [181]. . . . . . . . . . . . 130 248 list of figures 5.21 The distributions of the visible mass of the combination of the chosen tau candidate and chosen lepton are shown for the muon (a) and electron (b) channels. These distributions are shown following the full object selections and event selections, except for the visible mass window [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.22 An event display of a candidate Z → ττ → μτh event with a 3-prong hadronic tau decay, in the 2010 dataset [188]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.23 The μτh visible mass of events passing the full selection for the ATLAS Z → ττ observation. The red vertical lines indicate the 35–75 GeV mass window used as the final cut [146]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.24 Distributions of the pT and η of the selected leptons and tau candidates for events passing all signal selection [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.25 The distributions of the EmissT and ∆φ between the selected tau candidate and lepton, in the final visible mass window for the muon (a),(c) and electron (b),(d) channels [181]. . 136 5.26 The final track distribution after all cuts, except without the requirement of 1 or 3 tracks. The product of the reconstructed charges is required to be negative or zero (not samesign) [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.27 Muon and tau pT distributions in the W control region, following no tau identification (a)/(c) and tight (b)/(d) τ identification. Following tight tau identification, the Monte Carlo overestimates the W contribution. A similar effect is seen in the eτh channel [181]. 138 5.28 Diagrams of the control regions for two ABCD methods for estimating the multijet background. The figure on the left shows the regions for the primary estimate. The figure on the right shows regions for the cross-check method [181]. . . . . . . . . . . . . . . . . . 140 5.29 Plots demonstrating the stability of ROS/SS as a function of calorimeters isolation (top) and tau identification requirements (bottom), for the μτh (left) and eτh (right) channels [181]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.30 The combined measurement of the Z → ττ cross section in four final states: μτh, eτh, eμ, and μμ [113]. The combination of the ATLAS measurements of the Z → ee/μμ cross sections is shown for comparison [108]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 6.1 Kinematic distributions for the μτh channel. (top) The distribution of the absolute difference in φ between the selected muon and tau candidate in events with exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau. (middle) The distribution of the product of the reconstructed charges of the selected electron and tau candidate in events with the event preselection listed above, and requiring ∆φ(μ, τh) > 2.7. (bottom) The distribution of the E miss T in events with the above selection, and requiring opposite-sign charges for the μ and τh (the μτh baseline event selection) [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 6.2 Kinematic distributions for the μτh channel. (top) The distribution of pT(μ), (middle) the distribution of pT(τh), and (bottom) the distribution of m tot T (μ, τh, E miss T ) in events passing the μτh baseline event selection (MT ≡ mtotT ) [97]. . . . . . . . . . . . . 164 6.3 Kinematic distributions for the eτh channel. (top) The distribution of the absolute difference in φ between the selected electron and tau candidate in events with exactly one selected electron, no additional preselected electrons or muons, and exactly one selected 1-prong tau. (middle) The distribution of the product of the reconstructed charges of the selected electron and tau candidate in events with the event preselection listed above, and requiring ∆φ(e, τh) > 2.7. (bottom) The distribution of the E miss T in events with the above selection, and requiring opposite-sign charges for the e and τh [97]. . . . . . . . . 165 6.4 Kinematic distributions for the eτh channel. (top) The distribution of pT(e), (middle) the distribution of pT(τh), and (bottom) the distribution ofm tot T (e, τh, E miss T ) in events passing the eτh baseline event selection (MT ≡ mtotT ) [97]. . . . . . . . . . . . . . . . . . . . . . 166 6.5 Lepton isolation fake factors derived in the multijet control region for the μτh channel (left) and the eτh channel (right)[97]. . . . . . . . . . . . . . . . . . . . . . . . . . . 170 list of figures 249 6.6 (left) The distribution of the transverse mass of the combination of the selected lepton and the EmissT , mT(`, E miss T ). (right) The distribution of the impact parameter, d0 of the selected lepton. These plots include the requirements of: exactly one selected muon, no additional preselected electrons or muons, and exactly one selected 1-prong tau, except the (bottom-right) has the tau identification completely removed including the electonveto [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.7 Plots demonstrating that the multijet backgrounds are negligible at high mass for events passing the baseline event selections. (left) The mtotT distribution of the multijet estimate in μτh channel, showing that the multijet background falls to O(10−2) events for mtotT & 400GeV. (right) The mtotT distribution of the multijet estimate in eτh channel, with predictions for medium (used in the nominal selection), loose, and no jet-tau discrimination, The loosened mtotT distributions are scaled to the integral predicted by the nominal selection, JetBDTSigMedium. (MT ≡ mtotT ) [97]. . . . . . . . . . . . . . . . . . 172 6.8 Tau identification fake factors derived in the W + jets control region. The binning in η is defined as inner barrel: |η| < 0.8, outer barrel: 0.8 < |η| < 1.37, crack: 1.37 < |η| < 1.52, and end-cap: 1.52 < |η| < 2.47 [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 6.9 A diagram illustrating the combined use of the two data-driven methods to predict the multijet and W + jets backgrounds. First, the multijet contamination is estimated from the rate of non-isolated leptons in both the signal sample that passes tau identification, and the sample that fails. Then, the corrected number of tau candidates failing identification is weighted to predict the W + jets background. . . . . . . . . . . . . . . . . . . 175 6.10 (left) The distribution of mT(μ,E miss T ) near the W + jets control region, before applying a cut of mT(μ,E miss T ) > 70GeV. (right) Tau identification fake factors derived from modified control regions with various mT(μ,E miss T ) cuts applied, showing that the fake factors do not have a strong dependence on mT(μ,E miss T ) [97]. . . . . . . . . . . . . . . 175 6.11 Kinematic distributions for events passing the eτh baseline event selection, comparing estimates of the fake backgrounds with the nominal double-fake-factor method and the singlefake-factor method. The distribution of mtotT (e, τh, E miss T ) (top-left) and pT(τh) (topright) using the single-fake-factor method. The high-mass tail of the mtotT distribution using the nominal double-fake-factor method (bottom-left) and the single-fake-factor method (bottom-right) (MT ≡ mtotT ) [97]. The "Fake τh" estimate is meant to cover fake hadronic tau decays from W + jets and multijet events. Because it uses a tau fake factor derived in a W + jets sample, which is rich in quark-initiated jets, the fake estimate should over estimate the multijet contribution, which is more gluon-rich. . . . . . . . . 177 6.12 The distribution of mtotT (μ, τh, E miss T ) for the Z → μμ background of the μτh channel. The Z → μμ background is negligible at high mtotT , falling to 0.1 events with mtotT & 400 GeV compared to a total expected SM background of 15± 1 events. (MT ≡ mtotT ) [97]. . . . 178 6.13 Plots demonstrating that the Z → ee background is negligible at high mass for events passing the eτh baseline event selection. (left) The m tot T distribution of the Z → ee modeled with Alpgen Monte Carlo, divided into cases where the reconstructed tau candidate matched a true electron or a jet. (right) The mtotT distribution of the expected Z → ee background, with predictions for medium (used in the nominal selection), loose, and no electron-veto applied to the hadronic tau candidate. For the (right), the reconstructed tau candidate is required to match a true Monte Carlo electron [97]. . . . . . . . . . . . 178 6.14 The mtotT (τh, τh, E miss T ) distribution for the τhτh channel after the full selection (excluding the final mtotT window). The estimated contributions from SM processes and Z ′ SSM signal are stacked and theobserved events in data are overlayed. The uncertainty on the data/MC ratio includes only the statistical uncertainty from the data and the MC simulated samples, while the uncertainty on the multijet contribution is not included [212]. 181 250 list of figures 6.15 (left) The expected (dashed) and observed (solid) 95% credibility upper limits on the cross section times τ+τ− branching fraction, in the τhτh, μτh, eτh, and eμ channels, and for their combination. The expected Z ′SSM production cross section and its corresponding theoretical uncertainty (dotted) are also included. (right) The expected and observed upper limits for the combination including 1σ and 2σ uncertainty bands. Z ′SSM masses up to 1.40 TeV are excluded, in agreement with the expected limit in the absence of a signal of 1.42 TeV [212]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6.16 Generator-level kinematic distributions for a Z ′SSM with a mass of 1250 GeV, after the baseline event selection, with SSM (nominal), V −A, and V + A couplings. (top-left) and (top-right) show the visible pT of hadronic tau decay and lepton, respectively, in the `τh channel. (bottom-left) and (and bottom-right) compare the m tot T distributions in the τhτh and `τh channels, respectively. [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . 189 6.17 The relative change in signal acceptance for the V −A and V + A samples (in % of the nominal SSM signal) vs. the Z ′ mass for the τhτh channel (left) and the `τh channel (right) [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 6.18 The expected and observed upper limits for the combination, showing the change in expected limit for V −A and V + A couplings [97]. . . . . . . . . . . . . . . . . . . . . 190 7.1 Summary of several Standard Model total production cross section measurements, correcting for leptonic branching fractions, compared to the corresponding theoretical expectations. The W and Z vector-boson inclusive cross sections were measured with 35 pb−1 of integrated luminosity from the 2010 dataset. All other measurements were performed using the 2011 dataset or the 2012 dataset. The luminosity used for each measurement is indicated close to the data point [239]. . . . . . . . . . . . . . . . . . . . . . . . . . . 192 7.2 Mass reach of several ATLAS searches for new phenomena other than Supersymmetry. Dark blue lines indicate 8 TeV data results with the 2012 data [239]. . . . . . . . . . . 193 A.1 Diagrams illustrating that the QED fermion propagator (left) and the QED vertex (right) are inherently an infinite sum of indistinguisable quantum amplitudes that result in an effective mass and coupling, respectively, when renormalized [296, 297]. . . . . . . . . . 205 A.2 The interactions of the Standard Model [320]. . . . . . . . . . . . . . . . . . . . . . . . 216 A.3 Illustration of the Higgs potential, V (Φ). (left) The shape of the potential in any two components of: Re(φ+), Im(φ+), Re(φ0), Im(φ0). (right) A plot of the Higgs potential assuming mH = 126GeV, as shown in Table A.5 [328]. . . . . . . . . . . . . . . . . . . . 218 A.4 Mass range of the SM fermions [356]. For approximate values of the masses, see Table A.6. 223 A.5 (left) Pseudoscalar mesons (JPC = 0−+). (right) Pseudovector mesons (JPC = 1−−) [358]. 224 A.6 (left) Spin-3/2 baryon decuplet. (right) Spin-1/2 baryon octet [358]. . . . . . . . . . . . 224 A.7 NLO PDFs for the proton at Q2 = 10GeV2 (left) and Q2 = 104GeV2 (right) [54]. . . . 226 A.8 Constraints on the CKM (ρ, η) coordinates from the global SM CKM-fit. Regions outside the colored areas have been excluded at 95%. For the combined fit the yellow area inscribed by the contour line represents points with CL ≤ 95%. 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