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Search for new neutral high-mass resonances decaying into muon pairs with the ATLAS detector Viel, Simon 2014

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SEARCH FOR NEW NEUTRAL HIGH-MASS RESONANCESDECAYING INTO MUON PAIRS WITH THE ATLAS DETECTORbySimon VielB.Sc., Universite´ Laval, 2008A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2014c© Simon Viel, 2014AbstractThe question of physics beyond the Standard Model remains as crucial as it was before the discoveryof a Higgs boson at the Large Hadron Collider, as the theoretical and experimental shortcomingsof the Standard Model remain unresolved. Indeed, theoretical problems such as the hierarchy ofenergy scales, the Higgs mass fine-tuning and the large number of postulated parameters need tobe addressed, while the experimental observations of dark matter, dark energy and neutrino massesare not explained by the Standard Model. Many hypotheses addressing these issues predict theexistence of new neutral high-mass resonances decaying into muon pairs.This dissertation documents a search for this process using 25.5 fb−1 of proton-proton collisiondata collected by the ATLAS experiment in Run-I of the Large Hadron Collider. After evaluatingthe performance of the detector for reconstructing muons at very high momentum, the event yieldsobserved as a function of the invariant mass of muon pairs are compared with expected values fromStandard Model processes.The observed yields are found to be in good agreement with Standard Model predictions, andno significant excess of events is found. New gauge bosons with couplings to fermions equal tothese of the Standard Model Z boson and with masses lower than 2.53 TeV are therefore excludedat 95% confidence level. A statistical combination with the results of the search for the same particledecaying into electron pairs yields a lower mass limit of 2.90 TeV at 95% confidence level. Limitsare also placed in the context of two classes of models inspired by Grand Unification Theories:gauge theories with the E6 symmetry group, as well as Minimal Z′ Models.iiPrefaceThe research presented in this dissertation is based on the experimental data of the ATLAS exper-iment at the Large Hadron Collider. Thousands of researchers based at more than 170 institutionsfrom 38 countries participate in the ATLAS collaboration.All of the dissertation text was written by me, and not taken directly from previously publishedsources. Only versions of the text in Sections 7.2, 7.3, A.3.6 and A.3.7 have previously appearedin internal ATLAS documentation. All figures and tables for which a reference or figure credit isnot indicated in the caption represent my own work, often in collaboration with other researchersnamed below. Figures labeled “ATLAS”, “ATLAS Preliminary” and event displays with the ATLASlogo are public material released by the ATLAS collaboration. Figures labeled “ATLAS work inprogress” are previously unpublished material derived from ATLAS real and/or simulated data.Chapters 2, 3 and 4 present introductory material, with all sources referenced in the text.I participated in commissioning the Transition Radiation Tracker described in Section 4.3.3, andcontributed to developing and maintaining the data quality monitoring system described in Sec-tion 4.8.3. Section 5.1 also presents introductory material from the indicated references. From thematerial in Section 5.2, I have collaborated with L. Chevalier and H. Wang to produce Figure 5.3,and I have produced Figure 5.6.I was one of the lead investigators for the analysis presented in Section 5.3 and Chapters 6, 7,and 8. This work led directly to four publications, first with the full dataset collected by ATLASin 2010 [Phys. Lett., B700:163, 2011], then with the initial part of the dataset collected in 2011[Phys. Rev. Lett., 107:272002, 2011], the full dataset collected in 2011 [JHEP, 1211:138, 2012] andfinally with the full dataset collected in 2012 [Accepted by Phys. Rev. D, 2014].In addition, many other published analyses from the ATLAS collaboration have also made useof the primary muon selection described in Section 5.3, and in particular four of these have alsoused the methods described in Chapters 6 and 7, searching for a non-resonant excess of events usingthe same datasets collected in 2010 [Phys. Rev., D84:011101, 2011], in 2011 [Phys. Lett., B712:40,2012; Phys. Rev., D87:015010, 2013] and in 2012 [Submitted to Eur. Phys. J. C, 2014].My main roles toward these publications were as follows:• For the first two publications above, I was the main data analyst in the dimuon channel.iii• I then served as co-leader of the analysis with the full 2011 dataset, coordinating a team of 70researchers from 27 institutes. I was primarily responsible from the dimuon channel, whileS. Heim was co-leader for the dielectron channel. In addition to refining the techniques usedin the analysis, we have set stringent limits on a wide variety of theoretical models.• For the analysis with the full 2012 dataset, I continued to make crucial collaborations to theanalysis, indicated below.• I contributed importantly to writing these four publications, along with internal supportingdocumentation, and addressed comments during the review process.• I also contributed to estimating the background and signal predictions as well as the relateduncertainties for the four other publications listed.In detail, my original contributions to the material presented in the main body of this dissertationare as follows:• I contributed to developing the muon selection in Section 5.3.1 and characterizing the perfor-mance of the detector for these muons, as member of a task force coordinated by S. Willocq.• I carried out the studies described in Section 5.3.2 for the analysis with the full 2011 dataset,starting from code by D. Fortin. I collaborated with J. Coggeshall to replicate these studiesfor the analysis with the 2012 dataset.• I contributed to developing the event selection described in Section 6.1 and implemented it,starting from code by I. Nugent. The yield histograms in this section were produced in collab-oration with E. Laisne´, and the event display was produced in collaboration with L. Chevalier.• I performed the background and signal estimates described in Section 6.2, with the followinginputs provided by collaborators:– Real and simulated data prepared centrally by members of the ATLAS collaboration;– Theoretical corrections to the Z/γ∗ differential cross section calculated by T. Nunne-mann, J. Kretzschmar and U. Klein;– Fits to the tails of the sub-leading backgrounds performed by S. Heim and E. Fitzgerald;– Cosmic ray background estimate designed by P. Wagner;– Signal template re-weighting method designed by A. Kotwal and O. Stelzer-Chilton,with interference effects included by W. Fedorko, S. Heim, N. Hod and A. Kotwal.• I performed the comparison of data with background expectations in Section 6.3 in the firstthree rounds of analysis, starting from code by D. Hayden. Variants of my code were used forthe analysis with the 2012 dataset by R. Daya and E. Fitzgerald.iv• I developed the techniques used to evaluate theoretical and experimental systematic uncertain-ties discussed in Chapter 7, using inputs by T. Nunnemann and U. Klein for the theoreticaluncertainties on the Z/γ∗ yields. The experimental uncertainties were evaluated in collabora-tion with D. Fortin and O. Stelzer-Chilton for the analyses with the 2010 and 2011 datasets,and with J. Coggeshall and E. Fitzgerald for the analysis with the 2012 dataset.• I developed and managed the statistical framework used in Chapter 8, starting from code byB. Stelzer interfacing the Bayesian Analysis Tools. W. Fedorko and S. Heim also contributedto this framework.• I contributed to obtaining all the final results in Chapter 8, in collaboration with K. Allen,J. Coggeshall, R. Daya, F. Ellinghaus, O. Fedin, W. Fedorko, E. Fitzgerald, C. Goeringer,D. Hayden, S. Heim, B. Stelzer, O. Stelzer-Chilton, K. van Nieuwkoop and S. Zambito.• The expected limits presented in Chapter 9 are derived from work carried out primarily byT. Hryn’ova, U. Klein, J. Kretzschmar and me.In Appendix A, Sections A.1 and A.2 present introductory material relevant to the work pre-sented in Section A.3. My original contributions to this analysis in development are the following:• I investigated possible gains in sensitivity with the Matrix Element method, starting from codemainly by D. Schouten, and also by M. Bluteau, P. Chang, B. Stelzer and K. van Nieuwkoop.• I optimized the event pre-selection and the Boosted Decision Tree input variables, in collab-oration with B. Cerio, K. McLean, D. Schouten, B. Stelzer and K. van Nieuwkoop.• I performed modelling studies of variables and correlations, and estimated the Z/γ∗ back-ground in both search channels, starting from code by D. Schouten.• I quantified the effect of systematic uncertainties on the shape of the discriminant variable,starting from code by M. Venturi and T. Lenz.• I contributed to the statistical framework of the analysis group, and used it to quantify theperformance of the multivariate analysis developed in comparison to previous results.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 The Standard Model Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Forces and Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 The Englert-Brout-Higgs-Guralnik-Hagen-Kibble Mechanism . . . . . . . 62.1.3 Electroweak Interactions Revisited . . . . . . . . . . . . . . . . . . . . . . 82.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Successes of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 Asymptotic Freedom and Infrared Slavery . . . . . . . . . . . . . . . . . . 112.2.2 Calculation of Cross Sections and Decay Rates . . . . . . . . . . . . . . . 132.3 Limitations of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.1 Quantum Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.2 Dark Matter and Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . 222.3.3 Charge-Parity Violation and Matter-Antimatter Asymmetry . . . . . . . . 242.3.4 Neutrino Masses and Flavour Oscillation . . . . . . . . . . . . . . . . . . 24vi2.3.5 Hierarchy, Fine-Tuning and Elegance . . . . . . . . . . . . . . . . . . . . 253 Beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1 Hypotheses Beyond the Standard Model Predicting New High-Mass Resonances . 273.2 New Gauge Symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 The Sequential Standard Model . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Models from Grand Unified Theories . . . . . . . . . . . . . . . . . . . . 283.2.3 Experimental Limits on New Gauge Bosons . . . . . . . . . . . . . . . . . 324 The ATLAS Experiment at the Large Hadron Collider . . . . . . . . . . . . . . . . . 334.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1.1 Accelerator Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.1.2 Main Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.3 Delivered Luminosity and Beam Conditions in Run-I . . . . . . . . . . . . 374.2 The ATLAS Detector: Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2.1 Detector Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2.2 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.3.1 Pixel Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.2 Semiconductor Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.3 Transition Radiation Tracker . . . . . . . . . . . . . . . . . . . . . . . . . 454.3.4 Solenoid Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.4 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.4.1 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . 464.4.2 Hadronic Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.5 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.5.1 Toroid Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.5.2 Monitored Drift Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.5.3 Cathode Strip Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.5.4 Resistive Plate Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.5.5 Thin Gap Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5.6 Layout of the Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . 524.6 Missing Transverse Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.7 Luminosity Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.8 Trigger, Data Acquisition and Data Quality . . . . . . . . . . . . . . . . . . . . . 604.8.1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.8.2 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.8.3 Data Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62vii5 Muons at Very High Momentum in ATLAS . . . . . . . . . . . . . . . . . . . . . . . 635.1 Muon Reconstruction in ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2 High-Momentum Muon Performance . . . . . . . . . . . . . . . . . . . . . . . . 655.3 Dedicated Very-High Momentum Muon Selection . . . . . . . . . . . . . . . . . . 745.3.1 Selection of 3-Station Muons . . . . . . . . . . . . . . . . . . . . . . . . 745.3.2 Selection of 2-Station Muons . . . . . . . . . . . . . . . . . . . . . . . . 766 Event Selection and Comparison of Data with Standard Model Expectations . . . . 836.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.2 Background and Signal Expectation . . . . . . . . . . . . . . . . . . . . . . . . . 896.2.1 Simulated Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896.2.2 Data-Driven Background Estimates . . . . . . . . . . . . . . . . . . . . . 966.2.3 Generation of Signal Templates . . . . . . . . . . . . . . . . . . . . . . . 1006.3 Comparison of Data with Background Expectations . . . . . . . . . . . . . . . . . 1046.3.1 Kinematics of the Dimuon System . . . . . . . . . . . . . . . . . . . . . . 1056.3.2 Kinematics of Individual Muons . . . . . . . . . . . . . . . . . . . . . . . 1056.3.3 Missing Transverse Energy Distributions . . . . . . . . . . . . . . . . . . 1177 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1217.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1217.1.1 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 1227.1.2 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.2 Parton Distribution Function and QCD Uncertainties on Signal Cross Sections . . . 1267.3 Parton Distribution Function and QCD Uncertainties on the Z/γ∗ Cross Section . . 1287.3.1 Parton Distribution Function Variations . . . . . . . . . . . . . . . . . . . 1297.3.2 Parton Distribution Function Set Choice, QCD Scale and αS . . . . . . . . 1338 Statistical Methods and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1378.1 Signal Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1378.1.1 Local p-Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1388.1.2 Global p-Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1428.2 Limits on Z′SSM and E6 Z′ Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . 1468.3 Limits on Minimal Z′ Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1509 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15510 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159viiiA Search for Vector Boson Fusion H→WW ∗→ `ν`ν . . . . . . . . . . . . . . . . . . . 172A.1 Status of Higgs Boson Observations at the Large Hadron Collider . . . . . . . . . 172A.2 Analysis Goals and Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175A.2.1 Physical Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177A.2.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178A.2.3 Topology of VBF H→WW ∗→ `ν`ν Events . . . . . . . . . . . . . . . . 179A.2.4 Boosted Decision Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . 182A.2.5 Matrix Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 184A.3 Contributions to the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185A.3.1 Statistical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185A.3.2 Event Pre-Selection Optimization . . . . . . . . . . . . . . . . . . . . . . 186A.3.3 Boosted Decision Tree Optimization . . . . . . . . . . . . . . . . . . . . . 187A.3.4 Modelling Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188A.3.5 Correlation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194A.3.6 Background Estimation and Systematic Uncertainties for Z/γ∗→ τ+τ− . . 195A.3.7 Background Estimation and Systematic Uncertainties for Z/γ∗ → e+e−,µ+µ− in the Same-Flavour Channel . . . . . . . . . . . . . . . . . . . . . 196A.3.8 Effect of Object Systematic Uncertainties on the BDT Score Shape . . . . 199A.3.9 Comparison of Analysis Techniques . . . . . . . . . . . . . . . . . . . . . 200A.3.10 Matrix Element Method Investigation . . . . . . . . . . . . . . . . . . . . 206A.4 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209ixList of TablesTable 2.1 Gauge bosons in the Standard Model . . . . . . . . . . . . . . . . . . . . . . . 4Table 2.2 Fermions in the Standard Model, in flavour basis . . . . . . . . . . . . . . . . . 4Table 3.1 Values of γ ′ and θMin for three specific models: Z′B−L, Z′χ and Z′R . . . . . . . . 31Table 3.2 Previous experimental limits at 95% CL on the mass of new gauge bosons Z′ . . 32Table 5.1 Muon pT resolution parameters for simulated samples generated in 2011 at√s = 7TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Table 5.2 Muon pT resolution parameters for simulated samples generated in 2012 at√s = 8TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Table 5.3 Muon momentum smearing constants used in analyses at√s = 7TeV. The effectof SID1 is neglected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Table 5.4 Muon momentum smearing constants used in analyses at√s = 8TeV. . . . . . 70Table 5.5 PMS∗2 parameters measured in data and simulation at√s = 7TeV and correspond-ing smearing parameters SMS∗2 = PMS∗2,data	PMS∗2,MC. . . . . . . . . . . . . . . . . . 82Table 5.6 PMS∗2 parameters measured in data and simulation at√s = 8TeV. . . . . . . . . 82Table 6.1 Summary of the simulated samples for the analysis using the full dataset at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Table 6.2 Summary of the simulated samples for the analysis using the full dataset at√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Table 6.3 Expected and observed number of events for the analysis at√s = 7TeV . . . . . 106Table 6.4 Expected and observed number of events for the analysis at√s = 8TeV . . . . . 107Table 7.1 Summary of systematic uncertainties on the expected number of events for thesearch using data collected in 2011 at√s = 7TeV. . . . . . . . . . . . . . . . . 122Table 7.2 Summary of systematic uncertainties on the expected numbers of events for thesearch using data collected in 2012 at√s = 8TeV. . . . . . . . . . . . . . . . . 122Table 7.3 Uncertainty on Z′ cross sections due to PDF variations at 90% CL at√s = 7TeV. 128xTable 7.4 Uncertainty on Z′ cross sections due to PDF and αS variations at 90% CL at√s = 8TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Table 8.1 Observed and expected lower limits on the mass of Z′SSM and E6 Z′ bosons at95% CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Table 8.2 Observed and expected lower limits on the mass of Z′B−L, Z′χ and Z′R bosons at95% CL obtained in the context of Minimal Z′ Models . . . . . . . . . . . . . . 154Table 8.3 Range of the observed and expected lower limits at 95% CL on the Z′Min bosonmass for θMin ∈ [0,pi] and representative values of the relative coupling strengthγ ′. Both lepton channels are combined. . . . . . . . . . . . . . . . . . . . . . . 154Table 8.4 Range of the observed and expected upper limits at 95% CL on the relative cou-pling strength γ ′ for θMin ∈ [0,pi] and representative values of the Z′Min bosonmass. Both lepton channels are combined. . . . . . . . . . . . . . . . . . . . . 154Table A.1 Summary of the region definitions for the Z/γ∗ estimation technique used in theSF channel of the analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197xiList of FiguresFigure 2.1 Particle content of the Standard Model . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.2 Gauge couplings of the Standard Model as a function of energy scale . . . . . 12Figure 2.3 Feynman diagram for the contribution at Leading Order to the Drell-Yan process 15Figure 2.4 Feynman diagrams for examples of higher-order contributions to the Drell-Yanprocess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 2.5 Schematic illustration of parton interactions within a proton . . . . . . . . . . 17Figure 2.6 Proton NLO PDFs from the MSTW collaboration at two momentum transferscales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.7 Standard Model cross section predictions for proton-(anti)proton collisions . . 20Figure 2.8 Summary of several Standard Model production cross section measurementsperformed by the ATLAS collaboration . . . . . . . . . . . . . . . . . . . . . 21Figure 2.9 The Bullet Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 4.1 The CERN accelerator complex . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 4.2 Magnets in the LHC tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 4.3 LHC magnet components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 4.4 Placement of the dipole and quadrupole magnets responsible for bringing theLHC beams into collision at the ATLAS interaction point. Also shown are thepositions of the LUCID, Zero Degree Calorimeter and ALFA detectors . . . . 37Figure 4.5 Cumulative luminosity versus time delivered to ATLAS, recorded by ATLAS,and certified to be good quality data during stable beams and for proton-protoncollisions at 7 and 8 TeV centre-of-mass energy in 2011 and 2012 . . . . . . . 38Figure 4.6 Luminosity-weighted distribution of the mean number of interactions per cross-ing for the dataset collected in 2011 and 2012 . . . . . . . . . . . . . . . . . . 38Figure 4.7 Z → µ+µ− candidate event with reconstructed vertices from 25 simultaneousproton-proton interactions in the ATLAS detector . . . . . . . . . . . . . . . . 39Figure 4.8 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41xiiFigure 4.9 Illustration of the ways in which different particles are identified based on theirinteractions with the ATLAS detector . . . . . . . . . . . . . . . . . . . . . . 42Figure 4.10 Transverse view of the ATLAS Inner Detector components . . . . . . . . . . . 43Figure 4.11 Longitudinal view of the ATLAS Inner Detector components . . . . . . . . . . 43Figure 4.12 Average probability of a high-threshold hit in the TRT Barrel as a function ofthe Lorentz γ-factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 4.13 The ATLAS calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 4.14 The ATLAS Muon Spectrometer and toroid magnets . . . . . . . . . . . . . . 49Figure 4.15 Integrated magnetic field strength in the MS as a function of |η |, for φ = 0 andφ = pi/8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 4.16 Cross section of an MDT and mechanical structure of an MDT chamber . . . . 50Figure 4.17 Cross-section of an RPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Figure 4.18 Transverse view of Muon Spectrometer Barrel chambers, with the sector num-bering convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Figure 4.19 Layout of large and small standard sectors of the Muon Spectrometer . . . . . 56Figure 4.20 Number of detector stations traversed by muons in the MS as a function of ηand φ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 5.1 Determination of the sagitta based on the location of segments in the MuonSpectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 5.2 Design resolution of the ATLAS Muon Spectrometer as a function of muontransverse momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 5.3 Event with the highest dimuon invariant mass observed in data collected at√s = 7TeV by the ATLAS experiment . . . . . . . . . . . . . . . . . . . . . . 68Figure 5.4 Momentum scale corrections to Inner Detector and Muon Spectrometer tracksderived from data collected at√s = 8TeV . . . . . . . . . . . . . . . . . . . . 71Figure 5.5 Effect of corrections to the muon momentum scale and resolution in the Z peakregion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 5.6 Effect of muon resolution smearing on a Z′SSM resonant peak with a pole massof 2.25 TeV, and on the steeply falling background from Z/γ∗ production. . . 73Figure 5.7 Efficiency of the ATLAS detector for reconstructing combined muons as a func-tion of pseudorapidity, for data collected at√s = 8TeV and a correspondingsimulated Z→ µ+µ− sample . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 5.8 Example of a potential track curvature mis-measurement for a 2-station muonwhere one of the inner MDT chambers is out of alignment . . . . . . . . . . . 77Figure 5.9 Profile histograms demonstrating the linear relationship between q/p and∆θseg/Bint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77xiiiFigure 5.10 Example fit results for MS towers with good angular resolution in data at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 5.11 Example fit results for Muon Spectrometer towers with known poor angularresolution in data at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 5.12 Example fit results for selected 2-station muons from data at√s = 7TeV, inmomentum bins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Figure 5.13 Momentum resolution of 2-station muons in data at√s = 7TeV . . . . . . . . 80Figure 5.14 Momentum resolution of 2-station muons in simulation at√s = 7TeV . . . . . 81Figure 5.15 Momentum resolution of 2-station muons in simulation at√s = 7TeV fromcomparing the refit 2-station momentum to MC truth . . . . . . . . . . . . . . 81Figure 6.1 Signal acceptance times efficiency for a Z′SSM boson as a function of MZ′ . . . . 85Figure 6.2 Yield per pb−1 for each run, for the primary and secondary dimuon selection at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Figure 6.3 Yield per pb−1 for each run, for the primary and secondary dimuon selection at√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure 6.4 Event with the highest dimuon invariant mass observed in data collected by theATLAS experiment in Run-I of the LHC . . . . . . . . . . . . . . . . . . . . . 88Figure 6.5 Sketch of a proton-proton collision at high energy . . . . . . . . . . . . . . . . 89Figure 6.6 Perturbative QCD correction factor for Z/γ∗ → µ+µ− production as functionof mµ+µ− at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 6.7 Electroweak and photon-induced correction factor for Z/γ∗→ µ+µ− produc-tion as function of mµ+µ− at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . 92Figure 6.8 Generated Z pT spectra near the Z resonance region and at higher invariant masses 93Figure 6.9 Perturbative QCD, electroweak and photon-induced correction factors forZ/γ∗→ µ+µ− production as function of mµ+µ− at√s = 8TeV . . . . . . . . . 95Figure 6.10 Muon track-based isolation distribution, immediately before the isolation cut . 97Figure 6.11 Dimuon invariant mass distribution from events with two muons passing thereversed isolation requirement along with the rest of the selection . . . . . . . 98Figure 6.12 Dimuon invariant mass distribution after final selection for the first 1.21 fb−1 ofdata collected in 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Figure 6.13 Cosmic muon event with hits in all Barrel detectors . . . . . . . . . . . . . . . 99Figure 6.14 Example Z′SSM signal templates generated at√s = 8TeV . . . . . . . . . . . . 103Figure 6.15 Example 2D combined template of Z/γ∗ background and Z′Min signal generatedat√s = 8TeV, as a function of γ ′4 and mµ+µ− , for MZ′Min = 2.5TeV and θMin = 0. 104Figure 6.16 Dimuon invariant mass in the selected events at√s = 7TeV. . . . . . . . . . . 106Figure 6.17 Dimuon invariant mass in the selected events at√s = 8TeV. . . . . . . . . . . 107xivFigure 6.18 Dimuon transverse momentum and rapidity in the selected events at√s = 7TeV 108Figure 6.19 Dimuon transverse momentum and rapidity in the selected events at√s = 8TeV 109Figure 6.20 Dimuon transverse momentum in the first 1.21 fb−1 of data collected at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Figure 6.21 Transverse momentum of the leading muon and sub-leading muon in the se-lected events at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Figure 6.22 Transverse momentum of the leading muon and sub-leading muon in the se-lected events at√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Figure 6.23 Muon transverse momentum in the first 1.21 fb−1 of data collected at√s = 7TeV 113Figure 6.24 η and φ distributions for the selected muons at√s = 7TeV. . . . . . . . . . . 114Figure 6.25 η distributions for the leading muon and sub-leading muon in the selectedevents at√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Figure 6.26 φ distributions for the leading muon and sub-leading muon in the selectedevents at√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 6.27 Missing transverse energy in the selected events at√s = 7TeV. . . . . . . . . . 117Figure 6.28 Two-dimensional histograms of EmissT vs. mµ+µ− and EmissT vs. leading muon pTfor events passing the primary and secondary dimuon selection in collision dataat√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Figure 6.29 Missing transverse energy in the selected events at√s = 8TeV, for the primaryand secondary dimuon selection . . . . . . . . . . . . . . . . . . . . . . . . . 119Figure 6.30 Two-dimensional histograms of EmissT vs. mµ+µ− and EmissT vs. leading muon pTfor events passing the primary and secondary dimuon selection in collision dataat√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Figure 7.1 Fractional uncertainty at 90% CL on the quark-antiquark luminosity at√s = 7TeV due to PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Figure 7.2 Stopping power for positive muons in copper as a function of βγ = p/Mc . . . 125Figure 7.3 Muon critical energy for the chemical elements . . . . . . . . . . . . . . . . . 125Figure 7.4 Uncertainty on the background estimate due to the muon resolution as a func-tion of mµ+µ− at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 7.5 Z′ signal templates at 2 and 3 TeV for the primary dimuon selection at√s = 7TeV, with nominal smearing and over-smearing increasing the MS reso-lution smearing constants by their uncertainty . . . . . . . . . . . . . . . . . . 126Figure 7.6 Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8TeV as a functionof mµ+µ− due to each PDF eigenvector taken separately. Here eigenvectors 1 to8 are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130xvFigure 7.7 Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8TeV as a functionof mµ+µ− due to each PDF eigenvector taken separately. Here eigenvectors 9 to16 are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Figure 7.8 Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8TeV as a functionof mµ+µ− due to each PDF eigenvector taken separately. Here eigenvectors 17to 20 are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 7.9 Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8TeV as a functionof the dilepton invariant mass due to the four distinct PDF eigenvector groups . 134Figure 7.10 Symmetric uncertainty on the Z/γ∗ cross section at√s = 8TeV as a functionof the dilepton invariant mass resulting from the addition in quadrature of theuncertainties from the four PDF eigenvector groups . . . . . . . . . . . . . . . 135Figure 7.11 Symmetric uncertainty on the Z/γ∗ cross section at√s = 8TeV as a function ofthe dilepton invariant mass obtained using the MSTW prescription calculatedwith VRAP, shown along with the uncertainties due to the QCD scale, αS vari-ations, photon-induced corrections and higher-order electroweak corrections,as well as the difference between the cross section central values from ABM11and the PDF variation uncertainty envelope from MSTW, taken as an additionalsystematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Figure 8.1 Differences between data and expectation in the and dimuon and dielectronchannels at√s = 7TeV, with both the statistical and systematic uncertaintiestaken into account to derive a bin-by-bin local significance . . . . . . . . . . . 140Figure 8.2 Differences between data and expectation in the and dimuon and dielectronchannels at√s = 8TeV, with both the statistical and systematic uncertaintiestaken into account to derive a bin-by-bin local significance . . . . . . . . . . . 141Figure 8.3 Absolute value of the LLR used in the search, as a function of the Z′ signal massMZ′ and cross section σZ′ , using the√s = 7TeV dataset . . . . . . . . . . . . . 144Figure 8.4 Distribution of the most signal-like LLR found in each of 10,000 pseudo-experiments at√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Figure 8.5 Observed and expected upper limits at 95% CL on σB for Z′SSM and E6 Z′ bosonproduction at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Figure 8.6 Observed and expected upper limits at 95% CL on σB for E6 Z′ψ production at√s = 8TeV for the combination of the dielectron and dimuon channels . . . . . 148Figure 8.7 Observed and median expected upper limits at 95% CL on σB for Z′SSM pro-duction at√s = 8TeV for the exclusive dimuon and dielectron channels, andfor both channels combined . . . . . . . . . . . . . . . . . . . . . . . . . . . 149xviFigure 8.8 Ratio of the observed limits at 95% CL for the Z′SSM search to the Z′SSM crosssection times branching fraction for the combination of dielectron and dimuonchannels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Figure 8.9 Observed and expected limits at 95% CL on γ ′ as a function of the Z′ mass at√s = 7TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Figure 8.10 Observed and expected limits at 95% CL on γ ′ as a function of the Z′ mass at√s = 8TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Figure 8.11 Observed and expected limits at 95% CL on γ ′ as a function of θMin at√s = 8TeV153Figure 9.1 Ratios of the parton luminosity accessible at the LHC at√s = 13TeV comparedto that at√s = 8TeV for gluon-gluon, gluon-quark and quark-antiquark processes156Figure 9.2 Expected upper limits at 95% CL on σB for Z′SSM boson production for theprojected HL-LHC dataset in the dimuon channel . . . . . . . . . . . . . . . . 156Figure A.1 Higgs boson production cross section by channel as a function of MH . . . . . 173Figure A.2 Higgs boson cross section times branching fraction to observable final states asa function of MH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Figure A.3 Histograms with data from the ATLAS experiment displaying evidence for theproduction of a Higgs boson in four different channels . . . . . . . . . . . . . 174Figure A.4 Feynman diagram for VBF H→WW ∗ at Leading Order. . . . . . . . . . . . 175Figure A.5 Transverse mass mT used as discriminant in the final stage of the cut-basedsearch for VBF H→WW ∗→ `ν`ν . . . . . . . . . . . . . . . . . . . . . . . 176Figure A.6 Light-quark jet rejection factor as a function of the b-tagging efficiency for dif-ferent b-tagging algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Figure A.7 Possible spin configurations following a H →WW ∗ → `ν`ν decay where theW bosons have non-zero spin in the direction of motion . . . . . . . . . . . . . 180Figure A.8 VBF H→WW ∗→ `ν`ν candidate event . . . . . . . . . . . . . . . . . . . . 181Figure A.9 Schematic view of a simple decision tree . . . . . . . . . . . . . . . . . . . . 182Figure A.10 Illustration of the differences between a cut-based selection and one using adecision tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183Figure A.11 Schematic diagram of the analysis fit model. . . . . . . . . . . . . . . . . . . 186Figure A.12 Schematic diagram of the BDT optimization algorithm. . . . . . . . . . . . . 188Figure A.13 Histograms of the BDT score in the Top CR for the DF channel and the SF channel189Figure A.14 Histograms of the BDT training variables in the Top CR for the DF channel . . 190Figure A.15 Histograms of the BDT training variables in the Top CR for the SF channel . . 191Figure A.16 Histograms of the BDT training variables in the low-BDT VR for the DF channel192Figure A.17 Histograms of the BDT training variables in the low-BDT VR for the SF channel 193Figure A.18 Distribution of ρ(m``,mT ) in the low-BDT VR . . . . . . . . . . . . . . . . . 194xviiFigure A.19 Example pair of 2D correlation histograms . . . . . . . . . . . . . . . . . . . 195Figure A.20 Distributions of m`` and mττ in the Z/γ∗ → τ+τ− CR for the combination ofthe DF and SF channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196Figure A.21 Distributions of BDT score in the SF channel, for the low-EmissT Z CR, region Cand region D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198Figure A.22 Illustration of the absence of correlation between the BDT score and EmissT insimulated events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199Figure A.23 Example object systematic uncertainty, due to the pT,track resolution, on theBDT shape in the SR of the DF channel, for signal and the sum of all backgrounds200Figure A.24 Illustration of the sampling algorithm to generate pseudo-experiments . . . . . 201Figure A.25 Number of events in pseudo-datasets after the pre-selection of the BDT analysisand the selection of the cut-based analysis . . . . . . . . . . . . . . . . . . . . 202Figure A.26 Signal significance and strength observed in 200 pseudo-experiments, with aBDT score as the discriminating variable . . . . . . . . . . . . . . . . . . . . 203Figure A.27 Signal significance and strength observed in 200 pseudo-experiments, with mTas the discriminating variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Figure A.28 Differences in signal significance and strength observed in individual pseudo-experiments between the two analyses . . . . . . . . . . . . . . . . . . . . . . 204Figure A.29 Two-dimensional histograms of the signal significance and strength observed inindividual pseudo-experiments in the two analyses . . . . . . . . . . . . . . . 205Figure A.30 Linearity test between the two analyses, for the signal significance and signalstrength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205Figure A.31 Event-by-event probabilities calculated in a previous definition of the DFTop CR under the hypotheses of tt¯, WW , gluon-fusion Higgs, Z/γ∗ and VBFHiggs production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207Figure A.32 Event-by-event probabilities calculated in a previous definition of the blindedDF SR under the hypotheses of tt¯, WW , gluon-fusion Higgs, Z/γ∗ and VBFHiggs production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208Figure A.33 Measurements of the signal strength ratios between the bosonic and fermionicHiggs production channels for the individual final states and their combination. 210Figure A.34 Fit results for a parametrization of Higgs boson coupling strengths probing dif-ferent scale factors for fermions and bosons. . . . . . . . . . . . . . . . . . . . 210xviiiGlossaryBAT Bayesian Analysis ToolkitBDT Boosted Decision TreeBEE Barrel Endcap ExtraBI Barrel InnerBM Barrel MiddleBO Barrel OuterCKM Cabbibo-Kobayashi-MaskawaCL Confidence LevelCP Charge-ParityCR Control RegionCSC Cathode Strip ChamberDAQ Data AcquisitionDCS Detector Control SystemDF Different-FlavourEI Endcap InnerEE Endcap ExtraEM Endcap MiddleEO Endcap OuterEPD Event Probability DiscriminantxixGUT Grand Unified TheoriesHL-LHC High-Luminosity LHCID Inner DetectorLEP Large Electron-Positron ColliderLHC Large Hadron ColliderLLR Log-Likelihood RatioLO Leading OrderMC Monte CarloMDT Muon Drift TubeME Matrix ElementMS Muon SpectrometerNF Normalization FactorNLO Next-to-Leading OrderNNLO Next-to-Next-to-Leading OrderQCD Quantum ChromodynamicsQED Quantum ElectrodynamicsPMNS Pontecorvo-Maki-Nakagawa-SakataPDF Parton Distribution FunctionRPC Resistive Plate ChamberSCT Semiconductor TrackerSF Same-FlavourSM Standard ModelSR Signal RegionSSM Sequential Standard ModelTGC Thin Gap ChamberxxTMVA Toolkit for Multivariate Data AnalysisTRT Transition Radiation TrackerVBF Vector Boson FusionVR Validation RegionxxiAcknowledgementsMy journey as a graduate student at UBC has been a wonderful one, not least due to the people Ihave met along the way, both in beautiful Vancouver and abroad.First of all, I want to thank my supervisors, Colin Gay and Oliver Stelzer-Chilton, for havingbeen outstanding mentors. You have provided me with sound advice and strong support when Ineeded it, as well as flexibility and freedom regarding research projects and travel plans, and havetaught me the scientific knowledge and skills necessary to carry out cutting-edge research in particlephysics. Particularly to Oliver who has been my closest collaborator in the last 5 years: thank youso much for having made time to meet and review results and documents, sometimes on short noticewhen the situation required it. Few students have had the chance to have such a positive relationshipwith their supervisors.Thanks to Ashutosh Kotwal for your pragmatic advice, which taught me to concentrate my at-tention on non-negligible effects, and for sharing your insights in both theoretical and experimentaldomains. Thanks to Fabienne Ledroit for your attention to detail during the analysis and docu-mentation stages: this helped tremendously, both to speed up the approval process at the time, andalso to write this dissertation years later. Thanks to Bernd Stelzer for your help with statistics andanalysis methods, and for forming such a great duo with your twin brother.Thanks to Stephane Willocq, Dominique Fortin and all the other members of the very-high-momentum muon task force for your support as we worked towards understanding this crucialcomponent of our detector’s performance.To all collaborators from the Z′ analysis group, thank you for having been such a motivated,dedicated and strong team. It has been a pleasure to work with you, and may our paths cross again!Thanks also to everyone who contributed to writing or reviewing our internal and public documenta-tion of the analysis. Special thanks to Kathy Copic and Wojtek Fedorko for your extraordinary lead-ership towards our first publications, and to Sarah Heim for having been such a fantastic teammatein analysis and convenership. Thanks also to Kelsey Allen for having been an amazing researchassistant on this project.Thanks to collaborators who provided me with example computer programs to get me started onprojects, in particular to Ian Nugent and Doug Schouten for analysis frameworks. I am very gratefulxxiifor not having had to “re-invent the wheel”, allowing for faster progress in my research, and for theopportunity to learn by osmosis from your programming skills.Thanks to my colleagues participating on the Higgs to WW ∗ analysis, especially VBF analystsand multivariate analysis developers in particular: as the motto goes, “work hard, party hard”!More generally, thanks to the ATLAS collaboration and the LHC at large: this is true teamwork.It is an honour to be part of such an awesome international endeavour.Thanks to all my friends at UBC, TRIUMF and elsewhere for bringing sunshine in the work-place. I also want to thank UBC and TRIUMF for providing me the resources needed to carry outmy graduate program, and for being such lively working environments. Thanks to my supervisorycommittee members: Mark Halpern, Christopher Hearty and Gordon Semenoff.I acknowledge financial support from the Vanier Canada Graduate Scholarship program andthe Natural Sciences and Engineering Research Council of Canada. I am grateful for generousscholarships and also for the ATLAS Canada travel budget, which allowed me to travel to CERNmultiple times every year and to participate in several academic conferences worldwide. Thesetravels have enabled me to actively participate in the vibrant particle physics community.During my first three years in Vancouver, I have had the privilege of living at Green College, anoutstanding community at UBC where I formed close friendships, and even met my wife! Thanks toMark Vessey for your words of wisdom, wit and support, and may Green College keep blossoming.To my friends here: I sincerely hope that we will keep in touch after scattering from Vancouverin all directions. Here is to more board games, potlucks, pub nights and hikes!Merci a` Franc¸ois-Xavier Boulanger-Nadeau et Gwendoline Simon, pour m’avoir fait de´couvrirla physique des particules. Bonjour a` mes amis du Que´bec, c’est toujours un plaisir de se revoiraussi souvent que possible. Koulou spe´cial a` Hadrien Collin ! Aussi : cello, platypus, et toaster.A` mes parents, Johanne et Janot : merci, merci pour tout. Vous avez toujours eu une confianceabsolue en mes aptitudes et m’avez soutenu a` travers toutes les e´preuves que j’ai rencontre´es.Vous eˆtes les meilleurs parents du monde et je sais que vous serez e´galement des grands-parentsextraordinaires !Francis, Julie et Jean-Michel, je suis super chanceux de vous avoir comme fre`res et soeur, etj’aimerais eˆtre en mesure de passer plus de temps avec vous.Yuan, ma che´rie !!! Thank you for your patience and support during my research and the prepa-ration of my thesis. Especially during the many months I had to spend away from you traveling,I realized how truly special our love is. As much as I enjoy exploring the world, it is never thesame without you. You make each hour of our everyday life at home so much more meaningful.Your love and care mean the world to me. I love you more than ever, and am so excited to start ournew life as parents in the next months! And let’s hope that you will have as much fun reading mydissertation as I will with yours ,xxiiiA` ma famille :passe´e, pre´sente et futurexxivChapter 1IntroductionThe Standard Model of particle physics [108, 150, 160, 168] is the most successful theory of el-ementary particle physics so far. Its accuracy in describing physical phenomena in an extremelywide range of contexts is unparalleled, from the structure of atoms and molecules to the inner work-ings of their constituents. Experiments in high-energy particle physics represent another domainwhere the predictions of the Standard Model are verified. Building on the success of the CDF andD0 experiments at the Tevatron, where the top quark was discovered in 1995 [65, 89], the ATLASand CMS experiments at the Large Hadron Collider (LHC) are now at the forefront of the energyfrontier. The discovery in 2012 of a Higgs boson [23, 76], the last particle predicted by the StandardModel, is a momentous achievement.Nevertheless, the Standard Model’s description of nature is incomplete. First of all, it neglectsgravitational effects: a more fundamental theory is necessary to reconcile general relativity withquantum field theory. Additional theoretical problems such as the hierarchy of energy scales andthe large number of postulated parameters need to be addressed, while on the experimental side,the observation of dark matter, dark energy and neutrino masses are clear indications that there ismore to be discovered. For this reason, high-energy particle physics experiments are designed to besensitive to a wide range of new physics, exploring uncharted territory in hopes of detecting newphenomena that reach beyond the Standard Model.In particular, searches for resonances decaying into electron and muon pairs have a long andfruitful history [115]. Indeed, the discoveries in these channels of the J/ψ meson [37, 38], theϒ meson [116] and the Z boson [162, 164] all represent major breakthroughs in particle physics.The main advantage of this search signature are that the signal is fully reconstructible and forms apeak above relatively low and well-understood backgrounds. These features and the fact that manyhypotheses beyond the Standard Model predict the existence of such new resonances above the Zmass peak make the search for new physics in this channel especially promising.This dissertation describes searches for new neutral high-mass resonances decaying into muon1pairs using the full proton-proton collision dataset collected by the ATLAS experiment in Run-I ofthe LHC, including 5.0 fb−1 collected at a centre-of-mass energy of 7 TeV [25] and 20.5 fb−1 col-lected at a centre-of-mass energy of 8 TeV [36]. Chapter 2 describes the Standard Model of particlephysics in the framework of quantum field theory, and discusses its successes and limitations. Chap-ter 3 presents hypotheses that reach beyond the Standard Model, with particular emphasis on modelspostulating new gauge symmetries. The existence of these additional symmetries often implies thepresence of new particles to which this analysis could be sensitive. In Chapter 4, the LHC and theATLAS detector are described. The performance of the ATLAS detector for reconstructing muonsat very high momentum is assessed in Chapter 5, which also motivates the dedicated selection crite-ria that are employed. The next chapters describe the analysis itself: Chapter 6 describes the eventselection as well as the techniques used to predict background and signal yields, and presents acomparison of the background expectations to data, Chapter 7 discusses systematic uncertaintiesand Chapter 8 presents the statistical methods used and the results of the search. Finally, Chapter 9explores future directions and Chapter 10 concludes with a summary.In parallel with the work presented in this dissertation, significant contributions were also madeto the multivariate analysis looking for Vector Boson Fusion production of Higgs bosons decayinginto W boson pairs in final states with two electrons or muons. Measuring the production rate ofthe newly-discovered Higgs boson in this channel will provide one of the best constraints on theHiggs coupling to W bosons. Efforts toward completing the results of this analysis are still ongoingat the time of writing this dissertation, preventing their inclusion in this dissertation. Nevertheless,a summary of contributions to this Higgs boson analysis is presented in Appendix A.2Chapter 2The Standard Model of Particle PhysicsThis chapter presents the Standard Model of particle physics, which is so far the most successfultheory describing non-gravitational interactions. Instead of a historical presentation where experi-mental discoveries and theoretical advances are presented chronologically, a more axiomatic formatis followed1. Such a format allows for a more logical presentation of the theory, although it doesnot present the crucial experiments and early concepts that informed its development2.First, the Lagrangian of the Standard Model is presented in Section 2.1, and a few examplesof its successful predictions are discussed in Section 2.2. Section 2.3 describes the theoreticaland experimental shortcomings of the Standard Model, which are indicative of the challenges thathypotheses going beyond it have to meet.2.1 The Standard Model LagrangianThe Standard Model of particle physics is a renormalizable quantum field theory with local gauge in-variance. The gauge symmetry is postulated to be SU(3)C×SU(2)L×U(1)Y , where the subscriptsrepresent the conserved quantum numbers associated with each symmetry group. The conservedquantum numbers corresponding to SU(3)C are called “colours”, and the gauge bosons are named“gluons”. SU(2)L symmetry only interacts with left-handed fermions and their right-handed an-tiparticles, and the conserved quantity is the “isospin” T3. Finally, the conserved quantum numberof the U(1)Y symmetry is the “hypercharge” Y .2.1.1 Forces and MatterAs shown in Table 2.1, the vector bosons of the Standard Model correspond to the adjoint repre-sentations of SU(3)C and SU(2)L, with an additional vector field corresponding to U(1)Y which1 This chapter borrows many elements from Ref. [58] and from lecture notes by J. Ng. (unpublished).The metric convention used is ηµν = diag(−,+,+,+), the operator ∂µ ≡ ∂/∂xµ , and γµ are Dirac matrices.2 A captivating historical narrative can be found in Ref. [73].3transforms as a singlet. The notation (C,L,Y ) is used to describe how fields transform under theStandard Model gauge symmetry group: specifically, C gives the corresponding representation ofthe SU(3)C algebra, and similarly L for the SU(2)L algebra.Table 2.1: Gauge bosons in the Standard Model.Vector field SU(3)C SU(2)L U(1)YGαµ , α ∈ [1..8] 8 1 0W aµ , a ∈ [1..3] 1 3 0Bµ 1 1 0Table 2.2: Fermions in the Standard Model, in flavour basis. Colour indices c ∈ {r,g,b} forquarks and generation indices m ∈ [1..3] for all fermions are omitted.Fermion field SU(3)C SU(2)L U(1)YULDL 3 2 1/6UR 3 1 2/3DR 3 1 −1/3νL`L 1 2 −1/2`R 1 1 −1The Standard Model fermions come in three generations, and are collectively represented byψm, m ∈ [1..3]. Fermions in the second and third generations interact with gauge bosons in exactlythe same way as their counterparts in the first generation. They transform as fundamental repre-sentations of the gauge groups or as singlets, as detailed in Table 2.2. The fermions that interact4with SU(3)C are called “quarks”, and the ones that do not are called “leptons”. Fermions with left-handed helicity, ψm,L = 12(1+ γ5)ψm where γ5 = −iγ0γ1γ2γ3, transform differently from fermionswith right-handed helicity, ψm,R = 12(1− γ5)ψm. Specifically, the left-handed fermions are groupedtogether into SU(2)L doublets, with the ones on top having isospin T3 = 1/2, and the ones on thebottom having isospin T3 =−1/2. Right-handed fermions are assigned T3 = 0.The Lagrangian consisting of all renormalizable and gauge-invariant terms with the StandardModel fermion and gauge boson fields3 is the following:LGψ =−14GαµνGαµν −14W aµνWaµν −14BµνBµν −12(ψ¯mγµDµψm +h.c.) (2.1)where the covariant field strengths areGαµν = ∂µGαν −∂νGαµ +g3 f αβγGβµGγν (2.2)W aµν = ∂µW aν −∂νW aµ +g2εabcW bµW cν (2.3)Bµν = ∂µBν −∂νBµ (2.4)and the covariant derivative of the fermion fields isDµψm = (∂µ − ig1YψBµ −ig22σaW aµ −ig32λαGαµ )ψm (2.5)where the W aµ term only applies to left-handed fermions and right-handed antifermions, and theGαµ term only applies to quarks. Here the σa are Pauli matrices, the generators of SU(2), and the λαare Gell-Mann matrices, the generators of SU(3). The structure constants of SU(3) are representedby f αβγ and those of SU(2) are simply the fully antisymmetric εabc. The couplings g1, g2, g3 ∈ Rdetermine the strength of the interaction terms, and are discussed in more detail in Section 2.2.1.This Lagrangian has a rather surprising feature: because of the absence of left-right symmetryin the Standard Model, no mass term is allowed for any of the fields. For instance, while mass termsfor the fermions might have been written asLMψ =−Mmn2ψ¯mψn=−Mmn2(ψ¯m,Lψn,R + ψ¯m,Rψn,L)(2.6)these terms are not gauge-invariant under U(1)Y : in other words there is no combination of fieldsψ¯m,Lψn,R or ψ¯m,Rψn,L that is hypercharge-neutral. Direct mass terms for vector bosons are also for-bidden by gauge invariance. Since we observe that most fundamental particles do have an intrinsicmass, the absence of mass terms constitutes a significant theoretical problem.3 with a caveat discussed in Section 2.3.352.1.2 The Englert-Brout-Higgs-Guralnik-Hagen-Kibble MechanismThe solution to this problem is to add to the model a scalar field that retains a non-zero value in theground state and thereby breaks electroweak symmetry [96, 112, 117]. The simplest scalar field thatcan be used for this purpose transforms as (1, 2, 1/2):ϕ =[ϕ+ϕ0](2.7)where ϕ+ and ϕ0 are complex scalars. The potential of this scalar field can be parametrized asV (ϕ†ϕ) = λ (ϕ†ϕ−µ2/2λ )2= λ (ϕ†ϕ)2−µ2ϕ†ϕ+µ4/4λ(2.8)with λ and µ2 real and positive. This potential is minimized for ϕ†ϕ = µ2/2λ ≡ v2/2, where vis defined as the non-zero “vacuum expectation value” of the scalar field. A very useful form of ϕis obtained by performing a gauge transformation such that no quadratic vector-scalar cross termsremain: this gauge choice is called “unitary gauge” and the scalar field becomesϕ =[01√2(v+H)](2.9)with H a real scalar field named the Higgs boson. This gauge choice fixes the covariant derivativeof the scalar field as follows:Dµϕ = (∂µ −ig12Bµ −ig22σaW aµ )ϕ (2.10)=− ig22√2(W 1µ − iW2µ )(v+H)1√2∂µH− i2√2(g1Bµ −g2W 3µ )(v+H) (2.11)Then the Standard Model Lagrangian becomes:LSM =LGψ +LH (2.12)6withLH = − (Dµϕ)†(Dµϕ)−V (ϕ†ϕ)− (y`,mn[ν¯m,L ¯`m,L]`n,Rϕ+ yD ,mn[U¯m,L D¯m,L]Dn,Rϕ+ yU ,mn[U¯m,L D¯m,L]Un,Riσ2ϕ∗+h.c.)(2.13)= −12∂µH∂ µH−λv2H2−λvH3−λ4H4−g228(v+H)2|W 1µ − iW2µ |2−18(v+H)2(g1Bµ −g2W3µ )2−1√2(v+H)(y`,mn ¯`m,L`n,R + yD ,mnD¯m,LDn,R + yU ,mnU¯m,LUn,R +h.c.)(2.14)The complete Standard Model Lagrangian contains mass terms for most elementary particles.To see this more clearly, it is very useful to redefine the vector boson and fermion fields in the “massbasis”, in order to eliminate all quadratic mixed terms between fields. The vector boson fields areredefined as follows:W±µ =1√2(W 1µ ∓ iW2µ ) (2.15)Zµ =g2W 3µ −g1Bµ√g21 +g22≡W 3µ cosθW −Bµ sinθW(2.16)Aµ =g1W 3µ +g2Bµ√g21 +g22≡W 3µ sinθW +Bµ cosθW(2.17)defining θW , the weak mixing angle (or Weinberg angle). The fermion Yukawa terms are diagonal-ized using unitary matrices Uψ , which mix the fermion fields from different generations:ψ˜m,L =Uψ,mnψn,Lψ˜m,R =U∗ψ,mnψn,R(2.18)such that UTψ yψUψ ≡ yψ˜ is diagonal.These transformations simplify LH considerably; in the mass basis, LH becomesLH = −∂µH∂ µH−λv2H2−λvH3−λ4H4−g224(v+H)2W+µ Wµ−−18(v+H)2(g21 +g22)ZµZµ−yψ˜,m√2(v+H) ¯˜ψmψ˜m(2.19)7yielding the following masses, all directly proportional to v:MW =g22· v (2.20)MZ =√g21 +g222· v (2.21)Mψ˜m =yψ˜,m√2· v (2.22)MH =√2λ · v (2.23)From the experimental values of MW and MZ , we find v = 246 GeV.Nine gauge bosons remain massless: the eight gluons Gαµ , and Aµ which is identified as thephoton. This implies that the scalar field ϕ broke the symmetry of the Standard Model down fromSU(3)C×SU(2)L×U(1)Y to the low-energy SU(3)C×U(1)Q, where Q =Y +T3 is identified as theelectric charge. Gluons are often collectively represented by the letter g, and photons by the letter γ .The standalone study of U(1)Q interactions is called Quantum Electrodynamics (QED), and that ofSU(3)C interactions is called Quantum Chromodynamics (QCD) by analogy.Neutrinos are also strictly massless in the Standard Model, this time in conflict with experimen-tal results; this limitation is discussed in Section 2.3.4.2.1.3 Electroweak Interactions RevisitedWhile the field redefinitions of Equations 2.15-2.18 simplify LH , this comes at the cost of a moreintricate structure in LGψ . Gluon self-interactions are unaffected, but W and Z bosons interactwith photons in three electroweak self-interaction terms: WWγ , WWγγ and WWZγ . Additionalself-interaction terms WWZ, WWZZ and WWWW complete the list.Further, while electroweak interactions with fermions were originally diagonal in fermion gen-eration, as is manifest from Equation 2.1, the fermion field redefinitions of Equation 2.18 introduceterms in which a W boson interacts with two fermions from different generations. In other words,while in the initial basis, called the “flavour basis”, all interactions between W bosons and fermionspreserve fermion generation but propagation in the vacuum does not (a phenomenon called fermion“flavour oscillation”), in the mass basis fermions are perceived as preserving their identity as theypropagate in the vacuum but interactions with W bosons may occur between fermions of differentgenerations.Because all quarks have sizeable masses, the mass basis is privileged in the quark sector. Withincreasing generation index m, the mass-basis quarks um are named up (u), charm (c) and top (t)quarks, and the mass-basis quarks dm are named down (d), strange (s) and bottom (b) quarks. Quarksare collectively represented by the letter q.8The interaction terms of quarks with W bosons becomeLWq =ig2√2(Vmnu¯m,Lγµdn,LW+µ +(V †)mnd¯m,Lγµun,LW−µ ) (2.24)where V = U†u Ud using the Uψ from Equation 2.18 is the Cabbibo-Kobayashi-Maskawa (CKM)matrix:V =Vud Vus VubVcd Vcs VcbVtd Vts Vtb=1− 12λ2 λ Aλ 3(ρ− iη)−λ 1− 12λ2 Aλ 2Aλ 3(1−ρ− iη) −Aλ 2 1+O(λ 4)(2.25)The last line of Equation 2.25 defines the Wolfenstein parametrization of the CKM matrix, which isvalid to fourth order in λ ≈ 0.225, with A≈ 0.8, ρ ≈ 0.13 and η ≈ 0.35 [52]. The main advantageof this parametrization is that it highlights the relative size of the CKM matrix elements with respectto each other; in particular, the CKM matrix is nearly diagonal.On the other hand, because neutrinos are massless in the Standard Model, it is conventional toconceptualize leptons in the flavour basis. The charged leptons `m are the electron e, the muon µand the tauon τ , each with an associated neutrino, labeled respectively νe, νµ and ντ . The discoveryof neutrino flavour oscillations significantly enriched this description, as discussed in Section 2.3.4.The interaction terms of leptons with W bosons areLW` =ig2√2(ν¯m,Lγµ`m,LW+µ + ¯`m,Lγµνm,LW−µ ) (2.26)Finally, the fermion interactions with the neutral electroweak gauge bosons are described byL(Z/γ)ψ˜ = igEM ¯˜ψmγµQψ˜mAµ + igZ ¯˜ψmγµ(1+ γ52T3−Qsin2 θW)ψ˜mZµ (2.27)= igEM ¯˜ψmγµQψ˜mAµ + igZ ¯˜ψmγµ(1+ γ52gL +1− γ52gR)ψ˜mZµ (2.28)where in the last expression, gL ≡ T3−Qsin2 θW and gR ≡−Qsin2 θW . The first term is identi-fied with the Lagrangian of QED, with the factor gEM ≡ g1 cosθW = g2 sinθW identified as theelectromagnetic coupling constant, i.e. the elementary charge. The coupling to the Z boson isgZ ≡ g1/sinθW = g2/cosθW =√g21 +g22 = 2MZ/v. It is interesting to notice that in contrast withinteractions involving W bosons, these neutral interactions cannot change the type or flavour offermions.92.1.4 SummaryThe particle content of the Standard Model is encapsulated in Figure 2.1. In summary, it consists ofeight gluons, mediators of the strong force, the photon, which mediates the electromagnetic force,and the massive weak bosons W and Z, responsible for the weak force. Three generations of matterparticles are present: quarks interact with each other via all three forces, charged leptons interactvia both electroweak forces and neutrinos only interact via the weak force. Finally, the Higgs bosongives a mass to the quarks, charged leptons and weak bosons by interacting with all of them.Figure 2.1: Particle content of the Standard Model. Figure credit: Fermilab.2.2 Successes of the Standard ModelThe experimental discovery of all the particles postulated by the Standard Model is an exceptionalachievement, which certainly constitutes a major success of the theory. The latest discoveries ofmatter particles happened at Fermilab, where the top quark was observed in 1995 by the CDF andD0 experiments [65, 89], as well as the tau neutrino in 2000 by the DONUT experiment [95].This endeavour culminated in the discovery of a Higgs boson in 2012 by the ATLAS and CMSexperiments at the LHC [23, 76]. The experimental evidence so far indicates that this boson iscompatible with expectations from the Standard Model4, thereby validating our understanding of themechanism responsible for breaking the electroweak symmetry and for giving masses to elementaryparticles.4 More details in Appendix A10But the Standard Model is much more than simply the sum of its parts. The next sections discusstwo successful applications of the Standard Model, illustrating its ability to describe interactionsbetween particles. While many more useful calculations could be illustrated, such as the lifetimesof unstable particles and the probabilities for each combination of their decay products, quantumcorrections to the mass of particles, scattering amplitudes across different energy ranges, etc., thefollowing two are chosen because of their relevance to the main topic of this dissertation.First, implications of the specific values of the coupling strengths are discussed. These valuesare interpreted as originating from the evolution of the couplings with decreasing energy. Theyexplain why quarks and gluons must combine into hadrons and why matter is organized in atoms atlow energies. Then, the expected production rates for heavy particles at very-high energy collidersare discussed and compared with experimental results, with special attention given to the processpp→ Z/γ∗→ µ+µ−.2.2.1 Asymptotic Freedom and Infrared SlaveryThe larger size of the coupling g3 with respect to g1 and g2 explains why the corresponding forceis called the strong force. Indeed while at low energy scales the electroweak couplings g1,g2 1,which means that this part of the theory can be treated pertubatively, the coupling g3 is significantlylarger and, very importantly, gets larger towards low energies.An equivalent way to express the couplings is in terms ofαi(µ)≡g2i (µ)4pi (2.29)where µ is the renormalization scale, which when performing calculations is taken to be close to theenergy scale or momentum transfer scale of the process of interest. In particular, the strong couplingis αS ≡ α3:αS(µ)≡g23(µ)4pi (2.30)αS(MZ)≈ 0.117 (2.31)and the electromagnetic coupling isαEM(µ)≡g2EM(µ)4pi(2.32)αEM(MZ)≈ 1/128 (2.33)The dependence of the gauge couplings of the Standard Model as a function of µ , shown in11Figure 2.2, is described by the functionβ (α)≡ µ2 ∂α∂µ2 =∞∑i=0biα i+2 (2.34)Keeping only the first term of the sum, this is solved as1α(µ) =1α(µ0)−b0 lnµ2µ20(2.35)where a convenient choice for µ0 is MZ , as in the quoted values above. The coefficients b0 can becalculated explicitly, and the results for αS and αEM, valid for µ & Mt , areβ (αS)≈−7α2S2pi −O(α3S)< 0 (2.36)β (αEM)≈2α2EM3pi +O(α3EM)> 0 (2.37)Figure 2.2: Gauge couplings of the Standard Model as a function of energy scale [152].It follows that in contrast with the strong coupling, the electromagnetic coupling grows withenergy. This explains why while at very high energy scales µ ∼ 1014 GeV, called the “unificationscale”, all couplings of the Standard Model have similar values, at low energies their strength variesimportantly. Seen from another perspective, the strength of the electromagnetic force decreases asthe distance between particles increases (as is familiar from the classical Coulomb law in 1/r2), butthe effect of the strong force increases with the distance between quarks and gluons.12This implies that at very high energy, quarks and gluons essentially behave like free particleswith respect to each other: this feature of the strong interaction is called “asymptotic freedom”.Its counterpart is “infrared slavery”: at low energy, gluons and quarks must group together intocolourless bound states.There are a few different possibilities for quarks to bind together. First, a quark and an antiquarkcan join to form a “meson”. The most common mesons are the pions, consisting of up and downquark-antiquark pairs. Other common mesons in high-energy particle physics are made of one upor down quark or antiquark, while the other antiquark or quark is of a heavier flavour: dependingon this flavour such mesons are called kaons (strange), D-mesons (charm) and B-mesons (bottom).Charm quark-antiquark pairs called J/ψ mesons, and bottom quark-antiquark pairs called ϒ mesonsare also particularly interesting because of their resonant production and decay into lepton pairs.Alternatively, three quarks of different colours can join to form a “baryon”. Three antiquarkscan also join similarly to form antibaryons. The most common baryons found in nature are theproton, made of two up quarks and one down quark, and the neutron, made of one up quark andtwo down quarks. The relative strengths of the couplings in the low-energy limit of the StandardModel therefore explains the structure of atoms, with quarks and gluons bound together in protonsand neutrons forming atomic nuclei, and electrons in quantum orbits around these nuclei at effectivedistances inversely proportional to αEM.2.2.2 Calculation of Cross Sections and Decay RatesPerhaps the most important use of the Standard Model for physicists studying particle collisionsat very-high energy is to calculate the rates for all the different possible outcomes of a collision:these rates are called the cross sections of each process of interest. This section first introducesconcepts relevant when calculating cross sections, illustrated with an example, before comparingstate-of-the-art calculations in the Standard Model to experimental measurements.Scattering amplitudes and Feynman diagramsIn time-dependent perturbative quantum field theory, the amplitude connecting initial states |α〉 tofinal states |β 〉 is represented by the S-matrix:Sβα ≡ 〈β |S |α〉 (2.38)from which it is conventional to factor out the interaction matrix element MSβα = δβα − iMβα(2pi)4δ 4(kβ − pα) (2.39)13where pα represents the sum of the four-momenta of the initial-state particles, and kβ similarlyfor final-state particles. The link between the matrix element M and the Lagrangian density Ldiscussed earlier is via the interaction Hamiltonian density HI:S =∞∑n=0(−i)nn!∫ ∞−∞d4x1 .. d4xnT [HI(x1) ..HI(xn)] (2.40)where T is the time-ordering operator, ensuring that the interactions happen in the proper sequence.The key point of the perturbative approach is that each factor of HI carries with it one factor ofthe coupling between particles; if these couplings are small compared to unity, then the first termsconstitute a good approximation to the full amplitude. The matrix element M then becomesMβα = 〈β |HI(0) |α〉+(−i)22∫d4x〈β |T [HI(x)HI(0)] |α〉+ ... (2.41)When the initial state consists of a single particle, this matrix element allows to calculate itsdifferential decay rate dΓ as follows:dΓ=|Mβα |22Eα(2pi)4δ 4(kβ − pα)dβ (2.42)dβ ≡∏f∈βd3k f2E f (2pi)3(2.43)where E represents the energy of a particle, and k the three-momentum of final-state particles.Similarly, in the context of two-body scattering,M appears in the expression for the differentialcross section dσ :dσ =|Mβα |24√(p1 · p2)2−m21m22(2pi)4δ 4(kβ − pα)dβ (2.44)where the subscripts 1 and 2 refer to the incoming particles in the initial state.Feynman diagrams allow to conveniently calculate the matrix elements that enter such calcula-tions in quantum field theory, in addition to providing a simple way to visualize interaction processesbetween particles. This technique is used in the following section to calculate the leading contribu-tion to the Drell-Yan process at the LHC: pp→ Z/γ∗→ µ+µ−. The leading term in the series forthe matrix element M in this case will involve two interactions: one between constituents of theincoming protons and a Z boson or a photon, and one between the same electroweak boson and theoutgoing muons. Figure 2.3 shows the Feynman diagram corresponding to this term.A calculation keeping only this first term in the series expansion for M is called a calcula-tion at Leading Order (LO). Calculations keeping higher-order terms in the couplings are calledcalculations at Next-to-Leading Order (NLO), Next-to-Next-to-Leading Order (NNLO), and so on.Figure 2.4 shows examples of Feynman diagrams corresponding to higher-order contributions to the14Drell-Yan process. These additional contributions fall under two main categories: the emission ofradiation contributing to the final state, and the presence of particle loops during the interaction.Because each order of the perturbative series involves one more power of the interaction Hamil-tonian and therefore of the coupling, corresponding to an additional vertex in the correspondingFeynman diagrams, the number of diagrams increases factorially, making the calculation of eachsuccessive term in M harder than the precedent. This becomes an issue in the context of processesinvolving the strong interaction, especially in the low-energy regime where the coupling αS is large.Fortunately, this is not a concern for the main processes of interest here.Figure 2.3: Feynman diagram for the contribution at Leading Order to the Drell-Yan processpp→ Z/γ∗→ µ+µ−.Figure 2.4: Feynman diagrams for examples of higher-order contributions to the Drell-Yanprocess pp→ Z/γ∗→ µ+µ−: gluon emission in the initial state and photon emission inthe final state (left), and a gluon loop in the initial state (right).The Drell-Yan process at the LHC: pp→ Z/γ∗→ µ+µ−As illustrated in Figure 2.3, the leading contribution to the process pp→ Z/γ∗→ µ+µ− is simplythe annihilation of a quark and an antiquark into a virtual Z boson or photon, followed by the decayof the produced boson into a muon pair:q(p1)+ q¯(p2)→ µ−(k1)+µ+(k2) (2.45)15with each particle’s four-momentum indicated as p for initial-state particles, and k for final-stateparticles.At this point it is useful to introduce the Mandelstam variables:sˆ≡−(p1 + p2)2 =−(k1 + k2)2 (2.46)tˆ ≡−(p1− k1)2 =−(k2− p2)2 (2.47)uˆ≡−(p1− k2)2 =−(k1− p2)2 (2.48)Of the three, sˆ is the most intuitive as it corresponds to the centre-of-mass energy of the qq¯ collision.At LO, this also corresponds to the square of the invariant mass mµ+µ− of the muon pair; in otherwords, m2µ+µ− = sˆ = |r2| where r is the four-momentum of the gauge boson.The relevant parts of the interaction Lagrangian L(Z/γ)ψ from Equation 2.28 areL(Z/γ)q = igEMq¯γρQqqAρ + igZ q¯γρ(1+ γ52gqL +1− γ52gqR)qZρ (2.49)L(Z/γ)µ = igEMµ+γρQµµ−Aρ + igZµ+γρ(1+ γ52gµL +1− γ52gµR)µ−Zρ (2.50)where the space-time index ρ is used instead of the usual µ to avoid confusion with the particle.The matrix element associated with the diagram in Figure 2.3 can now be calculated usingthe Feynman rules, which convert each external line, internal line and vertex into a mathematicalexpression, and give a prescription for combining these factors to form the matrix element. Thecomplete list of Feynman rules can be found in references such as Ref. [58]. The result is:M =Mγ +MZ (2.51)= [µ+(k2)γρgEMQµµ−(k1)][q¯(p2)γνgEMQqq(p1)]ηρνr2− iε+[µ+(k2)γρgZ(1+ γ52gµL +1− γ52gµR)µ−(k1)]× [q¯(p2)γνgZ(1+ γ52gqL +1− γ52gqR)q(p1)]×1r2 +M2Z− iMZΓZ(ηρν +rρrνM2Z)(2.52)To enter the expression for the cross-section, the square of this matrix element must then be averagedover the four possible initial spin states and summed over the final spin states. The general resultis simplified in the ultra-relativistic limit, where sˆ M2ψ˜ for all ψ˜ except the top quark: then all16masses in this calculation except MZ can be neglected. After using the relations− ∑spinsψ˜(p) ¯˜ψ(p) = iγρ pρ −Mψ˜ → iγρ pρ (2.53)− ∑spinsψ˜(k) ¯˜ψ(k) = iγρkρ +Mψ˜ → iγρkρ (2.54)and taking all the traces involving the Dirac matrices, the result is|M |2 = |ALL|2uˆ2 + |ARR|2uˆ2 + |ALR|2tˆ2 + |ARL|2tˆ2 (2.55)whereAi j = g2EMQqQµsˆ+g2Zgqigµ jsˆ−M2Z− iMZΓZ(2.56)Introducing this expression into Equation 2.44 and integrating yields the cross sectionσ(qq¯→ Z/γ∗→ µ+µ−) = sˆ48pi(|ALL|2 + |ARR|2 + |ALR|2 + |ARL|2) (2.57)which is inversely proportional to sˆ for sˆM2Z , since then |Ai j|2 ∝ 1/sˆ2. The interference betweenthe individual contributions to the cross section due to the photon and the Z boson is manifest, ascross terms appear when squaring the matrix element. Similar interference effects can be importantin calculations involving new spin-1 particles such as Z′ bosons discussed in Section 3.2.One more step is necessary for the result of this calculation to become useful experimentally:after all, the initial state of collisions at the LHC consists not simply of quarks, but of protons. Inaddition to their three “valence quarks”, two up quarks and one down quark, protons are also madeof gauge bosons (mainly gluons) binding these valence quarks together, as well as quark-antiquarkpairs which are continually created and annihilated in interactions with these internal gauge bosons.This situation is illustrated in Figure 2.5. The quarks, antiquarks and gauge bosons making hadronslike the proton are collectively called “partons”.Figure 2.5: Schematic illustration of parton interactions within a proton. Figure credit: DESY.17It follows that in a typical proton-proton collision, one parton from each incoming proton inter-act in the main process of the event. The probabilities for the identity of each parton are parametrizedby Parton Distribution Functions (PDFs), which depend on the momentum transfer of the collisionand the fraction x of the proton momentum carried by each type of parton. They are evaluated usingdata from deep inelastic scattering experiments and from hadron colliders. For example, the PDFsof the proton as evaluated by the MSTW collaboration [132] for |r2|= 10 GeV2 and (100 GeV)2are shown in Figure 2.6.x-410 -310 -210 -110 1)2xf(x,Q00.20.40.60.811.2g/10dduuss,cc,2 = 10 GeV2Q)2xf(x,Qx-410 -310 -210 -110 1)2xf(x,Q00.20.40.60.811.2g/10dduuss,cc,bb,2 GeV4 = 102Q)2xf(x,QMSTW 2008 NLO PDFs (68% C.L.)Figure 2.6: Proton NLO PDFs from the MSTW collaboration at two momentum transferscales: |r2|= 10 GeV2 and (100 GeV)2 [132].The LO cross section for the process pp→ Z/γ∗→ µ+µ− must then include the sum over allpossibilities for the incoming quarks, weighted by their PDF. The Mandelstam variable s is nowtaken to represent the centre-of-mass energy of the proton-proton collision, and the quantity thatmust enter the cross section calculation is therefore x1x2s, where x1 and x2 represent the fraction ofthe proton momentum carried by the incoming partons. In addition, the average over quark coloursmust be taken, because the quark-antiquark annihilation can only occur if they have the same colour.This results in an additional factor of 1/3. With these changes,σ(qq¯→ Z/γ∗→ µ+µ−) = x1x2s144pi(|ALL|2 + |ARR|2 + |ALR|2 + |ARL|2) (2.58)where the change sˆ→ x1x2s also modifies the Ai j from Equation 2.56.18One last point to consider is that because in general x1 6= x2, the mediating boson will not be atrest in the centre-of-mass rest frame of the proton-proton system, but rather move along the beamaxis z with rapidityy =12ln(Er + rzEr− rz)=12lnx1x2(2.59)Finally, integrating over the PDF fq(x,r2) of both protons while imposing four-momentum con-servation gives the following expression for the differential cross section as a function of the mo-mentum transfer and rapidity:dσdr2dy(pp→ Z/γ∗→ µ+µ−) =∫ 10dx1dx2∑q( fq¯(x1,r2) fq(x2,r2)+ fq(x1,r2) fq¯(x2,r2))×|r2|144pi(|ALL|2 + |ARR|2 + |ALR|2 + |ARL|2)δ(|r2|− x1x2s)δ(y−12lnx1x2) (2.60)where as above Ai j = Ai j(r2) ∝ 1/|r2| for |r2| M2Z .This is an important result. It describes at Leading Order the behaviour of the Drell-Yan spec-trum above the Z peak in mµ+µ− , where this process constitutes the dominant background to thesearch for new neutral resonances decaying into muon pairs.State-of-the-art Standard Model calculations and comparison to measurementsIn practice, state-of-the-art cross section calculations at higher orders are not performed analytically,but rather use Monte Carlo (MC) simulation techniques including contributions from higher ordersin perturbative quantum field theory. This technique is described in more detail in Section 6.2.1.Figure 2.7 shows the Standard Model cross section predictions for selected outcomes of proton-antiproton and proton-proton collisions. With the exception of the total cross section σtot, which isbased on a parametrization from Ref. [52], they are calculated at NNLO in perturbative QCD withNLO electroweak corrections applied.The Standard Model is in fact remarkably accurate in predicting the rates of production anddecay of particles in high-energy collisions. Key examples of this are illustrated in Figure 2.8, whichshows the outcome of several Standard Model production cross section measurements performedby the ATLAS experiment, compared with the corresponding theoretical expectations.190.1 1 1010-710-610-510-410-310-210-110010110210310410510610710810910-710-610-510-410-310-210-1100101102103104105106107108109σZZσWWσWHσVBFMH=125 GeVWJS2012σjet(ETjet > 100 GeV)σjet(ETjet > √s/20)σggHLHCTevatronevents / sec for L = 1033 cm-2 s-1 σbσtotproton - (anti)proton cross sectionsσWσZσtσ   σ   σ   σ   (( ((nb)) ))√s  (TeV){Figure 2.7: Standard Model cross section predictions for proton-antiproton (shown for√s < 4 TeV) and proton-proton (shown for√s ≥ 4 TeV) collisions, at NNLO in per-turbative QCD with NLO electroweak corrections applied. Vertical lines indicate thecentre-of-mass energy at the Tevatron (√s = 1.96 TeV), and at the LHC (√s = 7,8 and13 TeV). Figure credit: W. J. Stirling.20Wtotal35 pb−1Ztotal35 pb−1t¯ttotal1.1 fb−120.3 fb−1tt−channeltotal1.0 fb−120.3 fb−1WWtotal4.6 fb−1Wttotal2.0 fb−120.3 fb−1WZtotal4.6 fb−113.0 fb−1ZZtotal4.6 fb−120.3 fb−1σ[pb]10−11101102103104105LHC pp √s = 7 TeVtheorydataLHC pp √s = 8 TeVtheorydataStandard Model Total Production Cross Section Measurements Status: March 2014ATLAS Preliminary Run 1 √s = 7, 8 TeVFigure 2.8: Summary of several Standard Model production cross section measurements performed by the ATLAS collaboration,compared with the corresponding theoretical expectations calculated at NLO or higher [33].212.3 Limitations of the Standard ModelIn spite of the outstanding success of the Standard Model of particle physics, there are strong exper-imental and theoretical indications that it is far from being a complete theory of physics at the mostfundamental level.2.3.1 Quantum GravityFirst, perhaps the most obvious shortcoming of the Standard Model is that it neglects gravitationaleffects. In Einstein’s general relativity, matter and force-carrying particles exist in curved space-time, and this curvature is in turn affected by the mass-energy distribution. Quantum field theo-ries like the Standard Model allow calculations for processes involving particles in curved space-time [100], but not for the quantum fluctuations of fields to affect the curvature. Our current under-standing of quantum gravitational effects would have such effects require non-renormalizable termsin the Lagrangian; in other words, quantum gravity is currently an effective field theory.Like in the case of Fermi’s interaction, a non-renormalizable four-fermion contact interactionsuccessful in describing radioactive decays, which were later understood as being mediated by Wbosons, effective field theories are valid up to a certain energy scale, or equivalently down to aminimum distance at which effects beyond the ones described by the theory become important. Forexample, calculations using Fermi’s interaction are valid for energies EMW .The presence of non-renormalizable terms in quantum theories of gravity might be indicativeof an underlying, more complete theory, the details of which remain to be understood. Efforts areongoing to design such a theory and reconcile general relativity with quantum field theory.2.3.2 Dark Matter and Dark EnergyOn the experimental side, astronomical observations indicate that ordinary matter as described bythe Standard Model only represents a small fraction of the mass-energy inventory of the Universe.One of the first indications towards this has been seen in the rotation velocity distributions of starsin spiral galaxies. By looking at the visible distribution of matter in these galaxies, it is possible tocalculate an expected velocity distribution for stars as a function of their distance from the galaxycentre. This expected velocity distribution does not match observations: stars outside the galacticbulge rotate faster than predicted [54, 149, 166], which hints towards the presence of invisiblematter, named “dark matter”, that would be present in every galaxy.The most definite evidence for dark matter comes from observations in the Bullet Clus-ter [74, 130], shown in Figure 2.9. This cluster is composed of two parts that have collided, andit is observed that the distribution of visible matter is manifestly different from the distribution ofinvisible matter inferred from gravitational lensing. In fact, the centre of the total mass is calcu-lated to be offset from the centre of visible mass with a statistical significance of 8σ [75]. This22phenomenon is attributed to interactions between the visible matter constituents during the collisionhaving slowed down these components of the cluster, while the weakly-interacting invisible matterpassed unhindered.Figure 2.9: The Bullet Cluster as seen by Magellan in the visible spectrum [75], withthe distribution of x-ray emitting gas as seen by Chandra shown in red [129],and the distribution of invisible matter inferred from gravitational lensing shown inblue [75]. Figure credit: X-ray: NASA/CXC/CfA/M.Markevitch et al.; Lensing Map:NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al.; Optical: NASA/STScI;Magellan/U.Arizona/D.Clowe et al.Another astronomical observation requiring an explanation beyond the Standard Model is thatthe expansion of the Universe is accelerating [142, 148], which points towards a very small but pos-itive value for the cosmological constant of general relativity. This constant is generally understoodas a form of energy, called “dark energy”, inherent to space itself, in other words the energy densityof the vacuum.Indications of the existence of dark matter and dark energy are also observed in the cosmic mi-crowave background, as successively observed with increasing precision by the COBE, WMAP andPlanck [143] satellites. The temperature map measured by these experiments is in fact very uniformacross the sky, but temperature differences of O(100 µK) exist between different directions. Thedistribution of these temperature fluctuations is sensitive to the composition of the Universe, and thePlanck data are compatible with a dark matter content of 26.8% and a dark energy content of 68.3%,with ordinary matter representing only 4.9% of the mass-energy inventory of the Universe [144]:another clear indication that the Standard Model is not a complete description of nature.232.3.3 Charge-Parity Violation and Matter-Antimatter AsymmetryAgain from the realm of astrophysics, a curious feature of the observable Universe is that most ofthe ordinary matter consists of particles, as opposed to antiparticles. This is surprising from theparticle physics viewpoint if the initial state of the Universe is assumed to be a state of pure energy,because then matter and antimatter would have been produced in equal amounts after the Big Bang,implying that equal amounts of matter and antimatter should be observed.One way to resolve this paradox involves interactions in particle physics that break the matter-antimatter symmetry, which implies violating the Charge-Parity (CP) symmetry, or equivalentlytime-reversal symmetry. There are indeed sources of such CP asymmetry in the flavour-mixingfeatures of the Standard Model, but their strength is not large enough to explain the observed im-balance. Therefore, if the assumption about the initial state of the Universe holds, new physicalprocesses, perhaps only occurring at very-high energies, must exist to contribute to this asymmetry.Such new physical processes would correspond to additional terms in the Lagrangian. In theStandard Model, all the renormalizable interactions that could appear given the model’s particlecontent are effectively realized in nature, with only one exception: an additional gluon interactionterm could have been present in LGψ in Equation 2.1LΘ =−g23Θ364pi2 εµνλρGαµνGαλρ (2.61)Similar terms for the electroweak gauge bosons would have no physical effect [58], but thisgluon interaction term would constitute an additional source of CP symmetry violation. How-ever, the existence of this term would imply a non-zero value for the electric dipole moment ofthe neutron δn, on which there are stringent experimental bounds. The best constraint to date is|δn|< 2.9×10−26e · cm at 90% Confidence Level (CL) [40]. This implies that the Θ3 term is ef-fectively absent: |Θ3| . 10−10 [52]. The matter-antimatter asymmetry of the Universe thereforeremains a mystery.2.3.4 Neutrino Masses and Flavour OscillationWhile in the Standard Model neutrinos have exactly zero mass, experiments worldwide have demon-strated that neutrinos are in fact massive, following from the observation of neutrino flavour oscilla-tions [111]. In fact, such oscillations are only possible if at least two neutrino flavours are massive.As a consequence, leptons in the mass basis are rotated from their representations in the flavourbasis, just like in the quark sector. The charged leptons are taken to remain the same, and neutri-nos in the mass basis are labelled ν1, ν2 and ν3. The equivalent of the CKM matrix is called thePontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [52]. The off-diagonal elements of the PMNSmatrix are large, implying that mixing is much more pronounced for neutrinos than for quarks.A possible mechanism to generate neutrino masses is called the see-saw mechanism. The main24idea is that it is possible to add right-handed neutrinos to the Standard Model, transforming assinglets: (1, 1, 0) under the Standard Model symmetries. This implies that right-handed neutrinos donot interact via any of the interactions of the Standard Model, and are therefore undetectable exceptindirectly because of their gravitational interactions. Combined with the fact that their masses couldbe large, this incidentally makes right-handed neutrinos a possible dark matter candidate.With right-handed neutrinos Nm, more terms appear in the Lagrangian, including a Majo-rana mass term. Such a term is allowed because right-handed neutrinos are singlets under allSU(3)C× SU(2)L×U(1)Y interactions, and can therefore have an explicit mass without breakinggauge invariance. The Lagrangian terms involving right-handed neutrinos are the following:LN =−12N¯m(γµ∂µ +Mm)Nm−yN,mn√2(v+H)ν¯mNn (2.62)To investigate the consequences of this Lagrangian, consider a simplified case where yN,mn is diag-onal. Then for each generation the neutrino mass matrix has the form[0 1√2yNv1√2yNv M](2.63)The positive-definite eigenvalues of this matrix are12∣∣∣∣M±√M2 +2y2Nv2∣∣∣∣ →y2Nv22M, M (2.64)with the values on the right in the limit M yNv.The largest of these eigenvalues, M, corresponds to the mass of right-handed neutrinos, anda very small mass is given to left-handed neutrinos in the process. Given the experimental upperbound on the sum of the masses of left-handed neutrinos of 0.23 eV at 95% CL [52], this meansthat the mass of right-handed neutrinos could range between O(100 GeV), for Yukawa couplingsyN ∼ y` ∼ 10−6, up to O(1014 GeV) for yN ∼ 1.The experimental study of neutrino oscillations and direct measurement of their masses is a veryrich field of study, however further discussion of this area is outside the scope of this dissertation.At any rate, the existence of non-zero masses for the left-handed neutrinos is a clear indication ofphysics beyond the Standard Model.2.3.5 Hierarchy, Fine-Tuning and EleganceThe hierarchy problem is a theoretical problem, raising the question of the existence of such a widerange of energy scales in nature. At the lower end of the spectrum, neutrino masses are thought tobe of O(0.1 eV), while the masses of other fermions range from the electron mass at 511 keV, to thetop quark mass at 173 GeV. In the Standard Model, the latter range is understood as arising from25the differences in strength of the Yukawa couplings between the Higgs boson and fermions, but theorigin of the precise values of these couplings is a mystery.The electroweak symmetry breaking scale is O(100 GeV) like the top quark mass, but then thescale of gravity is the Planck scale, O(1019 GeV). This is equivalent to the observation that whilethe three forces present in the Standard Model have couplings that are only a little smaller thanunity, gravity couples to matter in an extremely weak way, for reasons unknown.Linked to this hierarchy problem is the Higgs fine-tuning problem. While the Higgs mass is awell-defined quantity in the Standard Model, this parameter receives important radiative corrections,linked to the fact that the Higgs boson is assumed to be a fundamental scalar particle. The largestof these corrections comes from top quark loops. In the absence of new, currently undiscoveredparticles to cancel these quantum corrections, the natural value for the mass of the Higgs bosonwould be up at the Planck scale, only to be brought back to the observed value using an ad hoccorrection spanning 16 orders of magnitude. It is therefore theorized that the quantum correctionsto the Higgs mass must be cancelled by contributions from new particles, most naturally with massesnear the electroweak symmetry breaking scale. Other, more radical solutions to this problem alsoexist, and are described in Section 3.1.Finally, the Standard Model has 19 degrees of freedom, a number that grows to 26 if neutrinomasses and mixing angles are included. It is commonly thought that the simplest most fundamentaltheory of nature should have a smaller number of free parameters: this aesthetic elegance require-ment is yet another motivation to look for physics beyond the Standard Model.26Chapter 3Beyond the Standard ModelMany hypotheses reach beyond the Standard Model in attempts to address the limitations discussedin Section 2.3. This chapter first presents an overview of such hypotheses that predict new high-mass dilepton resonances in Section 3.1. Particular attention is devoted to models postulating newgauge symmetries in Section 3.2.3.1 Hypotheses Beyond the Standard Model Predicting NewHigh-Mass ResonancesSearches for new high-mass bosons decaying into lepton pairs are motivated by a wide variety ofnew models, each trying to address a subset of the Standard Model’s limitations. Many of thesemodels postulate that the gauge group of the Standard Model does not represent the most funda-mental symmetry realized in nature, but rather that the forces in the Standard Model are unified athigh energies under a larger gauge symmetry. The possibility of new gauge symmetries is exploredin more detail in Section 3.2.Alternatively, many models hypothesize the existence of additional dimensions of space-time:allowing gravity to propagate in these extra dimensions then explains why gravity is perceived asmuch weaker than the other forces of nature. As a result, the true strength of gravity is comparableto that of other forces, the actual Planck mass is comparable to the electroweak symmetry breakingscale and there is no hierarchy problem. Popular examples of this class of models include theRandall-Sundrum models [147], which predict excited states of the graviton that can decay intolepton pairs, and the models proposed by Arkani-Hamed, Dimopoulos and Dvali (ADD) [9]. Ifthe energy available at the collider is sufficiently above the actual Planck mass, quantum blackholes may also be produced, and decay in the dilepton final state [94, 106]. Variants of these extra-dimensional models, as well as TeV−1 models [7, 8, 39, 49], also allow gauge bosons to propagate inthe additional dimensions, predicting excited gauge boson states. Of these, the Kaluza-Klein spin-1bosons ZKK and γKK may also decay into lepton pairs.27Technicolour models propose another solution to the Higgs fine-tuning problem: to break elec-troweak symmetry using new strong dynamics. Many technicolour models are in fact incompatiblewith the properties of the newly-discovered Higgs boson, but some, such as Minimal Walking Tech-nicolour, include a composite Higgs boson with the right mass, spin and parity [93, 98, 99]. Sincethe Higgs boson is then a composite state, there is no fundamental scalar particle. This modelalso predicts other bound states called technimesons, which may be detected as resonances in thedilepton spectrum.Additional models predict new particles decaying into lepton pairs: models with new chiralbosons W ∗ and Z∗ [68–71], torsion models [50, 91, 145, 155], R-parity violating supersymme-try [43], and many others, further motivating the search. There is also the possibility of new particlesthat no one has yet imagined!In this dissertation, the interpretation of the search for new high-mass resonances decaying intomuon pairs will concentrate on models with new gauge symmetries; these are described in moredetail in the next section.3.2 New Gauge Symmetries3.2.1 The Sequential Standard ModelArguably the most simple extension to the Standard Model involves force-carrying particles withthe same couplings to fermions, the only difference between the new particles and the existingones being their predicted higher mass. Such a model is called the Sequential Standard Model(SSM) [123], and predicts new spin-1 bosons W ′SSM and Z′SSM, directly analogous to the W and Zbosons from the Standard Model. While the SSM is poorly motivated from a theoretical perspective,it provides a useful benchmark to compare the relative sensitivity of searches in different channelsor from different experiments.Unlike the W and Z bosons, which interact with each other in cubic and quartic interactionterms, the couplings of the bosons introduced in the SSM with each other and with the W and Z areassumed to be zero. This arbitrary choice is made for all Z′ bosons under study, in order to avoidintroducing additional model-dependent degrees of freedom into the interpretation of the search.3.2.2 Models from Grand Unified TheoriesMore interesting than the SSM is the possibility of new vector bosons from Grand Unified Theories(GUT). In GUT, the gauge group of the Standard Model is extended, usually to a simple group, toprovide a unifying picture of gauge interactions in which all fermions belong to the same multipletrepresentation of the group. These models are motivated by the fact that gauge couplings in theStandard Model seem to converge towards the same value at very high energy scales, as illustrated28in Figure 2.2. Further, GUT typically feature a reduction in the number of free parameters inthe theory, as well as natural neutrino masses due to the presence of right-handed neutrinos, andsometimes a cancellation of quadratic divergences of the Higgs mass in an attempt to solve thefine-tuning problem.Perhaps one of the most popular examples of GUT in high-energy particle physics is thesuperstring-motivated E6 model [127]. In particular, in a superstring theory with 10 space-timedimensions and an E8×E ′8 internal gauge symmetry, compactification to four dimensions reducesone of the E8 to E6. This E6 comprises the gauge symmetries of the Standard Model, while the E ′8interacts only gravitationally with ordinary matter and forces. While this hypothesis is fairly specu-lative and may not correspond to what actually occurs in nature, studying it is of particular interestbecause the predictions originating from its many different possible symmetry-breaking scenariosdo cover many of the different phenomenological possibilities explored in the literature. For in-stance, alternative symmetry-breaking scenarios such as E8 first breaking into SO(16) instead [45]give similar predictions at the energy scale explored by the LHC.The breakdown of the E6 gauge symmetry to SO(10)×U(1) is particularly appealing becausethen for each of three generations of matter, the Standard Model fermions plus a right-handed neu-trino are part of the same representation 16 of SO(10), while eleven additional exotic fermions forma 10 and a singlet. These exotic fermions can be given masses as high as the symmetry-breakingscale of E6, and will not be discussed further. While it is also possible for the E6 symmetry to breakdown following a different path, explicitly either E6→ SU(6)×SU(2) or E6→ [SU(3)]3, the mainexperimental prediction that follows from these scenarios is qualitatively the same: a Z′ boson mayexist at the TeV scale. All possibilities are explored in detail by London and Rosner in Ref. [127].SO(10) can then break down to the Standard Model following one of two scenarios: the Georgi-Glashow Model or the Pati-Salam Model.The Georgi-Glashow ModelA first symmetry-breaking scenario is via SU(5):E6→ SO(10)×U(1)ψ→ SU(5)×U(1)χ ×U(1)ψ→ SU(3)C×SU(2)L×U(1)Y ×U(1)θ→ SU(3)C×SU(2)L×U(1)Y→ SU(3)C×U(1)Q(3.1)Here all the symmetries of the Standard Model become unified at higher energies into the simplegroup SU(5). In the SU(5) model, first explored by Georgi and Glashow [105], the representations29containing the fermions from the Standard Model are one 5¯ and one 10 for each generation:d¯rd¯gd¯be−νL,1√20 u¯b −u¯g −ur −dr−u¯b 0 u¯r −ug −dgu¯g −u¯r 0 −ub −dbur ug ub 0 −e+dr dg db e+ 0L(3.2)The gauge bosons from the adjoint representation 24 of SU(5) include the Standard Modelgauge bosons, as well as leptoquarks. The latter can mediate experimentally unseen processes suchas proton decay (e.g. via p→ pi0e+) and K0→ µ±e∓. For this reason, the SU(5) breaking scale hasto occur at very high energies, thereby giving large masses to the leptoquarks.Nevertheless, the spontaneous symmetry breaking of E6 to SU(5) results in two additional U(1)gauge groups named U(1)ψ and U(1)χ , and the lightest linear combination of the associated massivegauge bosons Z′ψ and Z′χ could be accessible at the LHC if the symmetry breaking of SU(5) occursin two steps, with the breaking of U(1)θ involving a vacuum expectation value at the TeV scale.The experimental signature would then be a new gauge boson Z′θ , whereZ′θ = Z′ψ cosθE6 +Z′χ sinθE6 . (3.3)The couplings of Z′θ to fermions are detailed in Table I of Ref. [127].The Pati-Salam ModelAn even more interesting symmetry-breaking scenario involves the Pati-Salam Model [141], whichin turn breaks down to the Standard Model via the minimal left-right symmetric model as follows:E6→ SO(10)×U(1)ψ→ SU(4)C×SU(2)L×SU(2)R→ SU(3)C×SU(2)L×SU(2)R×U(1)B−L→ SU(3)C×SU(2)L×U(1)Y→ SU(3)C×U(1)Q(3.4)This particular mechanism makes a clear separation between the flavour and colour sectors of thetheory. On the flavour side, two triplets of weak bosons are present: the W and Z bosons from theStandard Model SU(2)L but also W ′R and Z′R from SU(2)R, making the left-right symmetry explicit.On the colour side, the strong force symmetry group is SU(4)C, with leptons joining quarks incolour quadruplets (charged leptons with down-type quarks, and neutrinos with up-type quarks).This unification also predicts leptoquarks, which gain large masses when SU(4)C is broken into the30familiar SU(3)C and the Abelian U(1)B−L of the minimal left-right symmetric model [46, 136, 154]where B is the baryon number, L is the lepton number and B−L is the conserved quantum number.The Standard Model is recovered when the symmetry SU(2)R×U(1)B−L breaks down to U(1)Y ,in a manner very similar to the electroweak symmetry breaking SU(2)L×U(1)Y →U(1)Q. If thislast step of the breakdown to the Standard Model happens near the TeV scale, then the W ′R, Z′R and/orZ′B−L bosons could be observable at the LHC.Minimal Z′ ModelsThe Minimal Z′ Models [151] constitute a parametrization aiming to describe a large section ofthe Z′ phenomenology potentially accessible at the LHC using only three parameters beyond theseof the Standard Model. The new parameters are the Z′Min mass MZ′Min , a coupling strength γ′ and amixing angle θMin. The latter two are related to the Z′Min coupling gY to the electroweak hyperchargeY , and its coupling gB−L to the B−L current, as follows:gY/gZ = γ ′ sinθMin (3.5)gB−L/gZ = γ ′ cosθMin (3.6)where gZ = 2MZ/v, and v = 246 GeV is the Higgs vacuum expectation value in the Standard Model.γ ′ therefore measures the overall coupling strength of the Z′Min boson relative that of the Z boson.As in the case of θE6 , certain values of θMin correspond to specific Z′ bosons: in this case they areZ′B−L, Z′R and Z′χ . The values of γ ′ and θMin for these three specific models are shown in Table 3.1.The Z′χ boson corresponds to the point in parameter space shared between Minimal Z′ Models andthe θE6 parametrization.Table 3.1: Values of γ ′ and θMin for three specific models: Z′B−L, Z′χ and Z′R.Z′B−L Z′χ Z′Rγ ′√58 sinθW√4124 sinθW√2512 sinθWsinθMin 0 −√1641 −√45cosθMin 1√2541√15SummaryTo summarize, in Grand Unified Theories all forces of nature originate from a unified gauge sym-metry. In the process of breaking this symmetry, additional SU(2) and U(1) groups appear at scalesabove that of the Standard Model. All additional U(1) symmetries would manifest themselves viathe production of Z′ gauge bosons, while an additional SU(2) symmetry would imply the exis-31tence of both W ′ and Z′ bosons. These additional gauge bosons might be observable directly athigh-energy colliders or indirectly in precision experiments.3.2.3 Experimental Limits on New Gauge BosonsPrevious experimental limits at 95% CL on the mass of new gauge bosons Z′ are shown in Table 3.2.The earliest TeV-scale limits on the existence of Z′ bosons came indirectly via limits on four-fermioncontact interactions [67]. Such interactions would interfere with fermion pair-production occur-ring via the Drell-Yan process, and impact the production cross sections and angular distributionsof the final-state fermions. The strongest indirect limits are set by the experiments at the LargeElectron-Positron Collider (LEP) [2, 92, 120, 140], which exclude at 95% CL a Z′SSM boson withMZ′ < 1.787 TeV [124].In their time, the CDF and D0 experiments at the Tevatron have set the strongest direct limits onthe existence of new gauge bosons, using proton-antiproton collision data at√s = 1.96 TeV. Theselimits are also shown in Table 3.2. The limits set by the D0 collaboration made use of 5.3 fb−1of data in the dielectron channel [90], and the limits set by the CDF collaboration made use of4.6 fb−1 of data in the dimuon channel [66].Finally, because the Large Hadron Collider currently holds the record for the highest centre-of-mass energy attained in a particle collider, it comes as no surprise that the most stringent direct limitsto date on the existence of new gauge bosons come from the ATLAS and CMS experiments. Usingproton-proton collision data amounting to 5 fb−1 at√s = 7 TeV and 4 fb−1 at√s = 8 TeV [78],the latest published results by CMS exclude at 95% CL a Z′SSM boson with MZ′ < 2.59 TeV anda Z′ψ with MZ′ < 2.27 TeV. The most recent preliminary results from CMS using 20 fb−1 of datacollected at√s = 8 TeV [77] exclude at 95% CL a Z′SSM boson with MZ′ < 2.96 TeV and a Z′ψ withMZ′ < 2.60 TeV. Results obtained by the ATLAS experiment are discussed in detail in Chapter 8.Table 3.2: Previous experimental limits at 95% CL on the mass of new gauge bosons Z′.CMS does not provide explicit limits on Z′χ ; they would be slightly better than the limitson Z′ψ . Results by the ATLAS collaboration are not shown here, but in Table 8.1.Collaboration Channel Mass limits at 95% CL [TeV]Z′SSM Z′ψ Z′χLEP combination e+e−→ e+e−,µ+µ−,τ+τ−,qq¯ 1.787 0.481 0.673D0 pp¯→ e+e− 1.023 0.891 0.903CDF pp¯→ µ+µ− 1.071 0.917 0.930CMS pp→ e+e−,µ+µ− 2.59 2.27 -CMS (preliminary) pp→ e+e−,µ+µ− 2.96 2.60 -32Chapter 4The ATLAS Experiment at the LargeHadron ColliderA truly international endeavour, the Large Hadron Collider (LHC) [51, 56, 57, 97] is the largestand most powerful particle accelerator ever built. This chapter first describes in Section 4.1 theLHC accelerator chain within the CERN accelerator complex, which accelerates protons to achievecollisions with record centre-of-mass energy and very high rates at four interaction points.Immense detectors are present at each of these interaction points to record the outcomes of thesecollisions and study the underlying physical processes: they are the ALICE, ATLAS, CMS andLHCb experiments. This dissertation makes use of data collected by the ATLAS experiment [12,13], described in Sections 4.2 to 4.8.4.1 The Large Hadron ColliderThe Large Hadron Collider is located at CERN near Geneva, Switzerland, in the 27-kilometre-long tunnel previously used by the Large Electron-Positron Collider (LEP) from 1989 to 2000. Itcurrently holds the record for the highest energy achieved in an artificial particle accelerator, havingsuccessfully accelerated protons to an energy of 3.5 TeV in 2010 and 2011, and 4 TeV in 2012. Itsdesign energy of 7 TeV per proton is projected to be attained in the next years. In comparison, theTevatron accelerated protons and antiprotons to an energy of 0.98 TeV. Unlike the Tevatron, theLHC is a proton-proton accelerator; this choice has been made to maximize the intensity of thebeam and therefore the instantaneous luminosity, related to the collision rate. The LHC is also usedto accelerate heavy ions, such as lead nuclei.334.1.1 Accelerator ChainThe accelerator chain leading to the main ring of the LHC consists of pre-existing machines, up-graded to meet the requirements of their new purpose as pre-accelerators. The chain starts at theproton source, a bottle of hydrogen gas. A duoplasmotron is used to ionize the hydrogen atoms, bybombarding them with electrons; electric fields then complete the separation, sending the resultingprotons into the accelerator chain. The CERN accelerator complex is shown in Figure 4.1.Figure 4.1: The CERN accelerator complex. Figure credit: CERN.The protons are first accelerated to an energy of 50 MeV by a linear accelerator, LINAC 2,which consists of radiofrequency cavities containing an alternating electric field. The length ofsuccessive cavities increases, matching the desired speed of the protons, so that protons in phasewith the electric field are uniformly accelerated, while others arriving later or earlier are acceleratedrespectively more or less. The net result is the formation of proton bunches, accelerating jointly.Quadrupole magnets ensure that the bunches remain focused in the transverse directions.34These proton bunches are then injected into the Proton Synchrotron Booster, the first of a seriesof synchrotrons, i.e. circular accelerators where the particles follow a fixed trajectory, with dipolemagnets providing the magnetic field to curve the particles’ path. This magnetic field must increaseas the particles are accelerated, in order to maintain the radius of the circular trajectory constant1.The maximal energy attainable by proton synchrotrons is limited by the strength of their dipolemagnets as compared with the radius of curvature imposed by the accelerator’s geometry. Thisimplies that there are two ways to reach higher energies: stronger magnets and larger rings. TheProton Synchrotron Booster actually consists of four superimposed synchrotron rings which accel-erate proton bunches to an energy of 1.4 GeV, before sending them into larger and more powerfulsynchrotrons.The proton bunches then enter the Proton Synchrotron, which once was the world’s most pow-erful particle accelerator when it first started in 1959. With a circumference of 628 meters, it canaccelerate protons up to an energy of 25 GeV. During its long service, this versatile machine hasalso served to accelerate heavier nuclei, as well as electrons, positrons and antiprotons.The next accelerator in the chain is the Super Proton Synchrotron, with a circumference ofnearly 7 km, bringing the beam energy to 450 GeV per proton. It is from proton-antiproton collisionevents obtained using this accelerator that the UA1 and UA2 experiments discovered the W andZ bosons in 1983 [161–164]. Finally, the proton bunches are injected into the LHC, in oppositedirections, for their final acceleration and eventual collision.4.1.2 Main RingThe LHC makes use of the LEP tunnel, shown in Figure 4.2, which only has room for a single ringof magnets. But unlike LEP or the Tevatron which accelerated beams with particles of equal andopposite charge, allowing both beams to share the same ultra-high vacuum tube and magnet system,the LHC’s two proton beams require dipole magnets of opposite polarity.The answer to this challenge is the “two-in-one” superconducting electromagnet design, illus-trated in Figure 4.3. In this economical configuration, the magnets share the same envelope, ironyoke and services. The magnets, made of a niobium-titanium alloy, are cooled down to a temper-ature of 1.9 K using liquid helium. At this temperature, helium is in the superfluid state, whichimplies excellent heat conduction properties. The use of superconducting technology is necessaryin order to reach the very high magnetic fields required: given the curvature imposed by the LHClayout, at the design energy of 7 TeV per proton the dipole magnets need to reach 8.33 T.In addition to the dipole magnets responsible for bending the beam’s trajectory, quadrupoleand sextupole magnets focus the beam in the transverse directions, while the longitudinal stabilityof proton bunches is provided by the superconducting radio-frequency cavities responsible for ac-1 This is in contrast with a cyclotron such as the one at TRIUMF, where the magnetic field in the accelerator is constantbut the radius of the particles’ trajectory increases as they are accelerated, resulting in an outward spiral path.35celerating the beam and compensating for any energy losses once the collision energy is attained.Additional magnets are used to improve the beam quality by compensating for second-order effectswithin the beams. Finally, at the interaction points, dedicated dipole magnets initiate beam recombi-nation and ensure beam separation on the other side of the crossing point, while dedicated triplets ofquadrupole magnets are responsible for focusing the beam to achieve the highest possible collisionrate. The placement of these magnets around the ATLAS interaction point is shown in Figure 4.4.Figure 4.2: Magnets in the LHC tunnel. Figure credit: CERN.Figure 4.3: LHC magnet components. Figure credit: CERN.36 V. Hedberg                                                                                ATLAS Technical Management Board  -  10.06.2004                                                                           1 Q1Q2Q3D1D2Q4Q5Q6IPTASTANbeam 2beam 1 DumpResistor Boxes17m140 m237m4mLUCIDZDCALFATop view of the LHCFigure 4.4: Placement of the dipole and quadrupole magnets responsible for bringing the LHCbeams into collision at the ATLAS interaction point. Also shown are the positions of theLUCID, Zero Degree Calorimeter and ALFA detectors discussed in Section 4.7 [12].4.1.3 Delivered Luminosity and Beam Conditions in Run-IFollowing the first proton-proton collisions obtained at a centre-of-mass energy of 900 GeV inNovember 2009, the accelerating power of the LHC was used to achieve a record energy of 2.36 TeVone week later. A centre-of-mass energy of 7 TeV was reached in March 2010, albeit with a lowluminosity. In total, 48.1 pb−1 of proton-proton collisions were delivered to the ATLAS experimentthat year, making possible the “re-discovery” of Standard Model processes and the first iteration ofmany searches for new physics at the LHC.The luminosity delivered to ATLAS increased dramatically in 2011, reaching 5.46 fb−1 ofcollisions at√s = 7 TeV by the end of the year. Then the centre-of-mass energy was raised to√s = 8 TeV in 2012, when 22.8 fb−1 of collisions were delivered to the ATLAS detector. In total,1.80× 1015 proton-proton collisions were recorded by the ATLAS detector in Run-I of the LHC.The cumulative progression of the luminosity delivered to ATLAS is shown in Figure 4.5, along withthe fraction of these data successfully recorded by ATLAS and passing all quality requirements, asdiscussed in Sections 4.7 and 4.8.In fact, the highest instantaneous luminosity achieved by the LHC in 2012 was7.73×1033 cm−2s−1, close to the design value of 1034 cm−2s−1 = 10 nb−1s−1. This was achievedwith half the proton bunch crossing rate originally planned: collisions occurred every 50 ns, insteadof the nominal time separation of 25 ns between bunches. This was compensated by a higher numberof protons in each bunch: specifically, instead of accelerating 2808 bunches with 1.15×1011 protonsper bunch, the LHC accelerated 1380 bunches with 1.7×1011 protons each.This implies that the reconstruction of detected collision events benefited from a greater separa-tion between bunch crossings, i.e. lower “out-of-time pileup”, but that a larger number of simultane-ous proton-proton interactions, or “in-time pileup”, occurred at each bunch crossing. The hardwareand event reconstruction software of ATLAS met this challenge, and operated successfully underthese conditions. The distributions of the observed number of interactions per crossing in 2011and 2012 are shown in Figure 4.6. Figure 4.7 displays a Z→ µ+µ− candidate event observed bythe ATLAS detector with reconstructed vertices from 25 simultaneous proton-proton interactions, anumber in the bulk of the distribution for collisions recorded in 2012.37Figure 4.5: Cumulative luminosity versus time delivered to ATLAS (green), recorded by AT-LAS (yellow), and certified to be good quality data (blue) during stable beams and forproton-proton collisions at 7 and 8 TeV centre-of-mass energy in 2011 and 2012 [33].Mean Number of Interactions per Crossing0 5 10 15 20 25 30 35 40 45/0.1]­1Recorded Luminosity [pb020406080100120140160180 Online LuminosityATLAS> = 20.7µ, <­1Ldt = 21.7 fb∫ = 8 TeV, s> =  9.1µ, <­1Ldt = 5.2 fb∫ = 7 TeV, sFigure 4.6: Luminosity-weighted distribution of the mean number of interactions per crossingfor the dataset collected in 2011 and 2012 [33].38Figure 4.7: Z → µ+µ− candidate event with reconstructed vertices from 25 simultaneousproton-proton interactions in the ATLAS detector. The two muons, which come fromthe same vertex, are highlighted in yellow [33].394.2 The ATLAS Detector: OverviewWith its extraordinary collision rates and beam energy, the LHC offers a tremendous technologicalchallenge for detector designers. The ATLAS detector, illustrated in Figure 4.8, was created to meetthis challenge: it serves as one of the two general-purpose detectors at the LHC, with the ambitiousgoal to search for the Higgs boson from the Standard Model in addition to being sensitive to avery wide range of new physics that might appear at the TeV scale. It also provides an opportunityto investigate much of the Standard Model’s high-energy spectrum, studying processes involvingthe top quark and flavour physics as well as performing precision tests of QCD and electroweakinteractions.To achieve these goals, precise and fast measurements of the physical objects in the final stateof collisions are essential, with the largest possible acceptance and efficiency for detecting signalprocesses. The next sections describe the technological features making such performance possible.4.2.1 Detector DesignATLAS is composed of four major subsystems, built in cylindrical layers: from the innermost tothe outermost part, they are the Inner Detector (ID), the Electromagnetic Calorimeter, the HadronicCalorimeters and the Muon Spectrometer (MS). Each of these subsystems is divided into threeregions: the central region is called the “Barrel”, bordered by “Endcap” regions on each side. Asillustrated in Figure 4.9, when particles produced in the LHC collisions interact with the detector,they produce distinctive patterns which make their identification possible.The ID, described in Section 4.3, measures tracks from charged particles: the momentum ofthese tracks is determined by their curvature in the magnetic field provided by a solenoid magnet.As well, the information from these tracks makes possible the reconstruction of primary vertices, al-lowing to distinguish different collision points, and the reconstruction of secondary vertices comingfor example from B-meson decays. The Electromagnetic Calorimeter, responsible for identifyingand measuring the energy of electrons and photons, and the Hadronic Calorimeters, which measurethe energy of hadrons while ensuring to stop them before they reach the MS, are briefly describedin Section 4.4.Particular attention is devoted to the MS described in Section 4.5, as it is the main subsystemused to detect and measure the momentum of muons, especially at very high momentum. One ofthe prominent features of ATLAS is its toroid magnet system, providing the strong magnetic fieldnecessary to perform this measurement: it is also described there.Section 4.6 defines the missing transverse momentum, a very useful observable making use ofthe information from all subsystems allowing the indirect detection of particles which do not interactwith any of the detector components, such as neutrinos. Section 4.7 outlines the strategies used tomonitor the luminosity delivered to ATLAS. Finally, sophisticated trigger and Data Acquisition40(DAQ) systems are responsible for the first stages of event selection, recording the outcome ofexperimentally interesting collision events and discarding the vast majority of the rest. As well,data quality monitoring ensures that all subsystems are working properly and that the collected dataare suitable for analysis. These systems are described in Section 4.8.4.2.2 Coordinate SystemThe ATLAS collaboration employs a right-handed coordinate system, with the z-axis along the beamdirection, also called the longitudinal direction. The origin is defined as the nominal interactionpoint in the centre of the detector. The x-axis points from this origin toward the centre of the LHCring, while the y-axis points upward. Cylindrical coordinates are often used, r being the radius inthe transverse plane (x,y) and φ being the azimuthal angle around the beam pipe defined from thepositive x-axis. When using spherical coordinates, the polar angle θ is defined from the positivey-axis. The transverse momentum of particles is defined in terms of θ and the momentum p aspT = psinθ , and the pseudorapidity is defined as η =− ln tan(θ/2).When describing the angular direction of particles following a collision, the coordinates (η , φ )are most often used because the differential production rates of particles are expected to be constantin φ and approximately constant in η . It is for the same reason that distances between particles,as well as cone sizes used when reconstructing objects from calorimetric clusters or when countingactivity near a reconstructed object, are most commonly expressed in terms of ∆R =√∆η2 +∆φ 2.Figure 4.8: The ATLAS detector [12].41Figure 4.9: Illustration of the ways in which different particles are identified based on theirinteractions with the ATLAS detector [33].4.3 Inner DetectorThe ATLAS Inner Detector, illustrated in Figures 4.10 and 4.11, is designed to identify tracks fromcharged particles and to reconstruct primary and secondary vertices using these tracks. Closest tothe beam pipe, it comprises the Pixel detector, the Semiconductor Tracker (SCT) made of siliconmicro-strips, and the Transition Radiation Tracker (TRT), which makes use of straw proportionaldrift tubes. The Pixel and SCT cover the range |η |< 2.5, while the TRT covers |η |< 2.0.The tracks from charged particles are bent using a solenoid magnetic field. As a result, theradius of curvature of the tracks is proportional to the transverse momentum of the correspondingparticles, and their charge is identified using the direction of curvature. The resolution of the ID formeasuring the momentum of tracks is discussed in detail in Section 5.2.42Figure 4.10: Transverse view of the ATLAS Inner Detector components [12].Figure 4.11: Longitudinal view of the ATLAS Inner Detector components [12].434.3.1 Pixel DetectorThe innermost part of the ATLAS detector is the Pixel detector, which is made of 1744 identicalsilicon pixel sensor modules, each with 46080 readout channels, for a striking total of more than80 million readout channels: about 50% of the number for the whole detector. Such a number isnecessary to provide the very fine detector granularity allowing to meet the stringent vertex recon-struction requirements imposed by the LHC collision rates.The dimensions of the pixels are 50 µm×400 µm in 90% of cases, and 50 µm×600 µm oth-erwise, with a thickness of 250 µm. They are arranged as three cylinders in the Barrel region; thefirst pixel layer, called the B-layer for its particular usefulness in reconstructing secondary verticesfrom B-meson decays, is closest to the beryllium beam pipe at a radius of 50.5 mm. On each layer,the modules are laid out in an overlapping way for redundancy, with the top of each module facingthe beam pipe in order to minimize the material in front of the detector. In each Endcap region, asillustrated in Figure 4.11, the modules are arranged in three wheels perpendicular to the beam axis.There the redundancy is achieved by alternating the sensors on each side of the supporting structure.When a charged particle passes through a semiconductor detector, it ionizes atoms in the lattice,resulting in the production of electron-hole pairs. These electrons and holes drift in opposite direc-tions, resulting in a measurable current at the electrodes. The pixels are made of radiation-tolerantdoped silicon, operating at a reverse bias voltage of 150 V initially. This voltage is foreseen to beincreased up to 600 V after 10 years of operation, to compensate for radiation damage.An additional inner layer for the Pixel detector, called the Insertable B-Layer [14], was insertedduring the shutdown between Run-I and Run-II, to further enhance the vertex reconstruction ca-pabilities of the ID. This new innermost pixel layer fits between the other pixel layers and a new,smaller beam pipe.4.3.2 Semiconductor TrackerThe SCT also makes use of semiconductor detector technology, with 15912 sensors of 768 activemicro-strips each. The silicon micro-strips measure 80 µm×12 cm, with a thickness of 285 µm.Their general layout is the same as for the Pixel detector, with four cylindrical layers in the Barreland nine wheels in each Endcap. The layers and wheels are instrumented on both sides, and a stereoangle of 40 mrad between micro-strips on each side allows 3D measurements of charged particletracks.For best operating conditions, both silicon detectors are operated at a temperature between−5 and −10 degrees Celsius. A laser interferometric monitoring system, able to monitor shape de-formations due to temperature variations to an accuracy of 10 µm, is used to maintain the alignmentof the SCT. Like the Pixel detector, the SCT is operated at a voltage of 150 V initially, foreseen tobe increased up to 350 V after 10 years of operation to maintain a good charge collection efficiency.444.3.3 Transition Radiation TrackerThe outermost part of the ID is the TRT, which makes use of straw proportional drift tubes to detectcharged particles. The straws have a diameter of 4 mm, a compromise between speed of responseand number of hits per track on one hand, and hit efficiency on the other. Indeed while smallerstraws are preferable for the first two requirements, with too small a diameter not enough ionizationwould take place in any straw. It is also important for tracking detectors to have high mechanicalstability and rigidity while minimizing the amount of material used. As illustrated in Figure 4.10,the straws in the Barrel are arranged in triangular clusters parallel to the beam axis. In the Endcaps,on the other hand, they form wheels perpendicular to the beam axis, as shown in Figure 4.11.When charged particles pass through a straw, they ionize the gas it contains; the ions pro-duced drift towards the cathode straw wall, which is kept at a negative tension of −1530 V, whilethe corresponding electrons drift towards a gold-plated tungsten anode wire with a small diameterof 31.5 µm. When electrons come close to the anode wire, an avalanche occurs with a gain of2.5×104, resulting in a signal proportional to the energy loss of the ionizing particle. The maxi-mum drift time, corresponding to ionization on the edge of a straw, is measured to be 50 ns, whichis satisfactory for operation at LHC collision rates. The drift-time accuracy of the straws is 130 µm.One distinguishing feature of the TRT is its use of transition radiation to distinguish electronsfrom more massive particles. Transition radiation is emitted when a charged particle crosses theboundary between two materials with different dielectric constants. This radiation is most abundantfor highly-relativistic particles with Lorentz factor γ > 103, and in this case the energy of the emittedphotons ranges from a few to tens of keV. To exploit this effect, the straw wall consists mainly of two25-µm kapton films, separated by a 5-µm polyurethane layer: these materials are chosen for theirlow density and relatively low atomic number Z. Indeed, since the photoelectric absorption crosssection per atom goes roughly as Z5 [52], a transition radiator with low Z keeps self-absorptionsmall and thus maximizes yield. On the other hand, it important for the gas mixture to absorbthe transition radiation photons: xenon is used for this purpose. The straw tubes are filled with aXe–CO2–O2 mixture at {70%, 27%, 3%}: CO2 ensures high drift velocities and photon-quenching,and O3, which is created from O2 during avalanches, prevents silicon and hydrocarbon deposits onthe anode wire. Unlike the silicon detectors and the liquid argon calorimeters, the TRT operates atroom temperature, which requires the presence of heaters.Two signal thresholds are used by the readout system: the low threshold is triggered by thesignal due to ionization energy loss from charged particles, and the high threshold, used for electronidentification, is triggered by the significantly stronger signal due to transition radiation. Figure 4.12shows the average probability of a high-threshold hit in the TRT Barrel as a function of the Lorentzγ-factor, as measured in the ATLAS combined test-beam. Electrons have a much higher high-threshold probability than pions, while muons are on the rise of the curve. Transition radiation thusallows the TRT to successfully distinguish electrons from pions.45Lorentz gamma factor10210 310 410 510High-threshold probability00.020.040.060.080.10.120.140.160.180.20.22Pions Muons Electrons ATLASFigure 4.12: Average probability of a high-threshold hit in the TRT Barrel as a function of theLorentz γ-factor for electrons (open squares), muons (full triangles) and pions (opencircles) in the energy range from 2 to 350 GeV [12].4.3.4 Solenoid MagnetThe superconducting solenoid magnet of ATLAS provides a magnetic field of 2 T parallel to thebeam axis. It consists of a single-layer coil made of aluminium-stabilized niobium-titanium, oper-ated at a nominal current of 7.73 kA and a temperature of 4.5 K. This choice of material and layoutminimizes the amount of material in front of the calorimeters. The magnetic field flux is returnedby the steel of the Tile Hadronic Calorimeter.4.4 CalorimetersThe ATLAS calorimeters are illustrated in Figure 4.13. Three cryostats, for the Barrel and thetwo Endcaps, house the calorimeters using liquid argon as the active material: the three parts ofthe Electromagnetic Calorimeter, the Hadronic Endcap Calorimeters and the Forward Calorimeters.They are operated at a temperature of 88 K, ensuring that the argon remains liquid. The cryostatsare surrounded by the Tile Hadronic Calorimeter, which extends above both the Barrel and Endcaps.4.4.1 Electromagnetic CalorimeterThe Electromagnetic Calorimeter makes use of lead absorbers between layers of liquid argon withkapton electrodes. An accordion shape is used, ensuring a complete symmetry in the φ coordinatewithout cracks in coverage. When charged particles traverse the lead absorbers, they emit photonsvia bremsstrahlung; these photons in turn convert into electron-positron pairs, which emit morephotons, the result being a shower of electrons and photons which continues until all the energy is46absorbed by the calorimeter. Photons may also initiate such a shower, with an initial conversion.Particles from the shower ionize the liquid argon, and the ions then drift toward the electrodesresulting in a signal proportional to the energy deposited.The thickness of the lead absorbers and the granularity of the instrumentation was optimized toprovide the best energy and position resolution possible for electrons and photons, especially in theprecision region of |η |< 2.5 corresponding to the acceptance of the ID. The design energy resolu-tion is σE/E = 10%/√E⊕0.7%. The coverage of this detector subsystem otherwise extends up to|η |= 3.2. Showers from photons and electrons are contained in the Electromagnetic Calorimeter,while showers from heavier particles reach the Hadronic Calorimeters.Figure 4.13: The ATLAS calorimeters [12].4.4.2 Hadronic CalorimetersThe Hadronic Endcap Calorimeters, located behind the corresponding parts of the ElectromagneticCalorimeter, are comprised of 32 identical wedge-shaped modules each. They make use of copperplates as absorbers, interleaved with gaps of liquid argon and instrumentation, and cover the range1.5 < |η |< 3.2.Between the Endcap Calorimeters and the beam pipe, Forward Calorimeters cover the range3.1 < |η |< 4.9. Instrumenting this region is especially challenging due to the high particle lumi-nosity coming from the collisions. Three modules are present in each Endcap: the first is made ofcopper and is optimized for electromagnetic measurements, and the others are made of tungsten tomeasure the intense hadronic interactions in the most compact way possible. Each of these modules47is designed as a metal matrix, with hollow tubes instrumented with metal rods parallel to the beamaxis. The very small gaps between the rods and the tube are filled with liquid argon.Around the three cryostats, the Tile Hadronic Calorimeter covers the range |η |< 1.7. Its namecomes from the scintillating tiles used as the active material, while steel is used as the absorber.Scintillators absorb the energy of charged particles and re-emit it in the form of photons; thesephotons then travel via fibre optics to readout photomultiplier tubes located around the calorimeter.The design energy resolution of the Hadronic Calorimeters is σE/E = 50%/√E⊕3%, ex-cept for the Forward Calorimeter which is limited by its high-radiation operating environment toσE/E = 100%/√E⊕10%. Overall, the Hadronic Calorimeters are as hermetic as possible, cover-ing the entire range |η |< 4.9 and limiting the amount of radiation reaching the Muon Spectrometer.4.5 Muon SpectrometerThe Muon Spectrometer is the most important detector subsystem for the analysis presented inthis dissertation, as it is used for the identification and precise momentum measurement of muontracks. After passing through the calorimeters, muon tracks are bent along the beam directionusing a toroidal magnetic field. Muon Drift Tubes (MDTs) measure the track curvature in thisdirection, in both the detector Barrel and Endcap regions. Cathode Strip Chambers (CSCs) arealso present in the very forward region of the detector to extend the muon tracking capability. Themuon trigger system comprises Resistive Plate Chambers (RPCs) and Thin Gap Chambers (TGCs);these chambers also provide measurements of the φ track coordinate. The resolution of the MS formeasuring the momentum of charged particle tracks, especially in the case of muons at very highmomentum, is discussed in detail in Sections 5.2 and 5.3.2.4.5.1 Toroid MagnetsThe eight-fold symmetric toroid magnets of ATLAS are its most distinctive feature. The magnetcoils are made of aluminium-stabilized niobium-titanium-copper, operated at a nominal current of20.5 kA and a temperature of 4.6 K, producing magnetic fields of approximately 0.5 T in the Barreland 1 T in the Endcaps. In the Barrel, the coils are encased in stainless-steel vacuum vessels, whilein the Endcaps the structure is made of aluminium.Figure 4.15 shows the integrated magnetic field strength in the MS as a function of |η |, for φ = 0and φ = pi/8. The variability of these field integral values, especially around the magnetic transi-tion region between the Barrel and Endcap toroids, illustrates the importance of using a dependablemagnetic field map for tracking muons. It also demonstrates that reliable track momentum mea-surements require adequate measurements of both angular track coordinates η and φ . Momentummeasurements are particularly challenging in the transition region, where the magnetic field integralbecomes small and even briefly changes sign.48Figure 4.14: The ATLAS Muon Spectrometer and toroid magnets [12].|η|0 0.5 1 1.5 2 2.5 m)⋅B dl     (T ∫-202468Barrel region regionEnd-capTransition region=0φ /8pi=φ Figure 4.15: Integrated magnetic field strength in the MS as a function of |η |, for φ = 0 andφ = pi/8 [13].494.5.2 Monitored Drift TubesThe MDT chambers constitute most of the precision tracking detectors in the MS. The drift tubesare made of aluminium with a diameter of 29.97 mm, and are filled with an Ar–CO2–H2O mixtureat {93%, 7%, 300 ppm}, at a pressure of 300 kPa. Muons passing through a tube ionize the gas,and the resulting electrons drift towards a central tungsten-rhenium anode wire with a diameter of50 µm, kept at a positive tension of 3080 V. When the electrons come close to the wire, an avalancheoccurs with a gain of 2×104, resulting in a measurable current. Because of the larger size of thetubes and the smaller CO2 gas concentration compared to the TRT, the maximum drift time in theMDTs is about 700 ns. Nevertheless, this is satisfactory because the track rates are significantlylower in the MS than in the ID, due to the shielding provided by the calorimeters: at the designLHC luminosity, the maximum counting rate measured by MDTs is expected to be 30 kHz.Figure 4.16 shows a schematic diagram of the cross section of an MDT, as well as the mechan-ical structure of an MDT chamber. The chambers are rectangular in the Barrel, and trapezoidal inthe Endcaps. They are made of an aluminium frame carrying two multi-layers of three or four drifttube layers each. In each chamber, an internal optical alignment system performs to a precision of10 µm, monitoring potential deformations due to temperature changes. Temperature sensors arepresent as well to quantify these effects. Barrel chambers placed at various horizontal angles arealso subject to gravitational sag, which is corrected using a mechanical system informed by the op-tical alignment system. Finally each chamber is equipped with two to four magnetic field sensors,to ensure a good mapping of the field. The drift-time resolution of individual MDTs is 80 µm,translating to an optimal tracking resolution of 30 µm for MDT chambers. The layout of MDTchambers and the global alignment system of the MS are discussed in Section 4.5.6.µ29.970 mmAnode wireCathode tubeRminFigure 4.16: Left: Cross section of an MDT. Right: Mechanical structure of an MDT chamber,showing the aluminium frame carrying two multi-layers of three or four drift tube layerseach, the internal optical alignment rays and the location of the readout electronics (RO)and high-voltage supplies (HV) [12].504.5.3 Cathode Strip ChambersThe CSCs are multi-wire proportional chambers designed to extend the MS coverage in areas wherethe counting rates are expected to be too high for MDTs to be successful. Each chamber consists ofparallel plates instrumented with metallic strips in orthogonal directions. The 5.0-mm gap betweenthe plates is filled with an Ar–CO2 gas mixture at {80%, 20%}. Anode wires having a diameter of30 µm, made of gold-plated tungsten with 3% rhenium, are placed mid-way between the plates atintervals of 2.5 mm and operated at a voltage of 1900 V. Electron avalanches at the wires followingby the passage of charged particles induce signals in the strips on both sides of the CSC.The precision coordinate η is measured using the strips perpendicular to the wires, with a hitresolution of 60 µm, and a coarser φ measurement is provided by the wider strips parallel to thewires, with a hit resolution of about 5 mm. The CSC wire signals are not read out.4.5.4 Resistive Plate ChambersThe RPCs have two objectives: first and foremost, to provide triggering capability in the Barrel ofthe MS, and second to complement the MDT chambers by measuring the non-precision coordinateφ of muon tracks. Trigger chambers must be as fast as possible, yet be able to recognize themultiplicity of tracks and perform a coarse measurement of their momentum.An RPC consists of two units of two rectangular gaseous parallel electrode-plate detectors, asillustrated in Figure 4.17. In each of these detectors, two resistive plates made of plastic laminateare separated by a 2-mm gap created with insulating spacers placed every 100 mm. The gap is filledwith C2H2F4–Isobutane–SF6 at {94.7%, 5%, 0.3%}. The chambers are operated at a voltage of9.8 kV, creating an electric field of 4.9 kV/mm: with such a high field, ionizing charged particlespassing through the gap instantaneously cause an avalanche of electrons which drift towards theanode plate in only a few nanoseconds. By capacitive coupling, this causes a signal on both sidesof the gap, and this signal is read out by metallic strips placed in 23–35 mm intervals on the otherside of the resistive plates. The strips are oriented to read out the η coordinate on one side and theφ coordinate on the other.In this way, a charged particle going through an RPC is measured twice in both η and φ , unlessit crosses in the 65-mm overlap region between units, in which case four measurements are availablefor each coordinate. The rate of accidental triggers is reduced by requiring independent coincidencesin both the η and φ coordinates, within and between RPCs.51Figure 4.17: Cross-section of an RPC, where two units are joined to form a chamber. Thedimensions are given in mm [12].4.5.5 Thin Gap ChambersA trigger detector with higher granularity is needed in the Endcaps, because of the higher radiationlevels and the presence of inhomogeneities in the magnetic field in the transition region. TGCs wereadopted as the solution in this case: they are multi-wire proportional chambers with a 2.8-mm gapfilled with a gas mixture of CO2–n-pentane at {55%, 45%}, providing a gain of 3×105. Gold-platedtungsten wires are placed every 1.8 mm, and are operated at a voltage of 2900 V.The wires are read out to obtain a measurement of η , while copper strips perpendicular to thewires provide measurements of φ . As a result of the use of a highly-quenching gas combined with asmall wire separation, the time resolution of a TGC is smaller than 25 ns for 99% of tracks, enablingthese detectors to act as trigger chambers.The TGCs are arranged in units of two or three chambers, and make use of coincidence algo-rithms like the RPCs. Because n-pentane is highly flammable, each TGC unit is surrounded by a gasenvelope with circulating CO2, which is monitored. The gas supplies and voltage are automaticallyswitched off if traces of n-pentane are found in the envelope, indicating the presence of a leak.4.5.6 Layout of the Muon SpectrometerThe layout in the transverse plane of the MS Barrel chambers is illustrated in Figure 4.18. Thechambers are placed in three concentric cylindrical layers, called “stations”, each with eight largeand eight small chambers matching the arrangement of the toroid magnets. The alternating large52and small sets of chambers are numbered as “sectors”, starting from sector 1 centred on the x-axis atφ = 0, with sector numbers increasing with φ . Thus sector 5 corresponds to the top of the detector,and sector 13 to the bottom. Air is utilized as the medium between the stations, for economicalreasons but also to minimize the amount of material traversed by the muons in the MS, and therebyreduce multiple-scattering effects.The MDT standard chambers are named based on their location and features: the detector region(Barrel or Endcap) is indicated first, followed by the station (Inner, Middle or Outer) and finally thesize (Large or Small). These names are often abbreviated as the corresponding three-letter acronyms(two-letter acronyms when the size is not specified). Exceptions to the above are necessary toaccommodate the supporting feet of the detector:• In sectors 11 and 15, the BIL chambers are replaced with two chambers named BIR and BIM;• In sectors 12 and 14, the BMS chambers are replaced with chambers named BMF, and theBOS chambers are replaced with two chambers named BOF and BOG.These special MDT chambers have proportions designed to match the geometry of the additionalsupporting material in this region.Because the toroid magnetic field bends the trajectories of muons in the longitudinal direction,it is crucial for the MS to precisely measure the η coordinate of hits: therefore, the orientation of allMDT chambers is such that the tubes are oriented in the φ direction. The Middle and Outer MDTchambers cover the range |η |< 2.7; on the other hand, the Inner MDT chambers cover |η |< 2.0,with the CSC providing coverage for 2.0 < |η |< 2.7.The RPCs are located on each side of the BM MDT chambers, on the outside of the BOLchambers and on the inside of the BOS chambers. One TGC double-layer is present on the insideof the EI chambers, one triple-layer is on the inside of the EM chambers, and two double-layersare on the outside of the EM chambers. The RPCs and TGCs thus provide triggering capabilityand φ track coordinate measurements for |η |< 1.05 and 1.05 < |η |< 2.4, respectively. Whereverpossible, trigger chambers are installed even where there is no space for MDT chambers, in orderto maximize the trigger acceptance.Figure 4.19 shows a longitudinal view of large and small standard MS sectors, namely sectors3 and 4 respectively: this allows to see the arrangement of both the Barrel and Endcap chambers.In addition to the EI, EM and EO chambers, two extra sets of MDT chambers are present:• The Endcap Extra (EE) chambers provide additional coverage in the η range between theBarrel and the edge of the EO chambers;• The Barrel Endcap Extra (BEE) chambers, situated around the Endcap toroid magnetcryostats, provide additional coverage in the region where the magnetic field integral changessign as shown in Figure 4.15.53Figure 4.18: Transverse view of Muon Spectrometer Barrel chambers, with the sector num-bering convention [12].Within given sectors, the MDT chambers are subdivided into “towers” defined projectively in the ηcoordinate. There are six well-defined towers in the Barrel, while in the Endcaps the arrangement ismore complicated, as illustrated in Figure 4.19. Further, unlike the EIL chambers, the EIS chamberscan only begin at |η | = 1.25 because of the Barrel toroid magnets; two additional BIS chambers,named BIS7 and BIS8, are therefore placed in compensation. The BEE and BIS8 chambers are eachmade of a single multi-layer of drift tubes, instead of the usual double multi-layer.The holes in coverage between the large MDT chambers near |η | = 0 are due to services forthe ID and the calorimeters. Services for the ID also require small holes between BIL chambersnear |η | = 0.64, while calorimeter services also require a small hole between BIL chambers, butonly in sector 13. Larger holes in the coverage of BML and BOL chambers in sector 13 are due tothe necessary elevator shafts at the bottom of the detector. Holes between BMS chambers around|η |= 0, |η |= 0.42 and |η |= 0.75 are needed for elements of the Barrel toroid magnet supportingstructure. Finally, there are no central EEL chambers in sector 5 to make room for pumps neededby the Endcap toroid magnets [47].54In addition to the internal optical alignment system present in each MDT chamber, a globalalignment system is necessary to monitor the position of each tube, in order to achieve a positionresolution of 30 µm. The BI, BM and BO chambers are connected to their neighbours using align-ment sensors, and between stations by projective optical lines corresponding to fixed values of η .Additional lines connect MDT chambers to the Barrel toroid magnets to provide a reference. In theEndcaps, the alignment is performed in two steps: optical lines corresponding to fixed values of θlink reference high-precision rulers together, and the EI, EE, EM, EO and CSC chambers are op-tically connected to these rulers and to neighbouring chambers. Unfortunately, the BEE, BIS7 andBIS8 chambers could not be linked to this global alignment system: this fact is taken into accountin the selection criteria for muons at very high momentum in Section 5.3.An important complement to the optical alignment system is the use of track-based alignmentalgorithms. In particular, straight tracks recorded from collision data taken with the magnetic fieldturned off provide key information allowing to further improve the alignment of the MS. Suchtrack-based algorithms are described in more detail in Section 5.2.There is one way in which the MS layout in Run-I differs from the nominal design describedabove: most of the EE chambers could not be installed in time. Before 2011, they were onlyinstalled in sectors 5 and 13 for both Endcaps, sector 11 for η > 0 and sector 15 for η < 0, and werenot linked to the alignment system. Figure 4.20 shows the number of detector stations traversedby muons in the MS as a function of η and φ : the effect of the EE chambers’ absence is seen bycomparing the graph for data collected in 2011 to the design layout.During the winter shutdown between 2011 and 2012, all the EE chambers for η < 0 were in-stalled, as well as the ones in sector 3 for η > 0, and the installed EE chambers were fully integratedinto to the alignment system. The installation of the remaining EE chambers was completed in thespring of 2013, for operation in Run-II.55Figure 4.19: Layout of large (top) and small (bottom) standard sectors of the MuonSpectrometer, specifically sectors 3 and 4 for η ≥ 0. Straight lines are drawn in in-crements of 0.1 in the η coordinate. Figure credit: F. Bauer.56Figure 4.20: Number of detector stations traversed by muons in the MS as a function of ηand φ as of March 2011 (top) compared with the design layout (bottom). Figure credit:A. Ouraou.574.6 Missing Transverse MomentumThe presence of particles which do not interact with any of the detector components can be inferredusing the vectorial sum of the transverse momentum measured by all the detector measurements.Among particles from the Standard Model, only neutrino production can cause real missing trans-verse momentum. On the other hand, many hypotheses beyond the Standard Model predict newparticles that cannot be detected directly. Conservation of momentum in the directions transverseto the beam axis implies that the overall transverse momentum vectorial sum from the objects de-tected after a collision would be zero in the absence of undetectable particles or mis-measurements.The same cannot be said from the longitudinal component of the sum, because the colliding partonshave different momenta along the beam axis.Missing transverse momentum is therefore defined as a 2D vector [21, 22, 28]. The magnitudeof this vector is commonly called missing transverse energy (EmissT ), and by an abuse of notationthis symbol is also used for its components:Emissi = Emiss,ei +Emiss,γi +Emiss,τi +Emiss,jetsi +Emiss,µi +Emiss,softi (4.1)with i ∈ {x,y}, where each term of the sum is the negative momentum sum over the calibratedreconstructed objects indicated:Emiss,αi =−∑ pαi (4.2)The order of the terms in Equation 4.1 reflects the priority with which calorimeter energy de-posits are associated to objects: electrons first, then photons, hadronic τ-lepton decays, jets withpT > 20 GeV and finally muons. The soft term comprises the calorimeter deposits from jets withpT < 20 GeV and from unassociated clusters with significant signal. In addition to calorimeterdeposits, the momentum of muon candidates entering the MS is also taken into account in themuon term, and the momentum of tracks with low pT detected by the ID but missed by the calorime-ters is included in the soft term.4.7 Luminosity MonitoringA measure of the number Ntot of collisions having happened inside the detector during a certainperiod of time is called the integrated luminosity Lint, defined as the integral of the instantaneousluminosity L:Lint =∫L dt =Ntotσtot(4.3)where σtot is the total inelastic proton-proton collision cross section, shown in Figure 2.7. Theprogression of the integrated luminosity during Run-I of the LHC was shown in Figure 4.5.Many experimental techniques are used to evaluate this quantity [27]. The main technique used58for calibrating the luminosity measurements outlined below is the van der Meer scan [165], whichmeasures the horizontal and vertical beam widths Σx and Σy allowing to calculate L usingL =nb frn1n22piΣxΣy(4.4)where nb is the number of proton bunches crossing at the interaction point, fr is the revolutionfrequency, and n1 and n2 are the numbers of particles in the colliding bunches.Then, it is possible to estimate the luminosity by counting the number Nevt of collision eventsdetected. These event-counting methods are calibrated during van der Meer scans, and can then beused during regular collision data collection to estimate the integrated luminosity. The detection oftracks in the ID and of energy clusters in the calorimeters are used for this purpose, in addition tothe information from dedicated detectors:• The Beam Condition Monitor, consisting of diamond sensors located near the beam pipe at|η |= 4.2 and z = 184 cm on each side of the interaction point, whose principal function is toprotect the detector by providing a fast abort signal in the event of large beam losses;• The Minimum Bias Trigger Scintillators, located at 2.09 < |η |< 3.84 and used to trigger asample of events with minimal collision activity;• The LUCID detector, covering 5.6 < |η |< 6.0, which detects Cherenkov photons producedwhen charged particles from collisions traverse its aluminium tubes filled with C4F10 gas;• The Zero Degree Calorimeter, designed to detect very forward neutral particles at |η |> 8.3using tungsten absorbers with embedded quartz rods read out by photomultiplier tubes.As an alternative to van der Meer scans, the ALFA detector, located about 240 m from the ATLASinteraction point, uses scintillators to measure elastic proton-proton scattering rates, which can alsoin principle calibrate the luminosity measurements. The placement of the LUCID, Zero DegreeCalorimeter and ALFA detectors along the LHC beam line around the ATLAS interaction point isshown in Figure 4.4.From the number of events detected, it is possible to obtain the average number λ of simulta-neous proton-proton interactions per bunch crossing. Using Poisson statistics, the probability for atleast one interaction to occur during a given bunch crossing isNevtNBC= 1− e−λ (4.5)and thereforeλ =− ln(1−NevtNBC)(4.6)59where NBC is the total number of bunch crossings having happened during the time Nevt was mea-sured. It follows that the instantaneous luminosity isL =λnb frσvis(4.7)where the visible cross section σvis is the quantity calibrated during van der Meer scans by compar-ing this result to the value measured using Equation 4.4.In practice, the formalism is more involved, taking into account bunch-by-bunch differences ininstantaneous luminosity and corrections due to pileup in the detector. As well, coincidence algo-rithms are used in addition to the simple counting algorithms described above in order to evaluatethe impact of non-collision backgrounds. The total integrated luminosity was calculated to a preci-sion of 1.8% for data collected in 2011 [27], and the corresponding preliminary uncertainty valuefor data collected in 2012 is 3.6%.It is also possible to convert the measured rates for the production of W and Z bosons into ameasure of the integrated luminosity using the theoretical cross section for these processes. Whilethis last technique is not used in general, in order to retain the possibility to carry out W and Z bosonproduction cross section measurements at ATLAS, it is effectively used in the search presented inthis dissertation, which normalizes the total background prediction to the measured event yields onthe Z peak. This is further explained in Sections 6.2.1 and 7.1.4.8 Trigger, Data Acquisition and Data Quality4.8.1 TriggerAs is readily seen from Figure 2.7 in Section 2.2.2, the different production cross sections at theLHC span many orders of magnitude, with processes involving b-quarks ranking factors 100 to 1000smaller than the total cross section, electroweak boson production another factor 104 smaller andHiggs boson production yet another factor 103 to 105 smaller. Processes beyond the Standard Modelare also expected to have very small rates compared to the total proton-proton inelastic cross section.In parallel, the available data collection bandwidth and storage capacity of ATLAS is significantlysmaller than the enormous event rate. A reliable and efficient trigger system is therefore crucial tothe success of the experiment, in order to select the collision data that contains physical processesof interest among very large backgrounds.ATLAS makes use of a dedicated trigger system that consists of three layers, respectively calledLevel-1, Level-2 and the Event Filter. The Level-1 trigger is a hardware-based trigger, which selectscollision events of interest based on features readily available during early reconstruction. Specifi-cally, it uses information from the trigger chambers of the MS and reduced-granularity informationfrom all the calorimeters to look for high-pT muons, electrons, photons, hadronic τ-lepton decays60and jets, as well as large EmissT . This first step, with an allocated decision time of 2.5 µs, alreadymakes possible a strong reduction of the event rate from 20 MHz (for a proton bunch time separationof 50 ns) to O(100 kHz).For each event selected by the Level-1 trigger, one or more “regions of interest” are defined,with information about the preliminary angular coordinates of interesting objects and the Level-1threshold passed. This information is passed to the two higher trigger levels, which use softwarealgorithms in order to determine which of these events are to be recorded for offline processing. TheLevel-2 trigger fully reconstructs all the event data from the region of interest identified at Level-1,which represents approximately 2% of the total event data, with an average event processing timeof 40 ms to further reduce the event rate to about 5 kHz. Then the Event Filter reconstructs thecomplete event in an average time of 4 seconds, finally reducing the rate to 400 Hz, including a5-Hz random trigger rate. Considering an average of about 20 interactions per crossing at 20 MHzin 2012, this means that out of all the proton-proton collisions observed by the ATLAS detector,only one out of a million is stored for analysis.In fact, some interesting physical processes have cross sections that are too large to allow thestorage all the produced events. This implies that the corresponding triggers have to be prescaled,meaning that only one in a number of events passing the triggers are kept. For example, in Run-I,events with a J/ψ meson quickly became too numerous to allow keeping them all; for Run-IIthis situation is even foreseen to affect W → `ν production. Nevertheless, in order to maximizethe signal sensitivity to new, rare physical processes, searches strive to make use of un-prescaledtriggers whenever possible.4.8.2 Data AcquisitionEach detector channel in ATLAS is linked to front-end electronics, which perform signal digitizationand provide buffers long enough to make possible the operation of the Level-1 trigger. Followingthe Level-1 decision, the selected events are stored in other buffers until they are transferred viareadout drivers to the Data Acquisition (DAQ) system, where the Level-2 and Event Filter triggeralgorithms are run and monitored.The DAQ system is configured for every data-taking period, or “run”, with a specific triggermenu corresponding to the objectives of the run. Each run is further subdivided into 1- or 2-minuteintervals called “luminosity blocks”: this segmentation allows the DAQ system to control the data-taking conditions without having to re-start the run, which would involve data losses.A hardware monitoring system called the Detector Control System (DCS) ensures that any ab-normal behaviour in the detector is reported to operators: automatic or manual corrective actions arethen taken. Example quantities monitored by the DCS include temperature, humidity, gas concen-tration and pressure values, magnetic field, voltage, etc. The DCS also handles the communicationbetween ATLAS subsystems, as well as between ATLAS and external systems at CERN.614.8.3 Data QualitySimilar to the fact that only a fraction of the collisions delivered to ATLAS are recorded by thedetector, only a fraction of the recorded collision events are suitable for use in analyses. As shownin Figure 4.5, this fraction is high: in 2011, 4.57 fb−1 out of 5.08 fb−1 (90.0%) of the recordedcollision data passing all quality requirements; for 2012 this proportion is even higher at 20.3 fb−1out of 21.3 fb−1 (95.3%).The quality of the data is first verified as it is being recorded: this is called “online monitoring”.A subset of the recorded events, called the Express Stream, is drawn and reconstructed in real-time.Many data quality verifications are performed automatically. In addition, data quality shifters in theATLAS Control Room manually monitor a series of histograms corresponding to a wide variety ofglobal quantities essential for the successful operation of the detector. For example, it is necessary toverify the synchronization of all detector subsystems with each other, as well as distributions of thenumber of hits observed in each subsystem, detector occupancy maps, magnetic field measurements,correlations between the parameters of the tracks observed in both the ID and the MS, etc.Physical objects are also monitored: electron, muon, and τ lepton candidates, as well as hadronsand missing transverse momentum. It is even possible to reconstruct J/ψ and ϒ mesons fromevents with pairs of opposite-sign muon candidates, and W and Z bosons in the electron and muonchannels, immediately as these objects are detected by ATLAS. Since the successful observation ofthese objects relies on the good performance of all detector subsystems, monitoring their observationrates as data are collected is an effective way to become aware of new detector problems as theyoccur. Indeed, online data quality monitoring shifters are often the first to identify such problems;this information is then transmitted to the shifters dedicated to the relevant subsystems.My main contributions to the ATLAS data collection were made in the context of this frame-work, by developing monitoring histograms and automatic algorithms, maintaining the softwarepackages and helping to define the instructions for data quality shifters in the ATLAS Control Room.Additional data quality verifications, called “offline monitoring”, are performed after the com-plete reconstruction of the data. They involve essentially the same quantities as in the case of onlinemonitoring, in addition to any validation which requires high statistics from complete runs. Whendetector problems are found, this information is stored in the data quality database [109], indicatingwhich luminosity blocks may not be used for certain purposes.The determination of the dataset suitable for analysis is finalized when dedicated lists of goodluminosity blocks are prepared from the data quality database, catering to the specific needs of thedifferent analysis categories. For instance, the search for new neutral resonances decaying intomuon pairs presented in this dissertation requires good data quality from the ID and from the MS.On the other hand, this analysis is insensitive to a number of data quality problems occurring in thecalorimeters, and thus benefits from a slightly higher integrated luminosity compared to analysesfor which all data quality requirements are necessary.62Chapter 5Muons at Very High Momentum inATLASIn order to successfully reconstruct an eventual resonant peak at dimuon invariant masses above theZ peak, while preventing a potential contamination of the signal region by false high-momentumtracks originating from mis-reconstruction, a detailed experimental understanding of muons at veryhigh momentum is absolutely necessary. Only the muon candidates traversing the regions of AT-LAS offering the best momentum resolution can be selected. Section 5.1 gives an overview of thedifferent types of muon objects reconstructed in ATLAS, and Section 5.2 details the performance ofthe type of muon candidates used in this search.The last section explains the exact muon candidate selection used in this analysis. Its firstpart, Section 5.3.1, concerns muon candidates with segments from all three stations of the MuonSpectrometer (MS), called “3-station muons” for short: these are the best-reconstructed muon tracksin ATLAS. The muon momentum measurement is derived from the curvature of the track, which for3-station muons is obtained from the sagitta, that is the distance between the middle track segmentand a straight line linking the inner and outer segments in the MS. The calculation of the sagitta isillustrated in Figure 5.1.While for this analysis the primary concern is to ensure that all selected muon tracks are well-measured, it is also very important to maximize the signal acceptance of the search, defined as thenumber of selected signal events over the total number present in the collision dataset. In orderto increase the signal acceptance in this analysis, the best muon candidates with two MS tracksegments are also considered: these are called “2-station muons”. In this case the track curvature ismeasured using the angular difference between the two measured segments. Dedicated studies arenecessary in order to ensure that the resolution of the selected 2-station muons is sufficient for usein this search: these studies are detailed in Section 5.3.2.63Figure 5.1: Determination of the sagitta based on the location of segments in the Muon Spec-trometer. Figure credit: P.-F. Giraud.5.1 Muon Reconstruction in ATLASFour different types of muon candidates are reconstructed from the raw ATLAS data, according tothe information available in the different subsystems [13, 32, 35]. The main information consists ofthe charged particle track measurements, performed independently in the ID and the MS. In the ID,the measurement comes from a fit to hits detected in the Pixel, SCT and TRT detectors.In the MS, the hits from the chambers in individual stations are first used to form track segments,which are then combined to form a track. These MS tracks extrapolated to the primary vertex ofthe event are called standalone muons. Energy depositions in the calorimeters are also taken intoaccount when extrapolating the tracks measured in the MS to the primary vertex of the event, byadding the energy losses of the muon candidate to the measurement from the MS. The methodsused to estimate these energy losses are explained in detail in Ref. [139].Combined muons are the best-measured muon candidates from the detector. They are formedwhen a standalone muon track is successfully matched to a track in the ID. This is only possiblewithin the acceptance of the ID, that is for detector |η | < 2.5, while only standalone muons areavailable in the range 2.5 < |η |< 2.7. During Run-I of the LHC, two independent algorithms havebeen used to reconstruct combined muons. One of them, named “Staco” or “chain 1”, performsa statistical combination of the standalone and ID muon track parameters using the covariancematrices of the track parameter measurements from each subsystem. The other, named “Muid”or “chain 2”, obtains combined muons by performing a global refit from the hits measured in boththe ID and the MS. This analysis makes use of the Muid algorithm.The last two types of muon objects, segment-tagged muons and calorimeter-tagged muons, areuseful in analyses prioritizing muon acceptance. In both cases the expected muon momentum hasto be small enough for the measurement from the ID to be reliable, as no momentum measurementis available from the MS. Segment-tagged muons consist of tracks measured in the ID that are64matched to single track segments in the MS. They can be used to recover muons in a few areasbetween the Barrel and Endcaps of the detector (1.1 < |η | < 1.3), where only one MS station isinstalled. Finally, services for the ID and the calorimeters pass in the most central region of thedetector for |η | < 0.1, implying the existence of multiple areas where no MS chamber could beinstalled. Calorimeter-tagged muons, consisting of ID tracks matched to energy depositions in thecalorimeter where these depositions are consistent with the ones expected from a minimum-ionizingparticle, can be used to recover acceptance in this region.5.2 High-Momentum Muon PerformanceIn this analysis, the muons at very high momentum expected from high-mass resonances requireprecise momentum measurements from the detector, and while signal acceptance is also very im-portant, it comes as a secondary concern. Only combined muons are therefore selected in thissearch.The momentum of muons is measured using the curvature of their tracks caused by the solenoidmagnetic field in the ID and the toroid magnetic field in the MS. Since this curvature is inverselyproportional to the muon momentum, the tracks of muons at very high momentum are very straight,and the uncertainty on the momentum measurement is dominated by the intrinsic resolution andalignment of the Muon Spectrometer. Specifically, this uncertainty can be parametrized as follows:σ(pT)pT=P0pT⊕P1⊕P2 · pT (5.1)where P0 is the resolution parameter related to energy loss fluctuations, P1 is related to multiplescattering, and P2 is related to the alignment and intrinsic resolution. Figure 5.2 illustrates thesedifferent contributions to the muon momentum resolution as a function of muon pT, as documentedat the time of the Muon Spectrometer Technical Design Report [11]. The design resolution at veryhigh momentum is σ(pT)/pT = 10%/ TeV. Given the intrinsic resolution described in Section 4.5,achieving this resolution for 3-station muons requires an alignment with sagitta bias lower than40 µm [107].Later estimates for the resolution parameters, which are used in simulated samples for the anal-yses at√s = 7 TeV and√s = 8 TeV, are respectively shown in Tables 5.1 and 5.2. They are deter-mined from the known geometry of the ATLAS detector including the distribution of material, thenumber of hits on each track and the intrinsic hit resolution, as well as magnetic field integrals andthe expected resolution of the detector as determined from the optical alignment system wheneverpossible. Most resolution parameters are taken to be constant in regions of η . The exception is thePID2 term for 2.0 < |η | < 2.5: since the TRT coverage ends at |η | = 2.0, the PID2 term, which isdependent on the muon track length in the detector active material, is proportional to sinh2η in thisregion.65Table 5.1: Muon pT resolution parameters for simulated samples generated in 2011 at√s = 7 TeV.Region PID1 [%] PID2 [TeV−1] PMS1 [%] PMS2 [TeV−1]|η |< 1.05 1.61 0.31 2.68 0.101.05 < |η |< 1.7 2.59 0.33 4.52 0.191.7 < |η |< 2.0 3.39 0.44 3.12 0.082.0 < |η |< 2.5 5.12 0.042sinh2η 2.64 0.05Table 5.2: Muon pT resolution parameters for simulated samples generated in 2012 at√s = 8 TeV.Region PID1 [%] PID2 [TeV−1] PMS1 [%] PMS2 [TeV−1]−2.50 < η <−2.25 4.88 0.0523sinh2η 3.09 0.208−2.25 < η <−2.00 4.88 0.0523sinh2η 3.09 0.208−2.00 < η <−1.70 3.30 0.447 3.44 0.208−1.70 < η <−1.50 2.50 0.322 4.77 0.287−1.50 < η <−1.05 2.50 0.322 4.77 0.287−1.05 < η <−0.80 1.58 0.299 3.25 0.188−0.80 < η <−0.40 1.58 0.299 3.25 0.188−0.40 < η < 0.00 1.58 0.299 3.25 0.1880.00 < η < 0.40 1.58 0.299 3.25 0.1880.40 < η < 0.80 1.58 0.299 3.25 0.1880.80 < η < 1.05 1.58 0.299 3.25 0.1881.05 < η < 1.50 2.59 0.316 5.25 0.3231.50 < η < 1.70 2.59 0.316 5.25 0.3231.70 < η < 2.00 3.28 0.450 3.60 0.1852.00 < η < 2.25 4.85 0.0516sinh2η 3.02 0.2192.25 < η < 2.50 4.85 0.0516sinh2η 3.02 0.21966Figure 5.2: Design resolution of the ATLAS Muon Spectrometer as a function of muon trans-verse momentum, for |η |< 1.5 (left) and |η |> 1.5 (right) [11].Measurements of the resolution of the detector are performed in situ using fits to the invariantmass peaks from J/ψ → µ+µ− and Z → µ+µ− candidate events. Such measurements mainlyconstrain the P0 and P1 terms from Equation 5.1. Additional constraints on P2 are obtained usingstraight tracks from collision data recorded in runs with the magnetic field turned off. In particular,sagitta measurements from these straight tracks indicate the sagitta bias of each MS tower. Themeasured sagitta bias values are found to be within the design resolution for many towers, andwithin 100 µm for almost all towers in the Barrel and Endcap, except in the CSC region1 wherebiases of up to 250 µm are observed [107].Muon tracks traversing overlapping sets of chambers in the MS are also used to quantify residualmis-alignments, by comparing the track segments measured by individual chambers in each station.The independent momentum measurements from the overlapping towers can also be compared di-rectly, by fitting the muon track once with the hits in the small sector only, and once with the hitsin the large sector only. The quantity (q/pT)small− (q/pT)large is then a measure of the momentumbias.The event with the highest dimuon invariant mass recorded in 2011, displayed in Figure 5.3,includes an excellent example of a muon candidate passing through overlapping MS chambers. It isalso worth noticing that the other muon candidate in the event passes the 2-station muon selection.The resolution performance of 2-station muons at very high momentum is described in more detailin Section 5.3.2.1 Recent updates to the MS alignment realized after the analyses presented here were completed have improved theresolution in all towers including in the CSC region, where the sagitta bias values are now within 80 µm.67Figure 5.3: Event with the highest dimuon invariant mass observed in data collected at√s= 7 TeV by the ATLAS experiment. Thetwo muon candidates have transverse momenta of 648 GeV and 583 GeV respectively, and the dimuon invariant mass is 1.25 TeV.The muon candidate in the upper half of the detector is a 2-station muon, and the other muon track passes through overlappingchambers in the MS.68To address differences between the resolution parameters observed in data with respect to thevalues used in simulations, corrections are applied to the transverse momentum pT of each simulatedmuon. This correction, applied independently in the ID and the MS, takes the form of a Gaussiansmearing of the quantity q/pT:δ (q/pT) = S1 ·g1 · (q/pT)+S2 ·g2 (5.2)where g1 and g2 are random Gaussian variables with zero mean and unit standard deviation, and S1and S2 are smearing constants. These smearing constants are determined as a function of pseudora-pidity by taking the differences in quadrature between the resolution parameters from data and theMonte Carlo simulations:Si =Pi,data	Pi,MC if Pi,data > Pi,MC0 otherwise(5.3)The correction to the combined q/pT is then the weighted average of the individual corrections inthe ID and MS:δ (q/pT)CB =1σ−2ID +σ−2MS·(δ (q/pT)IDσ2ID·pT,IDpT,CB+δ (q/pT)MSσ2MS·pT,MSpT,CB)(5.4)where pT,det are the un-smeared transverse momentum values, and σdet = σ(pT,det) are the expectedresolutions of the two subsystems calculated using Equation 5.1.The smearing constant values used are shown in Table 5.3 for analyses at√s = 7 TeV, and inTable 5.4 for analyses at√s = 8 TeV. For the latter, the nominal values of the smearing constantsSID1 and SMS2 are set to zero because the resolution parameters used in data turned out to be slightlybetter than the ones used in the simulation. Upper bounds on these parameters are still consideredwhen propagating systematic uncertainties to the analysis results [32].Table 5.3: Muon momentum smearing constants used in analyses at√s = 7 TeV. The effectof SID1 is neglected.Region SID2 [TeV−1] SMS1 [%] SMS2 [TeV−1]|η |< 1.05 0.19 ± 0.01 1.95 ± 0.04 0.10 ± 0.021.05 < |η |< 1.7 0.24 ± 0.03 3.97 ± 0.13 0.47 ± 0.021.7 < |η |< 2.0 0.50 ± 0.02 2.88 ± 0.14 0.20 ± 0.012.0 < |η |< 2.5 (0.015±0.004)sinh2η 1.82 ± 0.20 0.15 ± 0.0569Table 5.4: Muon momentum smearing constants used in analyses at√s = 8 TeV.Region SID1 [%] SID2 [TeV−1] SMS1 [%] SMS2 [TeV−1]−2.50 < η <−2.25 0.00 +0.49−0.00 (0.0073±0.0086)sinh2η 1.59±0.17 0.00 +0.16−0.00−2.25 < η <−2.00 0.00 +0.49−0.00 (0.0289±0.0041)sinh2η 1.57±0.13 0.00 +0.16−0.00−2.00 < η <−1.70 0.00 +0.17−0.00 0.340±0.028 1.64±0.15 0.00+0.16−0.00−1.70 < η <−1.50 0.00 +0.17−0.00 0.310±0.021 2.07±0.08 0.00+0.22−0.00−1.50 < η <−1.05 0.00 +0.13−0.00 0.275±0.016 1.35±0.10 0.00+0.22−0.00−1.05 < η <−0.80 0.00 +0.13−0.00 0.248±0.041 0.34±0.26 0.00+0.14−0.00−0.80 < η <−0.40 0.00 +0.08−0.00 0.206±0.019 0.30±0.11 0.00+0.14−0.00−0.40 < η < 0.00 0.00 +0.08−0.00 0.229±0.013 0.98±0.11 0.00+0.14−0.000.00 < η < 0.40 0.00 +0.08−0.00 0.208±0.016 1.03±0.10 0.00+0.14−0.000.40 < η < 0.80 0.00 +0.08−0.00 0.203±0.016 0.11+0.48−0.11 0.00+0.14−0.000.80 < η < 1.05 0.00 +0.13−0.00 0.237±0.007 0.53±0.11 0.00+0.14−0.001.05 < η < 1.50 0.00 +0.13−0.00 0.269±0.014 0.83±0.15 0.00+0.24−0.001.50 < η < 1.70 0.00 +0.17−0.00 0.284±0.023 2.15±0.16 0.00+0.24−0.001.70 < η < 2.00 0.00 +0.17−0.00 0.378±0.010 1.53±0.09 0.00+0.14−0.002.00 < η < 2.25 0.00 +0.49−0.00 (0.0310±0.0057)sinh2η 1.46±0.14 0.00 +0.17−0.002.25 < η < 2.50 0.00 +0.49−0.00 (0.0050±0.0028)sinh2η 1.22±0.21 0.00 +0.17−0.00The muon momentum scale is also constrained by the fit to the Z → µ+µ− mass peak. Asshown in Figure 5.4 for data collected at and√s = 8 TeV, these corrections are under 0.3% for allsimulated muons [32]. Corrections applied in for data at√s = 7 TeV are of the same order.The effect of the corrections to the muon momentum scale and resolution on the Z peak areshown in Figure 5.5. Figure 5.6 shows the impact of the corrections derived from data at√s = 7 TeVon a simulated Z′SSM resonant peak with a pole mass of 2.25 TeV, and on the steeply falling back-ground estimate in this region.The efficiency of the ATLAS detector for reconstructing muons is measured using a sample ofZ → µ+µ− events satisfying the requirement |mµ+µ− −MZ| < 10 GeV, with both muons havingpT > 20 GeV. The technique used is called “tag-and-probe”: one of the muon candidates, called the“tag”, is required to be a combined muon, while the requirements on the other muon track, calledthe “probe”, are looser. When measuring the reconstruction efficiency in the ID, the probe muon70is required to be a standalone muon, while ID tracks or calorimeter-tagged muons can be used asprobes when measuring the efficiency in the MS.The reconstruction efficiency in each detector subsystem then corresponds to the proportion ofprobes matching a second combined muon in the event. Finally, the efficiency for reconstructingcombined muons is the product of the track reconstruction efficiency in the ID with the MS re-construction efficiency given the presence of an ID track. Figure 5.7 shows the combined muonefficiency as a function of pseudorapidity, for data collected at√s = 8 TeV and a correspondingsimulated Z→ µ+µ− sample. In order to correct the muon efficiency in simulated samples to thevalues observed in data, event-by-event scale factors are applied for each simulated muon.Trigger efficiency is also estimated using a tag-and-probe technique, but here the measuredquantity is the proportion of probes matched to a triggered muon.Figure 5.4: Momentum scale corrections to ID (top) and MS (bottom) tracks derived fromdata collected at√s = 8 TeV [32].71Figure 5.5: Effect of corrections to the muon momentum scale and resolution in the Z peakregion. Data and simulated background are shown at√s = 8 TeV. The histogram on thetop left compares the uncorrected simulation to the data. On the top right, corrections tothe momentum resolution are applied, and corrections to both the scale and resolution areapplied on the bottom histogram. Additional shape differences are due to the emissionof initial-state and final-state radiation which was not fully taken into account in thesimulated events used for these histograms [32].72Figure 5.6: Effect of muon resolution smearing on a Z′SSM resonant peak with a pole mass of2.25 TeV, and on the steeply falling background from Z/γ∗ production.Figure 5.7: Efficiency of the ATLAS detector for reconstructing combined muons as a func-tion of pseudorapidity, for data collected at√s = 8 TeV and a corresponding simulatedZ→ µ+µ− sample [32].735.3 Dedicated Very-High Momentum Muon Selection5.3.1 Selection of 3-Station MuonsTo guard against false high-momentum tracks that could arise from mis-reconstruction, all selectedmuon candidates must pass stringent quality requirements. Combined muons with segments in allthree stations of the Muon Spectrometer constitute the major part of the muons selected in thisanalysis. The requirements on these 3-station muons for the analysis at√s = 8 TeV are as follows:• The measured muon transverse momentum must be above 25 GeV.• To guarantee the quality of the track in the Inner Detector, each muon must pass the followingrequirements on the number of detector hits:– At least one hit in the first layer of the Pixel detector, if such a hit is expected;– At least 1 hit in the Pixel detector, including Pixel dead sensors crossed;– At least 5 hits in the SCT, including SCT dead sensors crossed;– At most 2 Pixel or SCT holes (silicon detector holes are instances where an operationalsensor registers no hit but one is expected from the reconstructed track);– If the muon is within the range 0.1 < |η | < 1.9: require at least 6 TRT hits, includingTRT outliers, with outlier fraction under 90%;– Otherwise if |η | ≤ 0.1 or |η | ≥ 1.9: only if at least 6 TRT hits are observed, includingTRT outliers, require the outlier fraction to be under 90%.• Even more importantly, each muon candidate must pass strict requirements for MuonSpectrometer hits2:– To ensure that the momentum measurement is reliable, each muon track must have:∗ At least 3 hits in each of the BI, BM and BO MDT precision layers, or∗ At least 3 hits in each of the EI, EE and EM MDT precision layers, or∗ At least 3 hits in each of the EI, EM and EO MDT precision layers, or∗ At least 3 hits in each of the EM and EO MDT precision layers, along with at least 2unspoiled CSC hits (unspoiled hits are the ones for which a precise η measurementis available);– As well, no hit is allowed in the MDT chambers not connected to the optical alignmentsystem, namely the BEE, BIS7 and BIS8 chambers.2 using the naming convention for MS chambers explained in Section 4.5.674– For a correct estimate of the magnetic field along the track, it is necessary to require atleast one hit measuring the φ coordinate, in two different layers of the RPC, TGC orCSC.• To ensure that the momentum measurements are consistent between the different detectorsubsystems, for each muon candidate the difference between the standalone momentum mea-surements from the ID and MS must not exceed 5 times the sum in quadrature of the stan-dalone uncertainties from each subsystem.• In order to confirm that each muon candidate comes directly from the collision point, muontracks are required to be close to the primary vertex: within 0.2 mm in the transverse direction(d0) and within 1.0 mm in the longitudinal direction (z0).• The background due to the multi-jet background, discussed in Section 6.2.2, is significantlyreduced by requiring each muon candidate to be isolated: specifically, the sum of the pT ofall tracks with pT > 1 GeV in a cone with radius ∆R = 0.3 around the muon track must notamount to more than 5% of the muon pT.The selection used in 2011 at√s = 7 TeV is in general more restrictive than the one describedabove. First, muon candidates with hits in both the Barrel and one of the Endcaps could not be ac-cepted in 2011, because the track reconstruction software did not take into account potential globalmis-alignments of the Barrel with respect to the Endcaps. Following improvements in the trackreconstruction software, this uncertainty is correctly propagated for the analysis at√s = 8 TeV.The algorithm now operates as follows: it is first determined whether a given muon traverses pre-dominantly Barrel or Endcap chambers of the Muon Spectrometer, based on the number of hits.Then, hits from the corresponding region (Barrel or Endcap) are considered as usual in the track fits,while the error on the position hits from the other region is inflated by±7 mm, corresponding to theglobal alignment uncertainty. In effect, this algorithm therefore discards hits from Endcap chamberswhen reconstructing muons from the Barrel, and similarly discards hits from Barrel chambers whenreconstructing muons from the Endcap.A second, major improvement for the analysis at√s = 8 TeV is the inclusion of muon candi-dates with hits in EE chambers. In 2011, most EE chambers were not installed, and the ones alreadyinstalled had yet to be aligned and commissioned for use in analyses with high-momentum muons:muon tracks passing through these chambers were therefore vetoed by this analysis at the time. Af-ter the installation and alignment of many EE chambers in the winter shutdown between 2011 and2012, use of these chambers was approved following dedicated studies of their resolution.The ID hit requirements are a little tighter for the analysis in 2011: at least 2 Pixel hits arerequired instead of at least 1 (including Pixel dead sensors crossed), and at least 6 SCT hits arerequired instead of at least 5 (including SCT dead sensors crossed). Finally, at least 3 CSC hits intotal are required, instead of at least 2 unspoiled hits.755.3.2 Selection of 2-Station MuonsAdditional gains in acceptance are attained by selecting the best muon candidates which have twotrack segments in the MS instead of three. While for 3-station muons, the main constraint on thetrack curvature comes from the sagitta measurement in the MS, for 2-station muons this informationis unavailable. In this case the momentum measurement in the MS has to come from the angulardifference ∆θseg between the two measured segments, in addition to the magnetic field integral alongthe track. The result of the full track fit can be approximated as:p =K∆θseg∫B ·dl ≡K∆θsegBint (5.5)where K is a constant.For this reason, 2-station muons are expected to exhibit a worse momentum resolution than3-station muons, in addition to being more prone to large mis-measurement in cases where one ofthe MDT chambers is mis-aligned. An example of such a situation is illustrated in Figure 5.8: aposition mis-alignment in one of the MDT chambers can cause the curvature of a track having onlytwo MDT sections to be greatly underestimated, thereby resulting in a fake high-momentum muon.In other words, while for 3-station muons the momentum resolution is dominated by the sagittabias, for 2-station muons the primary cause of resolution degradation is the error on the segmentangle reconstruction in the bending direction.Dedicated studies are therefore carried out to identify which 2-station muons pass through MStowers where the alignment precision is sufficient to guarantee a reliable momentum measurement.This is first attempted in the Barrel for 2-station muons with hits in the BI and BO chambers, asthese muons have the best potential in terms of both acceptance gain and resolution.Study at√s = 7 TeVAs a first step, the angular resolution of segments in data, which by Equation 5.5 is translated intothe momentum resolution of 2-station muons, is quantified in data using 3-station muons in eachindividual MS tower. Figure 5.9 demonstrates that the relationship between q/p and ∆θseg/(KBint)is linear3, justifying this approach.Since the resolution of the momentum measurement using the information from all three stationsis negligible compared to that coming from the segment angular difference, the former is taken asthe reference to which the latter is compared. The momentum resolution of 2-station muons canthen be obtained from the standard deviation of the quantity p · |∆θseg|/(KBint) from neighbouring3-station muons. This is evaluated in each MS tower using Gaussian fits to the distribution. Afteran initial fit over the range [0..2] to initialize values for the mean µ and standard deviation σ , the fit3 The value K = 0.3 is used in this section for presentation purposes; it has no influence on the results.76Figure 5.8: Example of a potential track curvature mis-measurement for a 2-station muonwhere one of the inner MDT chambers is out of alignment. The actual muon path,that would correspond the the measurement using well-aligned BI and BO chambers,is represented with a continuous line. An error δ z in the position alignment of one ofthe chambers can cause the reconstructed track, represented by the dashed line, to bestraighter. Figure credit: P.-F. Giraud.Figure 5.9: Profile histograms demonstrating the linear relationship between q/p and∆θseg/Bint for muon candidates in large (left) and small (right) φ -sectors of the MS.is repeated with a range restricted to ±1.75σ of the previous fit until convergence. The momentumresolution is then given by σ/µ .Most towers have acceptable angular resolution: two typical fit results are shown in Figure 5.10.By contrast, a small number of towers are found where the alignment precision is insufficient for areliable 2-station momentum measurement: examples of these are shown in Figure 5.11.77Figure 5.10: Example fit results for MS towers with good angular resolution in data at√s = 7 TeV, from a large φ -sector (left) and from a small φ -sector (right). These resultsare typical of most towers. The Gaussian fits are for illustration only.Figure 5.11: Example fit results for MS towers with known poor angular resolution in dataat√s = 7 TeV. The Gaussian fits are for illustration only; the distributions are clearlynon-Gaussian, resulting in poor fits. These towers are vetoed in the analysis.78The selected 2-station muons must pass the same selection as described in the previous sectionfor 3-station muons, with the exception that the following criteria for Muon Spectrometer hits arerequired instead:• At least 5 hits in both the BI and BO MDT precision layers;• At least one RPC hit to measure the φ coordinate;• No hit is allowed in the MDT chambers not connected to the optical alignment system, namelythe BEE, BIS7 and BIS8 chambers.• In order to veto the towers with known poor angular resolution, no MDT hit:– in large (i.e. odd-numbered) φ -sectors with |η |> 0.85,– in φ -sector 2 with |η |> 0.85,– or in φ -sector 13 with 0.00 < η < 0.65;In addition to the specific requirements on the η coordinate used to veto muon candidates pass-ing through the vetoed towers, a general requirement of |η |< 1.00 is imposed to make sure to selectmuons from Barrel chambers only. Additionally, the difference between the standalone momentummeasurements from the ID and MS must not exceed 3 times the sum in quadrature of the standaloneuncertainties. This requirement is tighter with respect to that for 3-station muons, because 2-stationmuons rely more heavily on the ID track measurement.With this selection in hand, it is then possible to study the resolution of 2-station muons as afunction of momentum. Figure 5.12 shows fit results for selected 2-station muons from data in themomentum bin 200–300 GeV, taken as an example. The momentum resolution is obtained for eachmomentum bin in the same way as for individual towers. The result is shown for muon candidatesfrom data and simulated muons in Figures 5.13 and 5.14 respectively.The resolution parameters specific to high-momentum 2-station muons PMS∗2,data and PMS∗2,MC are thenderived respectively for data and simulation using fits with the functional form of Equation 5.1.The results are shown in Table 5.5, along with the corresponding smearing parameters given bySMS∗2 = PMS∗2,data	PMS∗2,MC.As a cross-check, another way to obtain the momentum resolution of simulated 2-station muonsis to compare their momentum values as measured by the virtual ATLAS detector to the real values(known as “MC truth”) from the event generator. The resolution is then given by the standard devi-ation of the quantity p/ptruth−1. Figure 5.15 shows the results as a function of momentum. Usinga fit with the same parametrization, the resolution parameter PMS∗2,MC is measured to be 0.41± 0.02for both the large and small φ -sectors, in agreement with the segment angular difference method.In addition to the 2-station muons with hits in the BI and BO chambers studied in this section,accepting additional 2-station muons with hits in the BI and BM chambers or in the BM and BO79Figure 5.12: Fit results for selected 2-station muons from data at√s = 7 TeV from large φ -sectors (left) and from a small φ -sectors (right), in the momentum bin 200–300 GeV.Figure 5.13: Momentum resolution of 2-station muons in data at√s = 7 TeV.chambers was briefly considered. Because for these muons the distance between the two MS stationsis half the distance between the Inner and Outer stations, angular differences are in general onlyhalf as large: as a result the angular resolution of segments fails to provide satisfactory momentumresolution for 2-station muons at very high momentum. Specifically, preliminary values for PMS∗2above 100%/TeV were observed for 2-station muons with hits in the BI and BM chambers or inthe BM and BO chambers. Similar conclusions were reached when considering 2-station muons inthe Endcaps with hits in the EI and EM chambers, in towers where the EE chambers were not yetinstalled.80Figure 5.14: Momentum resolution of 2-station muons in simulation at√s = 7 TeV. Here theresolution of simulated muons is obtained using the same method as for data.Figure 5.15: Momentum resolution of 2-station muons in simulation at√s = 7 TeV from com-paring the refit 2-station momentum to MC truth.81Table 5.5: PMS∗2 parameters measured in data and simulation at√s = 7 TeV and correspondingsmearing parameters SMS∗2 = PMS∗2,data	PMS∗2,MC.Sectors PMS∗2,data [TeV−1] PMS∗2,MC [TeV−1] SMS∗2 [TeV−1]Small 0.55 ± 0.02 0.45 ± 0.02 0.32 ± 0.04Large 0.54 ± 0.02 0.41 ± 0.02 0.35 ± 0.04Table 5.6: PMS∗2 parameters measured in data and simulation at√s = 8 TeV.Sectors PMS∗2,data [TeV−1] PMS∗2,MC [TeV−1]Small 0.46 ± 0.02 0.54 ± 0.02Large 0.42 ± 0.02 0.48 ± 0.02Results of the study at√s = 8 TeVThe same study is repeated for the analysis at√s = 8 TeV. The requirements on 2-station muonsare re-assessed and turn out to be the same as for the dataset collected in 2011, with the exceptionof the requirements on the η coordinate and vetoed chambers. The general requirement on η for2-station muons is relaxed to |η | < 1.05, and following a repetition of the tower-by-tower study,the vetoed chambers are located:• in φ -sectors 4 or 6 with |η |> 0.85,• in φ -sector 9 with 0.20 < |η |< 0.35,• and in φ -sector 13 with 0.00 < η < 0.20.Therefore the alignment of many towers vetoed in the 2011 dataset has improved in the 2012 dataset.The measured resolution parameters for these muon candidates are shown in Table 5.6. Like forthe 3-station muons in this dataset, the simulated resolution parameter PMS∗2 is observed to be betterin data than in simulations, and therefore no additional smearing is applied. Since the differencesin resolution between the simulation and data are small for 3-station muons, of which the selectedsample is mostly composed, the differences in resolution for 2-station muons are not expected toimpact the sensitivity of the search.82Chapter 6Event Selection and Comparison of Datawith Standard Model ExpectationsThis chapter first describes the criteria used to select the events considered in the search, in Sec-tion 6.1. Then, Section 6.2 explains the techniques used to evaluate the backgrounds to the searchand the expected signal contributions from the new physics models under consideration. Finally,Section 6.3 compares the observed data to these predictions.6.1 Event SelectionTo be considered in the search for high-mass resonances decaying to muon pairs, collision eventsare required to pass the following requirements:• Candidate events have to satisfy data-quality requirements, as discussed in Section 4.8.3.• Candidate events must have triggered the detector with at least one of the following single-muon triggers, requiring:– For events collected in 2011 at√s = 7 TeV:∗ At least one combined muon with pT > 22 GeV, or∗ At least one standalone muon in the Barrel with pT > 40 GeV.– For events collected in 2012 at√s = 8 TeV:∗ At least one combined muon with pT > 24 GeV and an isolation requirement(see below), or∗ At least one combined muon with pT > 36 GeV and no isolation requirement.• The primary vertex of the event, defined as the one with the largest ∑ p2T where the sum isover all tracks in the ID with pT > 0.4 GeV, must have at least 3 tracks, and be located within20 cm of the centre of the detector along the beam axis.83• Candidate events must have at least two high-momentum muons passing the selection detailedin Section 5.3.The standalone muon trigger chain is used to recover inefficiencies in the combined muon triggerchains for data collected at√s = 7 TeV. For data collected at√s = 8 TeV, the isolation requirementused in the trigger with a lower pT threshold is that the sum of the pT of all tracks with pT > 1 GeVin a cone with radius ∆R = 0.2 around the muon track must not amount to more than 12% of themuon pT. This requirement at trigger-level is significantly looser than the isolation requirementused in the analysis. Nevertheless, a non-isolated muon trigger chain is used to recover possibleinefficiencies, due to differences between the tracks used in the calculation of the isolation variableat trigger-level as compared with the tracks used for this purpose in the final recorded event.In each candidate event, high-momentum muons are used to build one opposite-sign muon pair.Following the classification explained in Section 5.3, the selected muon candidates can be 3-stationor 2-station muons. First, if two opposite-sign 3-station muon candidates are found, they are usedto make the pair: the pair is then said to pass the “primary dimuon selection”. If not, the paircan be built using one 3-station muon and one 2-station muon, in which case it is said to pass the“secondary dimuon selection”. If more than one pair passing the primary selection is found, the onewith the highest transverse momentum scalar sum is selected; similarly, if the event has no muonpair passing the primary selection but more than one passing the secondary selection, the muon pairwith the highest transverse momentum scalar sum is selected. Finally, events where the electriccharge of all muons is of the same sign are discarded.Figure 6.1 shows the signal acceptance times efficiency for a Z′SSM boson as a function of MZ′ .The values at MZ′ = 2.5 TeV for the analysis on the dataset collected in 2012 are 40.0% for the pri-mary dimuon selection and 3.2% for the secondary dimuon selection; these numbers are respectively36.2% and 2.9% for the analysis using data collected in 2011. The reasons for the improvement be-tween 2011 and 2012 are explained in Section 5.3.Figures 6.2 and 6.3 show the event yield per pb−1 per run for the full event selection describedabove. The yields are fairly constant as a function of time. For the analysis at√s = 7 TeV, twoslight efficiency losses are noticeable, due to the following causes:• A tighter Level-1 muon trigger, necessary to handle a higher instantaneous luminosity, wasused from the start of data period J (run 186516);• A timing problem in the RPC affects the trigger efficiency for runs 189205–189610 in dataperiod L.The observed event with the highest dimuon invariant mass is displayed in Figure 6.4. The eventpasses the primary dimuon selection, with the two 3-station muons having transverse momenta of652 GeV and 646 GeV respectively. The invariant mass of the muon pair is 1.84 TeV.84Figure 6.1: Signal acceptance times efficiency for a Z′SSM boson as a function of MZ′ . The re-gion MZ′ > 3 TeV was not considered for the analysis on the 2011 dataset. The width ofthe lines is representative of the uncertainty.85Run178044179710179771179939180124180149180212180242180448180636180776182284182424182454182486182519182766182879183003183045183079183129183272183391183426183580183780184066184088185353185649185761185976186156186179186216186361186456186532186673186753186877186933187014187453187543187811188921189028189090189242189372189481189536189602189660189751189822189875190046190120190297190608190643190689190933191138191150191218191425191513191635191920Yield [pb]050100150200250300350400B D E F G H I J K L MRun178044179710179771179939180124180149180212180242180448180636180776182284182424182454182486182519182766182879183003183045183079183129183272183391183426183580183780184066184088185353185649185761185976186156186179186216186361186456186532186673186753186877186933187014187453187543187811188921189028189090189242189372189481189536189602189660189751189822189875190046190120190297190608190643190689190933191138191150191218191425191513191635191920Yield [pb]0510152025303540B D E F G H I J K L MFigure 6.2: Yield per pb−1 for each run, for the primary (top) and secondary (bottom) dimuonselection at√s = 7 TeV.86Run200842200926200982201052201138201257201289201555202668202798203027203195203258203336203454203524203636203739203779203876204026204134204240204442204633204763204796204910204955205016205071206368206497206955207044207262207332207490207532207620207749207809207865207934208123208184208261208485208662208720208811208931209024209084209183209265209381209608209736209812209899210302211620211772211902212034212144212272212687212809212967213079213155213250213479213539213684213754213819213964214086214216214494214553214680214758215061215414215464215571Yield [pb]050100150200250300350400A B C D E G H I J LRun200842200926200982201052201138201257201289201555202668202798203027203195203258203336203454203524203636203739203779203876204026204134204240204442204633204763204796204910204955205016205071206368206497206955207044207262207332207490207532207620207749207809207865207934208123208184208261208485208662208720208811208931209024209084209183209265209381209608209736209812209899210302211620211772211902212034212144212272212687212809212967213079213155213250213479213539213684213754213819213964214086214216214494214553214680214758215061215414215464215571Yield [pb]0510152025303540A B C D E G H I J LFigure 6.3: Yield per pb−1 for each run, for the primary (top) and secondary (bottom) dimuonselection at√s = 8 TeV.87Figure 6.4: Event with the highest dimuon invariant mass observed in data collected by the ATLAS experiment in Run-I of the LHC.The muon candidates have transverse momenta of 652 GeV and 646 GeV respectively, and the dimuon invariant mass is 1.84 TeV.886.2 Background and Signal ExpectationThe main background contributions in this analysis are evaluated using simulated samples, de-scribed in Section 6.2.1. Contributions from multi-jet collision events and cosmic rays are evaluatedusing data-driven techniques, and turn out to be negligible: these techniques are described in detailin Section 6.2.2. Section 6.2.3 details how signal templates are obtained.6.2.1 Simulated SamplesAs already mentioned in Section 2.2.2, since protons are not fundamental particles, being madeof quarks and gluons (collectively partons), in a typical proton-proton collision event one partonfrom each incoming proton interacts in the main process of the event. Softer, simultaneous interac-tions constitute the underlying event, while partons that interact minimally with the proton bunchtraveling in the opposite direction are called beam remnants.Figure 6.5: Sketch of a proton-proton collision at high energy. Figure credit: F. Siegert.Figure 6.5 displays a sketch of such a high-energy proton-proton collision event. The event il-lustrated is a fully hadronic process: both the initial and the final states of the main process are con-stituted of quarks and gluons, which along with any emitted strongly coupled radiation undergo par-ton showering, fragmentation and hadronization before reaching the detector. The resulting object89is called a hadronic jet. In comparison, muons are relatively easier to model, because they only emitelectroweak radiation as they traverse the detector. It is nevertheless crucial that event simulationsused to calculate signal and background expectations take into account all of the effects describedabove if they are to describe collision data accurately.Event yield predictions using Monte Carlo simulationsConsidering an hypothesis H in a region of phase space, the expected number of collision eventsselected by the analysis is given byµ = Lint ∑i∈H(σBAε)i (6.1)where Lint is the integrated luminosity, σi is the cross section and Bi the branching fraction of a givenphysical process i into final states of interest, Ai is the acceptance of the detector for this processand εi is the efficiency for the accepted events to pass the analysis selection criteria. If H = H0 isthe null hypothesis, then µ represents the background expectation; on the other hand if H = HZ′includes a non-zero signal strength from a given Z′ boson, then µ represents the expectation fromthe sum of background and Z′ signal.In practice, the expected value µ is obtained using Monte Carlo simulation techniques, by gen-erating events for the physical processes of interest and simulating their interaction with a virtualrepresentation of the ATLAS detector. The quantity (Aε)i is then the fraction of simulated eventsthat are accepted by the virtual detector and pass the analysis selection criteria, over the to totalnumber of generated events:Aε =NpassNgen(6.2)Corrections described in the remainder of this section are applied to both Npass and Ngen. Thepassing events are then scaled by an additional weight wi = Lint(σB/Ngen)i such that their weightedsum gives the expectation:µ = ∑i∈H(wNpass)i = ∑i∈H(LintσBNpassNgen)i(6.3)This expression can be used to find the expected number of events in any region of phase space:these regions are typically represented by histogram bins in each variable of interest.Analysis at√s = 7 TeVTable 6.1 indicates the event generators used for the hard process and parton shower, as well asthe PDFs used to generate simulated samples for the analysis at√s = 7 TeV. Such samples areused to obtain Z′ signal templates and to evaluate the background yields from Z/γ∗, WW , WZ,90Table 6.1: Summary of the simulated samples for the analysis using the full dataset at√s = 7 TeV. The re-weighting of Z′ samples is discussed in Section 6.2.3.Process Main generator Parton shower PDFsZ/γ∗ PYTHIA 6.421 [158] PYTHIA 6.421 MRST2007LO** [156, 157]WW , WZ, ZZ HERWIG 6.510 [82, 83] HERWIG 6.510 MRST2007LO**tt¯, Wt MC@NLO 4.01 [101] HERWIG 6.510 CTEQ66 [137]Z′ PYTHIA 6.421 (re-weighted) PYTHIA 6.421 MRST2007LO**ZZ, tt¯ and Wt production in final states with at least two muons of opposite charge. With theexception of the samples involving top quarks, which are generated using matrix elements at NLO,all other samples are generated using LO event generators, making use of the modified LO PDF setMRST2007LO** [156, 157]. This modified PDF set was developed in an attempt to emulate thecalculation results from NLO generators when using LO generators. For all samples, the programPHOTOS [110] is used to simulate final-state photon radiation. The interactions of the generatedparticles with the ATLAS detector are then simulated using GEANT4 [104], and the events are fullyreconstructed using the ATLAS reconstruction software [15].The dominant, irreducible background to this search is Z/γ∗ → µ+µ−. To obtain the state-of-the-art prediction for the yields due to this process as a function of dimuon invariant mass,the Z/γ∗ cross section is calculated using PHOZPR [114] at NNLO in perturbative QCD, withMSTW2008NNLO PDFs [132]. The simulated Z/γ∗ samples are then re-weighted event-by-eventusing the ratio of this NNLO cross section to the prediction from the LO simulation: this correctionfactor is shown in Figure 6.6. Multiplicative correction factors such as this one are commonly called“K-factors”.Another event-by-event weight correction, displayed as a function of mµ+µ− in Figure 6.7, isalso applied to account for NLO electroweak corrections due to virtual heavy gauge boson loops,photon-induced processes (γγ → µ+µ−) and real radiation of W and Z bosons from the final-statemuons. The first two corrections are calculated at LO using HORACE 3.1 [64] with MRST2004QEDPDFs [131]. Real radiation is estimated based on the results of Ref. [48] to contribute an enhance-ment of about 2%/ TeV. The inclusive Z/γ∗ cross section with the above higher-order corrections,for mµ+µ− > 60 GeV, is σZ/γ∗ = 989±49 pb.Additional corrections not changing the total background normalization are applied to theweights of simulated events to account for known discrepancies with respect to data. To correctfor differences between the amount of pileup events in the simulated samples with respect to theobserved distribution shown in Figure 4.6, a correction is applied as a function of the number ofinteractions per proton bunch crossing. The corrections to simulated muons due to the detectorefficiency and resolution described in Section 5.2 are applied as well.In addition, a significant difference was found in the pT spectrum of Z bosons in simulated910.50.60.70.80.911.11.21.31.41.510 10 2 10 3mll [GeV]K-factorLHC 7TeVMSTW2008 NNLO/LONNLO/MRST2007 LO*NNLO/MRST2007 LO**NLO/LOFigure 6.6: Perturbative QCD correction factor for Z/γ∗→ µ+µ− production as function ofmµ+µ− at√s = 7 TeV. The purple dash-dotted line, representing the correction from theLeading Order calculation with MRST2007LO** to the Next-to-Next-to-Leading Ordercalculation with MSTW2008NNLO, is used in the analysis at√s = 7 TeV. Figure credit:T. Nunnemann.m [GeV]500 1000 1500 2000 2500 3000K factor0.80.850.90.9511.05 PDF + W/Z radiation correction (factor)aZ: muon: EW loop + initial Figure 6.7: Electroweak and photon-induced correction factor for Z/γ∗→ µ+µ− productionas function of mµ+µ− at√s = 7 TeV, taking into account corrections due to virtual Wand Z loops and real final-state radiation of W and Z bosons. A piecewise polynomial fitto the correction is shown in red. Figure credit: T. Nunnemann.92samples produced at√s = 7 TeV in 2011, compared to similar samples generated at the same centre-of-mass energy in 2010. This difference can be seen in Figure 6.8. While the earlier production isfound to describe collision data accurately, the later one does not. This difference was traced backto a re-tuning of event generator settings. A correction is therefore applied event-by-event as afunction of the generated Z pT and mµ+µ− to recover the spectrum from 2010 simulation.gent, Zp1 10 210 310N0100200300400500600700800900 DY75 MC10DY75 MC11aDY600 MC10DY600 MC11aFigure 6.8: Generated Z pT spectra near the Z resonance region (75 GeV<mµ+µ− < 120 GeV,in black) and at higher invariant masses (600 GeV < mµ+µ− < 800 GeV, in red). Samplesgenerated in 2010 and 2011 are respectively shown with closed and open markers. Figurecredit: J. Kretzschmar.Top-quark backgrounds, namely tt¯ and Wt production, also contribute opposite-sign pairs ofhigh-momentum muons when both W bosons in the event decay to µν . The tt¯ cross section is scaledto an approximate-NNLO prediction of σtt¯ = 160+11−15 pb [125, 135], and the single-top Wt cross sec-tion used is σWt = 14.4±1.0 pb. Diboson backgrounds evaluated from WW , WZ and ZZ simulatedprocesses are similarly scaled to NLO cross sections, calculated using MCFM [63] with an uncer-tainty of 5%. The values used are σWW = 45±2 pb, σWZ = 18.0±0.9 pb and σZZ = 6.0±0.3 pb.Because both the top-quark and diboson simulated background samples lack sufficient statis-tics at very high dimuon invariant masses, an extrapolation is performed by fitting the backgroundpredictions, with all corrections applied, to the functional formN(m) = p1 ·mp2 logm+p3 (6.4)where the pi are fit parameters and m is the invariant mass mµ+µ− . For top-quark backgrounds, thefit region is 200 GeV<mµ+µ− < 800 GeV, while for diboson backgrounds it is 450 GeV<mµ+µ− <93Table 6.2: Summary of the simulated samples for the analysis using the full dataset at√s = 8 TeV. The re-weighting of Z′ samples is discussed in Section 6.2.3.Process Main generator Parton shower PDFsZ/γ∗ POWHEG [3] PYTHIA 8.162 [159] CT10 [121]WW , WZ, ZZ HERWIG++ 2.5.2 [82, 83] HERWIG 6.520 CTEQ6L1tt¯, Wt MC@NLO 4.06 [101] HERWIG 6.520 CT10Z′ PYTHIA 8.165 (re-weighted) PYTHIA 8.165 MSTW2008LO [132]1450 GeV. Above these ranges in invariant mass, where the simulated statistics are insufficient, thebackground predictions are taken from Equation 6.4, using the parameters from the correspondingfits. Two sources of systematic uncertainties on this extrapolation are considered. First, the fit rangeis varied by 5 steps of 10 GeV about the starting value and 5 steps of 20 GeV before the endingvalue, resulting in 25 different fits, and the maximum discrepancy with respect to the nominal fit istaken. Second, a different functional form is tried: N(m) = p1 · (m+ p2)p3 . The sum in quadratureof the effects from these two variations is taken as the uncertainty on the estimated background yieldwhere it is taken from the fit.In the analysis using the first 1.21 fb−1 of data collected at√s = 7 TeV, the background fromW + jets processes, where one muon comes from the W → µν decay in the hard scatter and the otherfrom a meson decay in one of the jets, was also estimated. Simulated samples were generated usingALPGEN [128] interfaced with CTEQ6L1 PDFs [146], with HERWIG to simulate the parton showersand underlying event and JIMMY 4.31 [59] for multiple parton interactions. This background turnsout to be negligible, as can be seen in Figure 6.12, and was therefore not considered in subsequentiterations of the analysis.Finally, the sum of all backgrounds is normalized in the Z peak region, corresponding to mµ+µ−between 70 and 110 GeV. The number of events passing the full selection found in this normalizationregion is 985,180 and the corresponding scale factor is 1.01, with an uncertainty of 5% dominatedby that due to the theoretical Z cross section. This scale factor value is consistent with unity, and itscentral value lies within the 1.8% uncertainty on the integrated luminosity measurement.Analysis at√s = 8 TeVFor the analysis using data collected at√s = 8 TeV, background estimates are obtained followingthe same general strategy, using updated versions of the same event generators except for the Z/γ∗background, where POWHEG is used instead of PYTHIA for the hard process. The event generatorsused for the hard process and parton shower, as well as the PDFs used, are indicated in Table 6.2.Here the state-of-the-art prediction for the Z/γ∗ background is calculated at NNLO in pertur-bative QCD with NLO electroweak corrections using FEWZ [126, 134] with MSTW2008NNLOPDFs. The resulting K-factors applied to samples generated with POWHEG and PYTHIA are shown94in Figure 6.9. This calculation also includes photon-induced contributions, which are estimated atLO with MRST2004QED PDFs, as well as real final-state radiation of W and Z bosons estimatedusing MADGRAPH 5 [5] following the prescription outlined in Ref. [48]. The electroweak andphoton-induced corrections were verified by SANC [42, 53]. The Z/γ∗ cross section thus calcu-lated, integrated for mµ+µ− > 60 GeV is σZ/γ∗ = 1147±50 pb.Figure 6.9: Perturbative QCD, electroweak and photon-induced correction factors for Z/γ∗→µ+µ− production as function of mµ+µ− at√s = 8 TeV. The electroweak correction fac-tors take into account corrections due to virtual W and Z loops and real final-state radia-tion of W and Z bosons. Calculation by U. Klein.In a manner identical as explained above for the analysis at√s = 7 TeV, the appropriate correc-tions to the number of interactions per proton bunch crossing as well as to the detector efficiencyand resolution for reconstructing muons are also applied. On the other hand, no correction to thesimulated Z pT is necessary, following improvements in the Monte Carlo generator tune.Top-quark backgrounds are scaled to the cross section σtt¯ = 253+13−15 pb, obtained from a cal-culation performed at NNLO in perturbative QCD including the re-summation of next-to-next-to-leading logarithmic soft gluon terms with TOP++ 2.0 [44, 61, 85–88], assuming a top quark massof 172.5 GeV. The uncertainties on this prediction include PDF and αS uncertainties calculatedusing the PDF4LHC prescription [55] with the NNLO MSTW2008 [132, 133], CT10 [103, 121]and NNPDF2.3 [41] PDF error sets, QCD scale uncertainties and the effect of varying the top quarkmass by ±1 GeV. The single-top Wt cross section is taken to be σWt = 22.4±1.5 pb [119]. The95NLO cross section calculation for diboson processes is repeated at√s = 8 TeV with MCFM, andthe values obtained are σWW = 57±3 pb, σWZ = 21.5±1.1 pb and σZZ = 7.4±0.4 pb.For this version of the analysis, the diboson samples have sufficient statistics over the fullmµ+µ− spectrum. Top background contributions are extrapolated using a fit like for the analysisat√s = 7 TeV, using the functional form of Equation 6.4. The uncertainties are derived in the sameway, by varying the fit range and functional form.The normalization region is taken to be 80 GeV < mµ+µ− < 110 GeV. The number of eventspassing the full selection found in this normalization region is 5,075,739 and the corresponding scalefactor is 0.98, with a 4% theoretical uncertainty from the Z cross section. Here too, the scale factorvalue is consistent with unity, and its central value lies within the preliminary 3.6% uncertainty onthe integrated luminosity measurement.6.2.2 Data-Driven Background EstimatesThis section describes the data-driven background estimates of contributions from multi-jet pro-cesses and cosmic rays, using partial datasets collected at√s = 7 TeV. Both of these backgroundswere estimated to be negligible then, and re-evaluating them using the complete dataset is not nec-essary.Multi-jetsIn hadron colliders, fully hadronic processes have cross sections ranking orders of magnitude abovethe cross sections for hard-scattering processes with leptons in the final state; for illustration seeFigure 2.7 in Section 2.2.2. Following hadronization, jets originally from quarks and gluons canhave component particles which decay into muons, e.g. pi± → µ±ν or K± → µ±ν . While thesemuons from jets generally fail the tight isolation and impact parameter requirements used in thisanalysis, they constitute a potential background to the search in events where two of them pass allselection requirements.Using the first 1.21 fb−1 of data collected at√s = 7 TeV in 2011, a pure sample of muon pairswhere both muons come from jets is obtained by reverting the requirement on the isolation variableRiso = ΣptrkT (∆R < 0.3)/pµT , to 0.1 < Riso < 1.0 instead of Riso < 0.05 in the nominal selection. Thedistribution in the muon isolation variable immediately before the isolation requirement is appliedis shown on Figure 6.10, and the invariant mass distribution of events where two muon candidatespass the reversed isolation requirement along with the rest of the event selection is displayed inFigure 6.11. In both these histograms, the prediction from a simulated multi-jet background samplegenerated using PYTHIA is shown.The shape for the QCD multi-jet background is then taken from this Control Region (CR), and96µT / ptrkT pΣ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Muons / 0.0510210310410510610 Data 2011*γZ/DibosonttW+JetsQCDATLAS = 7 TeVs­1 L dt = 1.21 fb∫Figure 6.10: Muon track-based isolation distribution, immediately before the isolation cut.The QCD multi-jet background (yellow) is taken from PYTHIA MC simulation scaledby a factor 0.5.extrapolated to the Signal Region (SR) by applying a scaling factor as follows:Nexp,SRNexp,CR=(PMC(Riso < 0.05)PMC(0.1 < Riso < 1.0))2= (0.024±0.012)2= (5.8±5.8)×10−4(6.5)where PMC(Riso) is the probability for a muon from multi-jet processes to fall within a certain rangein the isolation variable, evaluated using PYTHIA simulation. The ratio has a statistical uncertaintyof 50%, which propagates to a 100% uncertainty on the multi-jet estimate in the SR.The resulting multi-jet background estimate can be seen in Figure 6.12, which shows the dimuoninvariant mass distribution after final selection selection for the first 1.21 fb−1 of data collected in2011. The multi-jet background is smaller than dominant backgrounds by many orders of magni-tude, and therefore negligible in this analysis.97 [GeV]µµm80 100 200 300 1000 2000Events­110110210310410Data 2011*γZ/DibosonttW+JetsQCD work in progressATLAS = 7 TeVs­1 L dt = 1.21 fb∫Figure 6.11: Dimuon invariant mass distribution from events with two muons passing the re-versed isolation requirement along with the rest of the selection. The QCD multi-jetbackground (yellow) is taken from PYTHIA MC simulation scaled by a factor 0.5. [GeV]µµm100 1000Events­210­110110210310410510610 Data 2011*γZ/DibosonttW+JetsQCDZ’(1000 GeV)Z’(1250 GeV)Z’(1500 GeV)ATLAS = 7 TeVs­1 L dt = 1.21 fb∫80 200 500 2000Figure 6.12: Dimuon invariant mass distribution after final selection for the first 1.21 fb−1 ofdata collected in 2011. Here the QCD multi-jet background (yellow) corresponds tothe data-driven estimate, i.e. the data shown in Figure 6.11 with extrapolation factorapplied. The cosmic ray background is too small to be shown.98Cosmic raysIn addition to being produced in the LHC collisions, high-momentum muons can also come fromcosmic rays. They are produced when high-energy protons from astronomical sources collide withmolecules in the Earth’s atmosphere, each producing a cascade of hadronic particles. Among theseparticles produced are mesons such as pions and kaons, which often decay into muons.Just like muons originating from the collider, high-momentum cosmic muons are minimum-ionizing particles, and have long lifetimes due to relativistic time dilation. They can thereforetraverse the atmosphere and the shielding above the ATLAS detector, before going through thedetector itself. In the event that a cosmic muon crosses all detector subsystems and coincides witha collision event at the interaction point before exiting under the detector, it can be mistakenlyreconstructed as a prompt dimuon event. An example of such an event, observed during a cosmic-ray run in 2008, is displayed in Figure 6.13.Figure 6.13: Cosmic muon event with hits in all Barrel detectors. Both solenoid and toroidmagnets were operational during this run, taken in 2008 [33].99A study estimating the cosmic ray background contamination in the high-mass dimuon sampleis conducted on the partial dataset consisting of the first 236 pb−1 of data collected in 2011. Thiscorresponds to the first 1.5 months of data taking, out of 7.5 months that year. A sample of probablecosmic ray events is obtained from this collision data by reverting the impact parameter cuts usedin the event selection, requiring 0.3 mm < d0 < 10 mm for the transverse impact parameter and3.0 mm < z0 < 200 mm for the impact parameter along the beam axis (instead of d0 < 0.2 mm andz0 < 1.0 mm in the nominal selection). Loose upper cuts on the impact parameters are kept for theCR, in order to maintain the same efficiency for detecting muons in the CR as in the SR.Two events are found to pass these reversed impact parameter cuts along with the rest of theevent selection. This number in the CR (Ncosmics,CR) is extrapolated to the number of cosmic rayevents expected in the SR (Ncosmics,SR). Assuming a constant cosmic ray distribution in spatialcoordinates perpendicular to the vertical, an upper bound is obtained by scaling the number in theCR using the ratio of the dimensions of the SR and CR along the x- and z-axes. This constitutes anupper bound because considering any correction along the y-axis would reduce the estimate. ThisyieldsNexp,SR < Ndata,CR ·d0,SRd0,CR,outer−d0,CR,inner·z0,SRz0,CR,outer− z0,CR,inner< (2.0±1.4) · 0.2 mm10 mm − 0.3 mm ·1.0 mm200 mm − 3.0 mm< (2.0±1.4) · (2×10−2) · (5×10−3)< (2.0±1.4)×10−4(6.6)Since the number of cosmic rays entering the detector scales with trigger live-time, the cor-responding bound on the number of cosmic events passing all selection requirements for the full√s = 7 TeV dataset is(2.0±1.4)×10−4 ·7.5 months1.5 months= (10±7)×10−4 (6.7)The cosmic ray contamination is therefore negligible in this analysis.Since the trigger live-time and the selection are similar for the√s = 8 TeV dataset, the cosmicray contamination is expected to be negligible there as well.6.2.3 Generation of Signal TemplatesThis search makes use of signal templates as a function of the dimuon invariant mass mµ+µ− , tointerpret the significance of differences between observed data and the expected backgrounds. Foreach signal hypothesis, the combined signal and background templates are compared to the data100using a likelihood fit: this is described in detail in Chapter 8. The main advantage of the templatemethod over a simple counting method using an invariant mass window is that templates make useof more information by taking into account signal contributions across the whole mass spectrum,therefore increasing the signal acceptance and allowing a better sensitivity.Nominally, a dedicated signal template is obtained for each Z′ pole mass MZ′ . In this approach,the relative width ΓZ′/MZ′ of the resonance is fixed, corresponding to that of the specific Z′ modelunder study: above the tt¯ production threshold, its value is 3.0% for Z′SSM, 1.2% for Z′χ and 0.5% forZ′ψ . The iterations of the analysis at√s = 7 TeV and√s = 8 TeV use different techniques to gener-ate these signal templates; both are described below. Moreover, this section also describes a thirdtechnique, used for generating signal templates as a function of the coupling γ ′ and mixing angleθMin from the Minimal Z′ Models described in Section 3.2.2. These templates have the additionaladvantage to fully take into account the interference between the Z/γ∗ and Z′ processes.In all cases, the same mass-dependent higher-order perturbative QCD corrections described inSection 6.2.1 are applied to Z′ signal template shapes, under the assumption that differences betweenthe initial-state quarks couplings to Z′ bosons and their couplings to Z bosons do not significantlychange these corrections. Higher-order electroweak corrections are not applied to the Z′ signal,since as mentioned in Section 3.2.1, the unknown couplings between Z′ and heavy gauge bosonsare assumed to be zero. Corrections due to experimental effects are applied, namely to the muonefficiency and momentum resolution, as well as the number of interactions per bunch crossing.Nominal Z′ signal templatesFor the nominal analysis at√s = 7 TeV, a sample of signal events is generated with a constant dis-tribution as a function of mµ+µ− , by modifying the expression for the differential Z′ cross section inPYTHIA at generator-level. This is accomplished first by removing the dependence on MZ′ and ΓZ′ ,by taking out a Breit-Wigner factor: this leaves a smoothly-falling event distribution as a function ofmµ+µ− . An exponential factor is then used to make this spectrum constant as a function of mµ+µ− .Mathematically, the transformation is the following:dσdm2dy→dσdm2dy× ((m2−M2Z′)2 +M2Z′Γ2Z′)× exp(0.00195 ·m) (6.8)where m is the dimuon invariant mass mµ+µ− . From this uniform distribution of events, templatescan then be obtained at any Z′ pole mass value using an event-by-event weightW , multiplying backa Breit-Wigner factor corresponding to the MZ′ and ΓZ′ values of interest and the reciprocal of thesame exponential factor. Explicitly,W (m) =exp(−0.00195 ·m)(m2−M2Z′)2 +M2Z′Γ2Z′(6.9)101This re-weighting method is validated using dedicated Z′ signal samples generated at differentvalues of MZ′ with un-modified PYTHIA code.For the analysis at√s = 8 TeV, another technique is used. Instead of re-weighting a dedicatedsample of signal events, Z′ signal templates are obtained by re-weighting background Z/γ∗ eventsgenerated at LO, to match every signal hypothesis considered. The aim is then to replace the matrixelements entering Equation 2.60, the LO differential cross section for Z/γ∗ production, by the onescorresponding to Z′ production:dσdm2dy(pp→ Z/γ∗→ µ+µ−) → dσdm2dy(pp→ Z′→ µ+µ−) (6.10)In practice, this is achieved by applying an event-by-event weight to Z/γ∗ events as follows:W (m,q) =∑i, j∈{L,R} |Ai j(Z′)|2∑i, j∈{L,R} |Ai j(Z/γ∗)|2(6.11)where in addition to depending on the invariant mass of the event, the event weight depends on theincoming quarks’ flavour q via their couplings to the Z′ boson appearing in Ai j(Z′). The latter isgiven byAi j(Z′) = g2Z′g′qig′µ jm2−M2Z′− iMZ′ΓZ′(6.12)where gZ′ is the universal part of the Z′ coupling and the charges g′ depend on the quantum numbersof the fermions, in accordance with the conventions set in Equation 2.28. The Z/γ∗ matrix elementAi j(Z/γ∗) is given in Equation 2.56 with sˆ = m2. Example Z′SSM signal templates generated withthis method are shown in Figure 6.14.Z′ signal templates including interferenceThe previous strategy can be improved to generate combined templates of Z/γ∗ background and Z′signal, with the interference between the two processes fully taken into account. This implies tosubstitute the matrix element in the numerator of the event weight as follows:W (m,q) =∑i, j∈{L,R} |Ai j(Z/γ∗)+Ai j(Z′)|2∑i, j∈{L,R} |Ai j(Z/γ∗)|2(6.13)with the Ai j as above. For this analysis, this method is used in the context of Minimal Z′ Models,for whichgZ′g′ = gYY +gB−L(B−L) (6.14)102Figure 6.14: Example Z′SSM signal templates generated at√s = 8 TeV, for MZ′ = 1.5, 2.5 and3.5 TeV. The bin width is constant in logmµ+µ− .or equivalently, using Equations 3.5 and 3.6:gZ′ = γ ′gZ (6.15)g′ = Y sinθMin +(B−L)cosθMin (6.16)In contrast with the nominal interpretation of the search, where the signal cross section is chosenas the parameter of interest, in the case of Minimal Z′ Models the parameters of interest are γ ′ andθMin, for this interpretation to remain as general as possible. Therefore, here it is not sufficientto generate signal templates as a function of mµ+µ− for each MZ′ of interest. Two-dimensionaltemplates are necessary: for each value on MZ′ and θMin under consideration, combined templatesof background and signal are generated as a function of both mµ+µ− and γ ′. An example of these2D combined templates is shown in Figure 6.15. In addition to correctly taking into account theinterference between Z/γ∗ and Z′ bosons, this approach varies the width ΓZ′ simultaneously withthe signal cross section, as required when varying the couplings between the Z′ boson and fermions.103Figure 6.15: Example 2D combined template of Z/γ∗ background and Z′Min signal generatedat√s = 8 TeV, as a function of γ ′4 and mµ+µ− , for MZ′Min = 2.5 TeV and θMin = 0.6.3 Comparison of Data with Background ExpectationsThis section compares the sum of background expectations to data collected by the ATLAS experi-ment in 2011 at√s = 7 TeV, and in 2012 at√s = 8 TeV.In practice, the search region is initially blinded for mµ+µ− > 400 GeV, in order to prevent theintroduction of potential biases in the event selection. The kinematic distributions of individualmuon candidates and the dimuon system (with the exception of mµ+µ−) are compared between dataand simulation to verify the quality of the simulation on which background estimates rely. Themissing transverse energy spectrum is also verified: if large and frequent mis-measurements ofmuon momentum were present in data and not in the simulation, the EmissT spectrum in data wouldexhibit a shift at higher values. Finally, two-dimensional histograms of EmissT vs. leading muon pTas well as EmissT vs. mµ+µ− are monitored in data, since correlations between these observables arecommon in events with mis-measured muons.Only after these verifications, when discrepancies are understood and the frozen selection isapproved in the first step of internal review by the collaboration, is the search region fully unblinded.The unblinded distributions are shown here.1046.3.1 Kinematics of the Dimuon SystemThe dimuon invariant mass spectrum is shown for mµ+µ− > 70 GeV with data at√s = 7 TeV inFigure 6.16, and for mµ+µ− > 80 GeV with data at√s = 8 TeV in Figure 6.17. Data are comparedto the stacked sum of expected backgrounds. Potential contributions from Z′SSM bosons are alsoshown above the expected backgrounds. These histograms are the most important in this analysis,because mµ+µ− is the discriminating variable used to search for new resonances.The number of observed events and the corresponding background expected from each sourcein the search region of the analysis are shown in Tables 6.3 and 6.4, in bins of mµ+µ− . No significantdifference between the data and expectations from the Standard Model is observed from these tables;a thorough statistical analysis of the level of agreement with the null hypothesis is carried out inSection 8.1.Figures 6.18 and 6.19 show the transverse momentum pT and rapidity y of the dimuon system.The rapidity distributions in data agree well with the expectations from Z/γ∗ background, howeveran excess of events in data is seen for both datasets at high dimuon pT. Indeed, while the agreementbetween data and the simulation is satisfactory in the bulk of the distributions, not enough simulatedevents remain in the tails, corresponding to a deficit in the amount of radiated gluons with very-highmomentum from the initial state of the collision in simulated events. It was verified using the first1.21 fb−1 of data collected at√s = 7 TeV that the dimuon pT is well-modelled when the Z/γ∗process is simulated using the ALPGEN generator, which is known to describe events with high jetmultiplicities more accurately. This comparison is shown in Figure 6.20.Ultimately, the results of the search are completely unaffected by this mis-modelling, becausethe invariant mass of the observed highly-boosted dimuon events is generally on the Z peak or lower.In other words, the mis-modelling in the tail of the dimuon pT spectrum does not significantly affectthe yield predictions in the search region. For the analysis, the Z/γ∗ samples generated with PYTHIAand POWHEG are chosen because of their significantly higher statistics at high invariant mass.6.3.2 Kinematics of Individual MuonsTransverse momentum spectra of individual muon candidates are shown in Figures 6.21 and 6.22,separately for the leading and sub-leading muons of each event, i.e. the muons with the highest andsecond-highest pT. Excesses are observed in the tails of the leading muon momentum distributionsin both datasets: this is completely due to the mis-modelling of dimuon pT and jet multiplicitiesdiscussed in the previous section. Indeed, it was verified explicitly that the events responsible forboth effects are the same, and that the tail of the muon pT spectrum is better described by simulationwith the ALPGEN generator. This comparison is shown in Figure 6.23.The angular distributions in the η and φ coordinates are shown in Figure 6.24 for the dataset at√s = 7 TeV, and in Figures 6.25 and 6.26 for the dataset at√s = 8 TeV. Here the agreement withthe Monte Carlo simulation is excellent.105 [GeV]µµm80100 200 300 1000 2000Events­310­210­110110210310410510610710Data 2011*γZ/DibosonttZ’(1500 GeV)Z’(2000 GeV)ATLAS­1 L dt = 5.0 fb∫ = 7 TeVsFigure 6.16: Dimuon invariant mass in the selected events at√s = 7 TeV.Table 6.3: Expected and observed number of events for the analysis at√s = 7 TeV. The errorsquoted include both statistical uncertainties and the systematic uncertainties discussed inChapter 7.mµ+µ− [GeV] 110–200 200–400 400–800 800–1200 1200–3000Z/γ∗ 21200±1200 2090±230 173±15 7.7±0.8 0.98±0.16tt¯, Wt 900±100 270±50 18±11 0.32±0.07 0.019±0.007WW , WZ, ZZ 289±32 97±24 11.8±2.7 0.59±0.26 0.087±0.016Total 22400±1200 2460±240 203±19 8.7±0.9 1.09±0.16Data 21945 2294 197 10 2106Events-110110210310410510610710Data 2012*γZ/Top quarkDibosonZ’ SSM (1.5 TeV)Z’ SSM (2.5 TeV)ATLAS      µµ →Z’       -1 L dt = 20.5 fb∫ = 8 TeV            s [TeV]µµm0.08 0.1 0.2 0.3 0.4 0.5 1 2 3 4Data/Expected0.60.811.21.4Figure 6.17: Dimuon invariant mass in the selected events at√s = 8 TeV.Table 6.4: Expected and observed number of events for the analysis at√s = 8 TeV. The errorsquoted include both statistical uncertainties and the systematic uncertainties discussed inChapter 7.mµ+µ− [GeV] 110–200 200–400 400–800 800–1200 1200–3000 3000–4500Z/γ∗ 111000±8000 11000±1000 1000±100 49±5 7.3±1.1 0.034±0.022tt¯, Wt 7100±600 2300±400 160±80 3.0±1.7 0.17±0.15 < 0.001WW , WZ, ZZ 1530±180 520±130 64±16 4.2±2.1 0.69±0.30 0.0024±0.0019Total 120000±8000 13700±1100 1180±130 56±6 8.2±1.2 0.036±0.023Data 120011 13479 1122 49 8 0107 [GeV]µµT,p100 200 300 400 500 600 700 800 900 1000Events­210­110110210310410510610 work in progressATLAS Data 2011*γZ/Dibosontt­1 L dt = 5.0 fb∫ = 7 TeVsµµy­3 ­2 ­1 0 1 2 3Events020406080100310× work in progressATLAS Data 2011*γZ/­1 L dt = 5.0 fb∫ = 7 TeVsFigure 6.18: Dimuon transverse momentum (top) and rapidity (bottom) in the selected eventsat√s = 7 TeV. The bin width of the pT histogram is constant in√pT.10830 40 50 60 70 100 200 300 400 1000Events­110110210310410510610710810 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVsData 2012*γZ/TopDiboson [GeV]µµT,p30 40 50 60 70 80 100 200 300 400 500 600 1000Data/Expected0.750.80.850.90.9511.051.11.151.21.25­3 ­2 ­1 0 1 2 3Events050100150200250 310× work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVsData 2012*γZ/µµy­3 ­2 ­1 0 1 2 3Data/Expected0.750.80.850.90.9511.051.11.151.21.25Figure 6.19: Dimuon transverse momentum (top) and rapidity (bottom) in the selected eventsat√s = 8 TeV. The bin width of the pT histogram is constant in√pT.109 [GeV]TDimuon p100 200 300 400 500 600Events­110110210310410510 Data 2011*γZ/DibosonttW+JetsATLAS = 7 TeVs­1 L dt = 1.21 fb∫ [GeV]TDimuon p100 200 300 400 500 600Events­110110210310410510 Data 2011* AlpgenγZ/DibosonttW+Jets work in progressATLAS = 7 TeVs­1 L dt = 1.21 fb∫Figure 6.20: Dimuon transverse momentum in the first 1.21 fb−1 of data collected at√s = 7 TeV. In the top histogram, the Z/γ∗ prediction is evaluated using the nomi-nal generator PYTHIA, while ALPGEN is used for the Z/γ∗ prediction in the bottomhistogram. The bin width is constant in√pT.110 leading [GeV]µT,p100 200 300 400 500 600 700 800 900 1000Events­210­110110210310410510610  work in progressATLAS Data 2011*γZ/DibosonttZ’(1500 GeV)Z’(1750 GeV)Z’(2000 GeV)­1 L dt = 5.0 fb∫ = 7 TeVs subleading [GeV]µT,p100 200 300 400 500 600 700 800 900 1000Events­210­110110210310410510610  work in progressATLAS Data 2011*γZ/DibosonttZ’(1500 GeV)Z’(1750 GeV)Z’(2000 GeV)­1 L dt = 5.0 fb∫ = 7 TeVsFigure 6.21: Transverse momentum of the leading muon (top) and sub-leading muon (bottom)in the selected events at√s = 7 TeV. The bin width is constant in√pT.11130 40 50 60 70 100 200 300 400 1000Events­110110210310410510610710810 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVsData 2012*γZ/TopDiboson [GeV]Tp30 40 50 60 70 80 100 200 300 400 500 600 1000Data/Expected0.750.80.850.90.9511.051.11.151.21.2530 40 50 60 70 100 200 300 400 1000Events­110110210310410510610710810 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVsData 2012*γZ/TopDiboson [GeV]Tp30 40 50 60 70 80 100 200 300 400 500 600 1000Data/Expected0.750.80.850.90.9511.051.11.151.21.25Figure 6.22: Transverse momentum of the leading muon (top) and sub-leading muon (bottom)in the selected events at√s = 8 TeV. The bin width is constant in√pT.112 [GeV]Tp100 200 300 400 500 600Muons­110110210310410510610 Data 2011*γZ/DibosonttW+JetsQCDZ’(1000 GeV)Z’(1250 GeV)Z’(1500 GeV)ATLAS = 7 TeVs­1 L dt = 1.21 fb∫ [GeV]Tp100 200 300 400 500 600Muons­110110210310410510610 Data 2011* AlpgenγZ/DibosonttW+JetsQCDZ’(1000 GeV)Z’(1250 GeV)Z’(1500 GeV) work in progressATLAS = 7 TeVs­1 L dt = 1.21 fb∫Figure 6.23: Muon transverse momentum in the first 1.21 fb−1 of data collected at√s = 7 TeV. In the top histogram, the Z/γ∗ prediction is evaluated using the nomi-nal generator PYTHIA, while ALPGEN is used for the Z/γ∗ prediction in the bottomhistogram. The bin width is constant in√pT.113η­3 ­2 ­1 0 1 2 3Muons / 0.1020406080100310×Data 2011*γZ/ATLAS­1 L dt = 5.0 fb∫ = 7 TeVsφ­3 ­2 ­1 0 1 2 3Muons / 0.220406080100120140310×Data 2011*γZ/ work in progressATLAS­1 L dt = 5.0 fb∫ = 7 TeVsFigure 6.24: η and φ distributions for the selected muons at√s = 7 TeV.114η-3 -2 -1 0 1 2 3Events / 0.1050100150200250310×ATLAS      µµ →Z’       -1 L dt = 20.5 fb∫ = 8 TeV            sData 2012*γZ/η-3 -2 -1 0 1 2 3Events / 0.1050100150200250310×ATLAS      µµ →Z’       -1 L dt = 20.5 fb∫ = 8 TeV            sData 2012*γZ/Figure 6.25: η distributions for the leading muon (top) and sub-leading muon (bottom) in theselected events at√s = 8 TeV.115φ-3 -2 -1 0 1 2 3Events / 0.2050100150200250300350 310×ATLAS      µµ →Z’       -1 L dt = 20.5 fb∫ = 8 TeV            sData 2012*γZ/φ-3 -2 -1 0 1 2 3Events / 0.2050100150200250300350 310×ATLAS      µµ →Z’       -1 L dt = 20.5 fb∫ = 8 TeV            sData 2012*γZ/Figure 6.26: φ distributions for the leading muon (top) and sub-leading muon (bottom) in theselected events at√s = 8 TeV.1166.3.3 Missing Transverse Energy DistributionsThe missing transverse energy spectrum at√s = 7 TeV is shown in Figure 6.27, and the two-dimensional histograms of EmissT vs. mµ+µ− and EmissT vs. leading muon pT observed in data areshown separately for the primary and secondary dimuon selections in Figure 6.28.The agreement in the EmissT distribution between data and the simulation is satisfactory, in spiteof the presence of an excess of observed events for 50 GeV < EmissT < 150 GeV. Perfect agreementis not expected here, since no data quality assessment from the calorimeters is required for thisanalysis1; it is more important that no mis-modelling is observed in the tail of the distribution, asthis implies that no large systematic mis-measurements of muon momentum are present in data.No correlation is seen in the two-dimensional histograms, with the possible exception of just oneoutlying event at high-mµ+µ− in the secondary dimuon selection. The results of the search areunaffected by the presence of this event.The corresponding histograms for the analysis at√s = 8 TeV are shown in Figures 6.29and 6.30. Here the EmissT spectrum is shown separately for the primary and secondary dimuonselections; in both of them, deficits in the number of observed events are present in the bulk of thedistributions, but the agreement between data and the simulation is good in the tails. No correlationis observed in the two-dimensional histograms for this dataset.Figure 6.27: Missing transverse energy in the selected events at√s = 7 TeV.1 Significantly better agreement is observed in dedicated EmissT analyses such as Ref. [22] and [28]117 [GeV]µµm0 200 400 600 800 1000 1200 1400 [GeV]missTE0100200300400500 work in progressATLAS­1 L dt = 5.0 fb∫ = 7 TeVs [GeV]TLeading Muon p0 100 200 300 400 500 600 700 800 900 1000 [GeV]missTE0100200300400500 work in progressATLAS­1 L dt = 5.0 fb∫ = 7 TeVs [GeV]µµm0 200 400 600 800 1000 1200 1400 [GeV]missTE0100200300400500 work in progressATLAS­1 L dt = 5.0 fb∫ = 7 TeVs [GeV]TLeading Muon p0 100 200 300 400 500 600 700 800 900 1000 [GeV]missTE0100200300400500 work in progressATLAS­1 L dt = 5.0 fb∫ = 7 TeVsFigure 6.28: Two-dimensional histograms of EmissT vs. mµ+µ− (left) and EmissT vs. leading muon pT (right) for events passing the primary(top) and secondary (bottom) dimuon selection in collision data at√s= 7 TeV.118 [GeV]missTE30 40 50 100 200 300 1000Events­110110210310410510610710 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVsData 2012*γZ/TopDiboson [GeV]missTE30 40 50 100 200 300 1000Events­210­110110210310410510610 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVsData 2012*γZ/TopDibosonFigure 6.29: Missing transverse energy in the selected events at√s = 8 TeV, for the primary(top) and secondary (bottom) dimuon selection. The bin width is constant in√EmissT .119 [GeV]µµm0 500 1000 1500 2000 2500 3000 3500 4000 4500 [GeV]missTE01002003004005006007008009001000 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVs [GeV]TLeading Muon p0 100 200 300 400 500 600 700 800 900 1000 [GeV]missTE01002003004005006007008009001000 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVs [GeV]µµm0 500 1000 1500 2000 2500 3000 3500 4000 4500 [GeV]missTE01002003004005006007008009001000 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVs [GeV]TLeading Muon p0 100 200 300 400 500 600 700 800 900 1000 [GeV]missTE01002003004005006007008009001000 work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVsFigure 6.30: Two-dimensional histograms of EmissT vs. mµ+µ− (left) and EmissT vs. leading muon pT (right) for events passing the primary(top) and secondary (bottom) dimuon selection in collision data at√s= 8 TeV.120Chapter 7Systematic Uncertainties7.1 OverviewIn this analysis, normalizing all backgrounds to data in the Z peak region simplifies the treatment ofsystematic uncertainties, as this makes the background estimate insensitive to all uncertainties inde-pendent of mµ+µ− , such as the uncertainty on the integrated luminosity. Only the mass-dependentsystematic uncertainties on the background prediction therefore need to be considered.On the other hand, by following this procedure the uncertainty on the signal expectation com-ing from mass-independent sources is traded for the systematic uncertainty from the theoreticalZ/γ∗ cross section in the normalization region. This is seen most clearly when considering a re-arrangement of Equation 6.1 applied to signal processes:(σB)Z′ =µZ′(Aε)Z′·1Lint→µZ′(Aε)Z′·(Aε)ZµZ(σB)Z(7.1)The uncertainty on (σB)Z is propagated accordingly. Following the conventions set in the Exoticsworking group of the ATLAS collaboration, no other theoretical uncertainty is applied on the signalprediction in the statistical model, because of the model-dependent nature of such calculations.The main systematic uncertainties to which this analysis is sensitive are listed in Tables 7.1and 7.2, respectively for the datasets collected in 2011 and 2012. For the analysis at√s = 7 TeV,theoretical uncertainties are quoted as a function of truth mµ+µ− , making them overly conservative.This is improved for the analysis at√s = 8 TeV, for which uncertainties are quoted with respect toreconstructed mµ+µ− , thereby taking into account muon momentum resolution effects. As it turnsout, a large fraction of events in the tail at high mµ+µ− comes from events with lower truth mµ+µ− ,and the relative effect of theoretical uncertainties on the total background yield is in fact smaller121Table 7.1: Summary of systematic uncertainties on the expected number of events for thesearch using data collected in 2011 at√s = 7 TeV.Source mµ+µ− = 1 TeV mµ+µ− = 2 TeV mµ+µ− = 3 TeVSignal Background Signal Background Signal BackgroundNormalization 5% N/A 5% N/A 5% N/APDF, αs, scale N/A 7% N/A 20% N/A 44%Electroweak corr. N/A 2% N/A 4.5% N/A 7%Efficiency 3% 3% 6% 6% 9% 9%Resolution < 3% 1% < 3% 3% < 3% 8%Total 6% 8% 8% 21% 10% 46%Table 7.2: Summary of systematic uncertainties on the expected numbers of events for thesearch using data collected in 2012 at√s = 8 TeV.Source mµ+µ− = 1 TeV mµ+µ− = 2 TeV mµ+µ− = 3 TeVSignal Background Signal Background Signal BackgroundNormalization 4% N/A 4% N/A 4% N/APDF variation N/A 5% N/A 12% N/A 17%PDF choice N/A < 1% N/A 6% N/A 12%αs N/A 1% N/A 3% N/A 4%Electroweak corr. N/A 1% N/A 3% N/A 3%γ-induced corr. N/A 2% N/A 3% N/A 4%Beam energy < 1% 2% < 1% 3% < 1% 3%Resolution < 3% 1% < 3% 3% < 3% 8%Total 4% 7% 4% 15% 4% 23%than implied by studies carried out at generator-level. Uncertainties having an impact smaller than3% on the expected number of events are neglected in the statistical model.7.1.1 Theoretical UncertaintiesThe dominant uncertainties in the analysis are theoretical in nature, and come from Parton Dis-tribution Functions (PDFs), introduced in Section 2.2.2. Indeed, Z/γ∗ production at invariantmasses comparable to the beam energy requires both a quark and an antiquark with high mo-mentum fraction x. As illustrated in Figure 7.1, because the PDFs of antiquarks are not well-known at such high x, the fractional uncertainty on the quark-antiquark luminosity gets large at high√sˆ/s =√x1x2, resulting in large uncertainties on the background and signal cross sections. Uncer-tainties due to αS and QCD scale variations are also considered. The methods used to evaluate thesetheoretical uncertainties are explained in detail in Sections 7.2 and 7.3.122 / ss-310 -210 -110Fractional uncertainty (90% C.L.)-0.2-0.15-0.1-0.0500.050.10.150.2 = 7 TeV)s) luminosity at LHC (q(qqΣW ZMSTW08 NLOCTEQ6.6CT10NNPDF2.1G. Watt     (March 2011)Fractional uncertainty (90% C.L.)Figure 7.1: Fractional uncertainty at 90% CL on the quark-antiquark luminosity at√s = 7 TeV due to PDFs, as a function of√sˆ/s =√x1x2. The uncertainty rise at highmomentum fraction is clearly visible [167]. Figure credit: G. Watt.For the analysis on data at√s = 7 TeV, the uncertainty on the electroweak corrections includesuncertainties in the calculation of real boson radiation, as well as the difference in the electroweakscheme definition between PYTHIA and HORACE, in addition to higher-order electroweak andO(ααS) corrections. This treatment was improved for the analysis at√s = 8 TeV: the calcula-tion is performed with higher precision with FEWZ, and uses a consistent electroweak scheme.There a smaller uncertainty is assigned, corresponding to the difference with an independent calcu-lation using the MCSANC [53] generator. The uncertainties on photon-induced corrections are alsotaken into account in both cases, and are dominated by the uncertainties on the photon PDF and onquark masses.Systematic uncertainties on sub-leading backgrounds, namely tt¯ and diboson production, arealso evaluated as discussed in Section 6.2.1. At high invariant masses the dominant contributioncomes from the extrapolation uncertainties. These uncertainties are large with respect to the corre-sponding backgrounds, but since the tt¯ and diboson backgrounds are an order of magnitude smallerthan the Z/γ∗ contribution, the resulting uncertainty on the total background is negligible.7.1.2 Experimental UncertaintiesOn the experimental side, the uncertainty on the muon trigger and reconstruction efficiency isdominated by the potential impact of catastrophic energy loss due to muon bremsstrahlung in the123calorimeters or in the MS. While muons detected in the ATLAS experiment are typically minimum-ionizing particles, which is the property that allows them to pass through the calorimeters with littleenergy loss and reach the Muon Spectrometer, muons at very high momentum enter the regimewhere radiative energy losses become important, as illustrated in Figure 7.2. In particular, radiativeenergy losses become larger than energy losses due to ionization for muon energy values above thecritical energy Eµc. As shown in Figure 7.3, Eµc ∼ 150− 300 GeV for the iron, copper, tungstenand lead used as absorbing materials in the ATLAS calorimeters, where most of the energy lossesoccur.As indicated in Section 5.1, energy depositions are taken into account when extrapolating thetracks measured in the MS to the primary vertex of the event. Nevertheless, if this procedure wasnot correctly calibrated for muons with very large energy losses, significant differences would beobserved between the track parameters measured in the ID and the standalone muon track, used intrack matching algorithms. This would in turn negatively impact the muon trigger and reconstruc-tion efficiency, especially for muons at very high momentum for which catastrophic energy lossesare more likely.For the analysis at√s = 7 TeV, this efficiency loss is estimated directly from simulation, byquantifying the efficiency as a function of the total energy loss from muons in simulated signalevents. Propagating this as a function of Z′ mass, the systematic uncertainty is found to be 3%/ TeV.This estimate is improved using more simulated statistics at√s = 8 TeV. Looking at muons passingthe full selection, no significant decrease in efficiency is observed for energy loss values up to 1 TeV.The systematic uncertainty due to this effect is therefore neglected for this dataset.The uncertainty on the muon resolution parameters described in Section 5.2 propagates tochanges in the background shapes and in the width of signal templates. To evaluate these effects, sig-nal and background estimates are repeated with the muon resolution parameters worsened by theirrespective uncertainties. The relative differences between the two estimates are then taken as thesystematic uncertainties. Figure 7.4 shows the uncertainty on the background estimate due to muonmomentum resolution uncertainties for the analysis at√s = 8 TeV, while Figure 7.5 demonstratesthat signal event migrations due to this effect are negligible. Results are similar at√s = 7 TeV.As discussed in Section 5.1, the muon momentum scale is calibrated using the Z→ µ+µ− peakto a precision of 0.1%. The effect of pileup on the signal acceptance is also negligible: it is checkedby varying the number of interactions per proton bunch crossing in simulated signal samples andverifying that the signal acceptance does not change significantly.Finally, for data collected at√s = 8 TeV, a systematic uncertainty of 0.65% on the beam energyof 4 TeV propagates to an uncertainty of 3% on the Z/γ∗ background yield at high dimuon invariantmass. This effect was not considered for the analysis at√s = 7 TeV. The effect on the signalnormalization is under 1% for all Z′ masses.124Figure 7.2: Stopping power for positive muons in copper as a function of βγ = p/Mc [52].Figure 7.3: Muon critical energy for the chemical elements [52].125]2 [TeV/c Simulation work in progressATLASµµ3+3 m0.2 0.3 0.4 1 2 3 4Combined resolution systematic00.20.40.60.81]2 [TeV/c Simulation work in progressATLASµµ3+2 m0.2 0.3 0.4 1 2 3 4Combined resolution systematic00.20.40.60.81Figure 7.4: Uncertainty on the background estimate due to the muon resolution as a functionof mµ+µ− , for the primary dimuon selection (left) and the secondary dimuon selection(right) at√s = 8 TeV.]2 [TeV/cµµm1 1.5 2 2.5 3Events00.20.40.60.81 Simulation work in progressATLAS NominalMSUP]2 [TeV/cµµm1 1.5 2 2.5 3 3.5 4 4.5Events00.010.020.030.040.050.06 Simulation work in progressATLAS NominalMSUPFigure 7.5: Z′ signal templates at 2 and 3 TeV for the primary dimuon selection at√s = 8 TeV,with nominal smearing (blue) and over-smearing increasing the MS resolution smearingconstants by their uncertainty (red). The vertical lines indicate the ±1 RMS ranges cor-responding to the nominal templates.7.2 Parton Distribution Function and QCD Uncertainties on SignalCross SectionsThe variation of PDFs and αS are expected to have a large impact on the Z′ cross section as a functionof mass. While by convention theoretical uncertainties on signal do not enter the statistical modelused in searches for new physics, it is important to be aware of them when converting limits on thesignal cross section into model-dependent mass limits. This section explains the techniques used tocalculate uncertainties on signal cross sections due to PDF and αS variations; variants of the sametechniques will be applied when quantifying the impact on background estimates in Section 7.3.In addition to central values of the PDFs, each PDF fit collaboration releases a set of PDFs126varied by their systematic uncertainties. These uncertainties are parametrized using mutually inde-pendent parameters, which are called the “eigenvectors” of the PDF set in function space, as theycan be varied in orthogonal directions to propagate the systematic uncertainties associated with PDFvariations to calculated quantities.For each PDF eigenvector, the Z′ cross section is calculated as a function of mass by generating100,000 simulated events in PYTHIA. This allows to calculate an asymmetric uncertainty at eachmass point using the following equations:∆σ+ =√n∑i=1(max(σ+i −σ0,σ−i −σ0,0))2 (7.2)∆σ− =√n∑i=1(max(σ0−σ+i ,σ0−σ−i ,0))2 (7.3)where n is the number of PDF eigenvectors, σ+i is the cross section for the higher value of the ithPDF eigenvector, σ−i is the cross section for the lower value of the ith PDF eigenvector, and σ0 isthe cross section for the central value PDF. The larger of the positive and negative variation is thentaken as the systematic uncertainty on the Z′ cross section.To generate the MC Z/γ∗ events used to obtain the Z′ signal templates for the analysis usingdata collected at√s = 7 TeV, ATLAS makes use of the modified LO PDF set MRST2007LO**, asdescribed in Section 6.2.1. In contrast with regular LO PDF sets, MRST2007LO** does not includeeigenvector variations. The closest LO PDF set, MSTW2008LO, is therefore used to estimate thePDF uncertainties on signal cross sections. In addition to central values, MSTW2008LO has 20orthogonal eigenvector variations, with high and low values for each eigenvector. The resultinguncertainties are shown in Table 7.3. It is also verified that the Z′ cross sections central valuescalculated using the CTEQ6L1 PDF are within these uncertainties.The same method is used for the analysis at√s = 8 TeV. There, MSTW2008LO is used toobtain the Z′ signal templates and for calculating the uncertainties due to PDF. Uncertainties dueto αS variations are also taken into account by calculating cross section values for αS between0.11365 and 0.12044, which correspond to the 90% CL αS limits of MSTW, and taking the extremalvariations summed in quadrature with the PDF uncertainty. The combined uncertainties due to PDFand αS variations are shown in Table 7.4. Here too, it is verified that the Z′ cross sections centralvalues calculated using a set from another PDF collaboration, in this case CT10, are within theseuncertainties.127Table 7.3: Uncertainty on Z′ cross sections due to PDF variations at 90% CL at√s = 7 TeV.Z′ mass Uncertainty using[GeV] MSTW2008LO at 90% CL100 +3.0% -2.1%200 +2.6% -2.6%500 +4.4% -3.7%1000 +5.5% -7.1%1500 +8.0% -9.8%2000 +8.5% -13.3%Table 7.4: Uncertainty on Z′ cross sections due to PDF and αS variations at 90% CL at√s = 8 TeV.Z′ mass Uncertainty using[GeV] MSTW2008LO at 90% CL200 +5.6% -4.7%500 +4.0% -5.0%1000 +6.8% -6.7%1500 +11.0% -10.6%2000 +17.6% -18.3%2500 +30.1% -29.7%3000 +42.5% -42.3%3500 +51.6% -52.8%4000 +62.1% -60.5%4500 +71.1% -71.9%7.3 Parton Distribution Function and QCD Uncertainties on the Z/γ∗Cross SectionIn addition to having an effect on signal cross sections, as described in Section 7.2, PDF variationshave an effect on the differential Z/γ∗ cross section as a function of the dimuon invariant massmµ+µ− . Indeed this effect represents the dominant source of uncertainty in this analysis.This section describes in detail how this uncertainty is evaluated, in addition to uncertaintiesdue to QCD scale and αS variations.1287.3.1 Parton Distribution Function VariationsIn a manner identical to the central estimate described in Section 6.2.1, the Z/γ∗ cross section iscalculated at NNLO as a function of mµ+µ− , using the program PHOZPR [114] for the analysis at√s = 7 TeV and VRAP [6] for the analysis at√s = 8 TeV, for each PDF eigenvector variation,at 90% CL in the MSTW2008NNLO parametrization [132]. The relative deviation of these crosssections from the values calculated using the nominal PDF is interpreted as the uncertainty on thecross section due to each PDF variation. The asymmetric uncertainties thus calculated are shownfor each PDF eigenvector in Figures 7.6, 7.7 and 7.8, for the analysis at√s = 8 TeV.Then, it is possible to calculate the total asymmetric uncertainty at each invariant mass pointusing Equations 7.2 and 7.3. This is the procedure followed for the analysis at√s = 7 TeV, andthen the larger of the positive and negative asymmetric uncertainties is taken as the total systematicuncertainty on the Z/γ∗ cross section. This symmetric uncertainty enters the likelihood functiondiscussed in Chapter 8 as a single nuisance parameter.However, it has been observed that using a single nuisance parameter for the uncertainty dueto PDFs can lead to an over-constraint. Since the PDF eigenvectors responsible for the uncertaintyat low mass are generally different from the ones responsible for the uncertainty at high mass, theuncertainty values in different mass ranges need to be treated as uncorrelated in the likelihood func-tion. While the most appropriate treatment would then be to assign a distinct nuisance parameter toeach of the 20 PDF eigenvectors, such a prescription would drastically increase the dimensionalityof the fit. As a result, in addition to introducing potential instabilities in the fit, such an approachwould be prohibitive in terms of the computing time required by the statistical framework.Therefore, the following procedure is implemented for the analysis at√s = 8 TeV, as a goodapproximation of the full statistical treatment. PDF eigenvectors are merged into four PDF eigen-vector groups, based on the similar shape of their corresponding uncertainty as a function of mµ+µ− .In the following list, a plus sign means that the eigenvector definition is taken as is, while a minussign means that the definition is inverted such that the downward eigenvector variation is exchangedwith the upward one; this is done so that eigenvectors in a given group behave in the same way.• Group A consists of eigenvectors 2+, 13+, 14-, 17-, 18+ and 20+. It is dominant nowhere, butits contribution is not negligible.• Group B consists of eigenvectors 3-, 4-, 9+ and 11+. It is dominant for mµ+µ− < 400 GeV.• Group C consists of eigenvectors 1+, 5+, 7+, and 8-. It is dominant in the range 400 GeV <mµ+µ− < 1500 GeV.• Group D consists of eigenvectors 10+, 12+, 15-, 16- and 19+. It is dominant for mµ+µ− >1500 GeV.129 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­1­0.500.51PDF eigenvector 1 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­3­2­10123PDF eigenvector 2 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­4­20246PDF eigenvector 3 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­0.3­0.2­0.100.10.20.30.40.5PDF eigenvector 4 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­2­10123PDF eigenvector 5 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­2­1012PDF eigenvector 6 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­4­3­2­1012345PDF eigenvector 7 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­1.5­1­0.500.511.522.53PDF eigenvector 8Figure 7.6: Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8 TeV as a functionof mµ+µ− due to each PDF eigenvector taken separately. Here eigenvectors 1 to 8 areshown.130 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­8­6­4­20246PDF eigenvector 9 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­2­1.5­1­0.500.511.52PDF eigenvector 10 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­20­1001020PDF eigenvector 11 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­20­100102030405060PDF eigenvector 12 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­20­15­10­50510152025PDF eigenvector 13 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­8­6­4­20246810PDF eigenvector 14 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­6­4­202468PDF eigenvector 15 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­8­6­4­20246PDF eigenvector 16Figure 7.7: Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8 TeV as a functionof mµ+µ− due to each PDF eigenvector taken separately. Here eigenvectors 9 to 16 areshown.131 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­3­2­1012PDF eigenvector 17 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­10­505101520PDF eigenvector 18 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­4­20246810PDF eigenvector 19 [GeV]llm500 1000 1500 2000 2500 3000 3500 4000 4500 5000Signed relative uncertainty [%]­20­15­10­50510PDF eigenvector 20Figure 7.8: Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8 TeV as a function ofmµ+µ− due to each PDF eigenvector taken separately. Here eigenvectors 17 to 20 areshown.The remaining eigenvector, number 6, has a shape that does not match any group, and its uncertaintycontribution is negligible.Within a group, the uncertainties from the constituent eigenvectors are combined in the follow-ing manner at each mass point:∆σ+G = signG√signGnG∑i=1sign(σ+i −σ0)(σ+i −σ0)2 (7.4)∆σ−G = signG√signGnG∑i=1sign(σ−i −σ0)(σ−i −σ0)2 (7.5)where the sum is over the nG PDF eigenvectors in a given group G, σ+i is the cross section forthe upward variation of the ith PDF eigenvector (downward variation, if inverted), σ−i is the crosssection for the downward variation of the ith PDF eigenvector (upward variation, if inverted), σ0 isthe cross section for the central value PDF, and signG is the sign of the sum inside the square root.This asymmetric uncertainty on the Z/γ∗ cross section as a function of mµ+µ− due to the four132distinct PDF eigenvector groups is shown in Figure 7.9, along with the total symmetric uncertaintyobtained using the MSTW prescription (which includes eigenvector 6).As a closure test, Figure 7.10 shows this same total symmetric uncertainty, compared to thesymmetric uncertainty resulting from the addition in quadrature of the uncertainties from the fourPDF eigenvector groups. The total symmetric uncertainty as calculated with FEWZ is also shownfor comparison. Above the invariant mass cut at 80 GeV used in the analysis at√s = 8 TeV, theapproximation results in a small overestimate of the total uncertainty, of under 0.35% below 3.5 TeV,and under 1% below 4.5 TeV, comparing calculations done with VRAP. The overestimate is slightlyworse when eigenvector 6 is taken into account as a fifth group. The uncertainties obtained withFEWZ and VRAP are in good agreement with each other.In conclusion, for the analysis on data collected at√s = 8 TeV in 2012, the uncertainty due toPDF variations on the Z/γ∗ cross section as a function of mµ+µ− is parametrized using four nuisanceparameters, corresponding to groups of PDF eigenvectors.7.3.2 Parton Distribution Function Set Choice, QCD Scale and αSIn addition to the uncertainty from PDF variations, we consider uncertainties coming from QCDscale and αS variations. These are also calculated using PHOZPR for the analysis at√s = 7 TeVand VRAP for the analysis at√s = 8 TeV. The QCD scale uncertainties are estimated by varyingthe renormalization and factorization scales simultaneously up and down by a factor of two. Theresulting maximum variations are taken as the uncertainties. To estimate the uncertainties due toαS variations, cross section values as a function of mµ+µ− are calculated for αS between 0.11365and 0.12044, corresponding to the limits on αS at 90% CL from MSTW2008 [133]. The extremalvariations, corresponding to these boundary values of αS, are taken as the asymmetric uncertainty.For the analysis at√s = 7 TeV, the central values for the Z/γ∗ cross section as a function ofmµ+µ− calculated with different PDF sets are compatible within uncertainties. When repeating thisverification at√s = 8 TeV by comparing MSTW2008 with the most recent predictions at NNLO andαS = 0.117 from the other PDF fit collaborations CT10 [103, 121], NNPDF2.3 [41], ABM11 [1] andHERAPDF1.5 [113], the central values from ABM11 are found to fall outside of the MSTW2008PDF uncertainty at 90% CL. An additional uncertainty is therefore assigned to reflect potentialdifferences in the underlying theoretical framework between the PDF fit collaborations. To avoiddouble-counting the uncertainty due to PDF variations, this additional uncertainty is taken as the dif-ference in quadrature between the cross section central values from ABM11 and the PDF variationuncertainty envelope from MSTW2008.A summary of the uncertainties on the Z/γ∗ background estimate is shown in Figure 7.11.133 [GeV]llm210 310Relative uncertainty [%]­80­60­40­20020406080PDF eigenvector group APDF eigenvector group BPDF eigenvector group CPDF eigenvector group DTotal symmetric PDF uncertainty from MSTW2008 [GeV]llm210 310Relative uncertainty [%]­20­15­10­505101520PDF eigenvector group APDF eigenvector group BPDF eigenvector group CPDF eigenvector group DTotal symmetric PDF uncertainty from MSTW2008Figure 7.9: Asymmetric uncertainty on the Z/γ∗ cross section at√s = 8 TeV as a function ofthe dilepton invariant mass due to the four distinct PDF eigenvector groups described inthe text. The total symmetric uncertainty is shown in black. The bottom graph zooms into show the low invariant mass region better.134 [GeV]llm210 310Relative uncertainty [%]010203040506070Total symmetric PDF uncertainty:Addition in quadrature of 4 PDF groups, calculated with VRAPUsing the MSTW prescription, calculated with VRAPUsing the MSTW prescription, calculated with FEWZ [GeV]llm210 310Relative uncertainty [%]012345678910Total symmetric PDF uncertainty:Addition in quadrature of 4 PDF groups, calculated with VRAPUsing the MSTW prescription, calculated with VRAPUsing the MSTW prescription, calculated with FEWZFigure 7.10: Symmetric uncertainty on the Z/γ∗ cross section at√s = 8 TeV as a function ofthe dilepton invariant mass resulting from the addition in quadrature of the uncertaintiesfrom the four PDF eigenvector groups (in red), compared to the total symmetric uncer-tainty obtained using the MSTW prescription calculated with VRAP (in black) andFEWZ (in green). The bottom graph zooms in the mass region from 80 to 1500 GeV.135 [GeV]llm210 310Relative uncertainty [%]­80­60­40­20020406080ScalesαHigher­order electroweakPhoton­induced correctionsPDF: MSTW2008ABM11 vs. MSTW2008: envelope diff. in quad. [GeV]llm210 310Relative uncertainty [%]­20­15­10­505101520ScalesαHigher­order electroweakPhoton­induced correctionsPDF: MSTW2008ABM11 vs. MSTW2008: envelope diff. in quad.Figure 7.11: Symmetric uncertainty on the Z/γ∗ cross section at√s = 8 TeV as a functionof the dilepton invariant mass obtained using the MSTW prescription calculated withVRAP, shown along with the uncertainties due to the QCD scale, αS variations, photon-induced corrections and higher-order electroweak corrections, as well as the differencebetween the cross section central values from ABM11 and the PDF variation uncertaintyenvelope from MSTW, taken as an additional systematic uncertainty. The bottom graphzooms in to show the low invariant mass region better.136Chapter 8Statistical Methods and ResultsThis chapter presents the statistical methods used in the search for new neutral high-mass resonancesdecaying into muon pairs, as well as the results of the analysis. First, the dimuon invariant massspectra of Figures 6.16 and 6.17 are scanned to look for positive deviations of the observed eventyields with respect to the expected backgrounds: significant excesses could be indicative of theexistence of a signal. The methods used to quantify this significance are detailed in Section 8.1.Following the signal search, in the case of a null result, limits are placed on the existence of newphenomena indicative of physics beyond the Standard Model. As indicated in Chapter 3, this searchis sensitive to a wide variety of hypotheses, and the interpretations considered here in Sections 8.2and 8.3 concern models predicting new gauge bosons. These results and many other interpretationswere published in Ref. [25] and [36]. Importantly, this search was also performed in the dielectronchannel, and published jointly. The results in the Z′ interpretation for the combination of bothchannels are also presented here1.8.1 Signal SearchTwo techniques are used to assess the significance of observed excesses in data above backgroundexpectations. In both cases this significance is quantified using a p-value, defined as the probability,assuming that a signal is absent, of observing an outcome at least as consistent with the existenceof signal as the one observed in data. This probability is often quoted in terms of the one-sidedintegral of a unit-width Gaussian distribution: for example, the integral beyond +3σ is equal to1.35×10−3. According to the convention used in experimental particle physics, a p-value smallerthan this number constitutes evidence for the existence of a signal; such evidence is then calleda “3σ effect”. Discoveries are only formally claimed when p < 2.87×10−7, corresponding to a“5σ effect”.1 In this chapter, the symbol `± therefore represents e± and µ± only, instead of e±, µ± and τ± as in Chapter 2.Among other differences the symbol L is used to represent likelihood functions instead of Lagrangians, etc.1378.1.1 Local p-ValuesThe first method used quantifies the significance individually for each histogram bin of the discrim-inating variable, in this case the dilepton invariant mass m``. This local significance is calculatedfollowing the methods from Ref. [72].Using Poisson statistics, the likelihood L to observe exactly N data events given µ expectedevents under hypothesis H is given byL (N|µ(H)) = µNe−µN!(8.1)If N > µ , there is an excess of observed events and the p-value then corresponds to the probabilityto have observed a number n≥ N events given the null hypothesis H0:p(n≥ N|µ(H0)) =∞∑k=Nµke−µk!= 1−N−1∑k=0µke−µk!(8.2)On the other hand if N < µ , there is an observed deficit with p-valuep(n≤ N|µ(H0)) =N∑k=0µke−µk!(8.3)Systematic uncertainties introduce an overall variance V on the expected number of events µ . Thisvariance is taken into account by setting a gamma distribution as the prior for µ:g(x;a,b) =baΓ(a)xa−1e−bx (8.4)where the parameters a and b are such thatµ = aband V =ab2⇒ a =µ2Vand b =µV(8.5)and Γ is the gamma function:∫ ∞0xa−1e−bxdx =Γ(a)ba(8.6)138Then the likelihood becomesL (N|µ(H),V (H)) =∫ ∞0xNe−xN!g(x;a,b)dx=∫ ∞0xNe−xN!·baΓ(a)xa−1e−bxdx=baN! Γ(a)∫ ∞0xN+a−1e−(1+b)xdx=baN! Γ(a)·Γ(N +a)(1+b)N+a(8.7)and hence the p-values arep(n≥ N|µ(H0),V (H0)) = 1−N−1∑k=0L (k|µ(H),V (H)) (8.8)p(n≤ N|µ(H0),V (H0)) =N∑k=0L (k|µ(H),V (H)) (8.9)Figures 8.1 and 8.2 present the dimuon and dielectron invariant mass spectra with data collectedin 2011 and 2012 respectively, with the bin-by-bin local significances calculated with this method.The histograms are shown in the search region: 128 GeV < m`` < 3000 GeV for the analysis at√s = 7 TeV and 128 GeV < m`` < 4500 GeV for the analysis at√s = 8 TeV. No local excess ordeficit with local significance beyond ±2σ is observed in any of the invariant mass histogram bins.The apparent presence of a global deficit in the dimuon dataset at√s = 7 TeV was investigatedby varying the muon momentum smearing parameters down beyond their uncertainties: this did notsignificantly impact the observed deficit. This leaves the overall normalization of the backgroundestimates obtained from simulation as a possible cause; this was investigated with the source of thiseffect remaining unascertained. Such a deficit does not appear in the dataset at√s = 8 TeV.139Figure 8.1: Differences between data and expectation in the and dimuon (top) and dielectron(bottom) channels at√s = 7 TeV, with both the statistical and systematic uncertaintiestaken into account to derive a bin-by-bin local significance, shown in blue.140Number of Events­210­110110210310410DataBackground expectationwith syst. uncertaintySignificance with stat.and syst. uncertainty work in progressATLAS­1 L dt = 20.5 fb∫ = 8 TeVs [TeV]µµm0.2 0.3 0.4 1 2 3 4significance­3­2­10123Number of Events­210­110110210310410DataBackground expectationwith syst. uncertaintySignificancewith stat. uncertaintySignificance with stat.and syst. uncertainty work in progressATLAS­1 L dt = 20.3 fb∫ = 8 TeVs [TeV]eem0.2 0.3 0.4 1 2 3 4significance­2­101234Figure 8.2: Differences between data and expectation in the dimuon (top) and dielectron (bot-tom) channels at√s = 8 TeV, with both the statistical and systematic uncertainties takeninto account to derive a bin-by-bin local significance, shown in blue.1418.1.2 Global p-ValuesWhile the method discussed in the previous section has the advantage of quantifying potential local-ized excesses in a general manner, that is independently of any signal hypothesis, another approachis needed to quantify the compatibility of data with specific signal hypotheses, taking the full rangeof the search region into account. For this purpose, this analysis interfaces the Bayesian AnalysisToolkit (BAT) [62] to calculate global p-values using a template shape fitting technique2. This tech-nique generalizes the likelihood from Equation 8.1 by taking the product of likelihood functionsfrom all histogram bins of the search region:L (N|µ(H)) =nbins∏j=1µ jN j e−µ jN j!(8.10)where for each bin j of the search region, µ j represents the expected number of events and N j theobserved number of events. Such a likelihood function takes into account the full background andsignal templates defined in Section 6.2, as well as the complete information from the selected data.Mass-dependent systematic uncertainties are incorporated into the likelihood function as nui-sance parameters θs, which control the magnitude of variations εs j of the expected number of eventsµ j in bin j due to each systematic uncertainty s. The nominal range of variations expected fromeach systematic uncertainty are detailed in Chapter 7. Specifically, the effect of these variations onthe expected yields isµ j → µ˜ j = µ j(1+nsyst∑s=1θsεs j) (8.11)The prior on each nuisance parameter is taken to be a Gaussian with zero mean and unit width. Thelikelihood therefore becomesL (N|µ(H),θ ,ε) =nbins∏j=1µ˜N jj e−µ˜ jN j!nsyst∏s=1e−θ2s /2√2pi(8.12)When multiple search channels are considered, the joint likelihood is the product of the individuallikelihoods from each channel. Systematic uncertainties that are fully correlated across channelsare assigned the same nuisance parameter, while uncorrelated systematic uncertainties are assigneddistinct nuisance parameters in each channel.To assess the compatibility of experimental data with a specific signal hypothesis HZ′ , as com-pared to the null hypothesis H0, a test is performed as a function of the Z′ signal cross section σZ′and mass MZ′ , using templates of Z′SSM signal. The chosen test is based on the Neyman-Pearsonlemma [138], which applied to this situation states that the most powerful test statistic to reject H02 The Bayesian Analysis Toolkit can be used to calculate p-values, although this concept is intrinsically frequentist.142in favour of HZ′ is the Log-Likelihood Ratio (LLR)LLR =−2lnL (N|µ(σˆZ′ ,MˆZ′), θˆ ,ε)L (N|µ(σZ′ = 0), ˆˆθ ,ε)(8.13)where σˆZ′ , MˆZ′ and θˆ are the best-fit values for the respective parameters given HZ′ , and ˆˆθ representsthe best-fit values of the nuisance parameters given H0. The best-fit values are the ones at the globalmaximum of the corresponding likelihood function given the data. Figure 8.3 shows the absolutevalue of the LLR as a function of the Z′ signal mass MZ′ and cross section σZ′ , using the√s = 7 TeVdataset, separately for both channels of the search.The global p-value in each channel is then the probability, assuming H0, of observing a value ofthe LLR test statistic at least as consistent with the existence of signal as the one observed in data,that isp = p(LLR≤ LLRobs|H0) (8.14)where because of the minus sign in the definition of the LLR, more negative values imply betteragreement with HZ′ compared to H0. The LLR distribution given H0 is obtained using pseudo-experiments, i.e. collections of events drawn from the background templates corresponding to theintegrated luminosity of the actual dataset. Figure 8.4 shows the LLR distributions obtained using10,000 pseudo-experiments at√s = 8 TeV. To obtain the global p-values, these distributions aresummed starting from the observed LLR toward more negative values. The p-value from eachchannel is then the value of this sum over the total number of pseudo-experiments considered. Thedata are found to be consistent with the null hypothesis, with p-values of 28% in the dimuon channeland 27% in the dielectron channel. Similar results are obtained in the analysis at√s = 7 TeV: therethe p-values are 68% in the dimuon channel and 36% in the dielectron channel.143 [pb]Z’σ0 0.02 0.04 0.06 [Tev]Z’M12300.511.52µµ →Z’ ATLASp = 0.675 = 7 TeVs­1 L dt = 5.0 fb∫Signal Scan, Best Fit [pb]Z’σ0 0.01 0.02 0.03 [Tev]Z’M12301234 ee→Z’  ATLASp = 0.361 = 7 TeVs­1 L dt = 4.9 fb∫Signal Scan, Best FitFigure 8.3: Absolute value of the LLR used in the search, as a function of the Z′ signal massMZ′ and cross section σZ′ , using the√s = 7 TeV dataset in the dimuon (top) and dielec-tron (bottom) channels. The most signal-like value of the LLR found is indicated with awhite marker.144LLR­18 ­16 ­14 ­12 ­10 ­8 ­6 ­4 ­2 0Pseudo­Experiments10210310410Pseudo­Experiments­ Dataµ+µObserved value in ATLAS = 8 TeVs­1 L dt = 20.5 fb∫: µµp=0.28Observed LLR­18 ­16 ­14 ­12 ­10 ­8 ­6 ­4 ­2 0Pseudo­Experiments110210310410Pseudo­ExperimentsObserved value in e+e­ DataATLAS = 8 TeVs­1 L dt = 20.3 fb∫ee: p=0.27Observed Figure 8.4: Distribution of the most signal-like LLR found in each of 10,000 pseudo-experiments at√s = 8 TeV, separately for the dimuon (top) and dielectron (bottom)channels. The most signal-like LLR found in data is indicated with the blue arrow, andthe p-value is the fraction of entries to the left of this arrow.1458.2 Limits on Z′SSM and E6 Z′ BosonsSince the data are found to be consistent with predictions from the Standard Model, limits are seton the existence of Z′ bosons, using BAT. This section presents limits set on the cross section σ forZ′ boson production times its branching fraction B in individual dilepton channels.As explained in Section 6.2.3, in this nominal approach to the analysis each choice of Z′ bosontype and mass MZ′ corresponds to a specific signal template, and the expected number of eventsµ(HZ′) only depends on σB. The general expression for the binned Poisson likelihood function inEquation 8.12 can then be reduced to a function of the parameter of interest, in this case σB, byperforming a numerical integration over the nuisance parameters using a Markov chain Monte Carloalgorithm. The marginalized likelihood function is thusL ′(N|σB) =∫L (N|σB,θ ,ε)nsyst∏s=1dθs (8.15)Using this function, the posterior probability density L ′(σB|N) is obtained using Bayes’ theorem:L ′(σB|N) =L ′(N|σB)pi(σB)pi(N) (8.16)where pi(σB) is the prior for σB, taken as a constant, and pi(N) is the prior for the observed numberof events, which does not depend on σB. The most probable signal strength given the data is givenby the maximum of L ′(σB|N).Limits at 95% CL are placed on σB by integrating the posterior probability density as follows,to find the limit value (σB)95 such that0.95 =∫ (σB)950 L′(σB|N)d(σB)∫ ∞0 L′(σB|N)d(σB) (8.17)Figure 8.5 shows the observed limits on σB for Z′SSM and E6 Z′ production calculated in this man-ner as a function of MZ′ , using data collected at√s = 7 TeV for the dimuon channel and for thecombined dielectron and dimuon channels. The range of expected limits calculated using pseudo-experiments is also shown for comparison. The limits using data collected at√s = 8 TeV are shownin Figure 8.6 for E6 Z′ production, and Figure 8.7 for Z′SSM production.Lower limits on the mass of Z′ bosons are obtained from the upper limits on σB by findingtheir intersection with the theory curves for σB as a function of MZ′ for the different hypothesesunder consideration. Table 8.1 shows the observed and expected values of these mass limits for thecombination of dielectron and dimuon channels. The ratio of combined limits on σ(Z′SSM→ `+`−)to the theoretical cross section is shown in Figure 8.8 for all four published results of this search bythe ATLAS collaboration [18, 19, 25, 36].146 [TeV]Z’M0.5 1 1.5 2 2.5 3 B [pb]σ­410­310­210­1101 Expected limitσ 1±Expected σ 2±Expected Observed limitSSMZ’χZ’ψZ’ATLASµµ →Z’  = 7 TeVs­1 L dt = 5.0 fb∫: µµ [TeV]Z’M0.5 1 1.5 2 2.5 3 B [pb]σ­410­310­210­1101 Expected limitσ 1±Expected σ 2±Expected Observed limitSSMZ’χZ’ψZ’ATLAS ll→Z’  = 7 TeVs­1 L dt = 5.0 fb∫: µµ ­1 L dt = 4.9 fb∫ee: Figure 8.5: Observed (red line) and expected upper limits on σB for Z′ boson production at√s = 7 TeV for the dimuon channel (top) and for the combined dielectron and dimuonchannels (bottom). The median expected limit is shown as a black dashed line, withthe ranges at ±1σ and ±2σ around the median shown as the yellow and green bands.The region above each of these lines is excluded at 95% CL. The three theory curvesfor Z′SSM and E6 Z′ boson production are also shown. Other theory curves belonging toE6-motivated models fall between the Z′ψ and Z′χ , since these signals respectively havethe smallest and largest σB. The dashed lines around the Z′SSM theory curve representthe theoretical uncertainty, which is similar for the other theory curves.147Table 8.1: Observed and expected lower limits at 95% CL on the mass of Z′SSM and E6 Z′bosons obtained by the ATLAS experiment.Centre-of-mass energy Channel Mass limits at 95% CL [TeV]Z′SSM Z′ψ Z′χobs. (exp.) obs. (exp.) obs. (exp.)√s = 7 TeV pp→ e+e−,µ+µ− 2.22 (2.25) 1.79 (1.87) 1.97 (2.00)√s = 8 TeV pp→ e+e−,µ+µ− 2.90 (2.87) 2.51 (2.46) 2.62 (2.60) [TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 B [pb]σ­510­410­310­210­1101Expected limitσ 1±Expected σ 2±Expected Observed limitχZ’ψZ’ATLAS ll→Z’  = 8 TeVs­1 L dt = 20.3 fb∫ee: ­1 L dt = 20.5 fb∫: µµFigure 8.6: Observed (red line) and expected upper limits on σB for the E6 Z′ψ boson pro-duction at√s = 8 TeV for the combination of the dielectron and dimuon channels. Themedian expected limit is shown as a black dashed line, with the ranges at ±1σ and ±2σaround the median shown as the yellow and green bands. The region above each ofthese lines is excluded at 95% CL. The two theory curves corresponding to Z′ψ and Z′χboson production are also shown. Other Z′ signals belonging to E6-motivated Modelsfall between these two cases, since Z′ψ and Z′χ respectively have the smallest and largestσB. The thickness of the Z′ψ theory curve represents the theoretical uncertainty, which issimilar for the Z′χ theory curve.148 [TeV]SSMZ’M0.5 1 1.5 2 2.5 3 3.5 B [pb]σ­410­310­210­110 µµExpected limit µµObserved limit Expected limit eeObserved limit eeExpected limit llObserved limit llSSMZ’ATLAS ll→ SSMZ’ = 8 TeVs­1 L dt = 20.3 fb∫ee: ­1 L dt = 20.5 fb∫: µµFigure 8.7: Observed and median expected upper limits on σB for Z′SSM boson productionat√s = 8 TeV for the exclusive dimuon and dielectron channels, and for both channelscombined. The region above each of these lines is excluded at 95% CL. The Z′SSM theorycurve is also shown; the grey area represents its theoretical uncertainty. [TeV]Z’M0.5 1 1.5 2 2.5 3 3.5SSMσ/limitσ-410-310-210-110110 )-1 20.5 fbµµ; -1 = 8 TeV (ee 20.3 fbsATLAS  )-1 5.0 fbµµ; -1 = 7 TeV (ee 4.9 fbsATLAS  ) -1 1.21 fbµµ; -1 = 7 TeV (ee 1.08 fbsATLAS  )-1 42 pbµµ; -1 = 7 TeV (ee 39 pbsATLAS ATLAS ll→Z’ Figure 8.8: Ratio of the observed limits for the Z′SSM search to the Z′SSM cross section timesbranching fraction for the combination of dielectron and dimuon channels. The regionabove each line is excluded at 95% CL. All four published results of this search by theATLAS collaboration are shown.1498.3 Limits on Minimal Z′ ModelsIn the context of Minimal Z′ Models, limits are placed not on the cross section times branchingfraction σB, but rather on the Z′ coupling γ ′ itself as a function of the mass MZ′ and of the mixingangle θMin.As indicated in Section 6.2.3, in this case signal templates are generated as a function of bothmµ+µ− and γ ′ for each pair of values of MZ′ and θMin under consideration. The likelihood functionis otherwise defined analogously: for each value of MZ′ and θMin, the expected number of eventsµ j(H) and systematic variations εs j now depend on both mµ+µ− and γ ′ instead of only on mµ+µ− .The marginalized likelihood function becomesL ′(N|γ ′) =∫L (N|γ ′,θ ,ε)nsyst∏s=1dθs (8.18)Bayes’ theorem is used with a prior pi(γ ′) constant in γ ′4: this is justified by the fact that the crosssection for Z′ boson production is proportional to γ ′4. Limits at 95% CL are then placed on γ ′ byintegrating the posterior probability density in the same way as in the previous section, to find γ ′95such that0.95 =∫ γ ′950 L′(γ ′|N)dγ ′∫ ∞0 L′(γ ′|N)dγ ′ (8.19)The resulting upper limits on γ ′ are shown as a function of MZ′ in Figure 8.9 for the datasetat√s = 7 TeV and in Figure 8.10 for the dataset at√s = 8 TeV. In the latter case, limits are alsodisplayed as a function of θMin for specific values of MZ′ in Figure 8.11.Lower limits on the Z′ boson mass can also be obtained in this framework, by finding the in-tersection of the upper limits on γ ′ with the nominal γ ′ values from theory given in Table 3.1, withsinθW = 0.48. The results are given in Table 8.2. The ranges of observed and expected limits on MZ′for θMin ∈ [0,pi] and representative values of γ ′ are given in Table 8.3, and the ranges of observedand expected limits on γ ′ for θMin ∈ [0,pi] and representative values of MZ′ are given in Table 8.4.150 [TeV]MinZ’M0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ’γ­1101 ]pi [0, ∈ θLimit range for Limit range (expected))3R(Z’θ ) (expected)3R(Z’θ )B­L(Z’θ ) (expected)B­L(Z’θATLASµµ → MinZ’ = 7 TeVs­1 L dt = 5.0 fb∫ [TeV]MinZ’M0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 ’γ­1101 ]pi [0, ∈ θLimit range for Limit range (expected))3R(Z’θ ) (expected)3R(Z’θ )B­L(Z’θ ) (expected)B­L(Z’θATLAS ll→ MinZ’ = 7 TeVs­1 L dt = 4.9 fb∫, ee: ­1 L dt = 5.0 fb∫: µµFigure 8.9: Observed and expected limits on γ ′ as a function of the Z′ mass at√s = 7 TeV,for the dimuon channel (top) and for the combined dielectron and dimuon channels (bot-tom). Two limit curves are displayed for representative values of θMin, which at specificvalues of γ ′ correspond to the Z′R and Z′B−L models. The collection of all limit curves forθMin ∈ [0,pi] forms the grey band. The region of parameter space above each limit curveis excluded at 95% CL.151 [TeV]MinZ’M0.5 1 1.5 2 2.5 3 3.5 ’γ­1101    ]pi  [0, ∈ Minθ Limit range for )χ(Z’Minθ )3R(Z’Minθ )B­L(Z’Minθ ATLASµµ → MinZ’ = 8 TeVs­1 L dt = 20.5 fb∫: µµ Exp.  Obs. [TeV]MinZ’M0.5 1 1.5 2 2.5 3 3.5 ’γ­1101    ]pi  [0, ∈ Minθ Limit range for )χ(Z’Minθ )3R(Z’Minθ )B­L(Z’Minθ ATLAS ll→ MinZ’ = 8 TeVs­1 L dt = 20.3 fb∫ee: ­1 L dt = 20.5 fb∫: µµ Exp.  Obs.Figure 8.10: Observed and expected limits on γ ′ as a function of the Z′ mass at√s = 8 TeV,for the dimuon channel (top) and for the combined dielectron and dimuon channels(bottom). Three limit curves are displayed for representative values of θMin, whichat specific values of γ ′ correspond to the Z′χ , Z′R and Z′B−L models. The collection ofall observed limit curves for θMin ∈ [0,pi] forms the grey band, while the grey dottedlines delimit the area containing the corresponding expected limit curves. The regionof parameter space above each limit curve is excluded at 95% CL.152Minθ0 0.5 1 1.5 2 2.5 3 ’γ­110110 = 3.5 TeVMinZ’M = 3.0 TeVMinZ’M = 2.5 TeVMinZ’M = 2.0 TeVMinZ’M = 1.5 TeVMinZ’M = 1.0 TeVMinZ’M = 0.5 TeVMinZ’MATLASµµ → MinZ’ = 8 TeVs­1 L dt = 20.5 fb∫: µµ Exp.  Obs.Minθ0 0.5 1 1.5 2 2.5 3 ’γ­110110 = 3.5 TeVMinZ’M = 3.0 TeVMinZ’M = 2.5 TeVMinZ’M = 2.0 TeVMinZ’M = 1.5 TeVMinZ’M = 1.0 TeVMinZ’M = 0.5 TeVMinZ’MATLAS ll→ MinZ’ = 8 TeVs ­1 L dt = 20.3 fb∫ee: ­1 L dt = 20.5 fb∫: µµ Exp.  Obs.Figure 8.11: Observed and expected limits on γ ′ as a function of θMin at√s = 8 TeV, for thedimuon channel (top) and for the combined dielectron and dimuon channels (bottom).The limits are set for seven representative values of MZ′Min . The region of parameterspace above each limit curve is excluded at 95% CL.153Table 8.2: Observed and expected lower limits at 95% CL on the mass of Z′B−L, Z′χ and Z′Rbosons obtained by the ATLAS experiment in the context of Minimal Z′ Models. Hereinterference effects are taken into account and the width ΓZ′ is varied simultaneouslywith σZ′ , resulting in slightly weaker limits for Z′χ than with the nominal approach.Centre-of-mass energy Channel Mass limits at 95% CL [TeV]Z′B−L Z′χ Z′Robs. (exp.) obs. (exp.) obs. (exp.)√s = 7 TeV pp→ e+e−,µ+µ− 2.13 (2.14) 1.89 (1.93) 2.11 (2.11)√s = 8 TeV pp→ e+e−,µ+µ− 2.80 (2.76) 2.51 (2.46) 2.73 (2.69)Table 8.3: Range of the observed and expected lower limits at 95% CL on the Z′Min boson massfor θMin ∈ [0,pi] and representative values of the relative coupling strength γ ′. Both leptonchannels are combined.Centre-of-mass energy γ ′ Range of limits on MZ′Min [TeV]obs. (exp.)√s = 7 TeV 0.1 0.67-1.43 (0.58-1.47)0.2 1.11-2.10 (1.17-2.07)√s = 8 TeV 0.2 1.24-2.28 (1.22-2.39)0.3 1.89-2.93 (1.83-2.82)0.4 2.09-3.12 (2.03-3.08)0.5 2.20-3.24 (2.16-3.19)0.6 2.31-3.39 (2.24-3.32)Table 8.4: Range of the observed and expected upper limits at 95% CL on the relative couplingstrength γ ′ for θMin ∈ [0,pi] and representative values of the Z′Min boson mass. Both leptonchannels are combined.Centre-of-mass energy MZ′Min [TeV] Range of limits on γ′obs. (exp.)√s = 7 TeV 1.0 0.08-0.16 (0.07-0.15)2.0 0.16-1.10 (0.17-1.01)√s = 8 TeV 1.0 0.08-0.16 (0.08-0.16)2.0 0.17-0.34 (0.15-0.37)3.0 0.33-1.71 (0.35-1.90)154Chapter 9OutlookLooking forward, Run-II of the LHC in 2015–2017 will be a very exciting opportunity to bringthis search to new heights. Increasing the centre-of-mass energy from 8 TeV to at least 13 TeVwill drastically improve the search prospects at high resonance masses: to give a specific example,the parton luminosity for quark-antiquark processes is expected to grow by a factor O(100) for aresonance mass of 4 TeV, as shown in Figure 9.1. As a result, the current limits on new neutralresonances are expected to be surpassed with as little as 5 fb−1 of Run-II data. By the end ofRun-II, with an integrated luminosity of 75 to 100 fb−1, the reach of the search will be extendedto even lower signal cross sections across the whole invariant mass spectrum. Then, a total of upto 300 fb−1 is expected in Run-III of the LHC, and up to 3000 fb−1 will be delivered at the High-Luminosity LHC (HL-LHC) by the year 2030 [26]. This will make possible a direct observationof the H → µ+µ− decay channel, thereby allowing to measure the Yukawa coupling of the Higgsboson to muons, in addition to any unexpected discoveries to come. Figure 9.2 shows the expectedlimits on Z′ boson production in the dimuon channel with the projected HL-LHC dataset: the lowerlimit at 95% CL on the mass of Z′SSM bosons is expected to reach 7.6 TeV.Such improvements will not come without hard work by the collaboration. The increased eventpileup coming from up to 70 interactions per proton-proton bunch crossing on average in Run-III,and up to 140 interactions per crossing on average at the HL-LHC, will bring tremendous gains ininstantaneous luminosity but also challenges in triggering and reconstructing these events. In partic-ular, the Inner Detector of ATLAS will need to be completely replaced to accommodate the highercharged track rates and number of collision vertices to identify. The calorimeters and the MuonSpectrometer will be upgraded in the forward region of the detector, in the first case to ensure thatthe liquid-argon calorimeter performance remains acceptable amid larger radiation levels, and in thesecond to mitigate the effects of increased fake muon backgrounds on the tracking efficiency andtrigger rates. As well, new front-end electronics will be necessary in order to read out the infor-mation from all detector subsystems faster, which along with developments in the trigger software155will considerably improve trigger decision times. Dedicated research and development is ongoingto ensure that the ambitious goals of the LHC machine are met by corresponding upgrades to itsdetectors, in order to enable their operation for years to come.1001000110100  gg  Σqq  qgWJS2013ratios of LHC parton luminosities: 13 TeV / 8 TeV luminosity ratioM X (GeV)MSTW2008NLO_Figure 9.1: Ratios of the parton luminosity accessible at the LHC at√s = 13 TeV compared tothat at√s = 8 TeV for gluon-gluon, gluon-quark and quark-antiquark processes. Figurecredit: W. J. Stirling.Figure 9.2: Expected upper limits on σB for Z′SSM boson production for the projected HL-LHC dataset in the dimuon channel. The median expected limit is shown as a blackdashed line, with the ranges at ±1σ and ±2σ around the median shown as the yellowand green bands. The region above each of these lines is excluded at 95% CL. The Z′SSMtheory curve is also shown [26].156Chapter 10ConclusionIn the search for new neutral high-mass resonances decaying into muon pairs performed by theATLAS experiment, the dimuon invariant mass spectrum was compared to expectations from theStandard Model of particle physics. A wide variety of hypotheses beyond the Standard Modelpredict the existence of a resonant peak in this spectrum corresponding to a new particle with amass larger than the Z boson mass.A detailed understanding of the performance of the detector for reconstructing muons at veryhigh momentum is absolutely necessary for this search to be successful, since only the best-measured reconstructed muon tracks from the detector have a momentum resolution that makespossible the reconstruction of a peak at the TeV scale. It is also crucial to prevent contaminationof the signal region from mis-measured tracks that falsely appear at high momentum. Therefore,stringent selection criteria were defined for the muon tracks used in the search: for example, mostof the selected muons are well-measured in all three stations of the Muon Spectrometer of ATLAS.The signal acceptance of the search was increased following dedicated studies, which found muontracks passing through two stations of the Muon Spectrometer but with acceptable momentum reso-lution. Other selection criteria on the isolation and impact parameter of muon tracks eliminated thebackgrounds due to physical processes with muons from hadronic jets and cosmic rays.Following the event selection, the observed event yields were compared with state-of-the-arttheoretical calculations for the expected dimuon invariant mass spectrum from the Standard Model,with the acceptance, efficiency and resolution of the detector for reconstructing muon tracks takeninto account using Monte Carlo simulations. Systematic uncertainties on this prediction were care-fully evaluated. The dominant uncertainty comes from our limited knowledge of PDFs at the highmomentum fraction values necessary for the production of a resonance at high mass.The agreement with the predictions from the Standard Model is remarkable. No significant ex-cess of observed events was found in the full proton-proton collision dataset collected at√s = 7 TeVand√s = 8 TeV in Run-I of the LHC, and limits were consequently placed on the existence of new157gauge bosons Z′. These new gauge bosons are predicted in theoretical hypotheses that reach beyondthe Standard Model in order to address some of its shortcomings. In particular, limits were set at95% CL excluding Z′ bosons from the Sequential Standard Model with masses below 2.90 TeV, andZ′ from Grand Unified Theories with masses below 2.51 to 2.80 TeV depending on the symmetrybreaking scenario. Limits on Z′ bosons set by the CMS collaboration are similar. These resultsrepresent an excellent improvement over previous limits, set around 1 TeV by the CDF and D0experiments at the Tevatron.Furthermore, alternative theoretical hypotheses predict other types of new neutral particles thatcan also decay into muon pairs, and this search is also sensitive to them. Public results by theATLAS collaboration [25, 36] place limits on a wide variety of these models using exactly the samemethods as detailed in this dissertation. As well, it is possible to recast these experimental results inorder to set bounds relevant to other hypotheses. The results of this analysis therefore help to guidefuture theoretical research by restricting the allowed parameter space for new models.The sensitivity of this search will keep improving in Run-II of the Large Hadron Collider andbeyond, as the energy and intensity frontiers are pushed further by technological developments. Thediscovery of a new neutral resonance would have a profound impact on our understanding of theuniverse. Should such a new particle be observed, an analysis of the angular distributions of thefinal-state leptons would provide key information towards identifying its properties. Otherwise, inthe case of a null result, increasing the exclusion limits will provide even more stringent boundson physics beyond the Standard Model. Either way, the continuation of this search, and moregenerally of the physics program of the ATLAS and CMS experiments at the LHC, will contributein fundamental ways to the advancement of knowledge about the elementary constituents of theworld we live in.158Bibliography[1] S. Alekhin, J. Blumlein, and S. Moch. Parton distribution functions and benchmark crosssections at NNLO. Phys. Rev., D86:054009, 2012. doi:10.1103/PhysRevD.86.054009,arXiv:1202.2281 [hep-ph]. → pages 133[2] ALEPH Collaboration, S. Schael et al. Fermion pair production in e+e− collisions at189-209 GeV and constraints on physics beyond the standard model. Eur. Phys. J., C49:411,2007. doi:10.1140/epjc/s10052-006-0156-8, arXiv:hep-ex/0609051. → pages 32[3] S. Alioli, P. Nason, C. Oleari, and E. Re. A general framework for implementing NLOcalculations in shower Monte Carlo programs: the POWHEG BOX. JHEP, 1006:043, 2010.doi:10.1007/JHEP06(2010)043, arXiv:1002.2581 [hep-ph]. → pages 94[4] J. Alwall, P. Artoisenet, S. de Visscher, C. Duhr, R. Frederix, M. Herquet, and O. Mattelaer.New developments in MadGraph/MadEvent. AIP Conf. Proc., 1078:84–89, 2009.doi:10.1063/1.3052056, arXiv:0809.2410 [hep-ph]. → pages 206[5] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer. MadGraph 5: Going beyond.JHEP, 1106:128, 2011. doi:10.1007/JHEP06(2011)128, arXiv:1106.0522 [hep-ph]. →pages 95, 206[6] C. Anastasiou, L. Dixon, K. Melnikov, and F. Petriello. High precision QCD at hadroncolliders: Electroweak gauge boson rapidity distributions at NNLO. Phys. Rev. D, 69:094008, 2004. doi:10.1103/PhysRevD.69.094008, arXiv:hep-ph/0312266. → pages 129[7] I. Antoniadis. A possible new dimension at a few TeV. Phys. Lett., B246:377–384, 1990.doi:10.1016/0370-2693(90)90617-F. → pages 27[8] I. Antoniadis, K. Benakli, and M. Quiros. Direct collider signatures of large extradimensions. Phys. Lett., B460:176–183, 1999. doi:10.1016/S0370-2693(99)00764-9,arXiv:hep-ph/9905311 [hep-ph]. → pages 27[9] N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali. The hierarchy problem and newdimensions at a millimeter. Phys. Lett., B429:263, 1998.doi:10.1016/S0370-2693(98)00466-3, arXiv:hep-ph/9803315. → pages 27[10] P. Artoisenet, V. Lemaitre, F. Maltoni, and O. Mattelaer. Automation of the matrix elementreweighting method. JHEP, 1012:068, 2010. doi:10.1007/JHEP12(2010)068,arXiv:1007.3300 [hep-ph]. → pages 206159[11] ATLAS Collaboration. ATLAS Muon Spectrometer: Technical design report. TechnicalReport CERN-LHCC-97-22, ATLAS-TDR-10, CERN, 1997. → pages 65, 67[12] ATLAS Collaboration. The ATLAS Experiment at the Large Hadron Collider. JINST, 3:S08003, 2008. doi:10.1088/1748-0221/3/08/S08003, arXiv:0901.0512 [hep-ex]. → pages33, 37, 41, 43, 46, 47, 49, 50, 52, 54[13] ATLAS Collaboration. Expected performance of the ATLAS experiment - detector, triggerand physics. 2009, arXiv:0901.0512 [hep-ex]. → pages 33, 49, 64[14] ATLAS Collaboration. ATLAS Insertable B-Layer: Technical design report. TechnicalReport CERN-LHCC-2010-013, ATLAS-TDR-19, CERN, 2010. → pages 44[15] ATLAS Collaboration. The ATLAS simulation infrastructure. Eur. Phys. J., C70:823, 2010.doi:10.1140/epjc/s10052-010-1429-9, arXiv:1005.4568 [physics.ins-det]. → pages 91[16] ATLAS Collaboration. Calibrating the b-tag efficiency and mistag rate in 35 pb−1 of datawith the ATLAS detector. Technical Report ATLAS-CONF-2011-089, CERN, 2011. →pages 178[17] ATLAS Collaboration. Commissioning of the ATLAS high-performance b-taggingalgorithms in the 7 TeV collision data. Technical Report ATLAS-CONF-2011-102, CERN,2011. → pages 178[18] ATLAS Collaboration. Search for dilepton resonances in pp collisions at√s = 7 TeV withthe ATLAS detector. Phys. Rev. Lett., 107:272002, 2011.doi:10.1103/PhysRevLett.107.272002, arXiv:1108.1582 [hep-ex]. → pages 146[19] ATLAS Collaboration. Search for high mass dilepton resonances in pp collisions at√s = 7 TeV with the ATLAS experiment. Phys. Lett., B700:163, 2011.doi:10.1016/j.physletb.2011.04.044, arXiv:1103.6218 [hep-ex]. → pages 146[20] ATLAS Collaboration. Measurement of the b-tag efficiency in a sample of jets containingmuons with 5 fb−1 of data from the ATLAS detector. Technical ReportATLAS-CONF-2012-043, CERN, 2012. → pages 177, 178[21] ATLAS Collaboration. Performance of missing transverse momentum reconstruction inproton-proton collisions at√s = 7 TeV with ATLAS. Eur. Phys. J., C72:1844, 2012.doi:10.1140/epjc/s10052-011-1844-6, arXiv:1108.5602 [hep-ex]. → pages 58, 178[22] ATLAS Collaboration. Performance of missing transverse momentum reconstruction inATLAS with 2011 proton-proton collisions at√s = 7 TeV. Technical ReportATLAS-CONF-2012-101, CERN, 2012. → pages 58, 117, 178[23] ATLAS Collaboration. Observation of a new particle in the search for the Standard ModelHiggs boson with the ATLAS detector at the LHC. Phys. Lett., B716:1, 2012.doi:10.1016/j.physletb.2012.08.020, arXiv:1207.7214 [hep-ex]. → pages 1, 10, 172[24] ATLAS Collaboration. Electron performance measurements with the ATLAS detector usingthe 2010 LHC proton-proton collision data. Eur. Phys. J., C72:1909, 2012.doi:10.1140/epjc/s10052-012-1909-1, arXiv:1110.3174 [hep-ex]. → pages 177160[25] ATLAS Collaboration. Search for high mass resonances decaying to dilepton final states inpp collisions at√s = 7 TeV with the ATLAS detector. JHEP, 1211:138, 2012.doi:10.1007/JHEP11(2012)138, arXiv:1209.2535 [hep-ex]. → pages 2, 137, 146, 158[26] ATLAS Collaboration. Physics at a high-luminosity LHC with ATLAS. 2013,arXiv:1307.7292 [hep-ex]. → pages 155, 156[27] ATLAS Collaboration. Improved luminosity determination in pp collisions at√s = 7 TeVusing the ATLAS detector at the LHC. Eur. Phys. J., C73:2518, 2013.doi:10.1140/epjc/s10052-013-2518-3, arXiv:1302.4393 [hep-ex]. → pages 58, 60[28] ATLAS Collaboration. Performance of missing transverse momentum reconstruction inATLAS studied in proton-proton collisions recorded in 2012 at√s = 8 TeV. TechnicalReport ATLAS-CONF-2013-082, CERN, 2013. → pages 58, 117, 178[29] ATLAS Collaboration. Measurements of Higgs boson production and couplings in dibosonfinal states with the ATLAS detector at the LHC. Phys. Lett., B726:88–119, 2013.doi:10.1016/j.physletb.2013.08.010, arXiv:1307.1427 [hep-ex]. → pages 172, 174, 175, 176[30] ATLAS Collaboration. Evidence for the spin-0 nature of the Higgs boson using ATLASdata. Phys. Lett., B726:120–144, 2013. doi:10.1016/j.physletb.2013.08.026,arXiv:1307.1432 [hep-ex]. → pages 172[31] ATLAS Collaboration. Evidence for Higgs boson decays to the τ+τ− final state with theATLAS detector. Technical Report ATLAS-CONF-2013-108, CERN, 2013. → pages 174[32] ATLAS Collaboration. Preliminary results on the muon reconstruction efficiency,momentum resolution, and momentum scale in ATLAS 2012 pp collision data. TechnicalReport ATLAS-CONF-2013-088, CERN, 2013. → pages 64, 69, 70, 71, 72, 73[33] ATLAS Collaboration. ATLAS Experiment – Public Results, 2014. URLhttps://twiki.cern.ch/twiki/bin/view/AtlasPublic. → pages 21, 38, 39, 42, 99, 181[34] ATLAS Collaboration. Updated coupling measurements of the Higgs boson with theATLAS detector using up to 25 fb−1 of proton-proton collision data. Technical ReportATLAS-CONF-2014-009, CERN, 2014. → pages 210[35] ATLAS Collaboration. Muon reconstruction efficiency and momentum resolution of theATLAS experiment in proton-proton collisions at√s = 7 TeV in 2010. Submitted toEur. Phys. J. C, 2014, arXiv:1404.4562 [hep-ex]. → pages 64[36] ATLAS Collaboration. Search for high-mass dilepton resonances in pp collisions at√s = 8 TeV with the ATLAS detector. Accepted by Phys. Rev. D, 2014, arXiv:1405.4123[hep-ex]. → pages 2, 137, 146, 158[37] J. J. Aubert et al. Experimental observation of a heavy particle J. Phys. Rev. Lett., 33:1404–1406, 1974. doi:10.1103/PhysRevLett.33.1404. → pages 1[38] J. Augustin et al. Discovery of a narrow resonance in e+e− annihilation. Phys. Rev. Lett.,33:1406–1408, 1974. doi:10.1103/PhysRevLett.33.1406. → pages 1161[39] G. Azuelos and G. Polesello. Prospects for the detection of Kaluza-Klein excitations ofgauge bosons in the ATLAS detector at the LHC. Eur. Phys. J., C39S2:1–11, 2005.doi:10.1140/epjcd/s2004-02-001-y. → pages 27[40] C. A. Baker et al. Improved experimental limit on the electric dipole moment of the neutron.Phys. Rev. Lett., 97:131801, 2006. doi:10.1103/PhysRevLett.97.131801. → pages 24[41] R. D. Ball et al. Parton distributions with LHC data. Nucl. Phys., B867:244, 2013.doi:10.1016/j.nuclphysb.2012.10.003, arXiv:1207.1303 [hep-ph]. → pages 95, 133[42] D. Bardin, S. Bondarenko, P. Christova, L. Kalinovskaya, L. Rumyantsev, A. Sapronov, andW. von Schlippe. SANC integrator in the progress: QCD and EW contributions. JETP Lett.,96:285–289, 2012. doi:10.1134/S002136401217002X, arXiv:1207.4400 [hep-ph]. → pages95[43] V. D. Barger, W. Y. Keung, and R. J. N. Phillips. Possible sneutrino pair signatures withR-parity breaking. Phys. Lett., B364:27–32, 1995. doi:10.1016/0370-2693(95)01225-1,arXiv:hep-ph/9507426 [hep-ph]. → pages 28[44] P. Ba¨rnreuther, M. Czakon, and A. Mitov. Percent level precision physics at the Tevatron:First genuine NNLO QCD corrections to qq¯→ tt¯ +X . Phys. Rev. Lett., 109:132001, 2012.doi:10.1103/PhysRevLett.109.132001, arXiv:1204.5201 [hep-ph]. → pages 95[45] I. Bars and M. Gu¨naydin. Grand unification with the exceptional group E8. Phys. Rev. Lett.,45:859–862, 1980. doi:10.1103/PhysRevLett.45.859. → pages 29[46] L. Basso, A. Belyaev, S. Moretti, and C. H. Shepherd-Themistocleous. Phenomenology ofthe minimal B−L extension of the Standard Model: Z′ and neutrinos. Phys. Rev., D80:055030, 2009. doi:10.1103/PhysRevD.80.055030, arXiv:0812.4313 [hep-ph]. → pages 31[47] F. Bauer. Private communication, 2011. → pages 54[48] U. Baur. Weak boson emission in hadron collider processes. Phys. Rev., D75:013005, 2007.doi:10.1103/PhysRevD.75.013005, arXiv:hep-ph/0611241. → pages 91, 95[49] G. Bella et al. A search for heavy Kaluza-Klein electroweak gauge bosons at the LHC.JHEP, 09:025, 2010. doi:10.1007/JHEP09(2010)025, arXiv:1004.2432 [hep-ex]. → pages27[50] A. S. Belyaev, I. L. Shapiro, and M. A. B. do Vale. Torsion phenomenology at the LHC.Phys. Rev., D75:034014, 2007. doi:10.1103/PhysRevD.75.034014, arXiv:hep-ph/0701002[hep-ph]. → pages 28[51] M. Benedikt, P. Collier, V. Mertens, J. Poole, and K. Schindl. LHC design report. 3. theLHC injector chain. Technical Report CERN-2004-003-V-3, CERN, 2004. → pages 33[52] J. Beringer et al. Review of particle physics. Phys. Rev., D86:010001, 2012.doi:10.1103/PhysRevD.86.010001. → pages 9, 19, 24, 25, 45, 125162[53] S. G. Bondarenko and A. A. Sapronov. NLO EW and QCD proton-proton cross sectioncalculations with mcsanc-v1.01. Comput. Phys. Commun., 184:2343, 2013.doi:10.1016/j.cpc.2013.05.010, arXiv:1301.3687 [hep-ph]. → pages 95, 123[54] A. Bosma. The distribution and kinematics of neutral hydrogen in spiral galaxies of variousmorphological types. PhD thesis, Groningen Univ., 1978. → pages 22[55] M. Botje et al. The PDF4LHC Working Group Interim Recommendations. 2011,arXiv:1101.0538 [hep-ph]. → pages 95[56] O. S. Bru¨ning, P. Collier, P. Lebrun, S. Myers, R. Ostojic, J. Poole, and P. Proudlock. LHCdesign report. 1. the LHC main ring. Technical Report CERN-2004-003-V-1, CERN, 2004.→ pages 33[57] O. S. Bru¨ning, P. Collier, P. Lebrun, S. Myers, R. Ostojic, J. Poole, and P. Proudlock. LHCdesign report. 2. the LHC infrastructure and general services. Technical ReportCERN-2004-003-V-2, CERN, 2004. → pages 33[58] C. P. Burgess and G. D. Moore. The Standard Model: A Primer. Cambridge UniversityPress, 2007. → pages 3, 16, 24[59] J. M. Butterworth, J. R. Forshaw, and M. H. Seymour. Multiparton interactions inphotoproduction at HERA. Z. Phys., C72:637–646, 1996. doi:10.1007/s002880050286,arXiv:hep-ph/9601371 [hep-ph]. → pages 94[60] M. Cacciari, G. P. Salam, and G. Soyez. The anti-kt jet clustering algorithm. JHEP, 0804:063, 2008. doi:10.1088/1126-6708/2008/04/063, arXiv:0802.1189 [hep-ph]. → pages 177[61] M. Cacciari et al. Top-pair production at hadron colliders with next-to-next-to-leadinglogarithmic soft-gluon resummation. Phys. Lett., B710:612, 2012.doi:10.1016/j.physletb.2012.03.013, arXiv:1111.5869 [hep-ph]. → pages 95[62] A. Caldwell, D. Kollar, and K. Kro¨ninger. BAT - The Bayesian Analysis Toolkit.Comput. Phys. Commun., 180:2197, 2009. doi:10.1016/j.cpc.2009.06.026, arXiv:0808.2552[physics.data-an]. → pages 142[63] J. M. Campbell and R. K. Ellis. An update on vector boson pair production at hadroncolliders. Phys. Rev., D60:113006, 1999. doi:10.1103/PhysRevD.60.113006,arXiv:hep-ph/9905386. → pages 93[64] C. M. Carloni Calame, G. Montagna, O. Nicrosini, and A. Vicini. Precision electroweakcalculation of the production of a high transverse-momentum lepton pair at hadron colliders.JHEP, 10:109, 2007. doi:10.1088/1126-6708/2007/10/109, arXiv:0710.1722 [hep-ph]. →pages 91[65] CDF Collaboration, F. Abe et al. Observation of top quark production in p¯p collisions.Phys. Rev. Lett., 74:2626–2631, 1995. doi:10.1103/PhysRevLett.74.2626,arXiv:hep-ex/9503002 [hep-ex]. → pages 1, 10163[66] CDF Collaboration, T. Aaltonen et al. Search for high mass resonances decaying to muonpairs in√s = 1.96 TeV pp¯ collisions. Phys. Rev. Lett., 106:121801, 2011.doi:10.1103/PhysRevLett.106.121801, arXiv:1101.4578 [hep-ex]. → pages 32[67] K. Cheung. Constraints on electron quark contact interactions and implications to models ofleptoquarks and extra Z bosons. Phys. Lett., B517:167–176, 2001.doi:10.1016/S0370-2693(01)00973-X, arXiv:hep-ph/0106251. → pages 32[68] M. V. Chizhov. A reference model for anomalously interacting bosons. Phys. Part. Nucl.Lett., 8:512, 2011. doi:10.1134/S1547477111060045, arXiv:1005.4287 [hep-ph]. → pages28[69] M. V. Chizhov and G. Dvali. Origin and phenomenology of weak-doublet spin-1 bosons.Phys. Lett., B703:593, 2011. doi:10.1016/j.physletb.2011.08.056, arXiv:0908.0924[hep-ph]. → pages[70] M. V. Chizhov, V. A. Bednyakov, and J. A. Budagov. Proposal for chiral-boson search atLHC via their unique new signature. Physics of Atomic Nuclei, 71:2096, 2008.doi:10.1134/S1063778808120107, arXiv:0801.4235 [hep-ph]. → pages[71] M. V. Chizhov, V. A. Bednyakov, and J. A. Budagov. Anomalously interacting extra neutralbosons. Nuovo Cimento, C33:343, 2010, arXiv:1005.2728 [hep-ph]. → pages 28[72] G. Choudalakis and D. Casadei. Plotting the differences between data and expectation.2011, arXiv:1111.2062 [physics.data-an]. → pages 138[73] F. Close. The Infinity Puzzle. Oxford University Press, 2011. → pages 3[74] D. Clowe, A. Gonzalez, and M. Markevitch. Weak lensing mass reconstruction of theinteracting cluster 1E0657-558: Direct evidence for the existence of dark matter.Astrophys. J., 604:596–603, 2004. doi:10.1086/381970, arXiv:astro-ph/0312273 [astro-ph].→ pages 22[75] D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randall, C. Jones, andD. Zaritsky. A direct empirical proof of the existence of dark matter. Astrophys. J., 648:L109–L113, 2006. doi:10.1086/508162, arXiv:astro-ph/0608407 [astro-ph]. → pages 22, 23[76] CMS Collaboration. Observation of a new boson at a mass of 125 GeV with the CMSexperiment at the LHC. Phys. Lett., B716:30, 2012. doi:10.1016/j.physletb.2012.08.021,arXiv:1207.7235 [hep-ex]. → pages 1, 10, 172[77] CMS Collaboration. Search for resonances in the dilepton mass distribution in pp collisionsat√s = 8 TeV. Technical Report CMS-PAS-EXO-12-061, CERN, 2013. → pages 32[78] CMS Collaboration. Search for heavy narrow dilepton resonances in pp collisions at√s = 7 TeV and√s = 8 TeV. Phys. Lett., B720:63, 2013.doi:10.1016/j.physletb.2013.02.003, arXiv:1212.6175 [hep-ex]. → pages 32[79] CMS Collaboration. Measurement of Higgs boson production and properties in the WWdecay channel with leptonic final states. JHEP, 1401:096, 2014.doi:10.1007/JHEP01(2014)096, arXiv:1312.1129 [hep-ex]. → pages 174, 175164[80] CMS Collaboration. Measurement of the properties of a Higgs boson in the four-lepton finalstate. Phys.Rev., D89:092007, 2014, arXiv:1312.5353 [hep-ex]. → pages 172[81] CMS Collaboration. Evidence for the 125 GeV Higgs boson decaying to a pair of τ leptons.Submitted to JHEP, 2014, arXiv:1401.5041 [hep-ex]. → pages 174[82] G. Corcella, I. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. Seymour,and B. Webber. HERWIG 6: an event generator for hadron emission reactions withinterfering gluons (including supersymmetric processes). JHEP, 0101:010, 2001.doi:10.1088/1126-6708/2001/01/010, arXiv:hep-ph/0011363. → pages 91, 94[83] G. Corcella, I. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. Seymour,and B. Webber. HERWIG 6.5 release note. 2002, arXiv:hep-ph/0210213. → pages 91, 94[84] G. Cowan, K. Cranmer, E. Gross, and O. Vitells. Asymptotic formulae for likelihood-basedtests of new physics. Eur. Phys. J., C71:1554, 2011. doi:10.1140/epjc/s10052-011-1554-0,arXiv:1007.1727 [physics.data-an]. → pages 188[85] M. Czakon and A. Mitov. Top++: A program for the calculation of the top-paircross-section at hadron colliders. 2011, arXiv:1112.5675 [hep-ph]. → pages 95[86] M. Czakon and A. Mitov. NNLO corrections to top-pair production at hadron colliders: theall-fermionic scattering channels. JHEP, 1212:054, 2012. doi:10.1007/JHEP12(2012)054,arXiv:1207.0236 [hep-ph]. → pages[87] M. Czakon and A. Mitov. NNLO corrections to top pair production at hadron colliders: thequark-gluon reaction. JHEP, 1301:080, 2013. doi:10.1007/JHEP01(2013)080,arXiv:1210.6832 [hep-ph]. → pages[88] M. Czakon, P. Fiedler, and A. Mitov. The total top quark pair production cross-section athadron colliders through O(α4S). Phys. Rev. Lett., 110:252004, 2013.doi:10.1103/PhysRevLett.110.252004, arXiv:1303.6254 [hep-ph]. → pages 95[89] D0 Collaboration, S. Abachi et al. Observation of the top quark. Phys. Rev. Lett., 74:2632–2637, 1995. doi:10.1103/PhysRevLett.74.2632, arXiv:hep-ex/9503003 [hep-ex]. →pages 1, 10[90] D0 Collaboration, V. M. Abazov et al. Search for a heavy neutral gauge boson in thedielectron channel with 5.4 fb−1 of pp¯ collisions at√s = 1.96 TeV. Phys. Lett., B695:88,2011. doi:10.1016/j.physletb.2010.10.059, arXiv:1008.2023 [hep-ex]. → pages 32[91] F. M. L. de Almeida Jr., A. A. Nepomuceno, and M. A. B. do Vale. Torsion discoverypotential and its discrimination at CERN LHC. Phys. Rev., D79:014029, 2009.doi:10.1103/PhysRevD.79.014029, arXiv:0811.0291 [hep-ph]. → pages 28[92] DELPHI Collaboration, J. Abdallah et al. Measurement and interpretation of fermion-pairproduction at LEP energies above the Z resonance. Eur. Phys. J., C45:589, 2006.doi:10.1140/epjc/s2005-02461-0, arXiv:hep-ex/0512012. → pages 32165[93] D. D. Dietrich, F. Sannino, and K. Tuominen. Light composite Higgs from higherrepresentations versus electroweak precision measurements: Predictions for LHC.Phys. Rev., D72:055001, 2005. doi:10.1103/PhysRevD.72.055001, arXiv:hep-ph/0505059.→ pages 28[94] D. Dimopoulos and G. Landsberg. Black holes at the LHC. Phys. Rev. Lett., 87:161602,2001. doi:10.1103/PhysRevLett.87.161602, arXiv:hep-ph/0106295. → pages 27[95] DONUT Collaboration, K. Kodama et al. Observation of tau neutrino interactions. Phys.Lett., B504:218–224, 2001. doi:10.1016/S0370-2693(01)00307-0, arXiv:hep-ex/0012035[hep-ex]. → pages 10[96] F. Englert and R. Brout. Broken symmetry and the mass of gauge vector mesons. Phys. Rev.Lett., 13:321–323, 1964. doi:10.1103/PhysRevLett.13.321. → pages 6[97] L. Evans and P. Bryant. LHC Machine. JINST, 3:S08001, 2008.doi:10.1088/1748-0221/3/08/S08001. → pages 33[98] R. Foadi, M. T. Frandsen, T. A. Ryttov, and F. Sannino. Minimal Walking Technicolor: Setup for collider physics. Phys. Rev., D76:055005, 2007. doi:10.1103/PhysRevD.76.055005,arXiv:0706.1696 [hep-ph]. → pages 28[99] R. Foadi, M. T. Frandsen, and F. Sannino. 125 GeV Higgs from a not so light technicolorscalar. Phys. Rev., D87:095001, 2013. doi:10.1103/PhysRevD.87.095001, arXiv:1211.1083[hep-ph]. → pages 28[100] L. H. Ford. Quantum field theory in curved space-time. 1997, arXiv:gr-qc/9707062 [gr-qc].→ pages 22[101] S. Frixione and B. R. Webber. Matching NLO QCD computations and parton showersimulations. JHEP, 0206:029, 2002. doi:10.1088/1126-6708/2002/06/029,arXiv:hep-ph/0204244. → pages 91, 94[102] Y. Fukui. Making an un-weighted event sample out of a weighted event sample. TechnicalReport Muon Collider Note 184, Fermilab, 2000. → pages 201[103] J. Gao, M. Guzzi, J. Huston, H.-L. Lai, Z. Li, P. Nadolsky, J. Pumplin, D. Stump, and C.-P.Yuan. The CT10 NNLO global analysis of QCD. Phys. Rev., D89:033009, 2014.doi:10.1103/PhysRevD.89.033009, arXiv:1302.6246 [hep-ph]. → pages 95, 133[104] GEANT4 Collaboration, S. Agostinelli et al. GEANT4: A simulation toolkit. Nucl.Instrum. Meth., A506:250, 2003. doi:10.1016/S0168-9002(03)01368-8. → pages 91[105] H. Georgi and S. L. Glashow. Unity of all elementary-particle forces. Phys. Rev. Lett., 32:438–441, 1974. doi:10.1103/PhysRevLett.32.438. → pages 29[106] S. B. Giddings and S. Thomas. High energy colliders as black hole factories: The end ofshort distance physics. Phys. Rev., D65:056010, 2002. doi:10.1103/PhysRevD.65.056010,arXiv:hep-ph/0106219. → pages 27166[107] P.-F. Giraud. Private communication, 2014. → pages 65, 67[108] S. Glashow. Partial symmetries of weak interactions. Nucl. Phys., 22:579–588, 1961.doi:10.1016/0029-5582(61)90469-2. → pages 1[109] T. Golling, H. S. Hayward, P. U. E. Onyisi, H. J. Stelzer, and P. Waller. The ATLAS dataquality defect database system. Eur. Phys. J., C72:1960, 2012.doi:10.1140/epjc/s10052-012-1960-y, arXiv:1110.6119 [physics.ins-det]. and referencestherein. → pages 62[110] P. Golonka and Z. Wa¸s. PHOTOS Monte Carlo: a precision tool for QED corrections in Zand W decays. Eur. Phys. J., C45:97, 2006. doi:10.1140/epjc/s2005-02396-4,arXiv:hep-ph/0506026. → pages 91[111] M. Gonzalez-Garcia and M. Maltoni. Phenomenology with massive neutrinos. Phys. Rept.,460:1–129, 2008. doi:10.1016/j.physrep.2007.12.004, arXiv:0704.1800 [hep-ph]. → pages24[112] G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble. Global conservation laws and masslessparticles. Phys. Rev. Lett., 13:585–587, 1964. doi:10.1103/PhysRevLett.13.585. → pages 6[113] H1 and ZEUS Collaborations, F. D. Aaron et al. Combined measurement and QCD analysisof the inclusive ep scattering cross sections at HERA. JHEP, 1001:109, 2010.doi:10.1007/JHEP01(2010)109, arXiv:0911.0884 [hep-ex]. → pages 133[114] R. Hamberg, W. L. van Neerven, and T. Matsuura. A complete calculation of the order α2Scorrection to the Drell-Yan K-factor. Nucl. Phys., B359:343–405, 1991.doi:10.1016/0550-3213(91)90064-5. → pages 91, 129[115] C. Hays, A. V. Kotwal, and O. Stelzer-Chilton. New techniques in the search for Z′ bosonsand other neutral resonances. Modern Physics Letters, A24:2387, 2009.doi:10.1142/S021773230903179X. and references therein. → pages 1[116] S. W. Herb et al. Observation of a dimuon resonance at 9.5 GeV in 400-GeV proton-nucleuscollisions. Phys. Rev. Lett., 39:252–255, 1977. doi:10.1103/PhysRevLett.39.252. → pages 1[117] P. W. Higgs. Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett., 13:508–509, 1964. doi:10.1103/PhysRevLett.13.508. → pages 6[118] A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, and H. Voss. TMVA:Toolkit for Multivariate Data Analysis. PoS, ACAT:040, 2007, arXiv:physics/0703039. →pages 182[119] N. Kidonakis. Two-loop soft anomalous dimensions for single top quark associatedproduction with a W- or H-. Phys. Rev., D82:054018, 2010.doi:10.1103/PhysRevD.82.054018, arXiv:1005.4451 [hep-ph]. → pages 95[120] L3 Collaboration, P. Achard et al. Measurement of hadron and lepton-pair production ine+e− collisions at√s = 192 GeV to 208 GeV at LEP. Eur. Phys. J., C47:1, 2006.doi:10.1140/epjc/s2006-02539-1, arXiv:hep-ex/0603022. → pages 32167[121] H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. M. Nadolsky, J. Pumplin, and C.-P. Yuan. Newparton distributions for collider physics. Phys. Rev., D82:074024, 2010.doi:10.1103/PhysRevD.82.074024, arXiv:1007.2241 [hep-ph]. → pages 94, 95, 133[122] W. Lampl, S. Laplace, D. Lelas, P. Loch, H. Ma, S. Menke, S. Rajagopalan, D. Rousseau,S. Snyder, and G. Unal. Calorimeter clustering algorithms: Description and performance.Technical Report ATL-LARG-PUB-2008-002. ATL-COM-LARG-2008-003, CERN, 2008.→ pages 177[123] P. Langacker. The physics of heavy Z′ gauge bosons. Rev. Mod. Phys., 81:1199, 2009.doi:10.1103/RevModPhys.81.1199, arXiv:0801.1345 [hep-ph]. → pages 28[124] P. Langacker. Z′ physics at the LHC. 2009, arXiv:0911.4294 [hep-ph]. → pages 32[125] U. Langenfeld, S. Moch, and P. Uwer. New results for tt¯ production at hadron colliders.2009, arXiv:0907.2527 [hep-ph]. → pages 93[126] Y. Li and F. Petriello. Combining QCD and electroweak corrections to dilepton productionin FEWZ. Phys. Rev., D86:094034, 2012. doi:10.1103/PhysRevD.86.094034,arXiv:1208.5967 [hep-ph]. → pages 94[127] D. London and J. L. Rosner. Extra gauge bosons in E6. Phys. Rev., D34:1530, 1986.doi:10.1103/PhysRevD.34.1530. → pages 29, 30[128] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau, and A. D. Polosa. ALPGEN, a generatorfor hard multiparton processes in hadronic collisions. JHEP, 0307:001, 2003.doi:10.1088/1126-6708/2003/07/001, arXiv:hep-ph/0206293 [hep-ph]. → pages 94[129] M. Markevitch. Chandra observation of the most interesting cluster in the universe. 2005,arXiv:astro-ph/0511345 [astro-ph]. → pages 23[130] M. Markevitch, A. H. Gonzalez, D. Clowe, A. Vikhlinin, L. David, W. Forman, C. Jones,S. Murray, and W. Tucker. Direct constraints on the dark matter self-interactioncross-section from the merging galaxy cluster 1E0657-56. Astrophys. J., 606:819–824,2004. doi:10.1086/383178, arXiv:astro-ph/0309303 [astro-ph]. → pages 22[131] A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne. Parton distributionsincorporating QED contributions. Eur. Phys. J., C39:155, 2005.doi:10.1140/epjc/s2004-02088-7, arXiv:hep-ph/0411040. → pages 91[132] A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt. Parton distributions for the LHC.Eur. Phys. J., C63:189, 2009. doi:10.1140/epjc/s10052-009-1072-5, arXiv:0901.0002[hep-ph]. → pages 18, 91, 94, 95, 129[133] A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt. Uncertainties on αS in global PDFanalyses and implications for predicted hadronic cross sections. Eur. Phys. J., C64:653,2009. doi:10.1140/epjc/s10052-009-1164-2, arXiv:0905.3531 [hep-ph]. → pages 95, 133[134] K. Melnikov and F. Petriello. Electroweak gauge boson production at hadron collidersthrough O(α2S). Phys. Rev., D74:114017, 2006. doi:10.1103/PhysRevD.74.114017,arXiv:hep-ph/0609070. → pages 94168[135] S. Moch and P. Uwer. Theoretical status and prospects for top-quark pair production athadron colliders. Phys. Rev., D78:034003, 2008. doi:10.1103/PhysRevD.78.034003,arXiv:0804.1476 [hep-ph]. → pages 93[136] R. N. Mohapatra and J. C. Pati. Left-right gauge symmetry and an isoconjugate model ofCP violation. Phys. Rev., D11:566, 1975. doi:10.1103/PhysRevD.11.566. → pages 31[137] P. M. Nadolsky et al. Implications of CTEQ global analysis for collider observables.Phys. Rev., D78:013004, 2008. → pages 91[138] J. Neyman and E. Pearson. On the problem of the most efficient tests of statisticalhypotheses. Phil. Trans. R. Soc. Lond. A, 231(694-706):289–337, 1933. → pages 142[139] K. Nikolopoulos, D. Fassouliotis, C. Kourkoumelis, and A. Poppleton. Muon energy lossupsteam of the muon spectrometer. Technical Report ATL-MUON-PUB-2007-002,ATL-COM-MUON-2006-019, CERN, 2006. → pages 64[140] OPAL Collaboration, G. Abbiendi et al. Tests of the standard model and constraints on newphysics from measurements of fermion pair production at 189 GeV to 209 GeV at LEP.Eur. Phys. J., C33:173, 2004. doi:10.1140/epjc/s2004-01595-9, arXiv:hep-ex/0309053. →pages 32[141] J. C. Pati and A. Salam. Lepton number as the fourth “color”. Phys. Rev. D, 10:275–289,1974. doi:10.1103/PhysRevD.10.275. → pages 30[142] S. Perlmutter et al. Measurements of Omega and Lambda from 42 high redshift supernovae.Astrophys. J., 517:565–586, 1999. doi:10.1086/307221, arXiv:astro-ph/9812133 [astro-ph].→ pages 23[143] Planck Collaboration, P. A. R. Ade et al. Planck 2013 results. I. Overview of products andscientific results. 2013, arXiv:1303.5062 [astro-ph.CO]. → pages 23[144] Planck Collaboration, P. A. R. Ade et al. Planck 2013 results. XVI. Cosmologicalparameters. 2013, arXiv:1303.5076 [astro-ph.CO]. → pages 23[145] N. J. Poplawski. Matter-antimatter asymmetry and dark matter from torsion. Phys. Rev.,D83:084033, 2011. doi:10.1103/PhysRevD.83.084033, arXiv:1101.4012 [gr-qc]. → pages28[146] J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. M. Nadolsky, and W. K. Tung. Newgeneration of parton distributions with uncertainties from global QCD analysis. JHEP,0207:012, 2002. doi:10.1088/1126-6708/2002/07/012, arXiv:hep-ph/0201195. → pages 94[147] L. Randall and R. Sundrum. A large mass hierarchy from a small extra dimension.Phys. Rev. Lett., 83:3370, 1999. doi:10.1103/PhysRevLett.83.3370, arXiv:hep-ph/9905221.→ pages 27[148] A. G. Riess et al. Observational evidence from supernovae for an accelerating universe anda cosmological constant. Astron. J., 116:1009–1038, 1998. doi:10.1086/300499,arXiv:astro-ph/9805201 [astro-ph]. → pages 23169[149] V. C. Rubin, W. K. J. Ford, and N. Thonnard. Rotational properties of 21 SC galaxies with alarge range of luminosities and radii, from NGC 4605 /R = 4kpc/ to UGC 2885 /R = 122kpc/. Astrophys. J., 238:471–487, 1980. doi:10.1086/158003. → pages 22[150] A. Salam. Elementary particle physics: Relativistic groups and analyticity. Eighth NobelSymposium, ed. N. Svartholm., page 367, 1968. → pages 1[151] E. Salvioni, G. Villadoro, and F. Zwirner. Minimal Z′ models: present bounds and earlyLHC reach. JHEP, 0911:068, 2009. doi:10.1088/1126-6708/2009/11/068, arXiv:0909.1320[hep-ph]. → pages 31[152] F. Sannino. Dynamical stabilization of the fermi scale: Phase diagram of strongly coupledtheories for (minimal) walking technicolor and unparticles. 2008, arXiv:0804.0182[hep-ph]. → pages 12[153] D. Schouten. Private communication, 2012. → pages 206[154] G. Senjanovic and R. N. Mohapatra. Exact left-right symmetry and spontaneous violation ofparity. Phys. Rev., D12:1502, 1975. doi:10.1103/PhysRevD.12.1502. → pages 31[155] I. L. Shapiro. Physical aspects of the space-time torsion. Phys. Rept., 357:113, 2002.doi:10.1016/S0370-1573(01)00030-8, arXiv:hep-th/0103093. → pages 28[156] A. Sherstnev and R. Thorne. Different PDF approximations useful for LO Monte Carlogenerators. 2008. doi:10.3360/dis.2008.149, arXiv:0807.2132 [hep-ph]. → pages 91[157] A. Sherstnev and R. S. Thorne. Parton distributions for LO generators. Eur. Phys. J., C55:553–575, 2008. doi:10.1140/epjc/s10052-008-0610-x, arXiv:0711.2473 [hep-ph]. → pages91[158] T. Sjo¨strand, S. Mrenna, and P. Z. Skands. PYTHIA 6.4 Physics and Manual. JHEP, 05:026, 2006, arXiv:hep-ph/0603175 [hep-ph]. → pages 91[159] T. Sjo¨strand, S. Mrenna, and P. Z. Skands. A brief introduction to PYTHIA 8.1.Comput. Phys. Commun., 178:852, 2008. doi:10.1016/j.cpc.2008.01.036, arXiv:0710.3820[hep-ph]. → pages 94[160] G. ’t Hooft and M. Veltman. Regularization and renormalization of gauge fields. Nucl.Phys., B44(1):189 – 213, 1972. ISSN 0550-3213.doi:http://dx.doi.org/10.1016/0550-3213(72)90279-9. → pages 1[161] UA1 Collaboration, G. Arnison et al. Experimental observation of isolated large transverseenergy electrons with associated missing energy at√s = 540 GeV. Phys. Lett., B122:103 –116, 1983. doi:http://dx.doi.org/10.1016/0370-2693(83)91177-2. → pages 35[162] UA1 Collaboration, G. Arnison et al. Experimental observation of lepton pairs of invariantmass around 95 GeV/c2 at the CERN SPS collider. Phys. Lett., B126(5):398 – 410, 1983.doi:http://dx.doi.org/10.1016/0370-2693(83)90188-0. → pages 1170[163] UA2 Collaboration, M. Banner et al. Observation of single isolated electrons of hightransverse momentum in events with missing transverse energy at the CERN p¯p collider.Phys. Lett., B122:476 – 485, 1983. doi:http://dx.doi.org/10.1016/0370-2693(83)91605-2.→ pages[164] UA2 Collaboration, P. Bagnaia et al. Evidence for Z0→ e+e− at the CERN p¯p collider.Phys. Lett., B129:130 – 140, 1983. doi:http://dx.doi.org/10.1016/0370-2693(83)90744-X.→ pages 1, 35[165] S. van der Meer. Calibration of the effective beam height in the ISR. Technical ReportCERN-ISR-PO-68-31, CERN, 1968. → pages 59[166] L. M. J. S. Volders. Neutral hydrogen in M 33 and M 101. Bulletin of the AstronomicalInstitutes of the Netherlands, 14:323, 1959. → pages 22[167] G. Watt. Parton distribution function dependence of benchmark Standard Model total crosssections at the 7 TeV LHC. JHEP, 1109:069, 2011. doi:10.1007/JHEP09(2011)069,arXiv:1106.5788 [hep-ph]. → pages 123[168] S. Weinberg. A model of leptons. Phys. Rev. Lett., 19:1264–1266, 1967.doi:10.1103/PhysRevLett.19.1264. → pages 1171Appendix ASearch for Vector Boson FusionH→WW ∗→ `ν`νThis appendix discusses the multivariate analysis looking for Vector Boson Fusion (VBF) produc-tion of Higgs bosons decaying into W boson pairs in the `ν`ν final states1. After a brief introductionto the status of Higgs boson observations at the LHC in Section A.1 and a description of the analy-sis goals and strategy in Section A.2, specific contributions to the upcoming result are presented inSection A.3 and future perspectives are outlined in Section A.4.A.1 Status of Higgs Boson Observations at the Large HadronColliderFollowing the discovery of a Higgs boson at the LHC in 2012 [23, 76], physicists started measuringits mass, spin, parity and couplings to the other particles. So far, the mass of the new particlehas been measured to be 125.5± 0.2 (stat.) +0.5−0.6 (syst.) GeV by the ATLAS collaboration [29] and125.6±0.4 (stat.)±0.2 (syst.) GeV by the CMS collaboration [80]. As well, the data favour the 0+spin-parity hypothesis over the 0−, 1+, 1− and 2+ hypotheses at 95% CL or higher [30, 80].The couplings of the new particle are obtained from measurements of its production and decayrates: it is therefore important to detect it in as many channels as possible. The four productionchannels with the highest cross sections are, in order, gluon fusion, VBF, associate production witha vector boson, and top quark fusion. Their relative size is shown as a function of the Higgs bosonmass MH in Figure A.1. On the other side, the cross section times branching fraction to observablefinal states following a Higgs boson decay are shown in Figure A.2.Of all the different combinations of initial and final states, only two have been decidedly ob-served so far: gluon fusion production with decays to γγ [29, 76], and ZZ∗→ `+`−`+`− [29, 80].1 In this appendix, the symbol `± represents e± or µ± only, with τ± indicated explicitly.172Figure A.1: Higgs boson production cross section by channel as a function of MH . Figurecredit: R. Tanaka.Figure A.2: Higgs boson cross section times branching fraction to observable final states as afunction of MH . Figure credit: R. Tanaka.173There is also very strong evidence for gluon fusion production decaying to WW ∗→ `ν`ν [29, 79]and for VBF production decaying in the τ+τ− final state [31, 81]. Figure A.3 shows the histogramsfrom the ATLAS collaboration corresponding to these four results; similar histograms are availablefrom the CMS collaboration.Figure A.3: Histograms with data from the ATLAS experiment displaying evidence for theproduction of a Higgs boson in four different channels: gluon fusion production fol-lowed by decays to γγ [29] (top left), ZZ∗→ `+`−`+`− [29] (top right) and WW ∗→`ν`ν [29] (bottom left), as well as VBF production decaying in the τ+τ− final state [31](bottom right).174A.2 Analysis Goals and StrategyThe goal of this analysis is to search for Vector Boson Fusion H →WW ∗ → `ν`ν . Measuringthe production and decay rate in this channel is particularly interesting, because the Higgs bosoncouples to W bosons in both the initial and the final states, as illustrated in Figure A.4. Although Zbosons also contribute in the initial state, the production is dominated by W boson fusion. Such ameasurement is therefore particularly sensitive to the coupling κW between the Higgs and W bosons.Explicitly:σ(VBF H→WW ∗) ∝ κ4W ⇒∆σσ = 4∆κWκW(A.1)which implies, for example, that achieving a relative uncertainty of 60% on the measurement of thecross section σ would constrain the coupling κW to a relative uncertainty of only 15%.Figure A.4: Feynman diagram for VBF H→WW ∗ at Leading Order.The decays of WW ∗ to `ν`ν have small branching fractions, because of the smaller branchingfraction of W bosons to leptonic final states than to hadronic final states. They are nevertheless themost promising ones, because the background rates are drastically reduced, especially from W + jetsand QCD multi-jet processes. In particular, the Different-Flavour (DF) channel, where one chargedlepton is an electron and the other is a muon, is the principal search channel because backgroundcontributions from Z/γ∗→ `+`− are absent. The channels with two electrons or two muons in thefinal state are merged, and named the Same-Flavour (SF) channel.Analyses looking for H→WW ∗→ `ν`ν have already been performed by the ATLAS and CMSexperiments. Based on the full Run-I dataset, the CMS collaboration has observed a signal strengthnormalized to the expectation from the Standard Model (SM) of σ/σSM = 0.62+0.58−0.47, correspondingto a significance of 1.3 standard deviations (2.1 expected) [79]. On the other hand, following afirst analysis of the full Run-I dataset, the ATLAS collaboration has observed σ/σSM = 1.4± 0.7,with a significance of 2.5 standard deviations (1.6 expected) [29]. Histograms showing the data andexpected yields corresponding to this last result are shown in Figure A.5. The discriminant variable175used in the final stage of the search is the transverse mass mT :mT =√(E``T +EmissT )2−|~p``T +~pmissT |2, where E``T =√|~p``T |2 +m2`` (A.2)Figure A.5: Transverse mass mT used as discriminant in the final stage of the cut-based searchfor VBF H→WW ∗→ `ν`ν , for the DF channel (top) and the SF channel (bottom) [29].The search described here aims to re-analyze the data collected in Run-I by the ATLAS ex-periment using multivariate analysis techniques. Such techniques are especially appropriate whenlooking for a small signal among a large variety of background processes, and many discriminat-176ing variables are available. Multivariate analysis exploits the power of correlations between thesevariables to achieve additional separation between signal and background.The remainder of this section first describes the physical objects that are observable in the finalstate of interest in Section A.2.1, and the background processes that yield the same final-state ob-jects in Section A.2.2. Section A.2.3 discusses the unique topological features of the signal process,linked to the variables that make its separation from background possible. Finally, the multivari-ate analysis techniques investigated are described: Boosted Decision Trees (BDTs) are explainedin Section A.2.4, and the Matrix Element (ME) method in Section A.2.5. Of the two, only themethod using BDTs is used for the analysis, primarily because the ME method was found to be toocomputationally demanding.A.2.1 Physical ObjectsIn this analysis, the final state of interest is diverse: two light-quark jets accompany the two Wbosons, which decay into final states with two electrons, two muons, or one electron and one muon,always with real missing transverse momentum (EmissT ) caused by the accompanying neutrinos.Because the charged leptons come from W decays, their expected momentum is relatively low andthus easier to measure well. Further, the two jets are expected to be very forward, often requiringthe use of the Forward Calorimeters in addition to the Endcap Calorimeters. This analysis thereforeprioritizes geometrical acceptance.The primary vertex of the event is defined as the one with the largest ∑ p2T where the sum isover all tracks in the ID with pT > 0.4 GeV, and must have at least 3 such tracks. Combined muons,reconstructed in both the ID and the MS, are selected where possible, with segment-tagged muonsand MS standalone muons accepted where necessary2 to extend the acceptance to the full range|η |< 2.7. Electron candidates are identified as clustered energy depositions in the ElectromagneticCalorimeter satisfying a set of requirements [24] on the longitudinal and transverse shower shapes,associated with a well-reconstructed track in the ID. Both charged leptons are required to be iso-lated, and their tracks are required to be close to the primary vertex. The leading charged leptoncandidate in the event is required to have pT > 22 GeV, and the sub-leading one is required to havepT > 10 GeV.Jets are measured as topological clusters [122] in the Hadronic Calorimeters, reconstructedusing the anti-kt algorithm [60] with a distance parameter R = 0.4. The measured transverse energyof jets, corrected to remove contributions from pileup events, is required to satisfy ET > 25 GeV for|η | < 2.4, and ET > 30 GeV for 2.4 < |η | < 4.5. To further reduce contributions from pileup, if ajet has ET < 50 GeV, at least 50% of the summed scalar pT of associated tracks must come fromtracks associated with the primary vertex. Light-quark jets are identified from b-quark jets usinga b-tagging algorithm [20] to define a veto. The algorithm is based on the presence of displaced2 The different muon reconstruction types are explained in Section 5.1177vertices, the impact parameter of tracks in the jets and the reconstruction of heavy-flavour hadronicdecays when possible. The light-quark jet rejection factor, defined as the inverse of the rate formistaking a light-quark jet for a b-quark jet, is shown as a function of the b-tagging efficiency fordifferent b-tagging algorithms in Figure A.6. The chosen working point is at a b-tagging efficiencyof 85%, corresponding to a light-quark jet rejection factor of 10.Missing transverse momentum [21, 22, 28] measured using calorimeter energy deposits wasdiscussed in Section 4.6. In addition, a track-based pmissT,track is defined using only the momentum oftracks as measured from the ID and the MS.Figure A.6: Light-quark jet rejection factor as a function of the b-tagging efficiency for differ-ent b-tagging algorithms [20]. The algorithm MV1, used in this analysis, is a based ona neural network taking the output weights from the IP3D, SV1 and JetFitterCombNNalgorithms as inputs; these algorithms are described in Ref. [17]. SV0, a predecessorto SV1, is described in Ref. [16]. The JetFitterCombNNc algorithm makes use of theJetFitterCombNN neural network trained to reject c-jets instead of light-quark jets [20].A.2.2 BackgroundsMany physical processes can produce the same final state as the signal. The main background to thissearch comes from top-quark backgrounds, namely tt¯ and single-top production, where one or moreb-quarks from the decay is mis-identified as light-quark jet. Diboson backgrounds from WW , WZ,Wγ(∗) and ZZ production in association with at least two jets in the initial state are also important,as well as gluon-fusion Higgs and Z/γ∗ production in association with at least two jets. Finally,178backgrounds where at least one jet is mis-identified as a charged lepton, namely W + jets and QCDmulti-jets, also contribute to the event expectation in the Signal Region (SR). They are evaluatedfrom data.The main challenge of this analysis is therefore to effectively separate the small signal frombackground processes with relatively large cross sections. This is most easily seen when compar-ing the cross section times branching fraction of the VBF Higgs signal in the `ν`ν channel (withMH = 125 GeV):σ(VBF H) ·B(H→WW ∗→ `ν`ν) = (1.58 pb)(1.0%) = 15.8 fb (A.3)which for an integrated luminosity of 20.7 fb−1 corresponds to a total expected number of only 327events, to the significantly larger cross sections for background processes illustrated in Figure 2.8.A.2.3 Topology of VBF H→WW ∗→ `ν`ν EventsFortunately, the VBF H →WW ∗ → `ν`ν signal has a unique topology which makes the searchpossible. First, as illustrated in the Feynman diagram of Figure A.4, two back-to-back, forward,light-quark jets are expected. As mentioned in Section A.2.1, a b-tag veto is imposed with anefficiency of 85% to reject b-quark jets measured within the acceptance of the Inner Detector, inorder to reject top-quark backgrounds.The jets in signal are further expected to have a large opening angle in rapidity ∆y j j and a highdijet invariant mass m j j. Vetoing events with additional jets between the two leading jets also helpsto reject background: this requirement is called the “central-jet veto”. Additionally, both jets areexpected to be more forward than the leptons from the W decays. Therefore, it is possible to definea variable called “lepton η-centrality”:Cη =∑`∣∣∣∣∣∑j∆η` j∆η j j∣∣∣∣∣(A.4)where the sums are over the two leading charged lepton candidates and the two leading jets. Thequantity inside the absolute value is equal to unity when the lepton is collinear with one of the jets,smaller when it is between the two jets, and larger otherwise. In top-quark decays, since one leptonand one (mis-tagged) jet come from each top quark, the separation between each lepton and theclosest jet is expected to be smaller than in signal; this is also captured by lepton η-centrality.Another powerful variable against the tt¯ background is ∑m` j, where the sum is over all four pairsmade from the two leading charged lepton candidates and the two leading jets. In tt¯ events, m` j <Mtfor two of these pairs, so ∑m` j is in general smaller for this background with respect to signal.The variable mT introduced in Equation A.2 also discriminates against tt¯ and other backgrounds.In what follows, pmissT,track is used in place of EmissT in the definition of mT to improve the resolution179of this observable. Background events with top quarks also tend to have a larger total transversemomentum, defined as the following vectorial sum:~ptotT =∑`~pT +∑j~pT +~pmissT,track (A.5)This variable is essentially a measure of the soft activity from initial-state radiation.Backgrounds from Z/γ∗ production are also important: decays to τ+τ− where both τ leptonsdecay leptonically potentially affect both search channels, while Z/γ∗→ e+e− and Z/γ∗→ µ+µ−only affect the SF channel. The photon and Z peak regions are vetoed using window cuts on theinvariant masses m`` and mττ , where mττ is computed under the assumption that neutrinos fromτ decays are collinear with their associated charged lepton. As well, since there is no real missingtransverse momentum coming from Z/γ∗ production in the SF channel, requiring large values ofEmissT and pmissT,track helps to reduce this background.Finally, signal events have two leptons of opposite electric charge, going preferentially in thesame direction due to spin correlations in the H→WW ∗ decay. Indeed, since the Higgs boson hasspin zero, the two W bosons must have opposite spin. Then, the W− decays to `−ν¯ , and the W+to `+ν . But antineutrinos always have right-handed helicity, i.e. their spin along the direction ofmotion is oriented in the same direction as their velocity, while neutrinos always have left-handedhelicity. It follows, as illustrated in Figure A.7, that following a H →WW ∗→ `ν`ν decay, if theW bosons have non-zero spin in the direction of motion, then the charged leptons travel in the samedirection, while the neutrinos travel in the other. As a result, the charged lepton candidates areexpected to have a small azimuthal separation ∆φ`` and a low dilepton invariant mass m``.Figure A.8 shows a candidate signal event found in the dataset collected in 2012, which displaysall the characteristics described above.Figure A.7: Possible spin configurations following a H → WW ∗ → `ν`ν decay where theW bosons have non-zero spin in the direction of motion. The thin arrows representvelocity, and the thick arrows represent spin. The charged leptons preferentially travelin the same direction. Figure credit: K. van Nieuwkoop.180Figure A.8: VBF H →WW ∗→ `ν`ν candidate event. The angular separation between the muon candidate (orange) and the electroncandidate (green) is small, with EmissT (red) opposite them. The two leading jets (blue) are very forward [33].181A.2.4 Boosted Decision TreesThe first multivariate analysis technique used in this analysis is based on BDTs, which constitutea machine-learning algorithm aiming to classify events as signal or background based on selecteddiscriminating variables. The implementation is based on the Toolkit for Multivariate Data Analysis(TMVA) environment [118].As a first step in any machine-learning algorithm, the sample of simulated background andsignal events is separated into two halves. The first half, called the “training sample”, is used totrain the algorithm to discriminate signal from background, while the other is an independent “testsample”, used to quantify the performance of the algorithm and provide background and signalpredictions in the SR. In practice, two different BDTs are trained: one on the first half of the sample,to apply on the second, and vice versa for the other. This procedure, called cross-evaluation, allowsto keep using the entire simulated sample to estimate the expected signal and background in the SR.In order to understand how a BDT algorithm differs from a traditional cut-based approach to dataanalysis, it is helpful to first consider a single decision tree. Decision trees consist of a successionof cuts over the discriminating variables: an example is shown in Figure A.9. First, starting from a“root node” containing all the events used for training, a scan is performed to find the cut that bestseparates signal from background. Each side of this cut then defines a sub-node, which is furthersplit. The process continues from each sub-node as long as the number of events in a node is abovea minimum value; otherwise, the node ceases to be split and is called a “leaf node”. Each leaf nodeis identified as a “signal node” or a “background node” based on its contents.Figure A.9: Schematic view of a simple decision tree, used to separate signal (S, blue) frombackground (B, red) [118].182Figure A.10 illustrates how using a single decision tree already constitutes an improvement overa simple cut-based analysis. For an example distribution of training background and signal events,the decision tree does find the region that would be selected using successive cuts, but also findsother signal-rich regions that would otherwise have not been identified. The importance of settinga minimal number of events per leaf node is also illustrated: not having this requirement can resultin overtraining, whereby unphysical signal-rich regions are found that are specific to the trainingsample. This would result in an unreliable decision tree that performs very well, by construction,on the sample used to train it, but not as well on statistically independent samples.Figure A.10: Illustration of the differences between a cut-based selection and one using adecision tree. Top left: distribution of background (red) and signal (blue) events beforeselection. Top right: selection using successive cuts. Bottom left: selection using asimple decision tree. Bottom right: selection using an overtrained decision tree.To further improve the discriminating power and stability of this method, the initial decision treeis then “boosted”. First, the events from the training sample that were mis-classified in the decisiontree are identified, and these events are given a higher weight. A second decision tree is then trainedfrom this re-weighted sample: by construction it will improve the classification of the events withlarger weights. This process is repeated until hundreds of decision trees are trained. The collectionof all the decision trees thus trained is the Boosted Decision Tree.183Finally, for each decision tree in the BDT, each event is given a score of −1 if it ended ina background node, and +1 if it ended in a signal node. The final discriminant, called the “BDTscore”, is defined for each event as the weighted average of the scores from all trees. The informationfrom the discriminating variables and correlations between them allowing to separate signal frombackground is thus summarized by a single value assigned to each event.A.2.5 Matrix Element MethodA complementary approach to machine-learning algorithms such as BDTs is the Matrix Element(ME) method, an elegant approach from first principles which aims to assign to each event a prob-ability to have been produced by a given physical process. Following a given physical process i,final-state particles with four-momenta y are produced with probability Pi(y). The probability toobserve a set of physical observables x in the detector is then given byPi(x) =∫Pi(y)T (x,y)dy (A.6)where the transfer functions T (x,y) relate the particle-level quantities to the physical observables.The transfer functions used are often Dirac δ -functions: this is justified by the good resolution ofthe detector to measure the angular coordinates and the momentum of charged lepton candidates,as well as the angular coordinates of jets. On the other hand, it is important to use Gaussian oreven more involved distributions for the energy of jets, to account for possible differences betweenmeasured and particle-level values due to the detector resolution and thereby improve the sensitivityof the method.Given the energy of collisions at the LHC, the mass of all final-state particles can safely beneglected. In the search for VBF H →WW ∗ → `ν`ν , the physical observables x are thereforethe three-momenta of the two charged lepton candidates and of the two leading jets, and the twocomponents of EmissT . In contrast, y represents the corresponding observable particle-level quantities:the three-momenta of the four leptons and of the two leading quarks or gluons in the final state.Four out of the six components of the neutrino three-momenta are unobservable, and are assignedT (x,y) = 1.In the context of a proton-proton collision with colliding partons q1 and q2, Equation A.6 be-comesPi(x) =1σi∫f (q1) f (q2)|Mi(y)|2T (x,y)dΦ(y)dq1dq2 (A.7)In this equation, the cross section σi of the process of interest is used to normalize the result, en-suring that Pi(x) is a probability density. The integrand includes the Parton Distribution Functionsf (q), which depend on the four-momenta q of initial-state partons, the square of the matrix elementMi(y), from which the method gets its name, and dΦ(y) represents the phase space over which theintegration is taken.184From the event-by-event probabilities calculated for signal and background processes, it is pos-sible to define the Event Probability Discriminant (EPD):EPD =PsigPsig + ∑i∈bkgαiPi(A.8)where the coefficients αi are optimized to find the EPD definition with the best discriminating power.In theory, these coefficients should be close to unity; in practice they can vary due to the fact thatthe acceptance and efficiency for distinct background sources differ.A.3 Contributions to the AnalysisThis section documents the main areas where contributions were made to this analysis in parallelwith the work presented in the main body of this dissertation.A.3.1 Statistical FrameworkThe implementation of the statistical analysis was conducted in parallel with the optimization andbackground estimation procedures described below, within an existing framework created for earlierversions of the analysis. Figure A.11 shows a schematic diagram of the analysis fit model. As indi-cated above, the search is divided into two channels, depending on the flavour of the leading chargedleptons: in the Different-Flavour (DF) channel, these leptons are one muon and one electron, whilein the Same-Flavour (SF) channel, they are either two electrons or two muons.All parameters are fitted simultaneously. Three Control Regions (CRs) are defined in order toconstrain the corresponding backgrounds using data:• Top CRs, defined by requiring exactly one b-tagged jet in the event, are used in both channelsto correct the normalization and shape of the predictions from MC simulations of backgroundprocesses involving top quarks. The CRs are distinct for the DF and SF channels in order tobenefit from the higher purity in the DF sample.• The Z/γ∗→ τ+τ− CR, discussed in Section A.3.6, is used to normalize the yields predictedby simulation of this background to those observed in data.• The Z/γ∗→ `+`− CR, discussed in Section A.3.7, is used in the SF channel to obtain a fullydata-driven estimate of this background.The parameters used to correct the simulations are called Normalization Factors (NFs), definedas the ratio Ndata,CR/NMC,CR. The expected number of events in the SR is then given byNexp,SR =Ndata,CRNMC,CR·NMC,SR =NMC,SRNMC,CR·Ndata,CR (A.9)185where the ratio in the second expression is commonly called the “extrapolation factor”.The systematic uncertainties are implemented as nuisance parameters which are then marginal-ized. The value for the VBF signal strength is extracted from the fit, along with the signal signif-icance. All optimizations below seek to maximize the expected significance, calculated from theestimated signal and background yields in the fit regions.Figure A.11: Schematic diagram of the analysis fit model.A.3.2 Event Pre-Selection OptimizationIn addition to the selection of physical objects described in Section A.2.1 and the b-tag veto, a fewmore criteria are applied to the events before applying the multivariate analysis techniques:• The requirement mττ < 66 GeV, called the Z/γ∗→ τ+τ− veto, is applied in both channels toallow the definition of the Z/γ∗→ τ+τ− CR.• The photon peak is absent from the Z/γ∗ background simulation; this is replicated in theanalysis by requiring m`` > 10 GeV in the DF channel and m`` > 12 GeV in the SF channel.The cut in the SF channel also removes potential background contributions from J/ψ and ϒmeson decays.• The region of the Z peak and above is set aside in the SF channel for use in the data-drivenestimate of the Z/γ∗ → `+`− background; the same is true of the low-EmissT region. Therequirements m`` < 75 GeV and EmissT > 45 GeV are therefore applied in this channel.186Further, it was found during the BDT optimization described in the next section that the sameBDT performs well in both the DF and SF channels, as long as additional cuts are applied to re-duce the background from Z/γ∗ → `+`−. This greatly simplifies the analysis, as the systematicuncertainties and NFs for most processes are then the same in both channels.The original cuts designed for this purpose were on the transverse momentum pT,``jets of thesystem consisting of all the lepton candidates and jets in the event, and the soft hadronic recoilfraction frecoil, defined as follows:pT,``jets =∣∣∣∣∣∑`~pT +∑j~pT∣∣∣∣∣(A.10)frecoil =|∑opp.jets~pT|pT,``jets(A.11)where in the definition of frecoil, the sum is over the jets opposite to the system of leptons andjets, i.e. over the jets with azimuthal separation from ~pT,``jets larger than 3pi/4. These variablesdiscriminate against the Z/γ∗ background because of the absence of neutrinos in this background’sfinal state, resulting in smaller values of pT,``jets and larger values of frecoil. A good operating pointconsists of the requirements pT,``jets > 25 GeV and frecoil < 0.2.On the other hand, it was later found that replacing these cuts by a more straightforward re-quirement on pmissT,track > 40 GeV gives the same performance, with less reliance on the modelling ofsoft jets. This later requirement was therefore adopted for the analysis. While any of these vari-ables could have been included in a dedicated BDT for the SF channel, the advantages of using thesame BDT in both channels are more important than the marginal increase in sensitivity that suchan approach would bring.A.3.3 Boosted Decision Tree OptimizationFollowing the event pre-selection, BDTs are trained and applied to separate background from signal.The identity of the input variables used in the BDTs is determined using the algorithm illustrated inFigure A.12, aiming to find the simplest BDT configuration that still maximizes performance.First, an initial BDT is trained with a large number N of input variables, and the performanceof this BDT is evaluated on the test samples using the expected significance as figure of merit. Thisvalue is considered the performance ceiling. The initial BDT is then simplified by considering Ndifferent BDT, each with one less input variable than the initial BDT. The input variable missingfrom the most performant of these simplified BDTs is the one that provides the least marginalimprovement. If the performance of this best simplified BDT is similar to that of the initial BDT,the algorithm is repeated using the best simplified BDT as the new initial one.It is following this procedure that eight variables described in Section A.2.3 were identified asthe best input variables for the BDT: mT , m``, ∆φ``, m j j, ∆y j j, ptotT , ∑m` j and Cη .187Figure A.12: Schematic diagram of the BDT optimization algorithm.The BDT configuration settings are also optimized, via a grid scan of the different possibilities.The optimal and most stable configuration is found to be a BDT made of 1000 trees, each witha maximum depth of 5 levels and a minimum of 1000 events in each leaf node, with additionalsettings related to the boosting algorithm also optimized.Finally, the binning of the BDT score used as the final discriminant is also optimized. Thebinning should be as fine as possible, to limit the loss of information, while being coarse enoughto make possible a reliable estimate of expected signal and background yields as a function of theBDT score. The problem being that the importance of statistical errors grows when finer bin sizesare used.A grid scan was originally used to find the optimal bin boundaries with the expected significanceas the figure of merit, however because of the need to repeat this step for each BDT tried (as opposedto the configuration settings which remain the same) the following, faster method is used instead.The bin boundaries are set by integrating the signal and background distributions from the high endof the BDT score distribution, to find the point maximizing the Poisson significanceZPoisson =√2(Nsig +Nbkg) · ln(1+Nsig/Nbkg)−2Nsig (A.12)This figure of merit is a closer approximation to the actual significance than the Gaussian approxi-mation Nsig/√Nbkg, which is only valid for Nsig Nbkg [84]. When a boundary is set, the integra-tion restarts from this point to find the next bin boundary. Three bin boundaries are typically set bythe algorithm, defining four bins. The three most signal-rich bins form the SR, and the background-rich bin with events having the lowest BDT scores is used as a Validation Region (VR), to verifythe modelling of input variables and correlations.A.3.4 Modelling StudiesSince the BDT is trained on MC simulated events, it is essential for the method to be valid thatthe modelling of data by the simulation is correct. The BDT score itself is verified in both search188channels in the Top CR, and these histograms are shown in Figure A.13. The BDT training variablesare also verified in both search channels, in the Top CR as well as in the low-BDT VR. Thesehistograms are shown in Figures A.14, A.15, A.16 and A.17. The agreement between data and thesum of expected backgrounds is satisfactory in all the distributions.Events / 0.11210410610 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→HBDT­1 ­0.5 0 0.5 1Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 0.1110210310410510 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→HBDT­1 ­0.5 0 0.5 1Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsFigure A.13: Histograms of the BDT score in the Top CR for the DF channel (top) and theSF channel (bottom). The uncertainties shown on the background estimate are statisti-cal only.189Events / 13 GeV200400600800 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]Tm50 100 150 200 250 300Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 20 GeV5001000ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]llm100 200 300 400Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 125 GeV1000200030004000 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]jjm0 500 1000 1500 2000 2500Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 175 GeV1000200030004000 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]lep,jetmΣ0 1000 2000 3000Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 0.16 rad200400600 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [rad]llφ∆0 1 2 3Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 0.45001000 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→Hjj Y∆0 2 4 6 8Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 7.5 GeV100020003000 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]totTp0 50 100 150Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsEvents / 0.1200400600800 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→Hη C0 0.5 1 1.5 2Data / Total 0.60.811.21.4 Data Totalt t Single top W+jetττ→*γ Z/ WW WZ ggF Higgsll→*γ Z/ VBF HiggsFigure A.14: Histograms of the BDT training variables in the Top CR for the DF channel. Theuncertainties shown on the background estimate are statistical only.190Events / 13 GeV100200300 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]Tm50 100 150 200 250 300Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsEvents / 20 GeV200400600 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]llm100 200 300 400Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsEvents / 125 GeV5001000 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]jjm0 500 1000 1500 2000 2500Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsEvents / 175 GeV5001000 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]lep,jetmΣ0 1000 2000 3000Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsEvents / 0.16 rad50100150 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [rad]llφ∆0 1 2 3Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsEvents / 0.4100200300400 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→Hjj Y∆0 2 4 6 8Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsEvents / 7.5 GeV200400600800 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]totTp0 50 100 150Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsEvents / 0.1100200300 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→Hη C0 0.5 1 1.5 2Data / Total 0.60.811.21.4 Data Totalt t Single topll→*γ Z/ W+jet WWττ→*γ Z/ WZ ggF Higgs VBF HiggsFigure A.15: Histograms of the BDT training variables in the Top CR for the SF channel. Theuncertainties shown on the background estimate are statistical only.191Events / 13 GeV50100150ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]Tm50 100 150 200 250 300Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsEvents / 20 GeV200400ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]llm100 200 300 400Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsEvents / 125 GeV200400600800 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]jjm0 500 1000 1500 2000 2500Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsEvents / 175 GeV200400600800 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]lep,jetmΣ0 1000 2000 3000Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsEvents / 0.16 rad50100150ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [rad]llφ∆0 1 2 3Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsEvents / 0.4100200300 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→Hjj Y∆0 2 4 6 8Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsEvents / 7.5 GeV200400600800 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→H [GeV]totTp0 50 100 150Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsEvents / 0.1100200300 ATLAS  work in progress = 8 TeVs 2j≥ + νµνe→WW*→Hη C0 0.5 1 1.5 2Data / Total 0.60.811.21.4 Data Totalt tττ→*γ Z/ WW Single top W+jet WZ ll→*γ Z/ ggF Higgs VBF HiggsFigure A.16: Histograms of the BDT training variables in the low-BDT VR for the DF chan-nel. The uncertainties shown on the background estimate are statistical only.192Events / 13 GeV50100 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]Tm50 100 150 200 250 300Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsEvents / 20 GeV100200300 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]llm100 200 300 400Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsEvents / 125 GeV100200300400 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]jjm0 500 1000 1500 2000 2500Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsEvents / 175 GeV100200300400 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]lep,jetmΣ0 1000 2000 3000Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsEvents / 0.16 rad50100 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [rad]llφ∆0 1 2 3Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsEvents / 0.450100ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→Hjj Y∆0 2 4 6 8Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsEvents / 7.5 GeV100200300400 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→H [GeV]totTp0 50 100 150Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsEvents / 0.1022.54567.590 ATLAS  work in progress = 8 TeVs 2j≥ + νµνµ/νeνe→WW*→Hη C0 0.5 1 1.5 2Data / Total 0.60.811.21.4 Data Totalt t ll→*γ Z/ WWττ→*γ Z/ Single top WZ ggF Higgs W+jet VBF HiggsFigure A.17: Histograms of the BDT training variables in the low-BDT VR for the SF channel.The uncertainties shown on the background estimate are statistical only.193A.3.5 Correlation StudiesIn addition to the BDT discriminating variables themselves, it is very important to verify that thecorrelations between these variables are well-modelled in the simulation, in order to guarantee thevalidity of the conclusions to be drawn from the BDT score distribution. Two ways to make thisverification are employed.The first way is based on the sample approximation to the Pearson correlation coefficient ρ:ρ(x,y) = (x− x¯)(y− y¯)√∑(x− x¯)2∑(y− y¯)2(A.13)where x¯ and y¯ are the sample means of the distributions of the variables x and y respectively, andthe sums in the denominator are taken over either data or the expected backgrounds. For each pairof variables used in the BDT, the distribution of ρ(x,y) is compared between data and the sum ofexpected backgrounds. An example of such a comparison is shown in Figure A.18. The agreementis reasonable for all pairs of variables.Figure A.18: Distribution of ρ(m``,mT ) in the low-BDT VR. The mean and its statistical un-certainty is indicated for background and data.As a more quantitative improvement on this method, it is also possible to monitor projections ofthe N-dimensional phase space onto 2D profile histograms. Figure A.19 shows an example of thistest: the mean value of one variable is shown in bins of the other, and vice versa. This test is repeatedfor all pairs of variables, as well as between all variables and the BDT score. χ2-probabilities are194calculated to quantify the agreement between data and the sum of expected backgrounds. In thelow-BDT VR, the χ2-probability is larger than 0.3% for all histograms but one (Cη vs. m``), andlarger than 5% for two others out of 72. In these three cases the deviations are evenly distributed oneach side of a unit ratio, and are therefore ascribed to statistical fluctuations.Figure A.19: Example pair of 2D correlation histograms, for data (black) compared with thesum of expected backgrounds (red). The green colour indicates that the χ2-probabilityis larger than 5%.A.3.6 Background Estimation and Systematic Uncertainties for Z/γ∗→ τ+τ−As mentioned in Section A.3.1, a Z/γ∗→ τ+τ− CR is used to estimate a Normalization Factor (NF)for this background in the DF channel. The Z/γ∗ → τ+τ− CR is defined in both the DF and SFchannels as follows:• All pre-selection cuts except the Z/γ∗→ τ+τ− veto;• m`` < 80 GeV in the DF channel (the SF channel pre-selection includes m`` < 75 GeV);• |mττ −MZ|< 25 GeV;• BDT score requirement corresponding to the SR definition.The cuts on m`` and mττ increase the Z/γ∗→ τ+τ− purity of the CR. Figure A.20 shows the m``and mττ distributions in the Z/γ∗→ τ+τ− CR for the combination of the DF and SF channels.The resulting NF, derived from this combined CR, is 0.9± 0.3 (statistical uncertainty only),which is compatible with unity. It is applied in the fit, and its uncertainty is considered as un-correlated between the different bins of the SR. Despite the fact that this statistical uncertainty isrelatively large due to the small event yield in the CR, its impact on the result is negligible becausethe contribution of the Z/γ∗ → τ+τ− process to the total background in the DF SR is small incomparison to the ones from dominant sources such as tt¯ production.195Events 24681012DataH ggF [125]Htautau [125]ttWWZtautauZleplepsingle topγWZ/ZZ/WQCDW+jetsH VBF [125] work in progressATLAS = 8 TeVsllm0204060801001201401601802000.60.811.21.4NF: WW 1.00, Top 1.00, Z 1.00, VBF 1.00Events 24681012DataH ggF [125]Htautau [125]ttWWZtautauZleplepsingle topγWZ/ZZ/WQCDW+jetsH VBF [125] work in progressATLAS = 8 TeVsττm0204060801001201401601802000.60.811.21.4NF: WW 1.00, Top 1.00, Z 1.00, VBF 1.00Figure A.20: Distributions of m`` (left) and mττ (right) in the Z/γ∗→ τ+τ− CR for the com-bination of the DF and SF channels.A.3.7 Background Estimation and Systematic Uncertainties for Z/γ∗→ e+e−,µ+µ− in the Same-Flavour ChannelTo estimate the Z/γ∗ background in the SR of the SF channel, the BDT analysis makes use of a fullydata-driven method inspired from ABCD techniques. In these techniques, the background estimatein one region of phase space, called region A (typically the SR), comes from three neighbouringregions. The shape of the background in terms of the variable of interest is taken from one of theseneighbouring regions, called region B, and the extrapolation factor going to region A from region Bis taken from the other two regions, called C and D.Here, the Z/γ∗ shape as a function of BDT score is taken from the data in a low-EmissT Z CR(25 GeV < EmissT < 45 GeV, using calorimeter-based EmissT ), corrected by subtracting the other back-ground contributions in this region. The Z/γ∗ estimate is extrapolated to the SR using the EmissT cutefficiency calculated from data on the Z peak. Table A.1 illustrates the regions used in this method:the indicated cuts are used in addition to the rest of the selection in the SF channel.The Z/γ∗ estimate in each BDT score bin i is then determined by:NSR,iZ/γ∗ = NB,iZ/γ∗ ·NCZ/γ∗NDZ/γ∗(A.14)where on the right-hand side NZ/γ∗ = (Ndata−Nnon-Z/γ∗MC). The resulting NFs are compatible withunity in each bin of BDT score. Figure A.21 shows the BDT score distributions from each region.The EmissT cut efficiency measured in data from regions C and D is 0.43±0.03, consistent withthe value of 0.47±0.04 measured from Z/γ∗ MC simulation. The statistical uncertainty on theefficiency measured from data is propagated to the fit, fully correlated across bins of BDT score.196Table A.1: Summary of the region definitions for the Z/γ∗ estimation technique used in theSF channel of the analysis.Region A (SR) Region CEmissT > 45 GeV EmissT > 45 GeVm`` < 75 GeV |m``−mZ|< 15 GeVRegion B (Z CR) Region D25 GeV < EmissT < 45 GeV 25 GeV < EmissT < 45 GeVm`` < 75 GeV |m``−mZ|< 15 GeVIt is important to note from Equation A.14 that the EmissT cut efficiency is not calculated in binsof BDT score, but rather obtained from the full sample after the selection: the EmissT cut efficiency isassumed to be the same across the BDT score spectrum. This is necessary because little to no eventsfrom the Z peak populate the bins at high BDT score. This method therefore relies on the absenceof correlation between the BDT score and EmissT . This fact is demonstrated by the similarity of theBDT score shapes from Z/γ∗ MC simulation in the SR and the Z CR, shown in Figure A.22. Eventhough the two shapes are compatible with each other within statistical uncertainties, the deviationfrom unity of the ratio between the two shapes in each bin is taken as an uncorrelated systematicuncertainty due to the non-correlation assumption.A second assumption that has to be satisfied for the method to be valid is the absence of corre-lation between EmissT and m``, which is necessary to extrapolate the EmissT cut efficiency value fromregions C and D to regions A and B. A closure test in Z/γ∗ simulation is performed to test thisassumption, with the non-closure between the four regions quantified using a double ratio:non-closure =NA,high-BDTZ/γ∗ / NB,high-BDTZ/γ∗NCZ/γ∗ / NDZ/γ∗(A.15)where “high-BDT” corresponds to the BDT score bins used in the fit. Closure is valid withinstatistical uncertainty, with a non-closure value of 0.87± 0.22. The deviation of this value fromunity is taken as a flat systematic uncertainty on the Z/γ∗ estimate in the SF channel.197­110110210310410510 Data ZleplepZ EW ZtautauH ggF [125] ttsingle top WWγWZ/ZZ/W QCDW+jets H VBF [125]Events  work in progressATLAS = 8 TeVsBDT­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 10.60.811.21.4Data/ExpectedNF: WW 1.00, Top 1.00, Z 1.00, VBF 1.00­110110210310410510610 Data ZleplepZ EW ZtautauH ggF [125] ttsingle top WWγWZ/ZZ/W QCDW+jets H VBF [125]Events work in progressATLAS = 8 TeVsBDT­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 10.60.811.21.4Data/ExpectedNF: WW 1.00, Top 1.00, Z 1.00, VBF 1.00­110110210310410510610 Data ZleplepZ EW ZtautauH ggF [125] ttsingle top WWγWZ/ZZ/W QCDW+jets H VBF [125]Events work in progressATLAS = 8 TeVsBDT­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 10.60.811.21.4Data/ExpectedNF: WW 1.00, Top 1.00, Z 1.00, VBF 1.00Figure A.21: Distributions of BDT score in the SF channel, for the low-EmissT Z CR (top),region C (bottom left) and region D (bottom right).198Unit Area Templates Simulation work in progressATLASBDT­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 1­210­1101RatioBDT­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.61.82Figure A.22: Illustration of the absence of correlation between the BDT score and EmissT insimulated events. Specifically, the BDT score distribution shape, normalized to unity, isshown for Z/γ∗ simulation for the SR selection (red) and in the Z CR selection (green).The rightmost three bins correspond to the fit SR, while the other two correspond tothe low-BDT VR. The shapes are compatible within the statistical uncertainties.A.3.8 Effect of Object Systematic Uncertainties on the BDT Score ShapeThe systematic uncertainties affecting this search form two main categories: theoretical systematicuncertainties originating from the background and signal estimation techniques, and experimentalsystematic uncertainties coming from the measurement and identification of the physical final stateobjects. The latter category includes, in decreasing order of importance, the uncertainties on theenergy resolution and scale of jets and electron candidates, the scale and resolution of missingtransverse momentum, the muon momentum scale and resolution, the jet b-tagging efficiencies, thelepton reconstruction and isolation efficiencies, and others.For each object systematic uncertainty source, dedicated signal and background samples areproduced with the same simulated events as the nominal samples, but with the object propertyaffected by the systematic uncertainty in question varied by the uncertainty range at 68% CL. Theevent selection is then applied on these samples, and a nuisance parameter is assigned to the shapedifferences in the discriminating variable between each varied sample and the nominal sample.An example object systematic uncertainty variation is shown in Figure A.23.199BDT0 0.5 1Rel. Diff.­0.0500.05Events0246work in progressATLASNominal, SignalSystematic Uncertainty Up, SignalSystematic Uncertainty Down, SignalBDT0 0.5 1Rel. Diff.­0.1­0.0500.050.1Events02040work in progressATLASNominal, BackgroundSystematic Uncertainty Up, SignalSystematic Uncertainty Down, SignalFigure A.23: Example object systematic uncertainty, due to the pT,track resolution, on the BDTshape in the SR of the DF channel, for signal (left) and the sum of all backgrounds(right). The bottom inset shows the ratio between the varied and nominal samples. Theyellow band represents the statistical uncertainty.A.3.9 Comparison of Analysis TechniquesThe new expected result based on BDT can be compared with the cut-based result to quantify thecompatibility of the two approaches. As a first step, the overlap between the events in the SRs ofthe two analyses is quantified in MC simulation: the result is that 99% of the events in the SR ofthe cut-based approach are selected in the BDT SR. On the other hand, the signal acceptance of theBDT SR is more than double that of the cut-based SR.Even then, the question of the compatibility of observed results remains: as it may turn out thatthe measured signal strength and significance will be very different between the two approaches,it is useful to quantify the expected range of differences between the two results. This question isaddressed using pseudo-experiments drawn from simulated events.In order to meaningfully compare the outcomes from the two analysis approaches, it is neces-sary to use the same pseudo-datasets in both cases. This forbids the method of drawing pseudo-experiments directly from the distributions of the discriminating variables, as was done for exampleis Chapter 8 to estimate expected limits and calculate p-values.Instead, actual pseudo-datasets consisting of simulated events are drawn randomly from the MCsamples used to evaluate the background and signal yields. The number of events drawn from eachsample is itself drawn from a Poisson distribution with a mean corresponding to the expected yieldfrom the given process following the event selection. Since the MC simulated events have differentweights, the sampling method must take this into account, in that the probability to draw a given200event must be proportional to its weight. The following algorithm [102], illustrated in Figure A.24,is used for this purpose:• For each sample, make a distribution of the cumulative event weight sum.• Draw a random number between zero and the total weight sum: this determines which partic-ular simulated event is picked-up.• Repeat until the desired number of events is drawn.Figure A.24: Illustration of the sampling algorithm to generate pseudo-experiments [102].The method is applied here in the DF channel of the search, with a nominal signal strengthcorresponding to Standard Model predictions (µ ≡ σ/σSM = 1) injected in the pseudo-datasets.Two hundred pseudo-experiments are generated. The pseudo-datasets are treated like observed datasamples in the statistical framework: for each of them in turn, the event selection is applied and thefits are run to obtain “observed” signal strength and significance values in each analysis method.First, as a validation step, histograms of the number of events passing the selection are produced:the results are shown in Figure A.25 for the selection taking place in each analysis. As expected,the distributions obtained from pseudo-datasets follow the Poisson distributions corresponding ineach case to the injected signal strength. This constitutes a non-trivial test that the pseudo-data arerepresentative: while the distributions of the number of events in each pseudo-dataset match thePoisson distribution by construction before the selection, this is not necessarily the case after theevent selection is applied.The observed signal strength µˆ and observed significance from pseudo-experiments are shown201 in SRobsN110011501200125013001350Pseudo-Experiments 01020304050Pseudo-Experiments = 0µPoisson,  = 1µPoisson,  Simulation work in progressATLAS in SRobsN0510152025303540Pseudo-Experiments 010203040506070Pseudo-Experiments = 0µPoisson,  = 1µPoisson,  Simulation work in progressATLASFigure A.25: Number of events in pseudo-datasets after the pre-selection of the BDT analysis(left) and the selection of the cut-based analysis (right).in Figure A.26 for the BDT analysis, and in Figure A.27 for the cut-based analysis3. On thesehistograms, the median expected significance from each analysis is also shown, and the median andaverage observed significances are shown to agree with these values. The agreement is also goodbetween the median and average observed signal strength and the injected value µ = 1.One possibly surprising feature of these distributions is their width: for example, the BDTanalysis has a percent-level chance to observe a significance as large as 4σ or, on the other side ofthe spectrum, not to observe any signal. For the cut-based analysis, this is explained by the width ofthe Poisson distributions shown in Figure A.25 (right): the low tail of the distribution with signal isaround the median of the distribution without signal, while the high tail is significantly outside. Thisfact, in turn, is explained by the low expected signal yields in the SR. A similar argument wouldhold for the distribution in the BDT analysis after a cut on the BDT score.For each pseudo-experiment, one can then directly compare the results obtained with the twoanalyses: histograms of the differences in signal significance and signal strength are shown in Fig-ure A.28. The median and average differences are consistent with zero, indicating the absence ofbias between the two analyses, however the width of this distribution indicates that potentially largedifferences are expected between the two observed results. This is explained like the variation inresults within each analysis, by the fact that the expected signal yields are small.Figure A.29 shows 2D histograms of the signal significance and strength observed in individualpseudo-experiments in the two analyses. The Pearson correlation coefficients are 0.63 for the ob-3 The significance values shown here represent the status of the two analyses as of October 2013, and the performancein both of them has improved since.202Observed significance00.511.522.533.544.55Pseudo-Experiments 051015202530354045Pseudo-ExperimentsMedian expected sig.Median observed sig.Average observed sig. Simulation work in progressATLASµ00.511.522.53Pseudo-Experiments 051015202530354045Pseudo-ExperimentsµExpected µMedian µAverage  Simulation work in progressATLASFigure A.26: Signal significance (left) and strength (right) observed in 200 pseudo-experiments, with a BDT score as the discriminating variable.Observed significance00.511.522.533.544.55Pseudo-Experiments 0102030405060Pseudo-ExperimentsMedian expected sig.Median observed sig.Average observed sig. Simulation work in progressATLASµ00.511.522.53Pseudo-Experiments 0102030405060Pseudo-ExperimentsµExpected µMedian µAverage  Simulation work in progressATLASFigure A.27: Signal significance (left) and strength (right) observed in 200 pseudo-experiments, with mT as the discriminating variable.served significance values, and 0.65 for the signal strength. In addition, linearity tests are performedon these distributions to ensure that the methods are unbiased with respect to each other: these areshown in Figure A.30. The response of the methods is shown to be linear in both cases.Notwithstanding these encouraging results, more verifications could be carried out in order todemonstrate that the results are representative of the expected range of possible outcomes:• Performing the representativity test in bins of the SRs in addition to the inclusive tests shown203Observed significance difference: BDT vs. MT-3-2-10123Pseudo-Experiments 01020304050Pseudo-ExperimentsMedian expected sig. diff.Median observed sig. diff.Average observed sig. diff Simulation work in progressATLASMTµ - BDTµ-3-2-10123Pseudo-Experiments 0102030405060Pseudo-Experiments diff.µExpected  diff.µMedian  diff.µAverage  Simulation work in progressATLASFigure A.28: Differences in signal significance (left) and strength (right) observed in individ-ual pseudo-experiments between the two analyses.here would ensure that there are little shape distortions induced by the sampling algorithm.• The signal strength distributions obtained with this event sampling algorithm could be com-pared, for individual analysis approaches, with the result of drawing pseudo-experiments di-rectly from the respective distributions of the discriminating variables.• Verifying the re-sampling distributions, i.e. histograms of the number of times each simulatedevent was drawn, would allow to quantify the maximum number of independent pseudo-experiments that can be drawn from the available simulated events.This study will be repeated once the implementation of the re-analysis is complete, immediatelybefore un-blinding the search.204Observed significance, BDT fit-2-1012345Observed significance, MT fit-2-10123450246810120246810 Simulation work in progressATLASBDTµ00.511.522.53MTµ00.511.522.53024681012141618024681012141618 Simulation work in progressATLASFigure A.29: Two-dimensional histograms of the signal significance (left) and strength (right)observed in individual pseudo-experiments in the two analyses.Observed significance, BDT fit-2-1012345Observed significance, MT fit -2-1012345 Simulation work in progressATLASBDTµ00.511.522.53MT µ 00.511.522.53 Simulation work in progressATLASFigure A.30: Linearity test between the two analyses, for the signal significance (left) andsignal strength (right).205A.3.10 Matrix Element Method InvestigationAs introduced in Section A.2.5, at the beginning of this multivariate analysis effort two optionswere considered: the BDT method, and the ME method. For this analysis, the event-by-eventprobabilities from the ME method were calculated using two environments: MADWEIGHT [4, 10](itself based on MADGRAPH [5]) for the tt¯ and WW background hypotheses as well as for the VBFsignal hypothesis, and independent software [153] for the Z/γ∗ and gluon-fusion Higgs backgroundhypotheses. These probabilities were then combined into an EPD using Equation A.8, with thecoefficients αi optimized using a grid scan with the Poisson significance as the figure of merit.Figure A.31 shows the modelling of the probability distributions in a previous definition ofthe Top CR in the DF channel. The agreement between data and the simulation is satisfactory.Figure A.32 shows the expected signal and background yields as a function of the event-by-eventprobabilities, illustrating the discriminating power of the method.One of the main drawbacks of the ME method is the large computing times it requires. Withintegration times reaching up to a few minutes per event, the use of extensive computing resourceswas necessary, and the flexibility and usability of the method was therefore hampered.Nevertheless, early results were very promising. The performance of both methods taken ontheir own were at first comparable, but it was observed that combining the EPD and the BDT scoreinto a combined discriminant performed best. The best such combination found was the productEPD*BDT. The performance obtained with the combined discriminant was found to be up to 15%better than with either the EPD or the BDT score alone.However, as the BDT optimization progressed, this additional gain started to fade, a plausibleexplanation being that the improvements to the BDTs were due to them making use of increasinglylarger fractions of the available information relevant to discriminating signal from background. Thedisappearance of the gain from using a combined discriminant, along with the prohibitive computingtimes of the event-by-event probabilities, justified shelving this multivariate analysis method infavour of an analysis based solely on BDTs.206Figure A.31: Event-by-event probabilities calculated in a previous definition of the DFTop CR under the hypotheses of tt¯ (top left), WW (top right), gluon-fusion Higgs(centre left), Z/γ∗ (centre right) and VBF Higgs production (bottom). On the mainhistograms, the signal contribution is magnified by a factor 200 for visibility. The redline in the bottom inset indicates the bin-by-bin Poisson significance of the VBF signal.207Figure A.32: Event-by-event probabilities calculated in a previous definition of the blinded DFSR under the hypotheses of tt¯ (top left), WW (top right), gluon-fusion Higgs (centreleft), Z/γ∗ (centre right) and VBF Higgs production (bottom). The red line in thebottom inset indicates the bin-by-bin Poisson significance of the VBF signal.208A.4 Conclusion and OutlookIn conclusion, the re-analysis of the Run-I dataset in the search for the process H→WW ∗→ `ν`νis well underway. Because the final state of interest is matched by a variety of diverse backgrounds,a multivariate analysis is found to be more powerful than a more traditional cut-based approach.Specifically, combined with refinements in the object selection, the new analysis strategy usingBDTs is expected to bring an improvement of 40% in expected significance compared to the pre-liminary result.Figure A.33 shows the preliminary ATLAS measurements from Run-I of the LHC of the signalstrength ratios between the bosonic and fermionic Higgs production channels for the individualfinal states and their combination. All values are currently compatible with a unit ratio. Figure A.34presents fit results for a parametrization of Higgs boson coupling strengths probing a universal scalefactor for fermion couplings (κF) and another for boson couplings (κV). The measured couplingsto fermions are compatible with predictions from the Standard Model, and although the couplingsto bosons are more compatible with higher values, the measured values are consistent with theStandard Model prediction given the uncertainties.Increasing the precision of Higgs boson coupling measurements might unveil a significant dis-crepancy, which could be indicative of physical processes beyond the Standard Model. Measuringthe Higgs boson production and decay rates using LHC data from Run-II and beyond will com-plement direct searches for new particles, and is therefore an indispensable part of the high-energyphysics programme for the next decades.209ggF+ttHµ / VBF+VHµ0 1 2 3 4 5ATLAS Prelim.-1Ldt = 4.6-4.8 fb∫ = 7 TeV s-1Ldt = 20.3 fb∫ = 8 TeV s = 125.5 GeVHm0.6-0.8+ = 1.2ggF+ttHµVBF+VHµγγ →H σ1 σ2  0.2- 0.2+ 0.2- 0.4+ 0.5- 0.7+0.9-2.4+ = 0.6ggF+ttHµVBF+VHµ 4l→ ZZ* →H σ1  0.2- 0.3+ 0.2- 0.6+ 0.9- 2.3+1.0-1.9+ = 1.8ggF+ttHµVBF+VHµνlν l→ WW* →H σ1  0.2- 0.5+ 0.4- 1.3+ 0.9- 1.4+1.2-∞ + = 1.7ggF+ttHµVBF+VHµττ →H  0.3-∞ + 0.6-∞ + 1.0- 5.3+0.5-0.7+ = 1.4ggF+ttHµVBF+VHµCombinedσ1 σ2  0.1- 0.2+ 0.2- 0.4+ 0.4- 0.5+Total uncertaintyσ 1± σ 2±(stat.)σ )theorysys inc.(σ(theory)σFigure A.33: Measurements of the signal strength ratios between the bosonic and fermionicHiggs production channels for the individual final states and their combination [34].Vκ0.60.70.80.911.11.21.31.41.51.6F κ-2-101234 bb→H  bb→H ττ →H ττ →H  4l→H  4l→H νlν l→H νlν l→H γγ →H γγ →H  bb→H ττ →H  4l→H νlν l→H γγ →H CombinedSMBest Fit-1Ldt = 20.3 fb∫ = 8 TeV s-1Ldt = 4.6-4.8 fb∫ = 7 TeV sATLASPreliminaryFigure A.34: Fit results for a parametrization of Higgs boson coupling strengths probing dif-ferent scale factors for fermions and bosons [34].210

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