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Search for new high-mass phenomena in events with two muons using the ATLAS detector at the Large Hadron… Rettie, Sébastien 2019

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Search for New High-MassPhenomena in Events with TwoMuons using the ATLAS Detector atthe Large Hadron ColliderbySébastien RettieB.Sc., University of Ottawa, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2019© Sébastien Rettie 2019The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the dis-sertation entitled:Search for New High-Mass Phenomena in Events with TwoMuons using the ATLAS Detector at the Large Hadron Collidersubmitted by Sébastien Rettie in partial fulfillment of the requirements forthe degree of Doctor of Philosophyin PhysicsExamining committee:Oliver Stelzer-Chilton, Physics & AstronomySupervisorColin Gay, Physics & AstronomySupervisory Committee MemberGary Hinshaw, Physics & AstronomySupervisory Committee MemberGordon Semenoff, Physics & AstronomySupervisory Committee MemberMoshe Rozali, Physics & AstronomyUniversity ExaminerAndrew MacFarlane, ChemistryUniversity ExamineriiAbstractElementary particles and their interactions are extremely well modeled bythe Standard Model of particle physics. However, experimental observationssuch as indirect detection of dark matter and theoretical problems such asthe hierarchy of energy scales cannot be explained entirely by this theory.Many extensions of the Standard Model which solve these shortcomingspredict the existence of new phenomena at high energies. In particular,there are numerous new resonance models, such as Grand Unified Theories,and contact interaction models leading to dimuon final states.This dissertation presents a search for new high-mass phenomena inevents with two muons using the ATLAS detector at the Large HadronCollider. The search results are found to be consistent with the StandardModel prediction. Interpretations are carried out in the context of bothresonant and non-resonant new physics models. In particular, lower limitson the mass of hypothetical Z ′ bosons are set between 4.0 TeV for the Z ′SSMmodel and 3.3 TeV for the Z ′ model, and lower limits on the contact inter-action energy scale Λ are set between 18 TeV and 30 TeV, depending on thechiral structure of the contact interaction.In addition to data analysis at the energy frontier, the performance ofmuon reconstruction and identification within the ATLAS experiment isdetailed. More precisely, calculations of muon trigger efficiencies for high-momentum muons using events containing a leptonically decaying W bosonand jets are presented. A new muon identification working point is alsoinvestigated.Finally, as the ATLAS experiment enters its second long shutdown, thefirst layer of the endcap regions of the muon spectrometer will be replacedwith the New Small Wheels (NSWs), in order to improve both the triggeringand tracking capabilities of the ATLAS detector. One of the two main tech-nologies used in the NSW is small-strip Thin Gap Chambers (sTGCs). Re-sults of various test beam campaigns carried out at Fermilab and at CERN,aimed at characterizing sTGCs, are presented. Position resolution mea-surements of less than 50 µm are obtained. Measurements using the latestelectronics readout chain of the sTGC detectors under realistic conditionsare also presented.iiiLay SummaryFour known fundamental forces act on the matter in our universe: grav-ity, electromagnetism, the strong nuclear force, and the weak nuclear force.While gravity is described by Einstein’s theory of General Relativity, thethree other forces are described by the Standard Model of particle physics.These theories are very successful, and have been experimentally validatedto high degrees of accuracy. However, they are incomplete. For example,they offer no explanation for the existence of dark matter, or the unificationof forces. To solve these shortcomings, extensions of the Standard Modelpredicting new forces of nature have been posited. This dissertation ana-lyzes the second dataset collected by the ATLAS experiment at the LargeHadron Collider, with a view to finding new forces of nature. While thesearch is found to be consistent with the Standard Model prediction, con-straints placed on new physics scenarios contribute to the advancement ofour knowledge of the universe.ivPrefaceThe ATLAS collaboration comprises over 3000 scientists from 183 insti-tutions worldwide, representing 38 countries. The work presented in thisdissertation would not have been possible without the efforts of all mem-bers of the collaboration both from a scientific standpoint and a computingresources standpoint. In addition, the successful operation of the LHC iscrucial to the realization of the physics experiments carried within the AT-LAS collaboration at CERN. In many cases, the material presented in thisdissertation relies on the work of many individuals.Figures with no reference in the caption have been produced by myself, attimes in collaboration with other researchers named below. Figures labeled“ATLAS”, “ATLAS Online”, or “ATLAS Preliminary”, are public resultsreleased by the ATLAS collaboration. Figures labeled “ATLAS Work InProgress” are not yet published but use either real or simulated ATLASdata.The results presented in this dissertation led to the publications listed be-low. The first publication is the analysis of the full Run 2 dataset. Althoughno results from this publication are directly presented in this dissertation, Iwas involved with the analysis group and contributed to the optimization ofthe muon channel selection, the investigation of the highest invariant massevents, the development of the analysis framework, and the writing of in-ternal documentation. In addition, I presented the latest results on behalfof the analysis team on several occasions during the internal ATLAS re-view process. The next two publications are related to the work describedin Chapters 9 to 11. Throughout my doctoral studies, I acted as the mainmuon channel analyzer for the search discussed in Chapters 9 to 11. I playeda major role in all aspects of the search, including the following:• Development of the analysis framework• Production of signal samples• Optimization of the event selection• Evaluation of the dominant systematic uncertaintiesvPreface• Background estimation• Signal estimation for numerous signal models• Statistical analysis• Investigation of the highest dimuon invariant mass eventsIn collaboration with D. Hayden and Y. Liu, I coordinated the cross-checks required between the different analyzers to ensure mutual consistency.I evaluated the performance of the ATLAS detector with respect to high-pT muon identification by investigating the highest dimuon invariant massevents with M. Bugge and the various Muon Combined Performance groupconveners G. Sciolla, M. Bellomo, S. Rosati, F. Sforza, and S. Zambito. Iprovided the inputs and ran the limit-setting analysis code with D. Hayden,W. Fedorko, and G. Artoni.The last publication in the list includes the work presented in Chapter 8.I participated in the test beam campaigns carried out both at Fermilab andCERN. During the Fermilab test beam campaign, I• Constructed and troubleshot the experimental setup in collaborationwith the authors of the publication• Led the small-strip Thin Gap Chamber standalone analysis with S.Viel• Obtained residual distributions• Addressed many referee comments during the review processDuring the CERN test beam campaigns, in addition to preparing theexperimental setup, I collected and analyzed data with L. Moleri, S. Sun,L. Guan, I. Ravinovich, N. Hod, D. Shaked-Renous, and S. Bressler. I alsospent three months at the Weizmann Institute of Science in Isreal thanksto the Mitacs Globalink Research Award. Part of the work I carried outwhile at the Weizmann Institute of Science led to the results presented inSection 8.3.3 in collaboration with M. Birman.ATLAS Collaboration Search for high-mass dilepton resonances using139 fb−1 of pp collision data collected at √s = 13 TeV with the ATLASdetectorPhysics Letters B, 796, Pages 68-87, (2019)viPrefaceATLAS Collaboration Search for new high-mass phenomena in the dilep-ton final state using 36 fb−1 of proton-proton collision data at √s =13 TeV with the ATLAS detectorJournal of High Energy Physics, 10, 182, (2017)ATLAS Collaboration Search for high-mass new phenomena in the dilep-ton final state using proton-proton collisions at √s = 13 TeV with theATLAS detectorPhysics Letters B, 761, Pages 372–392, (2016)sTGC Collaboration Performance of a Full-Size Small-Strip Thin GapChamber Prototype for the ATLAS New Small Wheel Muon UpgradeNuclear Instruments and Methods in Physics Research Section A, 817,Pages 85-92, (2016)In addition to the publications listed above, two publications that in-clude results from this dissertation are currently in preparation. The firstdescribes muon identification using the full Run 2 dataset collected at theLHC, and includes the work described in Chapter 6. As the liaison betweenthe ATLAS Exotics and Muon Combined Performance groups, I have hadthe pleasure of providing support for over 30 searches with muons in thefinal state. For example, I ensured the technical details regarding the latestMuon Combined Performance tools were propagated to the analyses ade-quately, and updated the relevant documentation web pages accordingly. Ialso contributed to the work carried out in the Muon Combined Performancegroup. Specifically, I used Alignment Effects On Track to improve the muonmomentum uncertainty estimation, and optimized the high-pT muon selec-tion working point for the ATLAS collaboration, as detailed in Section 6.2.I also employed Alignment Effects On Track to categorize muon tracks indifferent parts of the alignment system of the Muon Spectrometer withinATLAS in order to study the momentum resolution of tracks in differentdetector regions. The investigation of the gradient Working Point describedin Section 6.3 was performed with N. Hod.Finally, the last publication in preparation relates to the performanceof ATLAS muon triggers in Run 2. The efficiency measurements and ScaleFactor calculations presented in Chapter 7 were carried out by myself and A.Held. In particular, we wrote the framework which provides high-pT muontrigger Scale Factors for the entire ATLAS collaboration. I have served asone of the editors for the publication in preparation for the last year.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivAcronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxviAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . .xxix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The Standard Model of Particle Physics . . . . . . . . . . . . 32.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Gauge Bosons . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Leptons and Quarks . . . . . . . . . . . . . . . . . . . 62.1.3 The Higgs Mechanism . . . . . . . . . . . . . . . . . . 82.2 Parton Distribution Functions . . . . . . . . . . . . . . . . . . 102.3 Successes of the Standard Model . . . . . . . . . . . . . . . . 122.4 Limitations of the Standard Model . . . . . . . . . . . . . . . 142.4.1 Quantum Gravity . . . . . . . . . . . . . . . . . . . . 142.4.2 The Hierarchy Problem . . . . . . . . . . . . . . . . . 152.4.3 Neutrino Masses . . . . . . . . . . . . . . . . . . . . . 152.4.4 Dark Matter and Dark Energy . . . . . . . . . . . . . 16viiiTable of Contents3 Beyond the Standard Model . . . . . . . . . . . . . . . . . . . 173.1 New Gauge Symmetries . . . . . . . . . . . . . . . . . . . . . 173.1.1 Sequential Standard Model . . . . . . . . . . . . . . . 173.1.2 Grand Unified Theories . . . . . . . . . . . . . . . . . 183.1.3 Minimal Z ′ Models . . . . . . . . . . . . . . . . . . . . 193.2 Contact Interactions . . . . . . . . . . . . . . . . . . . . . . . 203.3 Extra-Dimensional Models . . . . . . . . . . . . . . . . . . . . 224 The ATLAS Detector at the Large Hadron Collider . . . . 234.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . 234.2 The ATLAS Detector: Overview . . . . . . . . . . . . . . . . 274.3 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3.1 Pixel Detector . . . . . . . . . . . . . . . . . . . . . . 314.3.2 Semiconductor Tracker . . . . . . . . . . . . . . . . . . 324.3.3 Transition Radiation Tracker . . . . . . . . . . . . . . 324.4 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.4.1 Electromagnetic Calorimeter . . . . . . . . . . . . . . 354.4.2 Hadronic Calorimeter . . . . . . . . . . . . . . . . . . 364.5 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . 374.5.1 Resistive Plate Chambers . . . . . . . . . . . . . . . . 424.5.2 Thin Gap Chambers . . . . . . . . . . . . . . . . . . . 434.5.3 Monitored Drift Tubes . . . . . . . . . . . . . . . . . . 444.5.4 Cathode Strip Chambers . . . . . . . . . . . . . . . . 455 Object Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 465.1 Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.3 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.3.1 b-jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.4 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.5 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.5.1 Medium Quality Muons . . . . . . . . . . . . . . . . . 535.5.2 Transverse Momentum Corrections . . . . . . . . . . . 535.5.3 Transverse Momentum Uncertainty . . . . . . . . . . . 545.6 Missing Transverse Momentum . . . . . . . . . . . . . . . . . 556 High-Momentum Muons . . . . . . . . . . . . . . . . . . . . . . 576.1 High-pT Working Point . . . . . . . . . . . . . . . . . . . . . 576.2 BadMuon Veto Optimization . . . . . . . . . . . . . . . . . . 606.3 Gradient Working Point . . . . . . . . . . . . . . . . . . . . . 64ixTable of Contents6.3.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 656.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 756.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 857 ATLAS Trigger System . . . . . . . . . . . . . . . . . . . . . . 867.1 Level-1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 867.2 High-Level Trigger . . . . . . . . . . . . . . . . . . . . . . . . 877.3 Muon Trigger Efficiency Measurements . . . . . . . . . . . . . 877.3.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . 887.3.2 Systematic Uncertainties . . . . . . . . . . . . . . . . . 907.3.3 Efficiency Measurements and Trigger Scale Factors . . 918 ATLAS Detector Upgrade . . . . . . . . . . . . . . . . . . . . . 958.1 The New Small Wheel . . . . . . . . . . . . . . . . . . . . . . 968.2 Small-strip Thin Gap Chambers . . . . . . . . . . . . . . . . 988.2.1 Readout Electronics . . . . . . . . . . . . . . . . . . . 998.3 Test Beam Results . . . . . . . . . . . . . . . . . . . . . . . . 1008.3.1 Fermilab Test Beam Campaign . . . . . . . . . . . . . 1008.3.2 CERN Test Beam Campaigns . . . . . . . . . . . . . . 1068.3.3 Pulser Board Tests . . . . . . . . . . . . . . . . . . . . 1119 Search for New High-Mass Phenomena . . . . . . . . . . . . 1149.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 1149.1.1 Background Processes . . . . . . . . . . . . . . . . . . 1169.1.2 Signal Processes . . . . . . . . . . . . . . . . . . . . . 1169.1.3 Higher-Order Corrections . . . . . . . . . . . . . . . . 1189.2 Dimuon Invariant Mass . . . . . . . . . . . . . . . . . . . . . 1209.3 Kinematic Distributions . . . . . . . . . . . . . . . . . . . . . 12210 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . 12910.1 Experimental Uncertainties . . . . . . . . . . . . . . . . . . . 12910.2 Theoretical Uncertainties . . . . . . . . . . . . . . . . . . . . 13210.3 Parton Distribution Function Uncertainties . . . . . . . . . . 13510.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13811 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 13911.1 Search Results . . . . . . . . . . . . . . . . . . . . . . . . . . 13911.1.1 Asymptotic Approximation . . . . . . . . . . . . . . . 14211.1.2 Look-Elsewhere Effect . . . . . . . . . . . . . . . . . . 14311.2 Exclusion Limits . . . . . . . . . . . . . . . . . . . . . . . . . 144xTable of Contents11.2.1 Z ′ Cross-Section and Mass Limits . . . . . . . . . . . 14511.2.2 Minimal Z ′ Model Limits . . . . . . . . . . . . . . . . 14711.2.3 Limits on Contact Interactions . . . . . . . . . . . . . 15012 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . 152Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154xiList of TablesTable 2.1 Summary of fermion field properties for the first gen-eration of fermions. Fermions in the second and thirdgeneration have identical properties. . . . . . . . . . . . 7Table 3.1 Summary of commonly motivated Z ′ models. . . . . . . 19Table 3.2 Summary of ′ and Min values for three specific mini-mal Z ′ models: Z ′W−a, Z ′, and Z ′3g. . . . . . . . . . . . 20Table 4.1 Summary of the ATLAS calorimeter system components. 35Table 4.2 Summary of the ATLAS MS stations. . . . . . . . . . . 39Table 6.1 Drop in selection efficiency per TeV due to catastrophicmuon energy loss for muons with pT S 200 GeV passingthe high-pT WP in different  ranges. . . . . . . . . . . 59Table 7.1 Summary of the samples used to evaluate the perfor-mance of high-pT muon triggers. . . . . . . . . . . . . . 89Table 7.2 Summary of the high-pT muon trigger SF calculationsfor muons passing either the HLT_mu50 trigger or theHLT_mu26_ivarmedium trigger. The last two columnsgive the statistical and systematic uncertainties thatcomprise the total uncertainty. . . . . . . . . . . . . . . 94Table 8.1 Amplitudes of the differential non-linearity correctionapplied to the three strip-cluster sizes considered in theposition resolution analysis. . . . . . . . . . . . . . . . 102Table 9.1 Summary of background processes considered in thissearch. The columns from left to right give the pro-cess of interest, generator, matrix element order, par-ton shower program, and PDFs adopted. . . . . . . . . 116xiiList of TablesTable 9.2 Summary of signal processes considered in this search.The columns from left to right give the process of in-terest, generator, matrix element order, parton showerprogram, and PDFs adopted. . . . . . . . . . . . . . . . 117Table 9.3 Expected and observed event yields in different mintervals. The quoted errors correspond to the com-bined statistical, theoretical, and experimental system-atic uncertainties. Expected event yields are reportedfor the Z ′ model, for two values of the pole mass. . . . 122Table 10.1 Summary of the pre-marginalized relative systematicuncertainties in the expected number of events at dimuonmasses of 2 TeV (4 TeV). The values quoted for thebackground represent the relative change in the totalexpected number of events in the corresponding mhistogram bin containing the reconstructed m massof 2 TeV (4 TeV). For the signal uncertainties, the val-ues were computed using a Z ′ signal model with a polemass of 2 TeV (4 TeV), by comparing yields in the coreof the mass peak, within the full width at half maxi-mum, between the distribution varied due to a givenuncertainty and the nominal distribution. . . . . . . . . 138Table 11.1 Observed and expected 95% CL lower mass limits forvarious Z ′ gauge boson models. The widths are quotedas a percentage of the resonance mass. . . . . . . . . . 147Table 11.2 Observed and expected 95% CL lower mass limits forvarious minimal Z ′ models. . . . . . . . . . . . . . . . . 149Table 11.3 Observed and expected 95% CL lower limits on Λ forthe LL, LR, RL, and RR chiral coupling scenarios, forboth the constructive (Const) and destructive (Dest)interference cases using a uniform positive prior in 1/Λ2or 1/Λ4. The limits are rounded to the nearest 100 GeV.151xiiiList of FiguresFigure 2.1 Particle content of the SM of particle physics [15]. . . 4Figure 2.2 Higgs potential k (ϕ) as a function of |ϕ| for 2 S 0(left) and 2 Q 0 (right). The values used for the SMparameters of the Higgs potential are  ≃ 0O129 and|2| ≃ (88O4 GeV)2. . . . . . . . . . . . . . . . . . . . . 9Figure 2.3 Illustration of the constituents of a proton, so-calledpartons. Quark-antiquark pairs are dynamically pro-duced and annihilated through interactions with glu-ons [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . 11Figure 2.4 PDFs of proton constituents at NLO in QCD as a func-tion of the momentum fraction x of the parton rela-tive to the proton momentum, for momentum trans-fers f2 = 10 GeV2 (left) and f2 = 104 GeV2 (right)obtained by the MSTW collaboration [24]. . . . . . . . 12Figure 2.5 Summary of several SM total production cross-sectionmeasurements [25]. . . . . . . . . . . . . . . . . . . . . 13Figure 2.6 Feynman diagram of the SM DY process. . . . . . . . 14Figure 3.1 Feynmann diagram representing a CI with energy scaleΛ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 4.1 The CERN accelerator complex [48]. . . . . . . . . . . 24Figure 4.2 Mean number of interactions per LHC bunch cross-ing [49]. . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 4.3 Luminosity delivered to the ATLAS detector as a func-tion of time [49]. . . . . . . . . . . . . . . . . . . . . . 26Figure 4.4 Total integrated luminosity recorded by the ATLASdetector as a function of time [49]. . . . . . . . . . . . 27Figure 4.5 Schematic diagram of the ATLAS detector [2]. . . . . 28xivList of FiguresFigure 4.6 Slice in the g−ϕ plane of the ATLAS detector. Start-ing from the IP, a particle will traverse the ID, theEM calorimeter, the hadronic calorimeter, and theMS. Different particles are reconstructed and identi-fied using all relevant sub-detectors. SM neutrinos areinvisible to the ATLAS detector [52]. . . . . . . . . . . 29Figure 4.7 The Inner Detector as seen in the transverse g − ϕplane. Particles traverse the beam pipe, three cylin-drical silicon pixel layers, four SCT layers, and ap-proximately 36 TRT straw tubes [2]. . . . . . . . . . . 30Figure 4.8 The Inner Detector as seen in the longitudinal plane.Immersed in a 2T solenoid magnetic field, the maincomponents are the pixel and SCT, covering || Q 2O5,and the TRT, covering || Q 2O0 [2]. . . . . . . . . . . 31Figure 4.9 Average probability of a high-threshold hit in the bar-rel TRT as a function of the Lorentz gamma factor forelectrons (open squares), muons (full triangles), andpions (open circles) in the energy range 2− 350 GeV [2]. 33Figure 4.10 The ATLAS calorimeter system. The EM calorime-ter, composed of alternating layers of lead and LiquidArgon, is closest to the beam pipe, and the hadroniccalorimeter, comprising the tile calorimeter, the hadronicendcap calorimeter, and the forward calorimeter, isfarther from the beam pipe [2]. . . . . . . . . . . . . . 34Figure 4.11 Schematic representation of a barrel module in the EMcalorimeter. The granularity in  and ϕ of the cells ofeach of the three layers and of the trigger towers isalso shown [2]. . . . . . . . . . . . . . . . . . . . . . . 36Figure 4.12 The ATLAS muon system. The magnetic field is pro-vided by one barrel toroid and two endcap toroids.Resistive Plate Chambers and Thin Gap Chambersare used for triggering, and Monitored Drift Tubesand Cathode Strip Chambers are used for precisiontracking [2]. . . . . . . . . . . . . . . . . . . . . . . . . 38Figure 4.13 Magnetic field integral in the MS as a function of ||for ϕ = 0 (red) and ϕ = .R8 (black) [2]. . . . . . . . . 39Figure 4.14 Cross-sectional view of one quadrant of the ATLASmuon system [2]. . . . . . . . . . . . . . . . . . . . . . 40Figure 4.15 Naming convention for the chambers within the AT-LAS muon system [54]. . . . . . . . . . . . . . . . . . 41xvList of FiguresFigure 4.16 g− ϕ cross-section of the ATLAS muon system [55]. . 42Figure 4.17 Schematic of a Resistive Plate Chamber layer withinthe ATLAS detector. The dimensions given are inmm [2]. 43Figure 4.18 Schematic of a single Monitored Drift Tube (left) anda Monitored Drift Tube chamber (right) [2]. . . . . . . 45Figure 5.1 Schematic representation of the topology of a typicalb-jet compared with jets produced by lighter quarksor gluons [59]. . . . . . . . . . . . . . . . . . . . . . . . 49Figure 5.2 Schematic representation of electron reconstruction inATLAS. The solid red line represents the path of anelectron, and the dashed red line corresponds to a pho-ton produced by the interaction of the electron withthe material in the ID [64]. . . . . . . . . . . . . . . . 51Figure 5.3 Schematic representation of the sagitta s of a curvedtrack with radius r [65]. . . . . . . . . . . . . . . . . . 52Figure 6.1 Acceptance times efficiency for the dielectron (solidblue) and dimuon (dashed red) selections as a functionof the Z ′ pole mass. Both plots are shown after thefull dilepton selection described in Section 9.1. . . . . 59Figure 6.2 Z ′ mass resolution for the dielectron (solid blue) anddimuon (dashed red) selections as a function of the Z ′pole mass. Both plots are shown after the full dileptonselection described in Section 9.1. . . . . . . . . . . . . 60Figure 6.3 qRp residual distribution for muons in the region 1O05 Q|| ≤ 1O3 with 700 GeV Q pT ≤ 1O3 TeV satisfying thehigh-pT WP (black), the high-pT WP and the newimplementation of the BadMuon veto (blue), and thehigh-pT WP and the old implementation of the Bad-Muon veto (red). . . . . . . . . . . . . . . . . . . . . . 62Figure 6.4 Summary of the efficiency gain of the optimized Bad-Muon veto with respect to its previous definition inthe five || regions studied. . . . . . . . . . . . . . . . 63Figure 6.5 Summary of the increase in the fraction of events inthe tails of the pT resolution distributions of the opti-mized BadMuon veto with respect to its previous def-inition in the five || regions studied. The tail fractionis defined as the fraction of events in the pT resolutiondistributions above one. . . . . . . . . . . . . . . . . . 63xviList of FiguresFigure 6.6 Digitized version of the MS TDR resolution, taken asthe ideal scenario to define the matching. The fits areextrapolated above 1 TeV. . . . . . . . . . . . . . . . . 67Figure 6.7 Two-dimensional distribution of q=pqRp as a function ofpT for baseline-selected fully truth-matched muons inthe barrel-endcap overlap region with the 95% quan-tile line overlaid in black. . . . . . . . . . . . . . . . . 69Figure 6.8 Summary of the 95% quantile fit in the barrel-endcapoverlap region. The quantiles of three samples areoverlaid: the misaligned single-muon sample (red), theperfectly aligned single-muon sample (green), and theperfectly aligned DYmass-sliced samples and Z ′ signalsamples (black). . . . . . . . . . . . . . . . . . . . . . 70Figure 6.9 SpWAT :pCBT integrity variable in any of the regions vetoedby the high-pT WP for the baseline selection (red), andthe baseline and all integrity cuts except the cut onSpWAT :pCBT (black). The cut is at SpWAT :pCBT S 10. . . . . . 73Figure 6.10 Categories of muons after the application of the in-tegrity cuts on data events taken during 2015-2016with dimuon invariant mass greater than 1 TeV. Allmuons here are recovered from the high-pT WP selec-tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 6.11 Muon pT as a function of the category of muons afterthe application of the integrity cuts on data eventstaken during 2015-2016 with dimuon invariant massgreater than 1 TeV. All muons here are recoveredfrom the high-pT WP selection. . . . . . . . . . . . . . 75Figure 6.12 Impact of the baseline selection (left) and high-pT WP(right) in the q=pqRp as a function of pT plane. While thebaseline selection does not impose any requirements onthe q=pqRp as a function of pT, the high-pT WP clearlysculpts the distribution through the use of the Bad-Muon veto described in Section 6.1. . . . . . . . . . . 76Figure 6.13 Impact of the gradient WP in the q=pqRp as a functionof pT plane. As the muon pT increases, larger val-ues of q=pqRp are allowed in order to accommodate theworsening pT resolution of the detector. . . . . . . . . 77xviiList of FiguresFigure 6.14 Efficiency as a function of truth ϕ (left) and truth (right) for the baseline selection (green), gradient WP(black), and high-pT WP (red). . . . . . . . . . . . . . 78Figure 6.15 Efficiency as a function of truth pT for the baselineselection (green), gradient WP (black), and high-pTWP (red). . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 6.16 Absolute gain in efficiency of the gradient WP, whichincludes the integrity cuts, with respect to the high-pTWP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Figure 6.17 Example qRp response distribution for the baseline se-lection (green), high-pT WP (red), and gradient WP(black). The purple line represents events passing thegradient WP, but failing the high-pT WP. . . . . . . . 81Figure 6.18 Variance of the response |qRp−qRptru|qRptru (left) and meanof the ratio qRpqRptru (right) used to compute the figureof merit shown in Figure 6.19. . . . . . . . . . . . . . . 82Figure 6.19 Resolution derived from the RMS of the truth-levelto reconstruction-level pT response distributions as afunction of truth pT. The figure of merit is the re-sponse variance over the ratio mean. A more preciseestimation of the resolution, obtained with Gaussianfits to the response itself, in bins of pT, is given inFigure 6.21. . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 6.20 Width  (left) and shifted mean +1 (right) obtainedfrom the Gaussian fitting of the qRp response distri-butions in various pT bins. . . . . . . . . . . . . . . . . 84Figure 6.21 Corrected qRp resolution +1 obtained from the Gaus-sian fitting of the qRp response distributions in variouspT bins. . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 7.1 Muon  distribution for the tt¯ selection. The disagree-ment between data and simulation is within system-atic uncertainties. . . . . . . . . . . . . . . . . . . . . . 90Figure 7.2 Trigger efficiencies for muons to pass either the HLT_mu50trigger or the HLT_mu26_ivarmedium trigger in thebarrel (top) and endcap (bottom) regions of the AT-LAS detector as a function of muon pT for theW+ jetsselection. The ratio plot in the lower panels give theSFs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92xviiiList of FiguresFigure 7.3 Trigger efficiencies for muons to pass either the HLT_mu50trigger or the HLT_mu26_ivarmedium trigger in thebarrel (top) and endcap (bottom) regions of the AT-LAS detector as a function of muon pT for the tt¯ se-lection. The ratio plot in the lower panels give theSFs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 8.1 L1 muon trigger signal (hashed blue) as a function of compared with the subset of matched muon candi-dates within a cone of ∆g = 0O2 with pT S 3 GeV(dotted blue) and offline-reconstructed muons withpT S 10 GeV (solid blue) [77]. . . . . . . . . . . . . . . 96Figure 8.2 Cross-sectional view of one quadrant of the ATLASdetector with the NSW installed. Tracks labeled Awill cause the trigger to fire, while tracks labeled Band C will not [77]. . . . . . . . . . . . . . . . . . . . . 97Figure 8.3 Schematic diagram of the small and large sectors com-prising the NSW. Each sector consists of eight MMplanes sandwiched between two sTGC quadruplets [78]. 98Figure 8.4 Internal structure of a small-strip Thin Gap Chamber.The high-voltage anode wires are sandwiched betweena strips cathode plane and a pads cathode plane, whichhave a resistive graphite layer to reduce sensitivity tofield fluctuations and prevent sparking [77]. . . . . . . 99Figure 8.5 Schematic overview of the experimental setup usedduring the Fermilab test beam campaign. The blueplanes correspond to the pixel detector telescope, andthe red planes correspond to the four sTGC layers ofthe quadruplet. The dimensions are not to scale [78]. . 101Figure 8.6 Residual distribution as a function of yrelsTGC, 0 before(left) and after (right) applying the differential non-linearity correction [78]. . . . . . . . . . . . . . . . . . 102Figure 8.7 Track quality parameter of pixel telescope tracks. Tracksused in the analysis are required to have a track qual-ity parameter less than 10. . . . . . . . . . . . . . . . 103Figure 8.8 Residual distributions for the pixel analysis (left) andthe standalone analysis (right). The intrinsic sTGCdetector position resolution is quoted as the width ofthe fitted Gaussian, . . . . . . . . . . . . . . . . . . . 104xixList of FiguresFigure 8.9 Summary of the pion beam position for the Fermilabdata-taking runs analyzed. Runs G to N do not havesynchronized data between the sTGC chamber and thepixel telescope, so only standalone analysis residualmeasurements are available for these runs [78]. . . . . 105Figure 8.10 Intrinsic sTGC position resolution measured using thepixel telescope analysis (left) and standalone analysis(right), for various periods of data-taking during theFermilab test beam campaign. Results for runs withno expected degradation due to sTGC detector sup-port structure or calibration are shown as black filledcircles. The horizontal line represents the average res-olution for these runs, and the hashed band representsthe RMS spread. Results for the remaining runs areshown as open circles. . . . . . . . . . . . . . . . . . . 106Figure 8.11 Schematic overview of the experimental setup usedduring the CERN test beam campaigns. The blueplanes correspond to scintillators used for triggering,and the red planes correspond to the four sTGC layersof the quadruplet. The dimensions are not to scale [78].107Figure 8.12 Beam profile from the QL1 module pads operating at2O8 kV. The beam is concentrated on one pad withinthe sTGC layer. The other pads with content 0 areinstrumented with readout electronics, but do not reg-ister any hits. The pads with no entries (white) arenot instrumented with readout electronics. . . . . . . . 108Figure 8.13 Beam profile from the QL1 module strips operating at2O9 kV. The dips in the profile at strip y positions of220 and 280 are caused by the spacer buttons withinthe sTGC chamber. . . . . . . . . . . . . . . . . . . . 109Figure 8.14 Charge spectrum from the QL1 module pads operat-ing at 2O8 kV. The red line corresponds to an overlaidLandau distribution. . . . . . . . . . . . . . . . . . . . 110Figure 8.15 Illustration of the Hough transform technique used toreconstruct tracks during the sTGC test beam cam-paigns. Each diagram (left, centre, right) representsthe various straight line possibilities (red, yellow, green,blue, magenta) for a particular measurement of ysTGCand z (black points) [82]. . . . . . . . . . . . . . . . . 111xxList of FiguresFigure 8.16 Experimental setup used for pulser board tests at theWeizmann Institute of Science. . . . . . . . . . . . . . 112Figure 8.17 Examples of pulses obtained during pulser board tests:noisy pulse coming from the oscilloscope before theaveraging procedure (left), clean pulse after averagingprocedure (centre), and signal from dead channel withno clear peak (right). . . . . . . . . . . . . . . . . . . . 113Figure 9.1 Number of events passing the event selection, nor-malized to the integrated luminosity, as a function ofrun number during the 2015 (top) and 2016 (bottom)data-taking periods. . . . . . . . . . . . . . . . . . . . 115Figure 9.2 Invariant mass distribution of the dimuon system forvarious Z ′ pole masses. As the pole masses get larger,the parton luminosity tails at lower invariant mass be-come more important. . . . . . . . . . . . . . . . . . . 118Figure 9.3 Invariant mass dependence of the total DY produc-tion cross-section predictions for modern NNLO PDFswith respect to the CT10NNLO PDFs (left) and QCDNNLO-to-NLOK-factors with respect to the CT10NLOPDFs (right). The top and bottom panels show thesame quantities, but with different y-axis ranges. Thecalculations are carried out assuming a centre-of-massenergy of √s = 14 TeV and are based on VRAP0.9and the PDFs as indicated in the legend [90]. . . . . . 119Figure 9.4 Higher-order Electroweak (EW) corrections for Drell-Yan (DY) production. The results of the factored (ad-ditive) approach based on Leading Order (LO) Quan-tum Chromodynamics (QCD) (Next-to-Leading Or-der (NLO) QCD) for√s = 7 TeV are shown with emptysquares (empty circles) and for √s = 14 TeV with fullsquares (full circles). All calculations are based onFEWZ 3.1.b2 and the PDFs as indicated in the leg-end [90]. . . . . . . . . . . . . . . . . . . . . . . . . . . 120xxiList of FiguresFigure 9.5 Invariant mass distribution of the dimuon system. Thedata are shown as black markers, while the SM back-ground processes are shown as filled histograms. Forillustration purposes, three different Z ′ signals areadded on top of the background distribution. Theshaded band in the lower panels illustrates the totalsystematic uncertainty. . . . . . . . . . . . . . . . . . . 121Figure 9.6 Reconstructed muon pT distribution for the leading(top) and subleading (bottom) muon after event selec-tion. The distributions are shown for dimuon invari-ant masses greater than 120 GeV.The data are shownas black markers, while the SM background processesare shown as filled histograms. For illustration pur-poses, three different Z ′ signals are added on top ofthe background distribution. The shaded band in thelower panels illustrates the total systematic uncertainty.123Figure 9.7 Reconstructed muon pT distribution for the sum of theleading and subleading muons (top) and dimuon sys-tem (bottom) after event selection. The distributionsare shown for dimuon invariant masses greater than120 GeV.The data are shown as black markers, whilethe SM background processes are shown as filled his-tograms. For illustration purposes, three different Z ′signals are added on top of the background distribu-tion. The shaded band in the lower panels illustratesthe total systematic uncertainty. . . . . . . . . . . . . 124Figure 9.8 Reconstructed muon  distribution for the leading (top)and subleading (bottom) muon after event selection.The distributions are shown for dimuon invariant massesgreater than 120 GeV.The data are shown as blackmarkers, while the SM background processes are shownas filled histograms. For illustration purposes, threedifferent Z ′ signals are added on top of the back-ground distribution. The shaded band in the lowerpanels illustrates the total systematic uncertainty. . . 125xxiiList of FiguresFigure 9.9 Reconstructed muon  distribution for the sum of theleading and subleading muons (top) and dimuon sys-tem (bottom) after event selection. The distributionsare shown for dimuon invariant masses greater than120 GeV.The data are shown as black markers, whilethe SM background processes are shown as filled his-tograms. For illustration purposes, three different Z ′signals are added on top of the background distribu-tion. The shaded band in the lower panels illustratesthe total systematic uncertainty. . . . . . . . . . . . . 126Figure 9.10 Reconstructed muon ϕ distribution for the leading (top)and subleading (bottom) muon after event selection.The distributions are shown for dimuon invariant massesgreater than 120 GeV.The data are shown as blackmarkers, while the SM background processes are shownas filled histograms. For illustration purposes, threedifferent Z ′ signals are added on top of the back-ground distribution. The shaded band in the lowerpanels illustrates the total systematic uncertainty. . . 127Figure 9.11 Reconstructed muon ϕ distribution for the sum of theleading and subleading muons (top) and dimuon sys-tem (bottom) after event selection. The distributionsare shown for dimuon invariant masses greater than120 GeV.The data are shown as black markers, whilethe SM background processes are shown as filled his-tograms. For illustration purposes, three different Z ′signals are added on top of the background distribu-tion. The shaded band in the lower panels illustratesthe total systematic uncertainty. . . . . . . . . . . . . 128Figure 10.1 Systematic uncertainties due to experimental sourcesrelated to muon performance. Shown are, from leftto right and top to bottom, the uncertainty relatedto muon reconstruction and selection, muon isolation,muon trigger, muon momentum scale, muon momen-tum resolution in the ID, and muon momentum reso-lution in the MS. . . . . . . . . . . . . . . . . . . . . . 131xxiiiList of FiguresFigure 10.2 Systematic uncertainties due to experimental sourcesrelated to accelerator performance. Shown are the un-certainty related to beam energy (top left), luminosity(top right), and pile-up (bottom). . . . . . . . . . . . . 132Figure 10.3 Systematic uncertainties due to theoretical sources.Shown are, from left to right and top to bottom, theuncertainty related to the strong coupling constant s,PI corrections, EW corrections, diboson backgroundestimation, and tt¯ background estimation. . . . . . . . 134Figure 10.4 Systematic uncertainties pertaining to the choice (left)and scale (right) of the PDFs of the incoming partons. 136Figure 10.5 Systematic uncertainties pertaining to the eigenvec-tor variations of the PDFs of the incoming partons.Shown are, from left to right and top to bottom, theuncertainty related to the seven eigenvector bundlesprovided by the CT14 authors. . . . . . . . . . . . . . 137Figure 11.1 Cumulative distribution function (left) and inverse ofthe cumulative distribution function (right) of the stan-dard Gaussian distribution. . . . . . . . . . . . . . . . 141Figure 11.2 Distribution of the q0 test statistic for background-only toys. The solid blue line shows the 2 distributionwith one degree of freedom scaled to the integral of theq0 distribution. . . . . . . . . . . . . . . . . . . . . . . 142Figure 11.3 Local p-value as a function of pole mass assuming Z ′signal shapes. Local (global) significance levels areshown as dashed grey (red) lines. . . . . . . . . . . . . 144Figure 11.4 Expected (dashed black line) and observed (solid redline) upper 95% CL limits on the product of the Z ′production cross-section and branching ratio to twomuons as a function of Z ′ pole mass. Theoretical un-certainties related to the Z ′SSM signal are shown as agrey band around the black line for illustration pur-poses, but are not included in the limit calculation. . . 146xxivList of FiguresFigure 11.5 Expected (dotted and dashed lines) and observed (filledarea and lines) 95% CL limits on the relative couplingstrength ′ as a function of the mass of the Z ′ bosonin the minimal Z ′ model. Limit curves are shown forthree representative values of the mixing angle, Min,between the generators of the (W − a) and the weakhypercharge n gauge groups. These are: tan Min = 0,tan Min = −2, and tan Min = −0O8, which corre-spond respectively to the Z ′W−a, Z ′3g, and Z ′ modelsat specific values of ′. The region above each line isexcluded. The grey band envelops all observed limitcurves, which depend on the choice of Min ∈ [0P .].The corresponding expected limit curves are withinthe area delimited by the two dotted lines. . . . . . . . 148Figure 11.6 Expected (empty markers and dashed lines) and ob-served (filled markers and lines) limits at 95% CL on′ as a function of Min. The limits are set for severalrepresentative values of the mass of the Z ′ boson inthe minimal Z ′ model. The region above each line isexcluded. . . . . . . . . . . . . . . . . . . . . . . . . . 149Figure 11.7 Expected (dashed black line) and observed (solid blackline) lower limits on the energy scale Λ at 95% CL,for the CI model with constructive (Const) and de-structive (Dest) interference for all considered chiralstructures using a 1RΛ2 prior. . . . . . . . . . . . . . . 150Figure 11.8 Expected (dashed black line) and observed (solid blackline) lower limits on the energy scale Λ at 95% CL,for the CI model with constructive (Const) and de-structive (Dest) interference for all considered chiralstructures using a 1RΛ4 prior. . . . . . . . . . . . . . . 151xxvAcronymsAEOT Alignment Effect On Track. vii, 68, 78ALICE A Large Ion Collider Experiment. 23ASIC Application-Specific Integrated Circuit. 99ATLAS A Toroidal LHC ApparatuS. v–vii, xii, xiv–xvi, xviii, xix, 1, 16,18, 23, 25–29, 31, 33–35, 37–43, 46, 48, 50–53, 55, 56, 58, 60, 72, 85–88,91–93, 95–97, 106, 113, 116, 117, 152BDT Boosted Decision Tree. 49BEE Barrel Endcap Extra. 40, 58, 65, 72BSM Beyond the Standard Model. 1, 2, 16, 17, 56, 57, 74, 87, 114, 116,129, 139, 140, 144, 145, 152CB Combined. 52–54, 57, 65, 68, 71CERN European Organization for Nuclear Research. v, vi, xiv, xx, 23, 24,100, 106, 107, 113CI Contact Interaction. xiv, xxv, 17, 20, 21, 144, 145, 150–152CL Confidence Level. xiii, xxiv, xxv, 145–151CMS Compact Muon Solenoid. 1, 18, 23CSC Cathode Strip Chamber. xv, 37–39, 45, 53, 61, 65, 72DAQ Data Acquisition. 99DY Drell-Yan. xiv, xvii, xxi, 13, 14, 21, 69, 70, 116–120, 122, 135, 138EM Electromagnetic. xv, 3, 5, 16, 28, 29, 33–37, 48, 50, 51, 88, 114xxviAcronymsEW Electroweak. xxi, xxiv, 17, 118–120, 134, 138EWSB Electroweak Symmetry Breaking. 8, 9, 15, 22FEB Front-End Board. 99GRL Good Run List. 88, 114GUT Grand Unified Theory. 17, 18HL-LHC High-Luminosity Large Hadron Collider. 95, 153HLT High-Level Trigger. 86, 87IBL Insertable B-Layer. 31, 32ID Inner Detector. xv, xvi, xxiii, 28–35, 46, 47, 50–54, 57, 71, 86, 87, 90,95, 129–131IP Interaction Point. xv, 28, 29, 33, 47, 52ITk Inner Tracker. 95L1 Level-1. xix, 86, 87, 96, 97LAr Liquid Argon. xv, 34–37, 88, 95LHC Large Hadron Collider. v, vii, xiv, 1, 2, 10, 20, 23, 25–28, 87, 88, 95,139, 152, 153LHCb Large Hadron Collider beauty. 23LO Leading Order. xxi, 117, 119, 120LS2 Long Shutdown 2. 95, 152MC Monte Carlo. 67, 87–89, 91, 114, 116, 118, 122, 138, 139MDT Monitored Drift Tube. xv, xvi, 37–39, 44, 45, 53ME Muon Extrapolated. 52, 53, 57, 71, 72MM Micromegas. xix, 95, 97, 98xxviiAcronymsMS Muon Spectrometer. vii, xii, xv, xvii, xxiii, 28, 29, 37–40, 42–44, 47,52–54, 57, 58, 64, 66, 67, 71, 72, 86, 87, 90, 95, 129–131NLO Next-to-Leading Order. xiv, xxi, 11, 12, 116, 118–120NNLO Next-to-Next-to-Leading Order. xxi, 116–119NSW New Small Wheel. xix, 2, 95–98, 106, 113, 152PDF Parton Distribution Function. xii–xiv, xxi, xxiv, 3, 11, 12, 116–120,129, 132, 135–138PI Photon-Induced. xxiv, 119, 132, 134, 138QCD Quantum Chromodynamics. xiv, xxi, 12, 116, 118–120, 133QED Quantum Electrodynamics. 5, 119RMS Root Mean Square. xviii, xx, 80, 81, 83, 84, 106RoI Region of Interest. 86, 87RPC Resistive Plate Chamber. xv, xvi, 37–39, 42, 43, 95RS Randall-Sundrum. 22SCT Semiconductor Tracker. xv, 30–32, 46, 47, 57, 58SF Scale Factor. vii, xii, xviii, xix, 87, 88, 91–94, 130, 152SM Standard Model. xiv, xv, xxii, xxiii, 1, 3–10, 12–21, 29, 34, 55, 74, 88,116, 121–128, 139, 140, 147, 152, 153SSM Sequential Standard Model. 17, 18sTGC small-strip Thin Gap Chamber. vi, xix, xx, 2, 95, 97–113, 152TDR Technical Design Report. xvii, 66, 67TGC Thin Gap Chamber. xv, 37–39, 43TRT Transition Radiation Tracker. xv, 30–33, 46, 57, 58WP Working Point. vii, xii, xvi–xviii, 49–51, 53, 54, 57–59, 61, 62, 64, 65,67, 70, 71, 73–81, 84, 85, 88, 89, 91, 114, 130, 152xxviiiAcknowledgementsFirst and foremost, I would like to thank my supervisor Oliver Stelzer-Chilton. You have been an outstanding supervisor. Your guidance andfeedback have been invaluable throughout my graduate studies. Your con-stant availability, even on short notice, and your flexibility regarding re-search projects have provided me with the ideal environment in which tocarry out my research. Not many graduate students can say they have en-joyed a fruitful and productive relationship with their supervisor, but I canunequivocally say that I have. I feel extremely privileged to have had theopportunity to have you as a mentor, and look forward to keeping in touchover the coming years. I would also like to thank my supervisory commit-tee members Colin Gay, Gary Hinshaw, and Gordon Semenoff for helpfuldiscussions during committee meetings.Thanks to the ATLAS collaboration as a whole, and in particular mycolleagues from the dilepton search group for the fun we had at CERN andduring the many workshops abroad. To Shikma Bressler, your hospitalityduring my time at the Weizmann Institute of Science in Israel was amazing.You really made me feel like a part of your group, and I hope we haveanother opportunity to collaborate together in the future.I gratefully acknowledge financial support from the Vanier Canada Grad-uate Scholarship and the Natural Sciences and Engineering Research Councilof Canada. In addition, I am thankful for the ATLAS Canada travel bud-get, which has allowed me to travel to CERN on several occasions and toparticipate in various academic conferences worldwide.To my fellow graduate students at UBC, the time spent with you bothin and out of the lab was fantastic. The thought of leaving such a wonderfulenvironment behind saddens me greatly. I sincerely hope our paths will crossagain! There is no way I can even come close to mentioning all of the fondmemories I have of my time at UBC, and no acknowledgements section cando justice to the friendships that I have had the privilege of creating. In noparticular order, thank you to Nicky for the awesome hikes and ski trips, toRobin for being the perfect gym buddy, to Robin for the climbing fun anddelicious cookies, to Chris for the late-night microwave fixing, to Felix forxxixAcknowledgementsthe moving help, to Elham for the enlightening discussions, to Vincent forthe wall storming, and to Alex for the interesting movie nights.Thank you to my family and friends that have supported me throughoutmy graduate studies. To my mother Estelle, I am forever indebted to you forthe unconditional love and support you’ve given me my entire life. Thankyou for always pushing me to be the best version of myself, and for teach-ing me to always be curious. To my brother William, you are a constantreminder of why I love doing physics. I am so proud of the young man youhave become. Even though I cannot spend as much time as I would likewith you, I know we will never lose touch even when we are on oppositesides of the planet. To my sister Julia, I hope we can spend more timetogether soon. To my father David, thank you for always being availableto proofread scholarship applications and the like, especially during crunchtimes. To the boys back home in Gatineau, I look forward to letting looseevery time I come back. Your support means the world to me, here’s tomany more years of fun!To Megan, I am so happy to have met you during our time togetherat TRIUMF all those years ago. To this day, every time I hear you laughI can’t help but smile. From traveling the world with you to trying tokeep up during hikes and meals, every moment spent with you is precious.Thank you for making me want to be a better person, and for supportingme throughout my graduate degree. I look forward to what the future hasin store for us.xxxChapter 1IntroductionWe currently live in one of the most exciting eras in particle physics. Atthe forefront of high-energy particle physics are two multipurpose particlephysics experiments located at the Large Hadron Collider (LHC) [1]: AToroidal LHC ApparatuS (ATLAS) [2], and the Compact Muon Solenoid(CMS) [3]. With the discovery of the Higgs boson by the ATLAS andCMS experiments in 2012 [4, 5], the last missing particle of the StandardModel (SM) of particle physics [6–9] has been observed. As the LHC nearlydoubles its centre-of-mass energy from 8 TeV to 13 TeV during its seconddata-taking period, so-called Run 2, the landscape of searches for new phys-ical phenomena is ripe with possibilities that could bring to light a morethorough understanding of our universe. To this effect, searches for newhigh-mass phenomena are one of the most promising avenues. Progress inexperimental particle physics often goes hand in hand with the discovery ofnew resonances. For example, the discoveries of the JR meson [10], the Υmeson [11], and the Z boson [12], have all led to definite breakthroughs inthis field.This dissertation will focus on three main topics, all centred aroundone common thread: the fundamental particle known as the muon [13].Chapter 2 presents the theoretical framework that underpins modern par-ticle physics: the SM of particle physics. In addition to the quantum fieldtheory formulation, both the successes and shortcomings of the SM are de-scribed. Chapter 3 details various theories that go Beyond the StandardModel (BSM) in attempts to solve its shortcomings. The ATLAS experi-ment and the LHC are presented in Chapter 4, with the experimental com-ponents such as the detector and accelerator technologies briefly outlined.The reconstructed objects used in various physics analyses are describedin Chapter 5. Particular emphasis is given to high-momentum muons inChapter 6, as these objects are of distinct importance for the main searchdescribed in this dissertation. The ATLAS trigger system is described inChapter 7, and the performance of the muon trigger system is evaluatedthrough trigger efficiency measurements. Chapter 8 gives an overview ofthe upgrade programme planned for the ATLAS detector in the coming1Chapter 1. Introductionyears, and details the New Small Wheel (NSW) upgrade in particular. Oneof the main technologies involved in the NSW upgrade, small-strip ThinGap Chambers (sTGCs), is characterized through various test beam cam-paigns. A search for new high-mass phenomena in events with two muonsin the final state is then presented in three distinct chapters: Chapter 9 de-scribes the event selection and presents various kinematic distributions thatcompare data and simulation; Chapter 10 summarizes the systematic un-certainties considered; and Chapter 11 details the statistical methods usedto search for BSM physics signals. The search uses 36.1 fb−1 of proton-proton collision data collected at the LHC. Finally, Chapter 12 concludesthe dissertation, and presents an outlook for the future of searches for newhigh-mass phenomena in events with two muons in the final state.2Chapter 2The Standard Model ofParticle PhysicsThere are four known fundamental forces acting on the matter in our uni-verse: gravity, electromagnetism, the strong nuclear force, and the weaknuclear force. The first of these, while being the most noticeable in ourday-to-day lives, plays a relatively insignificant role at the subatomic level.Indeed, gravity is described by Einstein’s theory of General Relativity, whichdeals mostly with objects on a macroscopic scale. The three other forces arebest described by the SM of particle physics. In this chapter, the theoreticalframework that makes up the SM is described in Section 2.11. Section 2.2presents the parton model, and in particular Parton Distribution Functions(PDFs). To give an idea of the current state of particle physics, the impres-sive successes of the SM are presented in Section 2.3, and the limitations ofthe model are described in Section 2.4.In the following, natural units where ℏ = x = 1 are used. In addition, theEinstein summation convention, where repeated indices imply a sum overall the values of the index, is used.2.1 TheoryThe SM is a very successful predictive theory, which explains the fundamen-tal interactions of elementary particles in the universe, with the exceptionof gravity. This quantum field theory comprises the elementary particlesdepicted in Figure 2.1. The quarks and leptons, more generally known asfermions, are spin-12 particles that interact with each other through the ex-change of integer-spin particles, the gauge bosons. For reasons yet unknown,the quarks and leptons exist in three so-called generations, with each gener-ation displaying similar properties. The three main forces described by theSM are the strong nuclear force, the weak nuclear force, and the Electro-magnetic (EM) force. These forces are mediated by the gluon (g), the weak1This section is loosely based on [14], and follows the conventions therein.32.1. Theorybosons (W± and Z0), and the photon (), respectively. Each particle in theSM has a corresponding antiparticle.Standard Model of Elementary Particlesthree generations of matter(fermions)I II IIIinteractions / force carriers(bosons)masschargespinQUARKSu22432.2 MeV/c²⅔½upd22434.7 MeV/c²−⅓½downc22431.28 GeV/c²⅔½charms224396 MeV/c²−⅓½stranget2243173.1 GeV/c²⅔½topb22434.18 GeV/c²−⅓½bottomLEPTONSe22430.511 MeV/c²−1½electronνe<2.2 eV/c²0½electronneutrinoμ2243105.66 MeV/c²−1½muonνμ<1.7 MeV/c²0½muonneutrinoτ22431.7768 GeV/c²−1½tauντ<15.5 MeV/c²0½tauneutrino GAUGE BOSONSVECTOR BOSONSg001gluonγ001photonZ224391.19 GeV/c²01Z bosonW224380.39 GeV/c²±11W bosonSCALAR BOSONSH2243125.09 GeV/c²00higgsFigure 2.1: Particle content of the SM of particle physics [15].The SM is a quantum field theory with local gauge invariance. In thegroup theoretical understanding of the SM, the gauge symmetry of the SMis expressed as the groupGhb = hj(3)X × hj(2)a × j(1)n P (2.1)where the subscript X corresponds to the conserved colour charge ofthe hj(3) group, the subscript a indicates that the hj(2) group acts onlyon left-handed particles or right-handed antiparticles, and the subscript n42.1. Theorycorresponds to the conserved weak hypercharge. The conserved quantityrelated to the hj(2) group is the weak isospin i3. The hj(3)X symmetryis unbroken and remains at low-energy scales. Quarks can carry one of threecolour charges, while gluons carry one colour and one anticolour charge. Asdescribed in Section 2.1.3, the remaining gauge symmetry of the SM breaksdown as the Higgs field reaches its ground state, generating gauge invariantmasses for the weak gauge bosons in the process:hj(2)a × j(1)n → j(1)fO (2.2)This j(1)f symmetry is the basis of Quantum Electrodynamics (QED),which is used to described the EM interaction present in nature. The con-served quantity of the resulting j(1)f symmetry is the usual electric charge,defined asf = i3 + nO (2.3)The gauge fields related to the hj(3)X , hj(2)a, and j(1)n groups aredefined as G, W a , and W, respectively. Recalling that the hj(c) (j(c))group has c2 − 1 (c2) generators, the SM gauge symmetry groups thushave 8 generators for hj(3)X , 3 generators for hj(2)a, and one generatorfor j(1)n . Hence, in the notation used throughout this chapter,  runs from1 to 8, and v runs from 1 to 3.The Lagrangian describing the fundamental particles in our universe canbe written as three separate terms:LSM = Lgauge +Lfermions +LHiggsO (2.4)Each of the three terms in Equation (2.4) will be described in the follow-ing sections: Lgauge, Lfermions, and LHiggs will be covered in Sections 2.1.1to 2.1.3, respectively.2.1.1 Gauge BosonsGauge bosons transform under the adjoint representation of their gaugesymmetry group. They mediate the SM forces between fermions, allowingthe fermions to interact. The Lagrangian characterizing the gauge bosons isLgauge = −14G,G, − 14W a,Wa, − 14W,W, P (2.5)52.1. Theorywhere G, , W a, , and W, are the field strength tensors for the hj(3)X ,hj(2)a, and j(1)n gauge fields, respectively. The field strength tensors aredefined as follows:G, = UG, − U,G + gsfGG, P (2.6)W a, = UWa, − U,W a + gϵabxW bW x, P (2.7)W, = UW, − U,WP (2.8)where f are the structure constants of the hj(3)X group and ϵabxare the structure constants of the hj(2)a group, i.e., the totally antisym-metric Levi-Civita symbol. The dimensionless coupling constants gs and gare coupling constants that quantify the strength of the interaction relatedto the hj(3)X and hj(2)a symmetry groups, respectively. It should benoted that Lgauge contains no explicit mass terms for the gauge boson. Ascopious experimental evidence has been found implying that gauge bosonshave mass [16], this is certainly a problem. The way to solve this issue isknown as the Higgs mechanism and is described in Section 2.1.3.2.1.2 Leptons and QuarksMost of the observable matter in our universe is composed of fermions.More specifically, leptons and quarks make up the basic building blocks ofnature. Fermions exist in three generations, which differ in mass. All threefermion generations interact with gauge bosons in exactly the same manner.For leptons, the electrically charged particles and their associated neutrinoscome in the three generations labeled electron (z), muon (), and tau ().Leptons do not carry any colour charge, and as such transform as a coloursinglet under the hj(3)X symmetry. For the quarks, the generational labelsare denoted as follows: up (u) and down (y) for the first generation, charm(x) and strange (s) for the second generation, and top (t) and bottom (b)for the third generation. Quarks carry a colour charge and transform astriplets under the hj(3)X symmetry. The fermion fields present in theSM are the lepton fields aa and zg, and the quark fields fa, ug, and yg,where the subscripts a and g correspond to left-handed and right-handedchirality, respectively. The left-handed quark fields act as a doublet underthe hj(2)a symmetry; positively-charged quarks have weak isospin i3 = 12 ,while negatively-charged quarks have weak isospin i3 = −12 . They also haveweak hypercharge n = 16 . The left-handed lepton fields also act as a doublet62.1. Theoryunder the hj(2)a symmetry; charged leptons have weak isospin i3 = −12 ,while neutrinos have weak isospin i3 = +12 . The left-handed leptons haveweak hypercharge n = −1R2. All right-handed fermion fields act as singletsunder the hj(2)a symmetry, and hence have weak isospin i3 = 0. Table 2.1summarizes the various properties of the fermion fields present in the SMfor the first generation of fermions.Fermion Type Field i3 n f ColourLeptons aa =(,aza)+ 1R2 −120 Singlet− 1R2 −1zg 0 −1 −1 SingletQuarksfa =(uaya)+ 1R2 +16+ 2R3 Triplet− 1R2 − 1R3ug 0 + 2R3 + 2R3 Tripletyg 0 − 1R3 − 1R3 TripletTable 2.1: Summary of fermion field properties for the first generation offermions. Fermions in the second and third generation have identical prop-erties.The Lagrangian describing the fermions of the SM and their interactionsis defined asLfermions =∑fields∑gen ¯iD P (2.9)where  denotes a generic fermion field and  represents the gammamatrices. The sum over generations (gen) implies summation over all threefermion generations for each fermion field. The D symbol in Equation (2.9)represents the most general form of a covariant derivative that can be writtenwith regard to the symmetry group of the SM:D = U − igsGtx − igW a taa − ig′WnP (2.10)where tx are the generators of the hj(3)X group and taa are the genera-tors of the hj(2)a group. The dimensionless coupling constant g′ representsthe strength of the interaction related to the j(1)n symmetry group. Thelast three terms in Equation (2.10) act only on the fields that transformnon-trivially in the appropriate group representation. For example, the termproportional to gs will not act on lepton fields, as they are colour singlets.72.1. TheorySimilarly to the expression for Lgauge, no explicit mass terms for theleptons and quarks are found in Lfermions, because they would not be gaugeinvariant. The solution to this discrepancy, i.e., that Lgauge and Lfermionspredict massless particles but experimental evidence supports massive par-ticles, is obtained via the Higgs mechanism described in Section 2.1.3.2.1.3 The Higgs MechanismAs alluded to above, gauge invariance would seem to imply the impossi-bility of any mass terms for gauge bosons, leptons, and quarks. However,as experimental evidence shows, these particles indeed carry mass. To ad-dress this issue, a mechanism1 is introduced in order to break the underlyinghj(2)a×j(1)n symmetry as in Equation (2.2), and in the process give riseto mass terms in the SM Lagrangian for gauge bosons and fermions [17–22].As the hj(2)a × j(1)n symmetry is broken down into a j(1)f symmetry,this process is called Electroweak Symmetry Breaking (EWSB). This is ac-complished by introducing an hj(2)a doublet of complex scalar fields withweak hypercharge n = 12 , which acts as an hj(3)X colour singlet, into thetheory:ϕ =(ϕ+ϕ0)O (2.11)The Lagrangian describing the Higgs sector of the SM is thenLHiggs = (Dϕ)†(Dϕ)− k (ϕ) +LYukawaP (2.12)where LYukawa describes the Yukawa interactions between the scalarHiggs field and the fermions, and the Higgs potential is defined ask (ϕ) = 2ϕ†ϕ+ (ϕ†ϕ)2O (2.13)If  = 0, no symmetry breaking occurs. If  is negative, the Higgspotential is unbounded from below, and no stable vacuum state exists. Asthis is considered unphysical,  is assumed to be positive. If the value of 2is positive, the potential has its minimum at |ϕ| = 0. This corresponds tothe Higgs potential before EWSB. However, if the value of 2 is negative,the Higgs potential minimum is not at |ϕ| = 0. This corresponds to theHiggs potential after EWSB. Figure 2.2 compares the Higgs potential as afunction of |ϕ| for the two possible cases discussed, i.e., when 2 S 0 and2 Q 0.1For brevity, this mechanism is denoted Higgs mechanism in this dissertation.82.1. Theory300− 200− 100− 0 100 200 300GeV φ1−01234(100 GeV)) φV( > 02µ(a)300− 200− 100− 0 100 200 300GeV φ1−01234(100 GeV)) φV( < 02µ(b)Figure 2.2: Higgs potential k (ϕ) as a function of |ϕ| for 2 S 0 (left) and2 Q 0 (right). The values used for the SM parameters of the Higgs potentialare  ≃ 0O129 and |2| ≃ (88O4 GeV)2.It is convenient to write the Higgs field in a gauge which minimizes thenumber of scalar degrees of freedom, i.e., the unitary gauge, asϕ =1√2(0v + h)P (2.14)where v represents the vacuum expectation value of the real Higgs field h.From Equation (2.13), it can be seen that the Higgs potential is minimizedfor ϕ†ϕ = −2R2. The vacuum expectation value is thus defined asv =√−2P (2.15)where 2 is negative. Inserting this definition into the first two termsof Equation (2.12) gives rise to mass terms for the massive gauge bosons inthe SM Lagrangian. No mass term appears for the photon, and as such itremains massless. In addition, a mass term for a spin-0 scalar particle, theHiggs boson, is obtained. Finally, interaction terms between the massivebosons are also obtained. Once the hj(2)a × j(1)n symmetry is broken,the usual electric charge becomes the conserved quantity, and is defined inEquation (2.3). After EWSB, the gauge fields of the hj(2)a×j(1)n groupmix to yield the physical states corresponding to the weak bosons (W± andZ) and the photon (V):W± =W 1 ∓ iW 2√2P (2.16)92.2. Parton Distribution FunctionsZ = cos lW3 − sin lWP (2.17)V = sin lW3 + cos lWP (2.18)where the weak mixing angle l is defined viacos l =g√g2 + g′2and sin l =g′√g2 + g′2P (2.19)and the coupling constants g and g′ have already been defined. Themasses of the bosons are given bym2l =g2v24, m2o =v2(g2 + g′2)4, m2h = 2v2O (2.20)The last term in Equation (2.12) is what allows the SM fermions to havemass. The Lagrangian describing Yukawa interactions between the fermionsand the Higgs field is defined asLYukawa =∑fields∑gen(yi ¯gϕ† a + hOxO)P (2.21)where  denotes a generic fermion field, the sum over fields includes allrelevant fermion fields present in the SM, the sum over generations (gen)implies summation over all three fermion generations for each fermion field,and hOxO denotes the Hermitian conjugate of the term before it. The Yukawacouplings yi represent the strength of the interaction between the Higgs fieldand the relevant fermion. Inserting the Higgs field given in Equation (2.14)into Equation (2.21) gives rise to fermion mass terms and interaction termsbetween the fermions and the Higgs field.2.2 Parton Distribution FunctionsProtons are composite objects. As such, each proton-proton interaction atthe LHC actually implies interactions between the underlying constituentsof the proton, so-called partons. Each proton is composed of three valencequarks: two up quarks and one down quarks. In addition, quark-antiquarkpairs are continuously produced and annihilated through interactions withgluons. Figure 2.3 illustrates the complex nature of the proton structure.102.2. Parton Distribution FunctionsFigure 2.3: Illustration of the constituents of a proton, so-called partons.Quark-antiquark pairs are dynamically produced and annihilated throughinteractions with gluons [23].Within the context of proton-proton collisions, the probability of a givenparton within a proton to interact with another parton of a different protonis given by PDFs. PDFs are obtained through deep inelastic scatteringexperiments, and depend on the momentum transfer of the collision, f, andthe fraction of the proton momentum carried by each parton involved in thecollision, x. Figure 2.4 depicts the PDFs of proton constituents at NLO as afunction of x for f2 = 10 GeV2 and f2 = 104 GeV2 obtained by the MSTWcollaboration [24].112.3. Successes of the Standard Modelx-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 2.4: PDFs of proton constituents at NLO in QCD as a function ofthe momentum fraction x of the parton relative to the proton momentum,for momentum transfers f2 = 10 GeV2 (left) and f2 = 104 GeV2 (right)obtained by the MSTW collaboration [24].2.3 Successes of the Standard ModelThe SM has been experimentally verified to astounding degrees of preci-sion. From the values of the coupling constants for the various forces to theproduction cross-sections of numerous processes, agreement between dataand simulated predictions is impressive. Figure 2.5 gives a summary ofvarious total production cross-section measurements performed by the AT-LAS experiment at a centre-of-mass energy corresponding to √s = 7 TeV,√s = 8 TeV, and √s = 13 TeV. The number of orders of magnitude spannedby the various measurements is a testament to the validity of the SM acrossa wide range of energy regimes.122.3. Successes of the Standard Modelpp500 µb−180 µb−1W Z t¯t tt-chanWt2.0 fb−1Htotaltt¯HVBFVHWW WZ ZZ ts-chant¯tW t¯tZ tZjWWWWWZ10−111011021031041051061011σ[pb]Status: March 2019ATLAS PreliminaryRun 1,2√s = 7,8,13 TeVTheoryLHC pp√s = 7 TeVData 4.5 − 4.6 fb−1LHC pp√s = 8 TeVData 20.2 − 20.3 fb−1LHC pp√s = 13 TeVData 3.2 − 79.8 fb−1Standard Model Total Production Cross Section MeasurementsFigure 2.5: Summary of several SM total production cross-section measure-ments [25].The third bin from the left in Figure 2.5 provides a parameter of partic-ular relevance for the results presented in this dissertation: the productioncross-section for the pp → RZ process. One of the most relevant SM pro-cesses to the search presented in this dissertation is the DY process, wheretwo incoming quarks interact to produce an intermediate Z boson or pho-ton, which subsequently decays to two outgoing muons. The DY processwithin the SM corresponds to the Feynman diagram depicted in Figure 2.6at leading order.132.4. Limitations of the Standard Modelqqγ/Z µ-µ+qqΛµ-µ++2Figure 2.6: Feynman diagram of the SM DY process.2.4 Limitations of the Standard ModelWhile the SM is an excellent theory in many particle physics regimes, thereare certain experimental measurements that cannot be explained solely bythe SM. For example, the existence of dark matter and massive neutrinosis not understood within the context of the SM. In addition, certain theo-retical issues arise that forbid the SM to be extrapolated to arbitrarily highenergies. In particular, a renormalizable quantum theory of gravity does notexist. Also, the vastly different energy scales present in the SM, while notnecessarily a problem, is certainly an aesthetically displeasing issue at thevery least. These shortcomings will be discussed in Sections 2.4.1 to 2.4.42.4.1 Quantum GravityOne of the most flagrant shortcomings of the SM is that it simply does notdescribe the gravitational force. Indeed, gravitational effects at the quan-tum level are not considered in the majority of particle physics experiments.The gravitational force is extremely weak at the subatomic level. Conse-quently, it is usually negligible compared with the other forces describedby the SM. Even though it is possible to write down a quantum theory ofgravity, this theory is non-renormalizable, and thus is valid only up to acertain energy scale. This theory would break down, e.g., when consideringextremely massive objects such as black holes, where gravitational effects atthe quantum level become important. Hence, a renormalizable theory thatreconciles General Relativity and quantum mechanics up to energy scales ofthe reduced Planck mass, bPl ≃ 2O4× 1018 GeV, is not provided by the SM.A possible explanation for why gravitational effects are so small comparedwith the forces described by the SM is that gravity propagates in extra142.4. Limitations of the Standard Modelspatial dimensions. Such a theory is briefly discussed in Section 3.3.2.4.2 The Hierarchy ProblemAs the Higgs boson is a scalar particle, its mass undergoes divergent quan-tum loop corrections. This is contrary to fermion or gauge boson masses,which are protected against divergent quantum loop corrections due to chi-ral symmetry and gauge invariance, respectively. In order to obtain a finitemass for the Higgs boson when including these corrections, countertermsmust be added when computing the mass, in order to renormalize it. This ispossible, but if the corrections required are larger than the bare Higgs bosonmass without any corrections applied, this would imply that the theory iscertainly not “natural”. In fact, to obtain a Higgs boson mass on the orderof 125 GeV, which is the experimentally measured value, the countertermsrequired imply a cancellation of terms up to the 30th decimal place. Thislarge amount of fine-tuning required for the Higgs boson mass seems to im-ply new physics, which would obviate the need for such fine-tuning of thecorrected Higgs mass. That the quantum corrections to the Higgs bosonmass are larger by several orders of magnitude than the bare mass is inex-plicable, as one would expect the corrections to be of the same magnitudein a natural theory.In addition to the Higgs mass issue, the fact that the particle contentof the SM has masses spanning several orders of magnitude, while not nec-essarily an issue, is quite puzzling. Finally, even though the SM does notdescribe gravity, it is not unreasonable to expect that the four fundamen-tal forces acting on the matter in our universe be approximately similar instrength; the fact that the weak nuclear force is ∼ 1024 times as strong asgravity is not understood with current models. Theoretically, it would bevery satisfying if some underlying principle could explain these seeminglyextremely large differences in a natural way.2.4.3 Neutrino MassesNeutrino oscillations have been experimentally observed [26–28]. These ob-servations imply that neutrinos have non-zero, albeit very small, masses. Asthe SM does not include right-handed neutrinos, no mass terms are gener-ated for these particles during EWSB. Hence, the SM predicts that neu-trinos are explicitly massless. Neutrino oscillation measurements are thuscertainly contradictory to SM predictions. In addition, the question of thedifferent scales between e.g., the neutrino masses and their corresponding152.4. Limitations of the Standard Modellepton masses, which are orders of magnitude larger, remains unanswered.This is clearly an indication of BSM physics as it is currently defined.2.4.4 Dark Matter and Dark EnergyMany experimental measurements point to the conclusion that the observ-able matter in our universe consists of only a small portion of the totalmatter present. The matter not visible through conventional measurementsis named dark matter. Its presence is inferred by many different sources.These include gravitational lensing [29], rotational velocities of galaxies [30],and even the cosmic microwave background [31]. A possible explanation fordark matter is the existence of a new particle that interacts via the gravi-tational force, and potentially the weak nuclear interaction, but has neutralEM and colour charge, so does not interact via the EM and strong nuclearforce. Such weakly interacting massive particles would account for the ex-perimental measurements alluded to above, but have eluded detection thusfar. Various BSM theories posit dark matter candidates through the exis-tence of new particles, and experimentally detecting such new particles withthe ATLAS experiment could help explain a vast array of cosmological prob-lems. Finally, while the visible matter and dark matter comprise 4.9% and26.8% of the energy density of the universe respectively, a staggering 68.3%of this energy density, named dark energy, is completely unaccounted forwithin the framework of the SM. The existence of dark energy is inferred bye.g., the measurements of the expanding universe carried out by the Planckcollaboration [31]. Therefore, the SM is certainly not a complete descriptionof nature.16Chapter 3Beyond the Standard ModelThe SM has been experimentally verified to extremely high degrees of pre-cision, and provides an exceptional description of nature. However, it isknown to be an effective theory in the sense that it is valid only in a low-energy regime, called the EW scale, and that it does not account for manyobserved experimental results. For example, it does not offer a satisfyingexplanation for dark matter. Essentially, the SM cannot be extrapolated tothe high energy regime of the Planck scale, i.e., the scale at which quantumeffects of gravity become strong, in a straightforward manner. Furthermore,from a theoretical point of view, the SM fails when it comes to explainingthe hierarchy problem, the unification of forces, etc. Hence, it is clear thatto fully understand and explain nature, a theoretical framework that goesbeyond the SM is required. While high-mass resonances and Contact In-teractions (CIs) do not offer a direct solution to the problems mentionedabove, many BSM theories predict their existence. Therefore, finding suchnew phenomena would help validate these theories, which do offer solutionsto the aforementioned problems. In this chapter, two types of BSM theorieswill be discussed: Section 3.1 will discuss models postulating new gaugesymmetries, and Section 3.2 will discuss CI models. Finally, Section 3.3briefly presents extra-dimensional models.3.1 New Gauge SymmetriesVarious BSM models predict the existence of new fundamental symmetriesof nature. These symmetries would manifest themselves as high-mass reso-nances, i.e., peak-like excesses in the dimuon invariant mass distribution. Ofparticular interest for this dissertation are the Sequential Standard Model(SSM), Grand Unified Theories (GUTs), and minimal Z ′ models.3.1.1 Sequential Standard ModelThe SSM [32] is the simplest extension to the SM. It assumes the existenceof heavier copies of the W and Z bosons present in the SM, described in173.1. New Gauge SymmetriesChapter 2, which would have the same couplings to SM fermions as theircounterparts. These new bosons are named W ′SSM and Z ′SSM, respectively.Contrary to the SM W and Z bosons, however, the couplings of the W ′SSMand the Z ′SSM bosons to each other are assumed to be zero. In addition, thecouplings between the SM W and Z bosons and the new SSM gauge bosonsare also assumed to be zero. While not very well motivated theoretically, theSSM is historically used as a benchmark model in order to compare results,e.g., between different experiments such as ATLAS and CMS [33, 34].3.1.2 Grand Unified TheoriesOther types of models that predict the existence of new gauge bosons areGUTs. GUTs often extend the gauge group of the SM, Ghb , to include ad-ditional U(1) symmetries. These additional symmetries provide a unifyingpicture of gauge interactions, in which all fermions belong to the same multi-plet of the group at the energy scale where the extended symmetries are un-broken. One interesting example of a GUT is the superstring-motivated Z6model [35]. The Z6 gauge group can follow the Georgi-Glashow symmetry-breaking pattern [36]Z6 → hd(10)× j(1) → hj(5)× j(1) × j(1) P (3.1)where SU(5) would break down into Ghb , and the additional U(1) sym-metries would manifest themselves via the production of Z ′ gauge bosons.These two neutral gauge bosons can mix with an angle Z6 , to yield a phys-ical state defined byZ ′(Z6) = Z′ cos Z6 + Z′ sin Z6 P (3.2)where Z6 ∈ [−.P .]. Table 3.1 lists the most commonly used valuesof Z6 and their corresponding physical states, according to the conventionused in [32].183.1. New Gauge SymmetriesModel Name Z ′ State Z6 Value Model Z ′ .R2 Model Z ′ . − arctan√5R3Neutral N Model Z ′c arctan√15Inert Model Z ′I arctan√3R5Secluded Sector Model Z ′h arctan(√15R9) Model Z ′ 0Table 3.1: Summary of commonly motivated Z ′ models.Another possible symmetry-breaking pattern is given by the Pati-Salammodel [37]:Z6 → hd(10)× j(1) → hj(4)X × hj(2)a × hj(2)g→ hj(3)X × hj(2)a × hj(2)g × j(1)W−a→ hj(3)X × hj(2)a × j(1)n P(3.3)where the last line in Equation (3.3) corresponds to Ghb . The left-right symmetry is made explicit in this model due to the hj(2)a × hj(2)gstructure. The model predicts a Z ′3g boson coming from the hj(2)g group ora Z ′W−a boson coming from the breaking of hj(4)X into hj(3)X×j(1)W−a,where 3g stands for the right-handed third component of weak isospin, andW (a) stands for the baryon (lepton) number, with (W − a) representingthe conserved quantum number [38–40]. Both the Z ′3g and the Z ′W−a arisein the minimal Z ′ models discussed in Section 3.1.3. The models above allassume that the coupling of the new Z ′ gauge bosons to SMW and Z gaugebosons is zero.3.1.3 Minimal Z ′ ModelsAn alternative approach to parameterising new gauge bosons is minimal Z ′models [41]. In these models, the new resonances are characterized by threeparameters: gWa, gn , and the mass of the hypothetical Z ′ boson. Both gWaand gn are effective coupling constants representing the coupling of a newZ ′ boson to the (W − a) current and weak hypercharge Y, respectively. Tosimplify the notation, it is convenient to defineg˜Wa ≡ gWaRgo and g˜n ≡ gn Rgo P (3.4)193.2. Contact Interactionswhere go = 2moRv, and mo and v = 246 GeV are the SM values cor-responding to the mass of the Z boson and the vacuum expectation valueof the Higgs boson, respectively. From these new quantities, two indepen-dent parameters can be defined, in order to specify completely a particularminimal Z ′ model: ′ and bin. These two parameters are defined by therelationsg˜Wa = ′ cos Min and g˜n = ′ sin MinO (3.5)In essence, Min corresponds to the mixing between the generators ofthe (W − a) and weak hypercharge Y gauge groups, while ′ measures thestrength of the Z ′ boson coupling relative to that of the SM Z boson. Ta-ble 3.2 summarizes the values of ′ and Min for three specific minimal Z ′models, which each have a specific Z ′ boson: Z ′W−a, Z ′, and Z ′3g.Z ′W−a Z′ Z′3g′√58 sin l√4124 sin l√2512 sin lcos Min 1√25411√5sin Min 0 −√1641 − 2√5Table 3.2: Summary of ′ and Min values for three specific minimal Z ′models: Z ′W−a, Z ′, and Z ′3g.3.2 Contact InteractionsNew phenomena in the dimuon invariant mass spectrum can also be ob-served by considering new interactions that occur at much higher energiesthan the energies in reach at the LHC. Such phenomena could, e.g., be four-fermion interactions, which would indicate that the interacting fermions, inthis case quarks and leptons, are composite objects. A particularly interest-ing new physics scenario would be that of CIs. CIs, depicted in Figure 3.1,would manifest themselves as broad excesses in the dimuon invariant massdistribution. The energy scale at which the CI occurs, denoted Λ, representsthe binding energy required to keep the fermion constituents together.203.2. Contact Interactionsqqγ/Z µ-µ+qqΛµ-µ++2Figure 3.1: Feynmann diagram representing a CI with energy scale Λ.The Lagrangian describing such CIs is given by [42, 43]LCI =4.Λ2[LL(q¯LqL)(u¯LuL) + RR(q¯RqR)(u¯RuR)+ LR(q¯LqL)(u¯RuR) + RL(q¯RqR)(u¯LuL)]P(3.6)where Λ is the CI scale, and qL,R and uL,R are left-handed and right-handed quark and lepton fields, respectively. The symbol  represents thegamma matrices, and the parameters ij , where iP j ∈ [aPg] with a (g)referring to left (right), define the chiral structure of the new CI. The signof ij determines whether the interference between the SM DY process andthe CI process is constructive (ij = −1) or destructive (ij = +1). Bysetting all but one of the ij parameters in Equation (3.6) to zero, andsetting the remaining ij parameter to ±1, different chiral structures of theCI are investigated. The total cross-section for the process qq¯ → ¯ canthen be written astot(m) = DY(m)− ij FIΛ2+FCΛ4P (3.7)where DY(m) is the cross-section of the SM DY process shown inFigure 2.6 and the last two terms represent the interference between the SMDY process and the CI process, and the pure CI process, respectively. FIand FC are both functions of the differential cross-section with respect tom, and do not depend on Λ.213.3. Extra-Dimensional Models3.3 Extra-Dimensional ModelsA different approach to solving the hierarchy problem is to introduce extraspacetime dimensions. New extra dimensions would reconcile the very dif-ferent energy scales of the Planck scale and the EWSB scale, by allowinggravity to propagate in these extra dimensions. By propagating in these ex-tra dimensions, gravity would thus be much weaker. One relevant exampleof these types of models is the Randall-Sundrum (RS) model [44]. The RSmodel posits the metricys2 = z−2krcϕ,yxyx, + r2xyϕ2P (3.8)where k is a scale on the order of the Planck scale, x are the usualspacetime coordinates, ϕ ∈ [0P .] is the angular coordinate parameterisingthe extra dimension, and rx, known as the compactification radius, sets thesize of the finite interval of ϕ. In other words, rx sets the size of the extradimension. Though outside the scope of this dissertation, it is possible tosolve the Einstein field equations for this metric and derive predictions forthe mass spectrum and couplings of the graviton Kaluza-Klein modes. Inparticular, a physical implication of this theory is the appearance of Kaluza-Klein graviton excitations with masses given by [45]mn = kxnz−krcP (3.9)where xn are roots of the Bessel function of order 1, i.e., x0 = 0P x1 =3O8317P x2 = 7O0156P O O O . Hence, the mass hierarchy between the physicalmass mn and the Planck scale is generated by an exponential function ofthe compactification radius. These excitations could give rise to high-massresonances at the TeV scale with various final states, including two muons.22Chapter 4The ATLAS Detector at theLarge Hadron ColliderThe results presented in this dissertation use data collected by the ATLASdetector at the LHC in the years 2015-2018, during the so-called Run 2 of theLHC. In this chapter, Section 4.1 gives an overview of the LHC acceleratorcomplex, and Section 4.2 describes the ATLAS detector in detail.4.1 The Large Hadron ColliderThe LHC is a proton-proton collider located at the European Organizationfor Nuclear Research (CERN), on the Franco-Swiss border near Geneva,Switzerland. Two beams of protons are accelerated in opposite directionsaround a 27 km ring located 100m underground, before colliding at oneof four interaction points. Each of these interaction points is surroundedby a multi-purpose particle detector: ATLAS, CMS, A Large Ion ColliderExperiment (ALICE) [46], or Large Hadron Collider beauty (LHCb) [47].The beams are steered along the ring using an 8O3T dipole field formedby superconducting magnets made of Nb-Ti. In order to bring the dipolemagnets to their superconducting state, liquid helium is used to cool thedipole magnets down to 1O9K. The LHC’s design centre-of-mass energyis √s = 14TeV. During Run 2, the LHC operated with a centre-of-massenergy of √s = 13 TeV.Figure 4.1 shows the CERN accelerator complex, with the LHC being thecentral component. Initially accelerated by a linear accelerator to 50 MeV,a series of smaller accelerators are subsequently used to inject bunches ofprotons into the LHC: the proton synchrotron booster accelerates the pro-tons to 1.4 GeV; the proton synchrotron accelerates them to 25 GeV; thesuper proton synchrotron accelerates them to 450 GeV. Finally, the pro-ton bunches are injected into the LHC, and accelerated to their maximumenergy of 6.5 TeV. The spacing between bunches of protons, the so-calledbunch spacing, is 25 ns. This equates to a bunch crossing rate of 40MHz.234.1. The Large Hadron ColliderLINAC 2North AreaLINAC 3IonsEast AreaTI2TI8TT41TT40CLEARTT2TT10TT66e-ALICEATLASLHCbCMSSPSTT20nppRIBsp1976 (7 km)ISOLDE19922016REX/HIE2001/2015IRRAD/CHARMBOOSTER1972 (157 m)AD1999 (182 m)LEIR2005 (78 m)AWAKEn-ToF2001LHC2008 (27 km)PS1959 (628 m)201120162015HiRadMatGIF++CENFp (protons) ions RIBs (Radioactive Ion Beams) n (neutrons) –p (antiprotons) e- (electrons)2016 (31 m)ELENALHC - Large Hadron Collider // SPS - Super Proton Synchrotron // PS - Proton Synchrotron // AD - Antiproton Decelerator // CLEAR - CERN Linear Electron Accelerator for Research // AWAKE - Advanced WAKefield Experiment // ISOLDE - Isotope Separator OnLine // REX/HIE - Radioactive EXperiment/High Intensity and Energy ISOLDE // LEIR - Low Energy Ion Ring // LINAC - LINear ACcelerator // n-ToF - Neutrons Time Of Flight // HiRadMat - High-Radiation to Materials // CHARM - Cern High energy AcceleRator Mixed field facility // IRRAD - proton IRRADiation facility // GIF++ - Gamma Irradiation Facility // CENF - CErn Neutrino platForm2017The CERN accelerator complexComplexe des accélérateurs du CERNFigure 4.1: The CERN accelerator complex [48].244.1. The Large Hadron ColliderWhen proton bunches collide at the centre of the ATLAS detector, theprimary interaction of interest is the so-called “hard scatter”, i.e., the in-teraction with the largest momentum transfer. A hard scatter takes placewhen a parton from one proton interacts with a parton from another pro-ton. In addition to the hard scatter, other parton-parton interactions takeplace during each bunch crossing. Pile-up is defined as the mean number ofinteractions per crossing, . Figure 4.2 shows the pile-up distributions forthe Run 2 data-taking period.0 10 20 30 40 50 60 70 80Mean Number of Interactions per Crossing0100200300400500600/0.1]-1Recorded Luminosity [pb Online, 13 TeVATLAS-1Ldt=146.9 fb∫> = 13.4µ2015: <> = 25.1µ2016: <> = 37.8µ2017: <> = 36.1µ2018: <> = 33.7µTotal: <2/19 calibrationFigure 4.2: Mean number of interactions per LHC bunch crossing [49].One of the key concepts for the LHC is that of luminosity. The number ofexpected events c for a particular process characterized by a cross-section can be obtained by considering the instantaneous luminosity a of the LHC:c =  ×∫dt aO (4.1)The instantaneous luminosity is measured in cm−2s−1, and can be ex-pressed as [50, 51]a =nbfrn1n22.ΣxΣyP (4.2)254.1. The Large Hadron Colliderwhere nb is the number of bunch pairs colliding per revolution, fr is therevolution frequency, n1 and n2 correspond to the number of protons perbunch in each proton beam, and Σx and Σy characterize the horizontal andvertical convolved beam widths. An integrated luminosity of 1 fb−1 cor-responds to approximately 1012 proton-proton collisions. During the firstrun of data-taking at the LHC, Run 1, the ATLAS experiment recordedan integrated luminosity totaling 25 fb−1 with a centre-of-mass energy of√s = 7 TeV and √s = 8 TeV and a bunch crossing rate of 20MHz. Duringthe second run of data-taking at the LHC, Run 2, the centre-of-mass en-ergy increased to √s = 13 TeV. The bunch crossing rate initially remainedat 20MHz, but was increased to the design value of 40MHz near the be-ginning of July 2015. A total of 36.1 fb−1 of data have been collected in2015-2016, and the entire Run 2 dataset totals 139 fb−1. Figure 4.3 showsthe evolution of the luminosity delivered to the ATLAS detector over time.Figure 4.4 shows the evolution of the total integrated luminosity recordedby the ATLAS detector during Run 2.Month in YearJan Apr Jul Oct]-1Delivered Luminosity [fb01020304050607080ATLAS Online Luminosity = 7 TeVs2011 pp   = 8 TeVs2012 pp   = 13 TeVs2015 pp   = 13 TeVs2016 pp   = 13 TeVs2017 pp   = 13 TeVs2018 pp  2/19 calibrationFigure 4.3: Luminosity delivered to the ATLAS detector as a function oftime [49].264.2. The ATLAS Detector: OverviewMonth in YearJan '15Jul '15Jan '16Jul '16Jan '17Jul '17Jan '18Jul '18-1fbTotal Integrated Luminosity 020406080100120140160ATLASPreliminaryLHC DeliveredATLAS RecordedGood for Physics = 13 TeVs-1 fbDelivered: 156-1 fbRecorded: 147-1 fbPhysics: 1392/19 calibrationFigure 4.4: Total integrated luminosity recorded by the ATLAS detector asa function of time [49].In summary, two proton beams are accelerated in opposite directionsto nearly the speed of light before colliding at the centre of multi-purposeparticle detectors. In particular, the detector used for the search describedin this dissertation is the ATLAS detector.4.2 The ATLAS Detector: OverviewATLAS is a multi-purpose particle detector used at the LHC. A detailedschematic of the ATLAS detector is shown in Figure 4.5.274.2. The ATLAS Detector: OverviewFigure 4.5: Schematic diagram of the ATLAS detector [2].The coordinate system used in ATLAS is a right-handed coordinate sys-tem with its origin at the nominal Interaction Point (IP) in the centre of thedetector and the z-axis along the beam pipe. The x-axis points from the IPto the centre of the LHC ring, and the y-axis points upwards. Cylindricalcoordinates (r, ϕ) are used in the transverse plane, ϕ being the azimuthalangle around the z-axis. A convenient quantity to note is the pseudorapidity, = − ln (tan (R2)) P (4.3)where  is the polar angle. The angular distance in the ATLAS detectoris measured in units of ∆g =√(∆)2 + (∆ϕ)2.The ATLAS detector is composed of three main parts: the Inner Detector(ID) described in Section 4.3, the EM and hadronic calorimeters describedin Section 4.4, and the Muon Spectrometer (MS) described in Section 4.5.Figure 4.6 illustrates a transverse slice (in theg−ϕ plane) of the detector andthe various detector technologies used to differentiate between the differenttypes of particles present in the detector during a collision event. Twomagnetic fields are present in the ATLAS detector: a 2T solenoid field inthe ID bends charged particles in the ϕ direction, and a toroid field startingafter the hadronic calorimeter and covering the entire MS bends charged284.2. The ATLAS Detector: Overviewparticles in the  direction. All three toroid fields, i.e., one in the barrelregion and two in the endcap regions of the detector, are formed by 8 coilsassembled radially and symmetrically around the beam axis.Figure 4.6: Slice in the g − ϕ plane of the ATLAS detector. Starting fromthe IP, a particle will traverse the ID, the EM calorimeter, the hadroniccalorimeter, and the MS. Different particles are reconstructed and identifiedusing all relevant sub-detectors. SM neutrinos are invisible to the ATLASdetector [52].Different particles are reconstructed and identified using all relevant sub-detectors in ATLAS. Electrons are reconstructed from ID tracks and com-bined with energy deposits in the EM calorimeters. Muons are reconstructedfrom tracks in the ID, calorimeter, or MS, depending on the quality of themuon. Quarks and gluons produced from proton-proton interactions willhadronize into colour-neutral states producing a shower of particles, col-lectively called a jet. Jets are reconstructed using energy deposits in thecalorimeters. A detailed description of object reconstruction in the ATLASdetector is presented in Chapter 5.294.3. Inner Detector4.3 Inner DetectorThe ID is immersed in a 2T solenoid magnetic field and is composed ofthree separate detector technologies: silicon pixel trackers described in Sec-tion 4.3.1, silicon micro-strip Semiconductor Trackers (SCTs) described inSection 4.3.2, and Transition Radiation Trackers (TRTs) described in Sec-tion 4.3.3. Arranged in concentric cylinders in the barrel and in disks per-pendicular to the beam axis in the endcaps, the detectors are used for thetracking of charged particles. These allow for electron and pion identifica-tion in the range || Q 2O5. Figures 4.7 and 4.8 show the transverse andlongitudinal views of the ID, respectively.Figure 4.7: The Inner Detector as seen in the transverse g−ϕ plane. Parti-cles traverse the beam pipe, three cylindrical silicon pixel layers, four SCTlayers, and approximately 36 TRT straw tubes [2].304.3. Inner DetectorFigure 4.8: The Inner Detector as seen in the longitudinal plane. Immersedin a 2T solenoid magnetic field, the main components are the pixel andSCT, covering || Q 2O5, and the TRT, covering || Q 2O0 [2].4.3.1 Pixel DetectorThe pixel detector is the innermost part of the ATLAS detector, and allowsfor precise tracking using 1774 identical silicon pixel sensor modules. Eachmodule has 46080 readout channels, equating to approximately 80 millionpixel readout channels throughout the pixel detector. Approximately 90%of the pixels have dimensions of 50 µm by 400 µm, while the remaining 10%have dimensions 50µm by 600 µm. All pixels have a thickness of 250 µm.The intrinsic resolution of the pixel detector in the barrel region is 10 µmin g − ϕ and 115 µm in z, while in the endcap regions it is 10 µm in g − ϕand 115 µm g. There are three concentric cylindrical layers of pixels inthe barrel region, and three disks perpendicular to the beam in each ofthe endcap regions. A typical track will cross three pixel layers. A newlayer of pixel detectors, the Insertable B-Layer (IBL), was commissioned forRun 2. Located only in the barrel region, the IBL consists of an additionalcylindrical layer of pixel detectors with a radius of 3O2 cm. The IBL providesa fourth layer of pixel detectors in the ID region and improves the precision314.3. Inner Detectorof the ID tracking capabilities. The pixel dimensions for the IBL are 50 µmby 250 µm.4.3.2 Semiconductor TrackerThe SCT consists primarily of two-sided silicon microstrip detector modules.The dimensions of one pixel microstrip is 80 µm by 12O8 cm. Each moduleconsists of two microstrips glued back-to-back at a 40mrad stereo angle.The intrinsic resolution in the barrel is 17 µm in g−ϕ and 580 µm in z, andin the endcap regions the intrinsic resolution is 17µm in g− ϕ and 580 µmin g. The barrel region consists of 4 cylindrical layers of modules, with thelength of the strips parallel to the beam axis. The endcap regions have 9planar discs per side, with the length of the strips extending radially fromthe beam axis. Cooled to between −5 ◦C and −10 ◦C, the SCT has over 6million readout channels in total. A typical track will cross four SCT layers,resulting in 8 SCT hits for a typical track.4.3.3 Transition Radiation TrackerThe last section of the ID to be traversed by particles is the TRT. The basicdetector element of the TRT consists of a straw tube with 4mm diameter.The tube has a 0O03mm diameter gold-plated tungsten wire in the centre,and it contains a gas mixture of Xenon, CO2 and O2. When a chargedparticle passes through a straw tube, it ionizes the gas. The ions drift to-wards the cathode straw wall, while the electrons drift towards the anodewire to be read out. The TRT has a total of 350,000 readout channels;the barrel portion of the TRT consists of 50,000 straws of length 144 cmthat are read out at each end, and the endcaps portion consists of 250,000straws of length 39 cm. A typical track will cross 36 TRT straws. The tubesare interleaved with polypropylene fibres in the barrel, and polypropylenefoils in the endcap regions. These polypropylene materials are what gener-ate transition radiation when charged particles traverse them. Transitionradiation is a form of electromagnetic radiation emitted when a chargedparticle passes through inhomogeneous media, such as a boundary betweentwo different media. The transition radiation produced when charged parti-cles traverse the polypropylene is exploited in order to distinguish electronsfrom pions. Because more transition radiation is produced for particles witha large gamma factor, i.e., more relativistic particles, more transition radi-ation is produced for electrons compared to pions or even muons. As theTRT measures the number of high-threshold hits produced by this transition324.4. Calorimetersradiation, i.e., hits that are above a certain threshold, electrons traversinga tube will produce more transition radiation on average compared withheavier particles such as pions, and hence the probability of generating high-threshold hits for electrons will be larger. Figure 4.9 depicts how this featureof transition radiation can be used in order to distinguish different particles.Lorentz gamma factor10 210 310 410 510High-threshold probability00.020.040.060.080.10.120.140.160.180.20.22Pions Muons Electrons Figure 4.9: Average probability of a high-threshold hit in the barrel TRT asa function of the Lorentz gamma factor for electrons (open squares), muons(full triangles), and pions (open circles) in the energy range 2−350 GeV [2].4.4 CalorimetersAfter having traversed the ID, particles coming from the IP reach thecalorimeters of ATLAS. Calorimeters are composed of dense layers of ab-sorber material, and active layers of material designed to read out the sig-nals generated by the interaction of the particles with the material. Thecalorimeters in ATLAS provide coverage in the range || Q 4O9, and consistof two main components: the EM calorimeter, used to detect particles in-teracting via the EM force, such as electrons and photons, and the hadroniccalorimeter, used to detect particles interacting via the strong force, such334.4. Calorimetersas quarks and gluons. The EM calorimeter is described in Section 4.4.1,and the hadronic calorimeter is described in Section 4.4.2. For the range|| Q 2O5, i.e., the range also covered by the ID, the EM calorimeter hasa fine granularity optimally suited for precision measurements of electronsand photons. Once particles pass through the EM calorimeter, they enterthe hadronic calorimeter. Ideally, all SM particles are contained within thecalorimeters of ATLAS, with the exception of muons and neutrinos, in or-der to limit punch-through into the muon system and obtain a better energymeasurement from the particles. Figure 4.10 depicts the ATLAS calorime-ter system. Table 4.1 summarizes the various components of the ATLAScalorimeter system.Figure 4.10: The ATLAS calorimeter system. The EM calorimeter, com-posed of alternating layers of lead and Liquid Argon, is closest to the beampipe, and the hadronic calorimeter, comprising the tile calorimeter, thehadronic endcap calorimeter, and the forward calorimeter, is farther fromthe beam pipe [2].344.4. CalorimetersCalorimeter Coverage Active Material Passive MaterialEM Barrel || Q 1O475 LAr LeadEM Endcap 1O375 Q || Q 3O2 LAr LeadTile Barrel || Q 1O0 Scintillating Tiles SteelTile Barrel Extended 0O8 Q || Q 1O7 Scintillating Tiles SteelHadronic Encdap 1O5 Q || Q 3O2 LAr CopperForward 3O1 Q || Q 4O9 LAr Copper & TungstenTable 4.1: Summary of the ATLAS calorimeter system components.4.4.1 Electromagnetic CalorimeterThe EM calorimeter is used to detect both photons and electrons. It is com-posed of alternating layers of lead and Liquid Argon (LAr), which are usedto initiate particle showers and measure energy deposits, respectively. TheLAr measures energy deposits by collecting the charge produced by the par-ticles passing through and ionizing the LAr. In total, the EM calorimeter isapproximately 22 radiation lengths thick, where a radiation length is definedas the mean distance over which an electron loses all but 1Rz of its energy bybremsstrahlung, or 7R9 the mean free path of a photon before producing anelectron-positron pair. An accordion geometry is used throughout the bar-rel, in order to obtain complete ϕ symmetry without azimuthal cracks. Thebarrel region of the EM calorimeter consists of two identical half-barrels sep-arated by a 4mm gap at z = 0, and covers || Q 1O475. Each endcap regionof the EM calorimeter consists of an inner wheel covering 2O5 Q || Q 3O2and an outer wheel covering 1O375 Q || Q 2O5. Starting after the ID, theEM calorimeter comprises a presampler, used for particles starting to showerbefore the EM calorimeter, followed by three main layers. The first layer,also known as the strips, is segmented finely along  in order to distinguishsingle photons from .0 →  decays. The fine segmentation corresponds to0O0031×0O098 in ×ϕ. The second layer, where most of the electron energyis deposited, has a granularity of 0O025 × 0O0245 in  × ϕ. The third layerof the EM calorimeter is used to capture the tails of the electron shower,and has a segmentation of 0O05 × 0O0245 in  × ϕ. Figure 4.11 depicts thegranularity of these layers in  × ϕ.354.4. Calorimeters∆ϕ = 0.0245∆η = 0.02537.5mm/83=34.6L3mm ∆η = 0.0031∆ϕ=0.0245x436.8mmx4 =147.3mmgrigger3gowergriggergower∆ϕ = 0.0982∆η = 0.116XC4.3XC2XC15CC3mm47C3mmηϕη = 0Strip3cells3in3Ltyer31Squtre3cells3in3 Ltyer321.7XCCells3in3Ltyer33 ∆ϕ×∆η3=3C.C245×C.C5Figure 4.11: Schematic representation of a barrel module in the EMcalorimeter. The granularity in  and ϕ of the cells of each of the threelayers and of the trigger towers is also shown [2].4.4.2 Hadronic CalorimeterThe hadronic calorimeter is used to detect strongly interacting particles suchas hadrons. Its thickness is 9.7 interaction lengths at  = 0, where an inter-action length is defined as the mean distance travelled by a hadronic particlebefore undergoing an inelastic nuclear interaction. It can be separated intothree main components: a tile calorimeter, a hadronic endcap calorimeter,and a forward calorimeter. The tile calorimeter is a sampling calorimeterusing steel as the absorber and scintillating tiles as the active material. Itsbarrel covers || Q 1O0 and its two extended barrels cover 0O8 Q || Q 1O7.The hadronic endcap calorimeter uses LAr as its active material and copper364.5. Muon Spectrometeras its passive material, and covers 1O5 Q || Q 3O2. Finally, the forwardcalorimeter uses LAr as its active material, and covers 3O1 Q || Q 4O9. Eachforward calorimeter consists of three modules in each endcap: the first ismade of copper and measures EM interactions, while the last two are madeof tungsten and measure mainly hadronic interactions.4.5 Muon SpectrometerThe MS is used to detect muons. The toroidal magnetic field present inthe MS allows for transverse momentum (pT) measurements by measuringthe curvature of the muon tracks magnetically deflected in the MS. The twomajor regions in the MS are the barrel region covering || Q 1O1 and the twoendcap regions covering 1O1 Q || Q 2O7. Four different types of detectorsare present in the MS: Resistive Plate Chambers (RPCs) and Thin GapChambers (TGCs) are used for triggering purposes, and Monitored DriftTubes (MDTs) and Cathode Strip Chambers (CSCs) are used for precisiontracking. Overall, the MS has a muon pT resolution ranging from 1.7% inthe barrel for pT ∼ 10 GeV to 4% in the endcaps for pT ∼ 100 GeV [53].More importantly for the analysis presented in this dissertation, the MSprovides muon momentum measurements with a relative resolution of upto 10% for muons with pT ∼ 1 TeV. In this section, RPCs and TGCs arediscussed in Sections 4.5.1 and 4.5.2, and MDTs and CSCs are described inSections 4.5.3 and 4.5.4. Figure 4.12 depicts the ATLAS muon system.374.5. Muon SpectrometerFigure 4.12: The ATLAS muon system. The magnetic field is provided byone barrel toroid and two endcap toroids. Resistive Plate Chambers andThin Gap Chambers are used for triggering, and Monitored Drift Tubesand Cathode Strip Chambers are used for precision tracking [2].The general idea of the MS is that each muon passes through a numberof so-called stations. In the barrel, three stations are arranged in concentriccylinders around the beam axis. In the endcap regions of the MS, threestations are also present and organized into three planar disks, or wheels.Ranging from 0O15T to 2O5T with an average value of 0O5T in the barrelregion, and from 0O2T to 3O5T in the endcap regions, the toroidal magneticfield bends electrically charged particles passing through it in order to mea-sure their momentum. The magnetic field integral as a function of || fortwo different values of ϕ is shown in Figure 4.13.384.5. Muon Spectrometer|η|0 0.5 1 1.5 2 2.5 m)⋅B dl     (T ∫-202468Barrel regionregionEnd-capTransition region=0φ /8pi=φ Figure 4.13: Magnetic field integral in the MS as a function of || for ϕ = 0(red) and ϕ = .R8 (black) [2].Various combinations of detector technologies are used for each station.A summary of the stations and their respective detector compositions isgiven in Table 4.2. In addition to the three stations described in Table 4.2,additional MDT chambers are installed between the inner and middle endcapstations, in order to improve tracking for muons passing through the barrel-endcap overlap regions. Figure 4.14 depicts a cross-sectional view of onequadrant of the ATLAS muon system and the relevant detector technologiespresent within it.Detector Region Station Detector TechnologyInner MDTBarrel Middle MDT, RPCOuter MDT, RPCInner CSC, MDT, TGCEndcap Middle MDT, TGCOuter MDTTable 4.2: Summary of the ATLAS MS stations.394.5. Muon SpectrometerFigure 4.14: Cross-sectional view of one quadrant of the ATLAS muon sys-tem [2].In order to ensure as much coverage as possible, overlapping sectors oflarge and small chambers are installed throughout the MS. Figure 4.15 givesa cross-sectional view of the same quadrant of the ATLAS muon systemshown in Figure 4.14 and highlights the positioning of the small and largechambers. The basic naming convention for the various MS chambers usesthree letters to identify specific chambers. The first letter indicates the re-gion of the detector and represents either the barrel (B) region or the endcap(E) regions. The second letter indicates the layer in the MS, and representseither the inner (I), middle (M), or outer (O) layer. Certain chambers havetheir second letter correspond to the transition region between the barreland the endcap, i.e., the extra (E) layer. The third letter represents thestation type, and can represent either small (S) or large (L) MS chambers.For example, the BIS chamber would refer to the inner chamber within thebarrel region with small chamber type. Some exceptions exist, such as thechambers in the barrel extended region mounted on the endcap toroid andelevator shafts, denoted as Barrel Endcap Extra (BEE), and the chambersin the feet region of the detector, denoted as BMG. Figure 4.16 depicts theg − ϕ cross-section of the MS, and focuses in particular on the chambernaming of the large and small barrel chambers.404.5. Muon SpectrometerFigure 4.15: Naming convention for the chambers within the ATLAS muonsystem [54].414.5. Muon SpectrometerFigure 4.16: g− ϕ cross-section of the ATLAS muon system [55].4.5.1 Resistive Plate ChambersRPCs are used for triggering on muon tracks contained within the barrel,i.e., || Q 1O05. There are three concentric layers of RPCs in the barrel:two layers in the middle station and one layer in the outer station of theMS, as shown in Figure 4.14. Each layer of RPCs has two rectangular gasgaps, allowing for a total of six measurements for a single particle track.Each RPC chamber contains overlapping units, as depicted in Figure 4.17.A single gas gap functions as a gaseous parallel electrode-plate detector,and consists of two parallel resistive plates separated by 2mm of insulatingspacers. The gas gap is filled with a mixture of C2H2F4 (94.7%), Iso-C4H10(5%), and SF6 (0.3%). Metallic strips are mounted on the outer faces of theresistive plates, with one side having the strips segmented in the  direction,and the other having the strips segmented in the ϕ direction. The operatingvoltage of each gap is 9O8 kV, and charged particles passing through thegap will ionize the gas and immediately create an avalanche of electrons todrift towards the anode plate due to the high electric field. This avalanche424.5. Muon Spectrometerwill induce a signal on the strips above and below the ionized region, viacapacitive coupling.Figure 4.17: Schematic of a Resistive Plate Chamber layer within the AT-LAS detector. The dimensions given are in mm [2].4.5.2 Thin Gap ChambersWith a timing resolution smaller than 25 ns for 99% of tracks, TGCs are usedfor their triggering capabilities, and provide a muon track measurement inthe ϕ direction. They cover the endcap regions 1O05 Q || Q 2O7. Theyfunction as multi-wire proportional chambers, with the cathode strips beingdistributed radially, and the anode wires being distributed perpendicularlyto the strips. The gas contained in the TGCs is a mixture of 55% CO2 and45% n-pentane. Each gap has a width of 2O8mm, and the wires are heldat a voltage of 2900V. The width of each wire is 50 µm, and the distancebetween consecutive wires within the TGC is 1O8mm. Due to the absenceof a magnetic field between the last two MS stations in the endcaps, theϕ coordinate in the outer MS station can be extrapolated from the middlestation measurement. Hence, no TGCs are present in the outer MS station.Seven layers (one triplet and two doublets) of TGCs are present in the middle434.5. Muon Spectrometerstation, while two layers (one doublet) are present in the inner station ofthe MS.4.5.3 Monitored Drift TubesMDTs provide precision measurements of the  coordinate of a muon track.They are the most pervasive detector technology within the MS, covering|| Q 2O7. The basic element within the MDT chambers is a pressurizeddrift tube with a diameter of 29O97mm. Each tube contains a gas mixtureof 93% Ar and 7% CO2, and a 50 µm tungsten-rhenium wire at its centre.The wire is kept at a voltage of 3080V. When a muon traverses the MDT, itionizes the gas and produces ions, which drift towards the cathode tube, andelectrons, which drift towards the anode wire. In order to keep the MDTchambers aligned with each other and with respect to the overall detector,the MDT chambers are monitored by alignment sensors that optically mon-itor any deviations from straight lines due to, e.g., temperature changes inthe environment. Magnetic field sensors are also implemented in the MDTsin order to map the magnetic field. The optimal tracking resolution of anMDT chamber is 30 µm. A schematic representation of an MDT is shown inFigure 4.18(a). MDT chambers are formed of three to four layers of tubesmounted on each side of a support structure, as depicted in Figure 4.18(b).444.5. Muon Spectrometerµ29.970 mmAnode wireCathode tubeRmin(a) (b)Figure 4.18: Schematic of a single Monitored Drift Tube (left) and a Moni-tored Drift Tube chamber (right) [2].4.5.4 Cathode Strip ChambersThe main purpose of the CSCs is to provide precision tracking in the in-nermost endcap regions where particle rates are beyond the MDT readoutlimits, i.e., 150HzRcm2. Able to operate at up to 1 kHzRcm2, they coverthe range 2O0 Q || Q 2O7. CSCs are multi-wire proportional chambers withanode wires distributed radially and cathode strips in the − ϕ plane. Oneside of the CSC has strips segmented perpendicularly to the wires, allowingfor a measurement of the  coordinate, while the other side has its strips seg-mented parallel to the wires, allowing for a measurement of the ϕ coordinate.Only the cathode strips of the CSCs are read out.45Chapter 5Object ReconstructionAfter having passed the trigger selection described below in Chapter 7,events of interest are fully reconstructed, and relevant physics objects aredefined. In this chapter, an overview of the different objects used in physicsanalyses carried out using the ATLAS experiment will be detailed. In partic-ular, Section 5.1 will describe tracks reconstructed in the ID, and Section 5.2will cover the definition of vertices within ATLAS. Furthermore, energy de-posits in the calorimeters that are reconstructed as jets will be presentedin Section 5.3. Next, charged lepton reconstruction will be presented: elec-trons will be discussed in Section 5.4, and muons will be reviewed in Sec-tion 5.5. While not directly relevant to the search for new physics presentedin this dissertation, an electron veto is applied in the analysis described inSection 7.3. As muons with large transverse momentum are of particularrelevance for the search for new physics presented in this dissertation, an in-depth description of muon reconstruction, with emphasis on high-pT muons,is presented in Chapter 6. Finally, missing transverse momentum (ZmissT )will be defined in Section 5.6.5.1 TracksCharged particles traversing the ID are bent due to the Lorentz force in thesolenoid magnetic field. This is exploited by the reconstruction procedurefor tracks, which includes global 2 and Kalman filter techniques [56]. Theprocedure is based on fitting a track model to a set of space point measure-ments. A space point is defined as a measurement of a particle’s position inthree dimensions. Tracks are obtained by using track seeds formed from acombination of space points from the pixel layers and the first layer of theSCT. Next, the track seeds are used to find track candidates, which includespace points from all SCT layers using a Kalman filter technique, in orderto take into account the material traversed by the charged particle. Finally,the track candidates are extended to include information from the TRT de-tector. Once the extended track candidates are obtained, the full track isrefitted with the full information of all three ID components. From the fit465.2. Verticesof the track, various measured quantities, b , are obtained:b = (y0P z0P ϕP P qRp)P (5.1)where y0 and z0 are the impact parameters, ϕ and  are the anglesdescribed in Section 4.2, and qRp represents the charge of the particle di-vided by its momentum. The impact parameters quantify the distance ofthe particle track to the IP. In particular, the transverse impact parame-ter y0 represents the distance between the track and the IP in the planetransverse to the proton beams, and the longitudinal impact parameter z0represents the distance between the track and the IP along the z-axis. IDtracks are used in both electron (muon) reconstruction; they are combinedwith calorimeter (MS) information to obtain the final measurement of theparticle parameters.5.2 VerticesAfter all ID tracks are identified, a vertex-finding algorithm based on thereconstructed tracks is used in order to find the vertices of each event [57].The collection of tracks described in Section 5.1 is refined in order to re-ject low-quality tracks. First, tracks are required to be consistent with theIP. Consistency with the IP is enforced by requiring the impact parame-ter y0 Q 4mm, and the impact parameter uncertainties y0 Q 5mm andz0 Q 10mm. Next, each track must have at least four hits in the SCT andat least nine hits overall when considering the combination of SCT and pixelhits. The track must also not contain any pixel holes. A hole is defined asan active detector region where no hit is found, but where a hit would beexpected based on the track information. Finally, the tracks used to re-construct vertices must have pT S 400 MeV. The vertex-finding procedurestarts by selecting a seed position for the first vertex consistent with the IP,and the collection of tracks satisfying the above criteria is used to estimatethe best vertex position with a fit. Iteratively, all tracks satisfying the cri-teria above are added to or removed from the vertex, in order to minimize a2 fit. If a track is not associated to the vertex, it is allowed to be associatedto another vertex. The procedure is repeated until either all ID tracks areassociated to a vertex or no additional vertex is found with the remainingunassociated tracks. When multiple vertices exist in an event, the primaryvertex is defined as the vertex within the event with the highest sum of trackpT squared.475.3. Jets5.3 JetsQuarks and gluons produced from proton-proton interactions will hadronizeinto colour-neutral states producing a collimated shower of particles, collec-tively called a jet. The amount of energy deposited in the hadronic calorime-ters in comparison with the EM calorimeters allow jets to be distinguishedfrom electrons or photons; jets usually have a much larger fraction of theirenergy deposited in the hadronic calorimeters. To reconstruct jets, the anti-kt algorithm [58] is used. This algorithm computes various distances anditerates over available entities. In the case of the ATLAS experiment, enti-ties are either tracks or energy clusters measured in the calorimeters. Thedistance between two entities labeled i and j, yij , or the distance betweenan entity labeled i and the jet beam labeled W, yiW, is computed usingyij = min(k−2ti P k−2tj )∆2ijg2and yiW = k−2ti P (5.2)where ∆2ij = (yi− yj)2+(ϕi−ϕj)2, and kti, yi, and ϕi are the transversemomentum, rapidity, and azimuthal angle of particle i, respectively. g is aradius parameter and varies depending on the analysis using the algorithm.A typical value of g is 0.4. The rapidity is defined asy =12ln(Z + pzZ − pz)P (5.3)where Z and pz are the energy and the momentum along the z-axis ofthe particle, respectively.For each entity, the algorithm compares yij and yiW and selects thesmaller of the two distances. If the smaller distance is yij , then the entitylabeled j is combined with the entity labeled i. If the smaller distance isyiW, then the entity labeled i is labeled a jet, and it is removed from thelist of entities. The algorithm terminates once the list of entities has beenexhausted and all entities have been classified.5.3.1 b-jetsA particular class of jets are those resulting from the decay of b quarks,which hadronize to b hadrons, so-called b-jets. The relatively long lifetimeof b hadrons implies that they will travel within the detector for severalmillimetres before decaying. The unique topology of such jets is exploitedin order to identify b-jets. In particular, a secondary vertex can be identifiedwhere the b hadron decayed. Figure 5.1 depicts the typical topology of a b-jet485.3. Jetsand highlights the distinction between the primary vertex and the secondaryvertex.Figure 5.1: Schematic representation of the topology of a typical b-jet com-pared with jets produced by lighter quarks or gluons [59].Machine learning algorithms use information relating to the secondaryvertex and its associated tracks in order to distinguish b-jets from jets orig-inating from lighter quarks or gluons [60–62]. In particular, the distancebetween the primary vertex and the secondary vertex, the impact param-eters of the tracks associated to the jet, and the information relating tothe secondary vertex, are used as inputs to low-level b-jet taggers. Theoutput of these individual low-level taggers are then used in a Boosted De-cision Tree (BDT), which enhances the separation power of the individuallow-level taggers. The BDT outputs a multivariate discriminant, so-calledmv2c10, which is used in order to quantify the probability of a jet originatingfrom a b quark, i.e., being a real b-jet. Various Working Points (WPs) aredefined based on the mv2c10 quantity, with the efficiency of identifying ab-jet as their main feature. For example, the mv2c10 70% WP has a b-jetselection efficiency of 70%. A higher b-jet selection efficiency comes at thecost of a higher fake rate due to jets originating from lighter quarks andgluons. Hence, a balance between the desired purity and selection efficiencyof b-jets must be struck. The b-jet veto applied to the analysis described in495.4. ElectronsSection 7.3 requires the absence of any b-jet satisfying the mv2c10 77% WP.5.4 ElectronsInformation from both the ID and the EM calorimeter is used to reconstructelectrons and obtain measurements of their properties. The EM calorimeter,described in Section 4.4.1, is used in order to measure the transverse energy,ZT, of the electrons. When reconstructing an electron candidate, ID tracks,described in Section 5.1, are matched with EM calorimeter clusters. Theseclusters are formed from energy deposits in the EM calorimeter. Specifically,the EM calorimeter is divided into so-called towers of dimension ∆×∆ϕ =0O025 × 0O025, corresponding to the granularity of the second layer of theEM calorimeter. The energy in all three EM calorimeter layers and in thepresampler is summed to obtain the total energy of each tower. In total,the ATLAS EM calorimeter comprises 200× 256 towers in ×ϕ. A sliding-window algorithm [63] searches for clusters using a window of size 3 × 5towers in  × ϕ, where the towers included have energy deposit greaterthan 2.5 GeV. EM calorimeter clusters are then matched to ID tracks toform electron candidates by requiring |cluster − track| Q 0O05 and −0O10 Qq × [∆(ϕclusterP ϕtrack)] Q 0O05, where q corresponds to the electron’s charge.After being matched to an ID track, the cluster is computed again using anextended window size of 3× 7 (5× 5) towers in the barrel (endcap) region.Figures 4.7, 4.8 and 4.11 give a summary of the ID and EM calorimetercomponents, and Figure 5.2 illustrates the sub-detectors involved in theelectron reconstruction process within the ATLAS detector.505.4. Electronssecond layerfirst layer (strips)presamplerthird layer hadronic calorimeterTRT (73 layers)SCTpixelsinsertable B-layerbeam spotbeam axisd0ηφ∆η×∆φ = 0.0031×0.098∆η×∆φ = 0.025×0.0245∆η×∆φ = 0.05×0.0245electromagnetic calorimeterFigure 5.2: Schematic representation of electron reconstruction in ATLAS.The solid red line represents the path of an electron, and the dashed red linecorresponds to a photon produced by the interaction of the electron withthe material in the ID [64].The electron veto applied to the analysis described in Section 7.3 uses theelectron candidates described above, which satisfy certain quality criteria.In particular, the likelihood-based Tight selection WP [64] is required. Theselection WP uses probability distributions of the input discriminating vari-ables to construct a likelihood ratio used to separate signal, i.e., real, promptelectrons, from background, i.e., fake electrons, such as those originatingfrom photon conversion inside the detector. The inputs to the likelihood-based discriminant relate to the electron candidate’s EM calorimeter clusterand track measurements. The complete list of input variables used in thelikelihood-based discriminant can be found in [64]. In addition to the se-lection WP, the Gradient isolation WP must be satisfied. The Gradientisolation WP uses information from the EM calorimeter and the ID in orderto quantify the level of activity surrounding the electron candidate. Requir-ing little activity around an electron object helps to reduce the number offake electrons selected. The efficiency of the electron isolation selection is90% (99%) at 25 GeV (60 GeV). Finally, electrons in the transition regionbetween the barrel and the endcaps, i.e., 1O37 Q || Q 1O52, are rejected,due to the large amount of inactive material present, which leads to pooridentification capabilities and energy resolution.515.5. Muons5.5 MuonsThe objects most relevant to the search presented in this dissertation aremuons. The muon transverse momentum is defined aspT = p sin  =sin |qRp| P (5.4)where qRp is the ratio of the muon charge to its momentum, and ismeasured from the track curvature. For muons with track segments comingfrom all three stations of the MS, the track curvature is obtained from thetrack sagitta. The sagitta of a curved track of radius r is defined as thedistance from the centre of the track arc to the centre of its base. Figure 5.3depicts the sagitta s for a curved track with radius r. For muons with tracksegments coming from only two stations of the MS, the track curvature isobtained from the angular difference between the two measured segments.srFigure 5.3: Schematic representation of the sagitta s of a curved track withradius r [65].The main types of muon tracks used within ATLAS are Combined (CB)muon tracks and Muon Extrapolated (ME) tracks [53]. A CB muon track isone where the track reconstruction for the muon is performed independentlyin the ID and the MS, and a combined track is formed with a global refitthat uses the hits from both the ID and MS sub-detectors. An ME muontrack is one where the track is reconstructed based only on the MS track,and a loose requirement on the compatibility of it originating from the IPis imposed. ME muons are used mainly to improve the muon acceptancein the 2O5 Q || Q 2O7 region of the detector, where no ID information isavailable.525.5. Muons5.5.1 Medium Quality MuonsThe default selection criteria required for muons used in ATLAS analyses aredefined as the Medium quality WP [53]. A Medium quality muon is definedas either a CB track or an ME track, with additional quality requirements.CB muons are required to have at least three hits in at least two MDT layers.CB muons in the central region || Q 0O1 are required only to have at leastone MDT layer, but no more than one MDT hole layer. Used only in theregion 2O5 Q || Q 2O7, ME muons are required to have at least three MDTor CSC layers hit. In order to avoid the selection of hadrons which decayin flight and get misidentified as muons, a requirement on the significancebetween the ID and MS pT measurements is placed, requiring SpIDT :pMST Q 7,where the significance between two measurements A and B is defined asSA:B = |A− B|√2A + 2BP (5.5)and A and B represent the uncertainties of the respective measure-ments. This is effective in rejecting hadrons that would leave a track in theID with large momentum and subsequently decay into a muon, resulting ina track with low momentum in the MS, e.g., kaons.5.5.2 Transverse Momentum CorrectionsThe muon momentum scale and resolution are simulated using Z →  sam-ples. In order to simulate the scale at the per mille level and the resolutionat the percent level, corrections to the simulated momentum are applied.With the aim of describing the collected data as precisely as possible, thecorrected transverse momentum in simulation is calculated usingpCor,DetT =pMC,DetT +1∑n=0sDetn (P ϕ)(pMC,DetT)n1 +2∑m=0∆rDetm (P ϕ)(pMC,DetT)m−1gmP (5.6)where pMC,DetT is the uncorrected transverse momentum in simulation,Det ∈ [ID, MS], gm is a normally distributed random variable with zero meanand unit width, ∆rDetm (P ϕ) describes the momentum resolution smearing,and sDetn (P ϕ) describes the scale corrections. These corrections are derivedfor various detector regions separately, ensuring uniform detector behaviorfor each set of corrections. The correction parameters are derived from data.535.5. MuonsThe numerator in Equation (5.6) describes the momentum scale, and thedenominator describes the momentum smearing that broadens the pT resolu-tion. The term sDet0 (P ϕ)models the inaccuracy of simulating the energy lossof muons due to interactions with material. In particular, sMS0 (P ϕ) is usedto model the muon energy loss between the interaction point and the MS,mostly due to interactions with the calorimeters. As there is very little ma-terial interactions between the interaction point and the ID, sID0 (P ϕ) = 0.sDet1 (P ϕ) is used to account for inaccuracies in the magnetic field integral.The pT resolution of muons can be parameterised aspTpT=r0pT⊕ r1 ⊕ r2 · pTP (5.7)where ⊕ denotes a sum in quadrature. The first term in Equation (5.7)models the fluctuations of the energy loss in the traversed materials. Asmuon energy loss affects mostly momentum scale, not resolution,∆rID0 (P ϕ) =∆rMS0 (P ϕ) = 0. The second term accounts for multiple scattering, localmagnetic field inhomogeneities, and local radial displacements of the hits.The last term, most important at high pT, describes intrinsic resolution ef-fects caused by the spatial resolution of the hit measurements and by residualmisalignments of the MS.The final corrected momentum for CB muons is obtained by combiningthe ID and MS corrected momenta from Equation (5.6) into a weightedaverage:pCor,CBT = f · pCor,IDT + (1− f) · pCor,MST P (5.8)where f is derived using an equation identical to Equation (5.8), butusing the uncorrected momenta values and solving for f .5.5.3 Transverse Momentum UncertaintyThe uncertainty on the transverse momentum is of prime importance, asit is used in the high-pT selection WP described in Section 6.1. From thetrack measurements in Equation (5.1), the covariance matrix for the trackmeasurement iscov(b) =2y0 z0;y0 ϕ;y0 ;y0 qRp;y0y0;z0 2z0ϕ;z0 ;z0 qRp;z0y0;ϕ z0;ϕ 2ϕ ;ϕ qRp;ϕy0; z0; ϕ; 2 qRp;y0;qRp z0;qRp ϕ;qRp ;qRp 2qRp O (5.9)545.6. Missing Transverse MomentumWe can expand pT in a Taylor series in order to get pT expressed as alinear combination of  and qRp:pT ≈ p0T +UpTU +UpTUqRpqRpO (5.10)In general, the error for a linear combinationf =n∑ivixiP (5.11)where vi are the linear combination coefficients and xi are the measuredvalues, is2f =n∑iv2i2i +n∑in∑j(j ̸=i)vivjij O (5.12)Now that pT is a linear combination of  and qRp, we can use the propa-gation of uncertainty method for linear combinations of correlated variablesto obtain2pT =(UpTU)2+(UpTUqRpqRp)2+ 2(UpTU)(UpTUqRp);qRpO (5.13)This result will be important when considering quantities that depend onthe uncertainty of muon momentum measurements, such as the uncertaintyof the dimuon invariant mass presented in Equation (9.3).5.6 Missing Transverse MomentumThe ATLAS detector cannot directly detect SM neutrinos. In order to ac-count for these particles in analyses, their presence is inferred using so-calledmissing transverse momentum, defined asZmissT = −all objects∑ipiT + Zxli P (5.14)where the sum includes the transverse momenta piT of all leptons, jets,and photons, and the Zxli term accounts for energy clusters in the calorime-ters over threshold which are not associated to any of the objects alreadyincluded in the sum. It should be noted that other unknown particles have555.6. Missing Transverse Momentumthe potential to leave the ATLAS detector without being detected. Thiswould leave a final state signature of large ZmissT , and certain searches forsuch BSM physics scenarios are undertaken within the ATLAS collabora-tion.56Chapter 6High-Momentum MuonsObjects with large transverse momentum are used in many searches for BSMphysics. In addition to the muons described in Section 5.5, of particularimportance for the search presented in this dissertation are muons withlarge transverse momentum. In particular, high-pT muons are key whensearching for new high-mass resonances, because of the very nature of thesearch; hints of new physics will manifest themselves as an excess of events inthe high-mass tail of the dimuon invariant mass distribution. Because higherinvariant mass events are characteristic of new and interesting physics, themain candidates for the final state objects are inherently high-pT muons.This chapter describes the treatment of high-pT muons and their relevanceto the search described in this dissertation. The high-pT WP is describedin Section 6.1, and the optimization of a component of the high-pT WP,the BadMuon veto, is presented in Section 6.2. Finally, the gradient WP,which investigates whether efficiency losses due to the high-pT WP selectioncan be recovered without compromising the pT resolution, is discussed inSection 6.3.6.1 High-pT Working PointThe high-pT WP consists of a set of criteria that a muon must satisfy. Inaddition to being a CB muon of quality Medium as described in Section 5.5,muons selected by the high-pT WP must satisfy the following criteria [53]:• At least three hits in at least three precision layers of the MS• Not excluded by geometrical  − ϕ chamber vetoes, described below• ID qRp measurement agrees with ME qRp measurement within 7 stan-dard deviations, i.e., SqRpID:qRpME Q 7• ID track has at least one pixel hit, at least five SCT hits, at least 10%of the TRT hits originally assigned to the track before the combined576.1. High-pT Working Pointfit (in the region of full TRT acceptance 0O1 Q || Q 1O9), and fewerthan three pixel or SCT holes• Satisfies the BadMuon veto, described belowWhile requiring three MS stations reduces the reconstruction efficiencyby approximately 20%, this requirement improves the pT resolution by ap-proximately 30% for muons with pT S 1O5 TeV. The geometrical vetoes areimposed in order to avoid chambers in the MS with poor alignment, whichwould lead to pT mismeasurements. The vetoed chambers include the re-gion where the barrel and endcaps overlap, i.e., 1O01 Q || Q 1O1, the BIS7/8chambers, and the BMG chambers located in the region accommodating thesupporting feet of the ATLAS detector. A muon passing through the BEEchambers is rejected if its track has fewer than four layers hit. Finally, if themuon passes through the overlap region between small and large MS cham-bers, i.e., if hits are found in both small and large chambers, the muon isrejected. The BadMuon veto is a cut on the relative qRp error measurement,and has been optimized in order to reject individual muon candidates withpoorly measured pT. The BadMuon veto depends on both the  and pT ofthe muon considered. The optimization of the BadMuon veto is discussedin Section 6.2.This muon selection has a pT-dependent efficiency. In particular, atlarger values of pT the efficiency degrades in part because of catastrophicmuon energy loss, i.e., the emission of energetic photons in the dense materialtraversed by muons. This effect in turn leads to an -dependent selectionefficiency loss of approximately 3% per TeV on average for muons with pT S200 GeV, and is folded into the high-pT WP as a systematic uncertainty.Table 6.1 summarizes the efficiency losses due to catastrophic muon energyloss for muons with pT S 200 GeV passing the high-pT WP in various ranges.586.1. High-pT Working Point Range Drop [%/TeV]0O1 Q || Q 1O0 2.74 ± 0.091O0 Q || Q 1O2 1.74 ± 0.281O2 Q || Q 1O3 4.09 ± 0.661O3 Q || Q 1O4 3.18 ± 0.751O4 Q || Q 1O7 12.03 ± 0.521O7 Q || Q 2O0 6.20 ± 0.702O0 Q || Q 2O5 12.25 ± 1.22Table 6.1: Drop in selection efficiency per TeV due to catastrophic muon en-ergy loss for muons with pT S 200 GeV passing the high-pT WP in different ranges.Figures 6.1 and 6.2 depict the acceptance times efficiency and the dilep-ton mass resolution as a function of Z ′ pole mass, respectively. The di-electron channel is beyond the scope of this dissertation, but it can be seenthat the efficiency in this channel is much higher compared with the dimuonchannel described in this dissertation. [TeV]χZ’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Acceptance x Efficiency0.20.30.40.50.60.70.80.91 SimulationATLAS = 13 TeVsDilepton Search Selection ee→Z’ µµ →Z’ Figure 6.1: Acceptance times efficiency for the dielectron (solid blue) anddimuon (dashed red) selections as a function of the Z ′ pole mass. Both plotsare shown after the full dilepton selection described in Section 9.1.596.2. BadMuon Veto Optimization [TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Mass resolution [%]0246810121416 ee→Z’ µµ →Z’ ATLAS Simulation= 13 TeVsDilepton Search SelectionFigure 6.2: Z ′ mass resolution for the dielectron (solid blue) and dimuon(dashed red) selections as a function of the Z ′ pole mass. Both plots areshown after the full dilepton selection described in Section 9.1.6.2 BadMuon Veto OptimizationThe goal of the BadMuon veto is to reject pathological muons residing inthe tails of the pT resolution distributions. The efficiency of this veto di-minishes with increasing pT because of a cut on the relative error of the qRpmeasurement. This cut is optimized in order to continue rejecting patholog-ical muons, but improve the efficiency of the selection as much as possible.Dedicated samples produced with realistic detector misalignments are usedfor these optimizations. The expected resolution of the momentum mea-surement is parameterised as a function of pT in 5 different  regions fol-lowing the parameterisation described in Equation (5.7). The  regions arechosen to coincide with specific regions of the ATLAS detector having vary-ing pT resolution, and are defined as follows: || ≤ 1O05, 1O05 Q || ≤ 1O3,1O3 Q || ≤ 1O7, 1O7 Q || ≤ 2O0, and || S 2O0. Assuming  is the expectedresolution of a muon candidate as expressed in Equation (5.7) given its and pT measurements, a cut on the relative error of the qRp measurement606.2. BadMuon Veto Optimizationof the muon is then applied:qRpqRpQ X(pT) · P (6.1)where X(pT) is a pT-dependent coefficient equal to 1.8 if pT ≤ 1 TeVwhich linearly decreases, or tightens, with pT if pT S 1 TeV. Two pos-sible optimizations are investigated: the pT value at which the tighteningstarts, and the initial value of X(pT). The tightening point is increasedfrom 1.0 TeV to 3.5 TeV in increments of 500 GeV. Increasing this valueshows minimal selection efficiency improvements, so a value of 1.0 TeV iskept. The initial value of X(pT) represents the multiple of the expectedresolution allowed when starting the tightening of the pT-dependent cut onthe relative error of the qRp measurement. This value is increased from 1.8to 2.0, 2.5, and 3.0, while maintaining the tightening point discussed aboveat 2.5 TeV. In all cases, the cut on the relative error of the qRp measure-ment is linearly tightened as a function of pT until the cut reaches a valueof 1  at pT = 5 TeV. Increasing this value improves the cut efficiencywhile still effectively removing the tails of the resolution distributions, butdiminishing returns are observed when increasing the initial value of X(pT)from 2.5 to 3.0. In the transition region, 1O3 Q || ≤ 1O7, and the CSCregion, || S 2O0, the cut is conservatively relaxed to allow for an initialvalue of X(pT) equal to 2.0. In all other detector regions, X(pT) is relaxedto start at 2.5. In summary, the new definition of the BadMuon veto isone where the pT value at which the tightening of the cut starts is 1.0 TeV,and the initial value of X(pT) is 2.5 everywhere, except in the transitionregion and in the CSC region, where it is 2.0. The optimized BadMuon vetoremoves the tails of the pT resolution distributions, defined as (pTRptruT )−1,where pT is the reconstructed transverse momentum and ptruT is the truth-level pT. Various  and pT configurations are investigated. In particular,the resolution distributions of the qRp measurements for the high-pT WP,the high-pT WP and the new implementation of the BadMuon veto, andthe high-pT WP and the old implementation of the BadMuon veto, in theregion 1O05 Q || ≤ 1O3 with 700 GeV Q pT Q 1O3 TeV, are shown in Fig-ure 6.3. Evidently, the old implementation of the BadMuon veto and theoptimized version of the BadMuon veto are both removing unwanted eventsin the tail of the qRp residual distribution, as intended. In addition, theoptimized BadMuon veto implementation is recovering events in the core ofthe residual distribution, allowing for an improved selection efficiency.616.2. BadMuon Veto Optimization5− 4− 3− 2− 1− 0 1 2 3 4 5) - 1tru((q/p)/(q/p)110210310Number Of Muons WPTHigh-p WP + New BadMuonVetoTHigh-p WP + BadMuonVetoTHigh-pATLAS Work In Progress| <= 1.3η1.05 < | <= 1.3 TeVtruT0.7 < pBadMuon Veto OptimizationFigure 6.3: qRp residual distribution for muons in the region 1O05 Q || ≤ 1O3with 700 GeV Q pT ≤ 1O3 TeV satisfying the high-pT WP (black), the high-pT WP and the new implementation of the BadMuon veto (blue), and thehigh-pT WP and the old implementation of the BadMuon veto (red).Figures 6.4 and 6.5 give a summary of the efficiency gain for the opti-mized BadMuon veto, and the increase in the fraction of events in the tails ofthe pT resolution distributions. An efficiency gain of up to 5% with respectto the previous definition of the BadMuon veto, i.e., starting the tighteningat 1.0 TeV with an initial value of X(pT) of 1.8, is seen in certain  regionswhile only increasing the tail fraction at the per mille level. The tail fractionis defined as the fraction of events in the pT resolution distributions aboveone.626.2. BadMuon Veto OptimizationTMuon Truth p  [GeV]0 1000 2000 3000 4000 5000E ff i ci en cy  Ga in  ( %)01234567| <= 1.05η|| <= 1.3η1.05 < || <= 1.7η1.3 < || <= 2.0η1.7 < || > 2.0η|ATLAS  Work In ProgressFigure 6.4: Summary of the efficiency gain of the optimized BadMuon vetowith respect to its previous definition in the five || regions studied.TMuon Truth p  [GeV]0 1000 2000 3000 4000 5000T ai l  F ra ct i on  I nc re as e ( %)00.10.20.30.4| <= 1.05η|| <= 1.3η1.05 < || <= 1.7η1.3 < || <= 2.0η1.7 < || > 2.0η|ATLAS  Work In ProgressFigure 6.5: Summary of the increase in the fraction of events in the tails ofthe pT resolution distributions of the optimized BadMuon veto with respectto its previous definition in the five || regions studied. The tail fractionis defined as the fraction of events in the pT resolution distributions aboveone.636.3. Gradient Working Point6.3 Gradient Working PointUntil 2015-2016, the analysis group searching for new high-mass phenom-ena in events with two muons used the high-pT WP described in Section 6.1.This WP results in a relatively good single-muon pT resolution and dimuonmass resolution, but has an inherently low efficiency, particularly when com-pared with the dielectron efficiency, as seen in Figures 6.1 and 6.2.The lower efficiency in the dimuon channel seen in Figure 6.1 is a directresult of the low efficiency of the single-muon identification WP. As can beseen in Figure 6.2, the dimuon mass resolution, which is inherently worsecompared with the dielectron resolution, is poor in absolute terms. The ideabehind the high-pT WP is to maximize selection efficiency while maintain-ing adequate single-muon pT resolution with a series of geometrical vetoes,a veto of 2-station muons, i.e. requiring at least three hits in at least threeprecision layers of the MS, and a cut on the relative error of the qRp measure-ment, i.e., the BadMuon veto. While the high-pT WP pT resolution is good,the WP has a very low efficiency. This section investigates whether thesignificant losses of efficiency due to the high-pT WP vetoes can be largelyrecovered without compromising the pT resolution. The simulated samplesused are dedicated samples produced with realistic detector misalignments:one sample with two muons per event having 300 Q pT Q 1000 GeV, onesingle-muon sample with 1O0 Q pT Q 3O0 TeV, and one single-muon samplewith 3O0 Q pT Q 5O0 TeV. The procedure is as follows:1. Define a single-muon truth-level acceptance selection, the so-calledtruth acceptance.2. Require a baseline selection consisting of simple kinematic and qualitycuts on single-muon reconstruction-level quantities.3. Require full truth-to-reconstruction matching between reconstructedbaseline muons and truth muons in acceptance.4. Plot the two-dimensional distribution of the reconstructed quantitiesqRpR(qRp) as a function of pT for the fully matched sample of muons.5. Derive the 95% quantile of the above distribution.6. Fit the 95% quantile. This fit is used as the gradient cut.7. Remove all muons above the 95% quantile fit, i.e., the gradient cut, inthe baseline sample where no truth-level cuts are applied.646.3. Gradient Working Point8. Apply the integrity cuts described below.9. Inspect the resulting acceptance times efficiency (A × ϵ) curve andresolution of the sample passing the baseline and gradient selection.10. Compare with the high-pT WP A× ϵ and resolution.The procedure is carried out separately for each of the geometrical orconceptual vetoes defined in the high-pT WP.6.3.1 AnalysisTruth-level acceptance selectionThe truth-level acceptance is a set of kinematic cuts on truth-level muonsto ensure they are within the geometrical and kinematic acceptance of thedetector. The selection is presented below.• ptruT S 30 GeV• |tru| Q 2O5Baseline selectionThe baseline selection is a set of standard kinematic, quality, and identifi-cation requirements.• pT S 30 GeV• || Q 2O5• Muon is type CB• Muon is of quality Medium• Muon is not in the CSC region vetoed by the high-pT WP• Muon is not in the BEE region vetoed by the high-pT WP656.3. Gradient Working PointTruth-level to reconstruction-level matchingThe new gradient algorithm is based on a tight truth-level to reconstruction-level matching scheme from which the quantiles are derived. First, in ad-dition to truth-level acceptance selection, spatial and charge matching arerequired; ∆g(truP rec) Q 0O01, qtru × qrec S 0. Next, the reconstructedmuon pT must match the pT of the truth muon assuming an ideal detector,i.e., considering the designed intrinsic resolution. This resolution is digi-tized from the MS Technical Design Report (TDR) [66], and is shown inFigure 6.6. The digitized points in Figure 6.6 are fitted and extrapolatedabove 1 TeV. The fits are done separately for the barrel and the endcapregions using higher-order polynomials. Since this is a digitized version ofthe TDR figure, the errors of the points are unavailable and are fixed toan arbitrarily small value. The pT matching scheme thus follows the idealresolution. The requirement is obtained from the fit, i.e.,∣∣ptruT − pT∣∣ptruTQ TDR(ptruT )P (6.2)where TDR(ptruT ) is the fit of the TDR resolution at a given value of ptruT .666.3. Gradient Working Point20 30 210 210×2 310 310×2 [GeV]TTruth p00.050.10.150.20.250.30.350.40.450.5Resolution|<1.5η||>1.5η||<1.5 Fitη||>1.5 Fitη||<1.5 Extrapolationη||>1.5 Extrapolationη|Digitized TDR resolutionFigure 6.6: Digitized version of the MS TDR resolution, taken as the idealscenario to define the matching. The fits are extrapolated above 1 TeV.Derivation of the gradient cutThe gradient WP exploits the correlation between the truth-level to reconstruction-level response, |qRp−qRptru|qRptru , and the relative error on the qRp measurement,q=pqRp . The response quantity is available in Monte Carlo (MC) simulationbut not in data as truth information is only available in simulated samples.Hence, the gradient cut is derived for the measurable quantity q=pqRp . To de-rive the correlation between q=pqRp and pT, the two-dimensional distributionof the baseline-selected fully truth-matched muons is used. This distribu-676.3. Gradient Working Pointtion represents a sample of muons having well-determined momentum byconstruction. An unbiased relative error, q=pqRp , is obtained by taking thenon-calibrated and non-smeared qRp or pT value in the denominator, as theerrors are not calibrated or smeared.During Run 1, the final uncertainties related to muon tracks were inflatedto account for alignment uncertainties. This amounted to a deweighting ofthe chambers in the CB track fit, and was only carried out in specific crit-ical situations such as the barrel-endcap overlap regions or the small-largeoverlap regions. In Run 2, a more realistic error on the qRp measurementis obtained by fitting the alignment discontinuities. In particular, the CBtrack fit is performed using a Gaussian constraint on the chamber hits, wherealignment uncertainties are used as Gaussian widths. This is accomplishedusing so-called Alignment Effects On Track (AEOTs). Each AEOT spec-ifies a position and angle uncertainty on the chamber hits to which it isassociated.The 95% quantile1 of the q=pqRp dimension of the two-dimensional distri-bution is calculated in each bin of pT. The result is a set of points in thetwo-dimensional space, below which 95% of the fully truth-matched muonsare found. The remaining 5% of the muons above these points naturallyhave the largest q=pqRp values. The set of points is then fit, in order to obtaina smooth description in the full pT range. This fit is used as the gradientcut. Figure 6.7 shows the two-dimensional distribution of q=pqRp as a functionof pT for baseline-selected fully truth-matched muons in the barrel-endcapoverlap region with the 95% quantile overlaid. Dedicated samples of singlemuons generated with a flat  and ϕ distribution with pT between 300 GeVand 5 TeV produced with realistic detector misalignments are used.1For reference, the 50% quantile is simply the median.686.3. Gradient Working Point40 210 210×2 310 310×2 [GeV]Tp00.10.20.30.40.50.60.70.80.91 / (q/p)q/pσ020004000600080001000012000140001600018000200002200024000Number of MuonsBarrel-Endcap Overlap RegionFigure 6.7: Two-dimensional distribution of q=pqRp as a function of pT forbaseline-selected fully truth-matched muons in the barrel-endcap overlapregion with the 95% quantile line overlaid in black.Figure 6.8 shows the summary of the 95% quantile fit for muons inthe barrel-endcap overlap region. The quantiles and fits of three samplesare overlaid: a single-muon sample with realistic detector misalignments, aperfectly aligned single-muon sample, and a DY mass-sliced sample with Z ′signal samples, assuming perfect alignment. The perfectly aligned samplesare not used in the gradient cut fits and are shown only for comparison.However, in the range below ∼ 300 GeV in muon pT, where there are veryfew or no entries in the misaligned samples, the quantiles of the DY andZ ′ samples are used. In this range of pT, the impact of misalignments isassumed to be negligible, and hence the procedure is assumed to be valid.696.3. Gradient Working PointThe misaligned sample’s quantiles are fit with higher-order polynomials inthe different regions considered.40 210 210×2 310 310×2 [GeV]Tp00.10.20.30.40.50.60.70.80.9 /  ( q/ p )q /pσ Z' + Drell-YanSingle Muon (aligned)Single Muon (misaligned)Single Muon (misaligned) fit [30, 4000] Barrel-Endcap Overlap RegionATLAS  Work In ProgressFigure 6.8: Summary of the 95% quantile fit in the barrel-endcap overlapregion. The quantiles of three samples are overlaid: the misaligned single-muon sample (red), the perfectly aligned single-muon sample (green), andthe perfectly aligned DY mass-sliced samples and Z ′ signal samples (black).In addition to the gradient cut, it is essential to independently ensurethat the pT measurement of the selected muons is accurate in the previouslyvetoed regions of the high-pT WP. This is accomplished by the integrity cutsdiscussed below.706.3. Gradient Working PointIntegrity cutsIn addition to the gradient cut described above, integrity cuts are defined inorder to ensure that the various pT measurements for a given muon areconsistent with each other when considering the previously-enforced ve-toes of the high-pT WP. This set of cuts is inspired by the existing cut onSqRpID:qRpME present in the high-pT WP. The cuts are tuned using simulatedsamples with realistic detector misalignments. In addition, 36.1 fb−1 of datataken in 2015-2016 is used to understand potential problems. The selectionused in this limited data-only study is the dimuon selection described inChapter 9 with the muon identification set to the Medium WP.The cuts make use of a set of significance variables using the four pTmeasurements: ID, ME, MS, and CB. The significance between two mea-surements is defined in Equation (5.5). The selection criteria applied aresuch that a muon is rejected if any of the criteria below are met.• SpCBT :pIDT S 10 to ensure consistent pT measurements between the IDmeasurement and the CB measurement• SpCBT :pMET S 10 to ensure consistent pT measurements between the MEmeasurement and the CB measurement• SpMST :pMET S 10 for pT Q 1 TeV or SpMST :pMET S 20 for pT S 1 TeV• ∆ID:ME:CB S 20, where ∆ID:ME:CB = |pIDT −pMET |pCBT• SpWAT :pCBT S 10, where pWAT =∑spsTR2psT∑s1R2psT, 2pWAT= 1∑s1R2psT, i ∈ [IDPME]An example distribution of one of these variables, SpWAT :pCBT , is shownin Figure 6.9. It can be seen that the integrity cuts already reduce thenumber of events with large SpWAT :pCBT even before the cut on this variable.Hence, it can be concluded that the set of integrity cuts applied are consis-tently removing events in the tails of the variables under consideration. Thesimulated samples used contain realistic detector misalignments, and theselection is the baseline selection described above. In addition to the base-line selection, the distribution for the baseline selection with all integritycuts except that of the specific variable plotted, i.e., the so-called N − 1distribution, is shown. The integrity cuts are optimized considering eventswithin the vetoed regions of the high-pT WP leading to the largest efficiency716.3. Gradient Working Pointlosses: 2-station muons, muons in the small-large and barrel-endcap overlapregions, and muons in the BIS7/8 region. The CSC and BEE vetoes arekept as part of the baseline selection, as they lead to very small efficiencylosses. While the MS pT measurement is never used independently in muonreconstruction for most analyses in ATLAS, the SpMST :pMET variable is impor-tant for determining the integrity of 2-station muons. The idea is to requirethe MS and ME measurements to be consistent with each other, in order toensure that the MS alone, although having only two stations participatingin the measurement, is capturing the muon’s true pT. The true pT shouldbe close to the one obtained by the ME algorithm because it accounts forenergy losses in the calorimeter.726.3. Gradient Working Point0 10 20 30 40 50 60 70 80 90 100CBT: pWATpS110210310410Nu mb er  Of  Mu on sAny Veto RegionAny Veto Region with integrity cutsATLAS Work In Progress < 2.1 TeVtruT1.8 TeV < pFigure 6.9: SpWAT :pCBT integrity variable in any of the regions vetoed by thehigh-pT WP for the baseline selection (red), and the baseline and all integritycuts except the cut on SpWAT :pCBT (black). The cut is at SpWAT :pCBT S 10.The impact of the integrity cuts is tested on 36.1 fb−1 of data taken dur-ing 2015-2016 using the sample of highest-mass dimuon events, i.e., eventshaving a dimuon invariant mass larger than 1 TeV, passing the event selec-tion described in Chapter 9, but where both muons pass theMedium qualitycriteria, and at least one of the muons fails the high-pT WP. Figures 6.10and 6.11 show the impact of the integrity cuts on the number of muonspassing the event selection after the application of the integrity cuts. Theevents appearing because of the new selection, which would otherwise berejected due to the high-pT WP, show no indication of muons with highly736.3. Gradient Working Pointinconsistent pT measurements. These events are of particular importance,as they allow for a gain in selection efficiency in the phase space most rele-vant to the search presented in Chapter 9. Indeed, even a few events at highdimuon invariant mass where the contribution from background processes issmall enough can lead to an excess of data compared to the SM prediction,which could indicate the presence of BSM physics. The fact that the pTmeasurements of the muons recovered from the high-pT WP fall within afew hundred GeV indicates that no pathological muons are preferentiallyaccepted as a result of the gradient WP procedure.2stations or S/L BIS7/8 B/E CSC BEE0510152025303540Nu mb er  Of  Mu on sAny overlapOverlap with 2-stations or S/LOverlap with BIS7/8Overlap with B/E, With integrity cutsMedium WP, Pass T > 1 TeV, Fail high-pµµmATLAS  Work In ProgressFigure 6.10: Categories of muons after the application of the integrity cutson data events taken during 2015-2016 with dimuon invariant mass greaterthan 1 TeV. All muons here are recovered from the high-pT WP selection.746.3. Gradient Working Point2stations or S/L BIS7/8 B/E CSC BEE1002003004005006007008009001000 [ Ge V]Tp012345678Nu mb er  Of  Mu on s, With integrity cutsMedium WP, Pass T > 1 TeV, Fail high-pµµmFigure 6.11: Muon pT as a function of the category of muons after theapplication of the integrity cuts on data events taken during 2015-2016 withdimuon invariant mass greater than 1 TeV. All muons here are recoveredfrom the high-pT WP selection.6.3.2 ResultsThe figures of merit used to evaluate the performance of the gradient WPare its impact on the dependence of q=pqRp as a function of pT, its muon selec-tion efficiency, and its pT resolution in comparison with both the baselineselection and the high-pT WP selection. In order to evaluate how the dif-ferent selections act on the same sample, it is informative to look at thetwo-dimensional distribution of q=pqRp as a function of pT for the given selec-756.3. Gradient Working Pointtions. Figures 6.12 and 6.13 show the impact of the selections in the q=pqRp asa function of pT plane for the baseline selection, the gradient WP, and thehigh-pT WP.500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσBaseline Selection500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσGradient WP500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσ WPTHigh-p(a)500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσBaseline Selection500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσGradient WP500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσ WPTHigh-p(b)Figure 6.12: Impact of the baseline selection (left) and high-pT WP (right)in the q=pqRp as a function of pT plane. While the baseline selection doesnot impose any requirements on the q=pqRp as a function of pT, the high-pTWP clearly sculpts the distribution through the use of the BadMuon vetodescribed in Section 6.1.766.3. Gradient Working Point500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσBaseline Selection500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσGradient WP500 1000 1500 2000 2500 3000 [GeV]Tp00.20.40.60.811.2 / (q/p)q/pσ WPTHigh-pFigure 6.13: Impact of the gradient WP in the q=pqRp as a function of pTplane. As the muon pT increases, larger values of q=pqRp are allowed in orderto accommodate the worsening pT resolution of the detector.The most important figures of merit are the selection efficiencies andpT resolutions. Figures 6.14 and 6.15 show a comparison of the selectionefficiency as a function of truth ϕ, , and pT. Figure 6.16 shows the absolutegain in efficiency of the gradient WP, including the integrity cuts, withrespect to the high-pT WP. A notable feature in Figure 6.14(b) is the lowerselection efficiency for the gradient WP compared to the high-pT WP in theregion || ∼ 1O5, corresponding to the region where the toroid magnetic field776.3. Gradient Working Pointtransitions from the barrel toroid to the endcap toroids. This is attributableto the fact that the relative error assigned to the qRp measurement in thisregion is larger, and as such, the 95% quantile cut on the relative qRp errorwill select fewer muons compared to the high-pT WP due to the nature ofthe gradient cut. This phenomenon indicates that the new implementationof the qRp uncertainty using AEOTs discussed in Section 6.3.1 is performingas desired.3− 2− 1− 0 1 2 3φTruth 00.20.40.60.811.21.4Ef f ic ie nc yBaseline SelectionGradient WP WPTHigh-p3− 2− 1− 0 1 2 3ηTruth 00.20.40.60.811.21.4Ef f ic ie nc yBaseline SelectionGradient WP WPTHigh-p210 310  [GeV]TTruth p00.20.40.60.811.21.4Ef f ic ie nc yBaseline SelectionGradient WP WPTHigh-pATLAS Work In Progress ATLAS Work In ProgressATLAS Work In Progress(a)3− 2− 1− 0 1 2 3φTruth 00.20.40.60.811.21.4Ef f ic ie nc yBaselin  S lectionGradient WP WPTHigh-p3− 2− 1− 0 1 2 3ηTruth 00.20.40.60.811.21.4Ef f ic ie nc yBaselin  S lectionGradient WP WPTHigh-p210 310  [GeV]TTruth p00.20.40.60.811.21.4Ef f ic ie nc yBaselin  S lectionGradient WP WPTHigh-pATLAS Work In Progress ATLAS Work In ProgressATLAS Work In Progress(b)Figure 6.14: Efficiency as a function of truth ϕ (left) and truth  (right) forthe baseline selection (green), gradient WP (black), and high-pT WP (red).786.3. Gradient Working Point3− 2− 1− 0 1 2 3φTruth 00.20.40.60.811.21.4Ef f ic ie nc yBaseline SelectionGradient WP WPTHigh-p3− 2− 1− 0 1 2 3ηTruth 00.20.40.60.811.21.4Ef f ic ie nc yBaseline SelectionGradient WP WPTHigh-p210 310  [GeV]TTruth p00.20.40.60.811.21.4Ef f ic ie nc yBaseline SelectionGradient WP WPTHigh-pATLAS Work In Progress ATLAS Work In ProgressATLAS Work In ProgressFigure 6.15: Efficiency as a function of truth pT for the baseline selection(green), gradient WP (black), and high-pT WP (red).796.3. Gradient Working Point210 310  [GeV]TTruth p0.1−0.05−00.050.1Ef f ic ie nc y Ga inATLAS  Work In ProgressFigure 6.16: Absolute gain in efficiency of the gradient WP, which includesthe integrity cuts, with respect to the high-pT WP.While Figure 6.17 illustrates an example of the qRp response distribution,Figures 6.18 and 6.19 show a comparison of the Root Mean Square (RMS) ofthe response distributions as a function of truth pT for the baseline selection,the gradient WP, and the high-pT WP. The chosen figure of merit is theRMS of the response divided by the mean of the ratio qRpqRptru , as this quantitygives the relative resolution of the distribution in each bin of truth pT, andavoids any momentum scale bias. The motivation to divide by the meanof the ratio qRpqRptru instead of taking the RMS of the response distributionas the resolution is as follows. If we scale qRp as qRp → f × qRp, whichis unphysical and does not represent the correct momentum scale, but is806.3. Gradient Working Pointa possible scaling nonetheless, the mean of the ratio qRpqRptru will be f timesthe mean of the original ratio before the transformation, and the RMS willtransform as qRp does. Thus, if we use the RMS as the resolution, it wouldbe artificially higher or lower after this operation, depending on the exactvalue of f . When looking at the response RMS over the ratio mean, thiseffect is not present. The shift in the RMS is present whenever the meanof the ratio qRpqRptru is not equal to 1. This occurs, e.g., in each of the threecurves in Figure 6.18(b).2− 1.5− 1− 0.5− 0 0.5 1 1.5 2tru) / (q/p)tru((q/p) - (q/p)110210310410510610710Nu mb er  Of  Mu on s WPTGradient WP & Fail High-pBaseline Selection WPTHigh-pGradient WPATLAS Work In Progress < 646 GeVtruT  558 GeV < pFigure 6.17: Example qRp response distribution for the baseline selection(green), high-pT WP (red), and gradient WP (black). The purple line rep-resents events passing the gradient WP, but failing the high-pT WP.816.3. Gradient Working Point210 310  [GeV]TTruth p00.20.40.60.811.21.4Re sp on se  Va ri an ceBaseline SelectionGradient WP WPTHigh-pResponse Variance210 310  [GeV]TTruth p0.80.911.11.21.31.41.5Ra ti o Me anBaseline SelectionGradient WP WPTHigh-pRatio Mean210 310  [GeV]TTruth p00.20.40.60.811.21.4Re sp on se  Va ri an ce  /  Ra ti o Me anBaseline SelectionGradient WP WPTHigh-pResponse Variance / Ratio MeanATLAS Work In ProgressATLAS Work In ProgressATLAS Work In Progress(a)210 310  [GeV]TTruth p00.20.40.60.811.21.4Re sp on se  Va ri an ceBaseline SelectionGradient WP WPTHigh-pResponse Vari nce210 310  [GeV]TTruth p0.80.911.11.21.31.41.5Ra ti o Me anBaseline SelectionGradient WP WPTHigh-pRatio Mean210 310  [GeV]TTruth p00.20.40.60.811.21.4Re sp on se  Va ri an ce  /  Ra ti o Me anBaseline SelectionGradient WP WPTHigh-pResponse Vari nce / Ratio MeanATLAS Work In ProgressATLAS Work In ProgressATLAS Work In Progress(b)Figure 6.18: Variance of the response |qRp−qRptru|qRptru (left) and mean of the ratioqRpqRptru (right) used to compute the figure of merit shown in Figure 6.19.826.3. Gradient Working Point210 310  [GeV]TTruth p00.20.40.60.811.21.4Re sp on se  Va ri an ceBaseline SelectionGradient WP WPTHigh-pResponse Variance210 310  [GeV]TTruth p0.80.911.11.21.31.41.5Ra ti o Me anBaseline SelectionGradient WP WPTHigh-pRatio Mean210 310  [GeV]TTruth p00.20.40.60.811.21.4Re sp on se  Va ri an ce  /  Ra ti o Me anBaseline SelectionGradient WP WPTHigh-pResponse Variance / Ratio MeanATLAS Work In ProgressATLAS Work In ProgressATLAS Work In ProgressFigure 6.19: Resolution derived from the RMS of the truth-level toreconstruction-level pT response distributions as a function of truth pT. Thefigure of merit is the response variance over the ratio mean. A more preciseestimation of the resolution, obtained with Gaussian fits to the responseitself, in bins of pT, is given in Figure 6.21.Figure 6.20 shows a similar comparison to that of Figure 6.18, where theresolution is derived from fits to the response distributions in bins of truthpT. The response distributions are fit with a Gaussian between the distribu-tion mean minus 1O5 × RMS and the distribution mean plus 1O5 × RMS.The width of the Gaussian fit, , as a function of truth muon pT, is shown836.3. Gradient Working Pointin Figure 6.20(a). The shifted mean of the Gaussian fit, + 1, is shown inFigure 6.20(b). Given that  + 1, which is equivalent to the ratio qRpqRptru , isnot equal to 1 throughout the entire range for all three selections, the ratioof the width to + 1 is taken in order to correct for different scales, as ex-plained in the text above for the numerical RMS procedure. The correctedresolution is seen in Figure 6.21. The dip in resolution as the muon pT getsvery large is obtained by construction; the 95% quantile gradient cut selectsmore muons at high pT values compared to the high-pT WP. In turn, theresidual distributions for higher values of pT will have more events in thebulk of the distribution for the gradient WP, resulting in a better resolution.Indeed, by looking at Figures 6.12 and 6.13, it is clear that the gradient WPselects more muons at high pT values compared to the high-pT WP.0 500 1000 1500 2000 2500 3000 [GeV]TTruth p0.10.20.30.40.50.60.70.8σF it t ed  Ga us si an  Baseline Selection WPTHigh-pGradient WP WPTGradient WP & Fail High-pATLAS  Work In Progress(a)0 500 1000 1500 2000 2500 3000 [GeV]TTruth p11.11.21.31.41.5 + 1µF it t ed  Ga us si an  Baseline Selection WPTHigh-pGradient WP WPTGradient WP & Fail High-pATLAS  Work In Progress(b)Figure 6.20: Width  (left) and shifted mean  + 1 (right) obtained fromthe Gaussian fitting of the qRp response distributions in various pT bins.846.3. Gradient Working Point0 500 1000 1500 2000 2500 3000 [GeV]TTruth p0.10.20.30.40.50.60.70.8 + 1)µ/ (σF it t ed  Ga us si an  Baseline Selection WPTHigh-pGradient WP WPTGradient WP & Fail High-pATLAS  Work In ProgressFigure 6.21: Corrected qRp resolution +1 obtained from the Gaussian fittingof the qRp response distributions in various pT bins.6.3.3 SummaryA new algorithm is presented as an alternative to the current high-pT muonidentification WP, which provides good resolution but is inefficient. The newalgorithm comprises two independent components: a gradient cut and a setof integrity cuts. The gradient cut is applied in the previously vetoed regionsof the high-pT WP and in the regions outside of these vetoes, while theintegrity cuts are applied only in the previously vetoed regions. Overall, thenew algorithm delivers a better efficiency and similar resolution throughoutthe entire pT range. The algorithm can be used by many other analyses inATLAS other than the analysis presented in this dissertation. For example,the gradient WP is ideal for analyses which work at lower values of muonpT and want to use a more robust selection WP compared to the MediumWP, but cannot use the high-pT WP because of the associated efficiencyloss. The new algorithm is thus a good compromise in terms of robustnessand efficiency for these analyses.85Chapter 7ATLAS Trigger SystemProton bunches collide within the ATLAS detector at a rate of 40MHz.Recording all collision events is impossible, both from a data collection band-width standpoint and from a data storage capacity standpoint. Hence, theATLAS experiment uses a two-level trigger system in order to select eventsof interest and reject events with little potential to be of interest from aphysics point of view. This chapter introduces the two levels of the ATLAStrigger system: the Level-1 (L1) trigger is described in Section 7.1, and theHigh-Level Trigger (HLT) is described in Section 7.2. Particular consid-eration is given to the muon trigger system in Section 7.3, because of therelevance of muon triggers and their efficiencies to the analysis containingtwo high-momentum muons in the final state described in this dissertation.7.1 Level-1 TriggerThe fast hardware-based L1 trigger enables the reduction of the event ratefrom 40MHz to ∼ 100 kHz. The L1 trigger uses detectors that are fastenough to accurately identify the bunch crossing of an event, thus allowingto filter out uninteresting events each time a proton-proton collision occurs.The information used by the L1 trigger is obtained from the trigger cham-bers of the MS and from the calorimeters with reduced-granularity; no IDinformation is used for the L1 trigger. The MS trigger chambers identifyhigh-pT muons, while the calorimeters allow the detection of electrons, pho-tons, jets,  leptons, and ZmissT . The decision time allocated for the L1trigger is 2O5 µs. If an event passes the L1 trigger, one or several coarseRegions of Interest (RoIs) are defined with preliminary measurements in and ϕ using a subset of detectors. Events passing the L1 trigger are sent toget processed by the software-based HLT.867.2. High-Level Trigger7.2 High-Level TriggerThe HLT employs dedicated offline algorithms to reconstruct particles andestimate their parameters. Starting from the RoIs obtained by the L1 trig-ger, the full granularity of the calorimeters and the MS is exploited to mea-sure the properties of the particles traversing the detector within the RoIs.The average processing time for objects found in the ROIs is 40ms. Next,track matching with the ID is carried out. Finally, events are fully re-constructed at the HLT in approximately 4 s, and a final decision is madewhether to write the event to permanent storage for offline analysis. Theevent rate after the HLT is reduced from the ∼ 100 kHz accept rate comingfrom the L1 trigger to ∼ 1 kHz. In cases where the accept rate of a particulartrigger is still too large to handle after having passed the HLT, e.g., JR meson production events, the trigger must be prescaled, i.e., only one in anumber of events passing the trigger is kept. However, whenever possible,triggers that are not prescaled are used, in order to make the most of thevaluable data produced by the LHC.7.3 Muon Trigger Efficiency MeasurementsMeasuring the performance of high-pT muon triggers used in the ATLAS ex-periment is vital for understanding the detector. Their performance needsto be evaluated in data to determine whether MC simulations are reliableenough for use in physics analyses. This is achieved by performing measure-ments of the trigger efficiencies in events containing a leptonically decayingW boson and jets (W+ jets), and events with muons from top quark pairproduction (tt¯). From these measurements, data-to-simulation correctionfactors, so-called Scale Factors (SFs), which will be applied to physics anal-yses to correct for any mismodelling of the triggers in simulation, can bederived. This is of direct relevance in searches for BSM physics, in particu-lar in searches for high-mass phenomena, because the final states consideredhave two high-momentum muons in each event.The method used to calculate the efficiencies of muon triggers is the so-called “tag and probe” method. This approach uses a “tag” trigger to selectdesired events. Once events pass the tag trigger, the various “probe” triggerefficiencies are evaluated in both data and MC by calculating the fraction ofevents passing both the tag and the probe triggers in the sample of eventspassing the tag trigger. For low-pT (medium-pT) muons, i.e., muons withpT ≲ 10 GeV (10 ≲ pT ≲ 100 GeV), this method is used with events where877.3. Muon Trigger Efficiency Measurementsa SM JR meson (Z boson) decays into a pair of muons. In this case, oneof the muons causes the tag trigger to record the event, and the other muonis used to measure the probe trigger performance without bias. For high-pTmuons, i.e., muons with pT ≳ 100 GeV, two distinct types of events areutilized for the tag-and-probe method: tt¯ events and W+ jets events. Thetag trigger used in this study is a trigger based on selecting events withhigh ZmissT , defined in Equation (5.14). The scale factors are then calculatedaccording toSF = ϵdataϵMCP (7.1)where ϵm is defined as the ratio of the number of probe muons matchedto at least one trigger object to the total number of probe muons:ϵm =cmprobzcmtag +cmprobzP (7.2)where m ∈ [data, MC].In the following, Section 7.3.1 presents the samples and event selectionapplied in order to perform efficiency measurements of high-pT muon trig-gers. Section 7.3.2 describes the systematic uncertainties considered whencalculating the trigger SFs. The efficiency measurements and trigger SFcalculations are presented in Section 7.3.3.7.3.1 Event SelectionBoth the data and simulated samples undergo a series of cuts in order toselect a high-purity sample of W+ jets or tt¯ events. Cuts are applied bothat the event level and at the object level. The object-level requirementsfor the selected muons are that each pass the Medium quality WP withno isolation requirements. At the event level, data events are required tobe in the so-called Good Run List (GRL) as defined by the ATLAS dataquality group. An event is contained in the GRL if it occurred during aperiod where the proton beams in the LHC were stable and all relevantdetector systems were functioning nominally. In addition, events must notbe flagged as incomplete, and must pass LAr and Tile error requirements.This provides protection against noise bursts and data corruption in the EMand hadronic calorimeters, respectively. Each event must contain a primaryvertex, defined as the vertex in the event with the highest sum of track pTsquared, and must pass either the tag or the probe trigger. The tag trigger887.3. Muon Trigger Efficiency Measurementsused, HLT_xe100_L1XE60, requires at least 100 GeV of ZmissT . The probetriggers, HLT_mu50 or HLT_mu26_ivarmedium, require at least one muon withpT S 50 GeV or one isolated muon with pT S 26 GeV, respectively. Eventsmust contain exactly one muon with pT S 26 GeV, and contain no electrons.The ZmissT present in the event must also be greater than 200 GeV, in orderto avoid the turn-on curve of the ZmissT tag trigger. The requirements abovecan be applied in the context of high-pT trigger efficiency studies for both tt¯and W+ jets event topologies. Specific to the W+ jets selection, events arerequired to have between 1 and 4 jets with pT S 25 GeV inclusively, and tocontain no b-jets, which are defined using the mv2c10 77% WP defined inSection 5.3.1. For the tt¯ selection, events are required to have at least 4 jetswith pT S 25 GeV, and at least one b-jet. The b-jet requirement ensures theorthogonality of the W+ jets and tt¯ measurements. The samples used tostudy high-pT muon triggers, and their associated MC generators, are listedin Table 7.1.Process GeneratorW+ jets Sherpa 2.2.1 [67]Z+ jets Sherpa 2.2.1 [67]Diboson Sherpa 2.1 [68]Single Top Powheg [69] + Pythia 6 [70]tt¯ Powheg [69] + Pythia 8 [71]tt¯ + V MadGraph5/aMC@NLO [72] + Pythia 8 [71]Table 7.1: Summary of the samples used to evaluate the performance ofhigh-pT muon triggers.The collected Run 2 data are compared to the simulated samples in var-ious kinematic regions, in order to validate the agreement between data andsimulation. Figure 7.1 shows an example of a relevant kinematic distribu-tion for events passing the tag trigger requirement and the offline ZmissT cutof 200 GeV: the  distribution of the muons for the tt¯ selection. The dis-agreement between data and simulation is within systematic uncertainties.897.3. Muon Trigger Efficiency Measurements2.5− 2− 1.5− 1− 0.5− 0 0.5 1 1.5 2 2.5ηmuon 0.60.811.21.4Da ta  /  Pr ed . 0200040006000800010000120001400016000180002000022000E ve nt sDatattW+jetsSingle topZ+jetsDibosonOtherATLAS Work In Progresss = 13 TeV, 135.7 fb-1tt selectionFigure 7.1: Muon  distribution for the tt¯ selection. The disagreementbetween data and simulation is within systematic uncertainties.7.3.2 Systematic UncertaintiesVarious sources of systematic uncertainty were considered for the efficiencymeasurements presented in Section 7.3.3. All contributions are added inquadrature to obtain the total systematic uncertainties. In addition to thesources of systematic uncertainty described below, systematic variations onthe smearing of the muon ID tracks, the smearing of the muon MS tracks,and the scale of the muon momentum were also studied and found to benegligible.The identification of b-jets can affect the efficiency measurements be-907.3. Muon Trigger Efficiency Measurementscause of the b-jet requirements described in Section 7.3.1. This effect is esti-mated by measuring the muon trigger efficiency while changing the object-level selection for b-jets from the mv2c10 77% WP to the mv2c10 70% WP.Depending on how the ZmissT is reconstructed, different efficiencies can be ob-tained for the high-pT muon triggers. The systematic uncertainty associatedwith the ZmissT reconstruction is estimated by measuring the muon triggerefficiency while changing the ZmissT event-level selection from 200 GeV to150 GeV. Because of the large number of jets present in the final state con-sidered for the efficiency measurements, the pT cut applied to selected jetswill affect the overall muon trigger efficiencies. By varying the pT cut appliedto selected jets from 25 GeV to 30 GeV, the systematic uncertainty relatedto the jet pT cut is evaluated. Muon selection criteria are also consideredwhen calculating systematic uncertainties. In particular, the muon isolationand selection WPs are varied. For the isolation, the systematic uncertaintyis estimated by measuring the efficiency when applying the FCTight or theFCTightTrackOnly isolation [53]. The larger difference between either ofthese settings and the nominal efficiency, calculated with no isolation crite-ria, is used as an uncertainty. For the selection WP, the systematic uncer-tainty is estimated by changing the muon quality WP from the Medium WPto the high-pT WP described in Section 6.1. The largest source of systematicuncertainty is the choice of the selection WP. All systematic uncertaintiesare below 3%.7.3.3 Efficiency Measurements and Trigger Scale FactorsThe efficiency described in Section 7.3 is measured for the relevant high-pT muon triggers used within ATLAS: HLT_mu50 or HLT_mu26_ivarmedium.Sample distributions of trigger efficiencies as a function of muon pT areshown in Figure 7.2 for the W+ jets measurements and in Figure 7.3 for thett¯ measurements. In particular, the efficiencies plotted are those of a muonpassing either the HLT_mu50 trigger or the HLT_mu26_ivarmedium trigger.The final SFs are obtained by taking the ratio between the data and MCsimulation efficiencies.917.3. Muon Trigger Efficiency Measurements0 100 200 300 400 500 600 [GeV]TMuon p0.811.2Data/MC0.40.50.60.70.80.91Trigger efficiencyData 2016Data 2017Data 2018ATLAS Work In Progress-1 = 13 TeV, 135.7 fbsW + Jets, Barrel(a)0 100 200 300 400 500 600 [GeV]TMuon p0.811.2Data/MC0.60.70.80.911.11.2Trigger efficiencyData 2016Data 2017Data 2018ATLAS Work In Progress-1 = 13 TeV, 135.7 fbsW + Jets, Endcaps(b)Figure 7.2: Trigger efficiencies for muons to pass either the HLT_mu50 trig-ger or the HLT_mu26_ivarmedium trigger in the barrel (top) and endcap(bottom) regions of the ATLAS detector as a function of muon pT for theW+ jets selection. The ratio plot in the lower panels give the SFs.927.3. Muon Trigger Efficiency Measurements0 100 200 300 400 500 600 [GeV]TMuon p0.811.2Data/MC0.40.50.60.70.80.91Trigger efficiencyData 2016Data 2017Data 2018ATLAS Work In Progress-1 = 13 TeV, 135.7 fbs, Barreltt(a)0 100 200 300 400 500 600 [GeV]TMuon p0.811.2Data/MC0.60.70.80.911.11.2Trigger efficiencyData 2016Data 2017Data 2018ATLAS Work In Progress-1 = 13 TeV, 135.7 fbs, Endcapstt(b)Figure 7.3: Trigger efficiencies for muons to pass either the HLT_mu50 triggeror the HLT_mu26_ivarmedium trigger in the barrel (top) and endcap (bot-tom) regions of the ATLAS detector as a function of muon pT for the tt¯selection. The ratio plot in the lower panels give the SFs.937.3. Muon Trigger Efficiency MeasurementsTable 7.2 summarizes the SF calculations and their associated uncertain-ties. The total uncertainty is the sum in quadrature of the statistical andsystematic uncertainties, with the systematic uncertainty being equal to thesum in quadrature of the various effects discussed in Section 7.3.2.Year Selection Region SF (%) Unc. (%) Stat. (%) Syst. (%)2016tt¯ Barrel 90O5 1O2 0O9 0O8tt¯ Endcaps 96O7 2O6 0O9 2O5W+ jets Barrel 90O7 1O1 0O8 0O8W+ jets Endcaps 98O2 0O9 0O5 0O72017tt¯ Barrel 86O9 1O0 0O8 0O6tt¯ Endcaps 96O7 1O1 0O8 0O7W+ jets Barrel 86O8 0O7 0O6 0O4W+ jets Endcaps 96O6 1O1 0O5 1O02018tt¯ Barrel 88O3 1O7 0O7 1O6tt¯ Endcaps 95O8 1O7 0O7 1O5W+ jets Barrel 86O9 1O2 0O5 1O1W+ jets Endcaps 95O5 0O8 0O4 0O7Table 7.2: Summary of the high-pT muon trigger SF calculations for muonspassing either the HLT_mu50 trigger or the HLT_mu26_ivarmedium trigger.The last two columns give the statistical and systematic uncertainties thatcomprise the total uncertainty.94Chapter 8ATLAS Detector UpgradeThe LHC entered the Long Shutdown 2 (LS2) at the end of 2018, which willlast approximately two years. During Run 2, the design instantaneous lu-minosity of 1× 1034 cm−2s−1 was attained, and surpassed, reaching a peakinstantaneous luminosity of 2× 1034 cm−2s−1. Following the third run ofdata-taking of the LHC in 2021− 2023, so-called Run 3, the instantaneousluminosity is expected to increase by up to a factor of three compared withthe Run 2 conditions. The data-taking period after Run 3, the so-calledHigh-Luminosity Large Hadron Collider (HL-LHC), promises to deliver anastounding 3000 fb−1 of proton-proton collision data, and is scheduled tostart in 2026. To cope with these harsher luminosity conditions, a series ofupgrades are foreseen to be implemented within the ATLAS detector. Inparticular, the upgrade programme consists of two main phases: Phase-Iupgrades will be installed during LS2, and Phase-II upgrades will be in-stalled during the third long shutdown. The largest Phase-II upgrade is theInner Tracker (ITk) [73, 74], which will replace the existing ID with a new,entirely silicon-based, detector. The ITk will provide higher granularity andincreased radiation hardness with respect to the current ID. Among others,anticipated Phase-II upgrades include the replacement of the electronics re-lated to the trigger system for the LAr calorimeters [75], and the installationof additional RPC chambers in the MS [76]. These upgrades will allow theATLAS detector to remain compatible with the higher trigger rates expectedduring the HL-LHC and gain efficiency in the barrel, respectively.The largest Phase-I upgrade to the ATLAS detector is the replacement ofthe inner-most station of the MS, the Small Wheel. Described in Section 8.1,the NSW will be integrated into the ATLAS detector during LS2. One ofthe two technologies used in the NSW is sTGCs. This technology, andresults of test beam campaigns undertaken with the goal of characterizingsTGCs, will be presented in Sections 8.2 and 8.3, respectively. The otherdetector technology employed in the NSW are Micromegas (MM). A detaileddescription of MM is beyond the scope of this dissertation.958.1. The New Small Wheel8.1 The New Small WheelThe L1 muon trigger rate in the forward region of the ATLAS detector iscurrently very high, and comprises approximately 90% fake muon triggers, asseen in Figure 8.1. With the upcoming increase in instantaneous luminosity,the situation will only get worse.Figure 8.1: L1 muon trigger signal (hashed blue) as a function of  comparedwith the subset of matched muon candidates within a cone of ∆g = 0O2 withpT S 3GeV (dotted blue) and offline-reconstructed muons with pT S 10GeV(solid blue) [77].The NSW is an upgrade to the ATLAS detector, aimed at reducingfake muon triggers while maintaining an acceptable trigger bandwidth andimproving the tracking performance in the forward region of the detector.In addition, the NSW will allow the pT thresholds of the muon triggersto remain low. This is accomplished by providing an additional means ofrejecting fake triggers coming, e.g., from activation of material in the ATLASdetector toroids. Figure 8.2 depicts a cross-sectional view of one quadrantof the ATLAS detector with the NSW installed. The current trigger systemwithin ATLAS accepts all tracks in the diagram, i.e., tracks labeled A, B, and968.1. The New Small WheelC. The desired tracks that should fire the trigger are only the tracks labeledA. With the installation of the NSW, the required coincidence between thebig wheel trigger and small wheel trigger will help to reduce the fake triggerscoming from tracks labeled B and C. The tracks labeled B will be rejectedbecause no corresponding track in the NSW is found. The tracks labeled Cwill be rejected because the corresponding NSW track does not point backto the interaction point.New Small WheelIP Zend-captoroid∆θLL_SV_NSWABCEIBig Wheel EMFigure 8.2: Cross-sectional view of one quadrant of the ATLAS detectorwith the NSW installed. Tracks labeled A will cause the trigger to fire,while tracks labeled B and C will not [77].One NSW will be installed on either side of the interaction point. EachNSW consists of 16 detection layers: 8 sTGC layers and 8 MM layers. Start-ing from the interaction point, a particle will cross four layers of sTGCs (aquadruplet), eight layers of MM, and another four layers of sTGCs. EachsTGC-MM-sTGC grouping is referred to as a sector. There are two types ofsectors: small and large sectors. Figure 8.3 depicts the arrangement of smalland large sectors of the NSW detector components. The NSW will recon-struct muon tracks with high precision and provide information for the L1trigger using sTGCs as the primary trigger system and MM as the primary978.2. Small-strip Thin Gap Chambersprecision tracking detectors. The performance requirements for the NSWare 1mrad angular resolution and 100 µm position resolution per detectorlayer.Figure 8.3: Schematic diagram of the small and large sectors comprisingthe NSW. Each sector consists of eight MM planes sandwiched between twosTGC quadruplets [78].8.2 Small-strip Thin Gap ChamberssTGCs are similar to multi-wire proportional chambers. The anode plane,realized with 50 µm gold-plated tungsten wires with a 1O8mm pitch, liesbetween two cathode planes, at a distance of 1O4mm, which have a resistivegraphite layer to reduce sensitivity to field fluctuations and prevent sparking.One cathode plane uses thin readout strips with a 3O2mm pitch. The othercathode plane uses readout pads to determine which strips to read out forthe trigger. The wires are held at a voltage of approximately 3 kV. Thechamber is filled with a gas mixture of 55% O2 and 45% n-pentane. Chargedparticles passing through the sTGC ionize the gas and create an avalancheof electrons on the high-voltage wire, which induces a signal related to thecharge deposited on the pads and strips. The internal structure of sTGCsis shown in Figure 8.4.988.2. Small-strip Thin Gap ChambersFigure 8.4: Internal structure of a small-strip Thin Gap Chamber. Thehigh-voltage anode wires are sandwiched between a strips cathode planeand a pads cathode plane, which have a resistive graphite layer to reducesensitivity to field fluctuations and prevent sparking [77].Four individual chamber layers, or gaps, are assembled into quadruplets,or modules. The naming convention for sTGC modules follows the conven-tion “QXY”, where X ∈ [S, L] refers to small (S) or large (L) sectors, andY ∈ [1, 2, 3] refers to the distance from the beam pipe, with 1 being closestto the beam pipe and 3 being farthest away from the beam pipe. Eachmodule has a trapezoidal shape, as shown in Figure 8.3, with surface areasbetween 1m2 and 2m2.8.2.1 Readout ElectronicsThe readout chain of sTGCs comprises multiple electronic components. AnApplication-Specific Integrated Circuit (ASIC), the so-called VMM chip, isused as the first step in the readout chain. Multiple versions of the VMMASIC are used throughout the test beam campaigns discussed in this chap-ter. The VMM chips are placed on Front-End Boards (FEBs), and are usedto amplify and digitize the hits coming from the pads, strips, and wires ofthe sTGC chamber. The data from the FEBs are then sent to the DataAcquisition (DAQ) system through Twinax cables. The DAQ system han-dles triggering, configures the FEBs, reads all data, and forwards hit datato computerized storage for offline analysis. Finally, event building is doneoffline after all hits are recorded.998.3. Test Beam Results8.3 Test Beam ResultsIn order to characterize the sTGC modules and understand their perfor-mance and limitations, a series of test beam campaigns are carried out. Thegoals of the campaigns vary, but in general the tracking and timing reso-lution are important quantities to measure. The readout electronics of thechambers must also be understood, as several versions of the readout chipsare produced. Section 8.3.1 details the test beam campaign carried out atFermilab, and Section 8.3.2 presents results obtained during subsequent testbeam campaigns carried out at CERN.8.3.1 Fermilab Test Beam CampaignDuring the summer of 2014, a test beam campaign was undertaken at Fermi-lab, and aimed at characterizing the spatial resolution of a prototype QS2sTGC detector built in Israel [78]. The prototype consists of four sTGCstrip and pad layers. The position resolution measurements are done withthe strip layers. A 32 GeV pion beam is provided by Fermilab and usedto irradiate the sTGC detector prototype. The detector is placed betweenthe two arms of an external silicon pixel telescope with intrinsic resolutionof 5O3 µm. Each arm of the pixel telescope comprises three pixel detectorplanes, for a total of six pixel detector planes overall. Figure 8.5 gives aschematic overview of the experimental setup used during the Fermilab testbeam campaign and the coordinate system used for the ensuing analysis. Inparticular, the positive z-axis is in the same direction as the incoming beam,the y-axis is perpendicular to the strips in the chamber, and the x-y planecorresponds to the surface of the sTGC strip layer under study.1008.3. Test Beam ResultsBEAM	  ypix xpix zsTGC (0,0,0) y’pix x’pix Pixel (0,0,0) Figure 8.5: Schematic overview of the experimental setup used during theFermilab test beam campaign. The blue planes correspond to the pixeldetector telescope, and the red planes correspond to the four sTGC layersof the quadruplet. The dimensions are not to scale [78].Strip clustering is done by fitting a Gaussian to the charge distributioncoming from the set of strips having a signal above threshold and usingthe mean of the fitted Gaussian as the position of the cluster, ysTGC, 0.The strip-cluster multiplicities considered in this analysis are 3, 4, and 5.In addition to alignment corrections, a correction accounting for differentialnon-linearity effects in the detector is applied, based on the number of stripsin each cluster. The need for this correction stems from the discrete natureof the strips; the spatial coordinate measured by the sTGC results from adiscrete sampling of measured charge on the strips. The correction is derivedby fitting the residual distribution with respect to the pixel telescope trackas a function of relative y position, measured in number of strip pitches.The corrected position ysTGC is then given byysTGC = ysTGC, 0 − vi sin(2. yrelsTGC, 0)P (8.1)where ysTGC, 0 is the uncorrected position of the cluster, yrelsTGC, 0 is the1018.3. Test Beam Resultsrelative position of the cluster with respect to the closest inter-strip gapcentre, and the values of vi depend on the number of strips in the cluster,with i ∈ [3P 4P 5] corresponding to the strip-cluster multiplicity. The val-ues of vi are obtained by fitting the residual distribution as a function ofyrelsTGC, 0 with a sine wave and extracting the fitted amplitudes for the variousstrip-cluster multiplicities. Figure 8.6 shows the residual distribution as afunction of yrelsTGC, 0 before and after applying the differential non-linearitycorrection. Table 8.1 summarizes the amplitudes used for the differentialnon-linearity corrections applied to the strip-cluster sizes considered in theposition resolution analysis. As all amplitudes are consistent, a universalcorrection is applied using the amplitude for the strip-cluster multiplicity of3 for all strip-cluster multiplicities. [strip-pitch]relsTGC, 0y0.5− 0.4− 0.3− 0.2− 0.1− 0 0.1 0.2 0.3 0.4 0.5m]µ [pix - ysTGC, 0y400−300−200−100−0100200300400(a) [strip-pitch]relsTGC, 0y0.5− 0.4− 0.3− 0.2− 0.1− 0 0.1 0.2 0.3 0.4 0.5m]µ [pix - ysTGCy400−300−200−100−0100200300400(b)Figure 8.6: Residual distribution as a function of yrelsTGC, 0 before (left) andafter (right) applying the differential non-linearity correction [78].Strip-Cluster Multiplicity i Amplitude Parameter vi3 205 ± 94 206 ± 45 211 ± 5Table 8.1: Amplitudes of the differential non-linearity correction applied tothe three strip-cluster sizes considered in the position resolution analysis.In order to avoid multiple scattering effects within the sTGC chambers,only straight tracks are selected for the analysis. This is accomplished byrequiring that the track quality parameter of the selected pixel telescope1028.3. Test Beam Resultstracks be less than 10. The track quality parameter is based on the 2 ofthe pixel telescope track fit, and is depicted in Figure 8.7Pixel telescope track quality parameter0 20 40 60 80 100 120 14005001000150020002500300035004000Nu mb er  of  ev en tsFigure 8.7: Track quality parameter of pixel telescope tracks. Tracks usedin the analysis are required to have a track quality parameter less than 10.The main goal of the test beam campaign at Fermilab is to measurethe position resolution of the first full-size sTGC prototype detector. Theintrinsic position resolution for each sTGC layer is estimated in two ways.First, the extrapolated beam particle trajectory reconstructed by thetelescope, ypix, is compared with the measurements in each of the four sTGCquadruplet planes. A Gaussian model is adopted to fit the residual distri-bution between the sTGC position measurement and the pixel telescopeposition measurement, and the width of the Gaussian fit, , is quoted asthe resolution of the sTGC layer. Figure 8.8(a) shows the residual distri-bution obtained with the pixel telescope analysis for a representative run ofdata-taking.The second position resolution measurement uses the difference betweentwo independent measurements of the beam particle position determinedin two different sTGC layers. This standalone analysis assumes that two1038.3. Test Beam ResultssTGC strip layers are identical. The differential non-linearity correctionderived from the pixel telescope analysis is also applied to the standaloneanalysis. The width of the residual distribution of pairwise sTGC striplayer position measurements, pair, is then used to compute the positionresolution of a single layer,  = pairR√2. Figure 8.8(b) shows the residualdistribution obtained with the standalone analysis for a representative runof data-taking.m]µ [pix - ysTGCy400− 300− 200− 100− 0 100 200 300 400Events0100200300400500600 Run A, layer 4 mµ 0.8 ± = 43.4 σ(a)m]µ [2 / sTGC,L4 - ysTGC,L2y-400 -300 -200 -100 0 100 200 300 400E ve nt s0100200300400500600700σ = 40.8 ± 0.6 µm Run A(b)Figure 8.8: Residual distributions for the pixel analysis (left) and the stan-dalone analysis (right). The intrinsic sTGC detector position resolution isquoted as the width of the fitted Gaussian, .The data collected throughout the test beam campaign are analyzed byboth methods. Data-taking runs are labeled by a letter corresponding to aparticular location on the sTGC quadruplet where the beam is impinging forthat data-taking run. Figure 8.9 depicts the positions of the pion beam forthe various runs of data-taking during the test beam campaign. Runs G toN do not have synchronized data between the sTGC chamber and the pixeltelescope, so only standalone analysis residual measurements are availablefor these runs.1048.3. Test Beam ResultsFigure 8.9: Summary of the pion beam position for the Fermilab data-takingruns analyzed. Runs G to N do not have synchronized data between thesTGC chamber and the pixel telescope, so only standalone analysis residualmeasurements are available for these runs [78].Figure 8.10 shows the intrinsic sTGC resolution  for various periodsof data-taking during the Fermilab test beam campaign for both the pixeltelescope analysis and the standalone analysis. The black markers indicatepoints where data are taken with no expected degradation due to sTGCdetector support structure or calibration. The white markers indicate the1058.3. Test Beam Resultsresolution measurements for the remainder of the runs, and are not in-cluded in the calculation of the average position resolution. In both thepixel telescope and sTGC standalone analysis, the average position resolu-tion is about 45 µm, with an RMS spread of 8 µm, well below the 100 µmrequired by ATLAS for the NSW upgrade project.Run, layer0 1 2 3 4 5 6m]µ [σ3035404550556065707580A1 2 3 4B1 2 3 4C1 2 3 4D1 2 3 4E1 2 3 4F1 2 3 4(a)Run Identifier0 1 2 3 4 5 6 7 8 9 10 11 12m]µ [σ3035404550556065707580A B C E F G H I J K L M NsTGC Standalone Analysis(b)Figure 8.10: Intrinsic sTGC position resolution measured using the pixeltelescope analysis (left) and standalone analysis (right), for various periodsof data-taking during the Fermilab test beam campaign. Results for runswith no expected degradation due to sTGC detector support structure orcalibration are shown as black filled circles. The horizontal line representsthe average resolution for these runs, and the hashed band represents theRMS spread. Results for the remaining runs are shown as open circles.8.3.2 CERN Test Beam CampaignsFollowing the initial test beam campaign described in Section 8.3.1, a seriesof subsequent test beam campaigns was carried out at CERN. In particu-lar, a campaign with a QS2 module was carried out in October 2017, anda campaign with a QL1 module was carried out in September 2018. Bothcampaigns were held at the H8 beamline at CERN. The H8 beamline pro-vides 150 GeV muons to the sTGC module under test. While conceptuallysimilar to the experimental setup of the test beam campaign described inSection 8.3.1, the experimental setup used at CERN does not include apixel telescope, as shown in Figure 8.11. Triggering is performed by requir-ing the coincidence between two scintillators placed before and after thesTGC chamber under test.1068.3. Test Beam ResultsBEAM	  L1 L2 L3 L4 Sc0 Sc1 Pad n Figure 8.11: Schematic overview of the experimental setup used during theCERN test beam campaigns. The blue planes correspond to scintillatorsused for triggering, and the red planes correspond to the four sTGC layersof the quadruplet. The dimensions are not to scale [78].The coordinate system used for the analysis of the test beam data issuch that the positive z-axis is in the same direction as the incoming beam,the y-axis is perpendicular to the strips in the chamber, and the x-y planecorresponds to the surface of the sTGC strip layer under study.The main goal of these test beam campaigns, in addition to measuringthe spatial resolution of the prototype detectors, is to test the operationof full-sized sTGC quadruplets with complete 4-layer VMM readout frompads and strips. In particular, the efficiency of the pads is investigated, andthe performance of sTGC chambers is characterized under high-backgroundenvironments. Two distinct clustering algorithms are employed during theoffline analysis of the test beam data. The first clustering algorithm is similarto the one described in Section 8.3.1, where the strip charge distribution isfit with a Gaussian function, and the mean of this Gaussian is taken as theysTGC position. The second clustering algorithm uses the centroid of the1078.3. Test Beam Resultsstrip charge distribution, defined asysTGC =∑chitsi=0 Xiyi∑chitsi=0 XiP (8.2)where chits is the total number of hits in a given sTGC layer, and Xi isthe charge of the ith hit with position yi. No major difference is observedbetween the two clustering algorithms. As no pixel telescope is availableto calculate the correction parameters, the differential non-linearity correc-tion is not applied in these test beam campaigns. Figure 8.12 shows thebeam profile recorded by the QL1 module pads. In particular, the beam isconcentrated on one pad within the sTGC layer.050001000015000200002500035000Layer 1 as seen when looking into the beam1 2 3 4 5 6 7Pad x position in layer 124681012141618P ad  y  po si t i on  i n  l a ye r 13000Nu mb er  of  Hi t sFigure 8.12: Beam profile from the QL1 module pads operating at 2O8 kV.The beam is concentrated on one pad within the sTGC layer. The otherpads with content 0 are instrumented with readout electronics, but do notregister any hits. The pads with no entries (white) are not instrumentedwith readout electronics.The same beam can also be profiled using the sTGC strips, as shown inFigure 8.13. The dips in the profile at strip y positions of 220 and 280 arecaused by the spacer buttons within the sTGC chamber.1088.3. Test Beam Results50 100 150 200 250 300 350 400Strip y position in layer 1050100150200250310×C ou nt s50 100 150 200 250 300 350 400Strip y position in layer 200.20.40.60.81C ou nt sh_strips_hitsProfile_layer2h_strips_hitsProfile_layer2Entries  0Mean        0Std Dev         050 100 150 200 250 300 350 400Strip y position in layer 300.20.40.60.81C ou nt sh_strips_hitsProfile_layer3h_strips_hitsProfile_layer3Entries  0Mean        0Std Dev         050 100 150 200 250 300 350 400Strip y position in layer 400.20.40.60.81C ou nt sh_strips_hitsProfile_layer4h_strips_hitsProfile_layer4Entries  0Mean        0Std Dev         0Figure 8.13: Beam profile from the QL1 module strips operating at 2O9 kV.The dips in the profile at strip y positions of 220 and 280 are caused by thespacer buttons within the sTGC chamber.The signals induced by charged particles traversing the sTGC chamberare related to the charge deposited within the chamber by the particles. Thecharge spectrum should follow a Landau distribution [79]. Figure 8.14 showsthe charge spectrum recorded by the QL1 module pads.1098.3. Test Beam Results0 200 400 600 800 1000ADC pad charge in layer 1010002000300040005000E ve nt sFigure 8.14: Charge spectrum from the QL1 module pads operating at2O8 kV. The red line corresponds to an overlaid Landau distribution.In order to reconstruct tracks, a feature extraction technique used inimage analysis, the Hough transform [80, 81], is employed. In particular,tracks are parameterised as straight lines with two parameters:ysTGC = mz + bP (8.3)where the two parameters are the slope m and the intercept b of the line.For each layer in the quadruplet, the ysTGC and z positions are measured.From these measurements, all possible values of the slope m and intercept bwhich parameterise a line compatible with the ysTGC and z measurements fora given sTGC layer are iterated over, and the so-called accumulator is filledwith the corresponding (bPm) pair. Each point in the accumulator spacecorresponds to a line going through the measured ysTGC and z positions fora given sTGC layer. The point in the accumulator space where the lines ofall four sTGC layers intersect corresponds to the values of the (bPm) pairof the straight line passing through all four measured points. Figure 8.15illustrates the conceptual procedure of the Hough transform using the (P r)parameterisation of a straight line instead of the (bPm) parameterisation1108.3. Test Beam Resultsused in this analysis:r = z cos  + ysTGC sin O (8.4)Each coloured line represents a particular combination of  and r thatis compatible with the measured values of ysTGC and z. Possible straightlines (coloured lines) are iterated over for each data point (black points), inorder to fill an accumulator. Clearly, the line best describing all three blackpoints, i.e., independent measurements of ysTGC and z, is the blue line.Θ = 15°r = 189 Θ = 45°r = 407Θ = 75°r = 340Θ   r    15  189.030  282.045  355.760  407.375  429.4Θ   r    15  318.530  376.845  407.360  409.875  385.3Θ   r    15  419.030  443.645  438.460  402.975  340.1Figure 8. 5: Illustration of the Hough transform technique used to recon-struct tracks during the sTGC test beam campaigns. Each diagram (left,centre, right) represents the various straight line possibilities (red, yellow,green, blue, magenta) for a particular measurement of ysTGC and z (blackpoints) [82].8.3.3 Pulser Board TestsAs mass production of sTGC modules progresses, it is imperative to test thequality of each detector module. In particular, it is crucial to test the elec-trical connectivity and functionality of all readout elements of a quadruplet:pads, strips, and wires. This is accomplished by using the so-called pulserboard. The experimental setup used at the Weizmann Institute of Sciencein Israel in order to carry out pulser board tests is shown in Figure 8.16.1118.3. Test Beam ResultsTitle TextPulse GeneratorOscilloscope MonitorQuadruplet Under TestPulser Board & ArduinoAdapter BoardFigure 8.16: Experimental setup used for pulser board tests at the WeizmannInstitute of Science.A high-voltage signal is injected into the chamber. The signal is a squarewave with a peak-to-peak amplitude of 20V. The signal propagates throughthe chamber, and the response signal from the external adapter boards ismeasured. The signals coming from the various quadruplet elements are pro-cessed through the pulser board and digitized with an oscilloscope. As theanalog signal coming from the chamber is inherently noisy, the digitized sig-nal produced by the oscilloscope remains noisy, as shown in Figure 8.17(a).The pulser board software includes an averaging function that smooths thenoisy waveform from the oscilloscope and produces a cleaner signal for anal-ysis use, as shown in Figure 8.17(b). The pulser board tests provide theability to detect bad channels in the sTGC module by distinguishing goodpulses from pulses such as the one shown in Figure 8.17(c) and reporting thisto the user. In particular, the amplitude, mean, and variance of each chan-nel’s pulse is computed, and good channels will tend to have clear regionsof high variance and large amplitude.1128.3. Test Beam ResultsTitle Text(a)Title Text(b) (c)Figure 8.17: Examples of pulses obtained during pulser board tests: noisypulse coming from the oscilloscope before the averaging procedure (left),clean pulse after averaging procedure (centre), and signal from dead channelwith no clear peak (right).Currently used at the Weizmann Institute of Science, the pulser boardtesting system allows the construction site to assess the quality of con-structed sTGC chambers and the functionality of their readout electron-ics. If channels on the chamber are flagged as faulty by pulser board tests,bad connections can, e.g., be re-soldered in order to ensure a fully functionalchamber upon arrival at CERN and integration into the NSW of the ATLASdetector.113Chapter 9Search for New High-MassPhenomenaThe search presented in this dissertation selects events based on a number ofcriteria aiming to detect any potential signal of BSM physics. The dimuonfinal state is advantageous because of its clean signature and simplicity.In this chapter, Section 9.1 describes the event selection applied to bothMC simulation and data. Section 9.2 presents the discriminating variableused for this search. Comparisons between MC simulation and data arepresented for various kinematic distributions relating to the dimuon systemin Section 9.3.9.1 Event SelectionIn order to select events with two muons in the final state, a series of cutsis applied to each event. A successful event satisfies all of these cuts. Threetypes of cuts are applied in this analysis: event-level cuts, muon-level cuts,and cuts relating to the dimuon system.In terms of event-level cuts, each event is required to be in the GRL, asdefined in Section 7.3.1. Next, each event passes at least one of the muontriggers mu26_ivarmedium (mu26_imedium for 2015 data) or mu50, whichrequire at least one isolated muon with pT greater than 26 GeV or one muonwith pT greater than 50 GeV, respectively. Event cleaning is then applied,where events are rejected if they are flagged as incomplete. An incompleteevent is one where noise bursts or data corruption occurs in the EM orhadronic calorimeter. At least one reconstructed proton-proton interactionvertex is required for each event, with the primary vertex defined as the onewith the highest sum of track pT squared.Each event is required to contain at least two muons with pT greaterthan 30 GeV satisfying the high-pT WP described in Section 6.1. Muonsare also required to fulfill track-based isolation requirements, in order toreduce the background from light and heavy hadron decays inside jets. In1149.1. Event Selectionparticular, the quantity pvarcone30T RpT is used to ensure a 99% efficiency thatis constant across  and pT. The quantity pvarcone30T is the scalar sum ofthe transverse momenta of the tracks with pT S 1 GeV within a cone ofsize ∆g = min(10 GeVRpTP 0O3) around the muon of transverse momentumpT. The dimuon pair is selected from the muons in the event using thepair having the highest scalar sum pT. The pair must have opposite signcharge, as well as have an invariant mass larger than 80 GeV, because thesearch is mainly interested in the higher invariant mass spectrum. Figure 9.1shows the number of dimuon events passing the event selection, normalizedto the integrated luminosity, for each data-taking run during the 2015-2016data-taking period.Run276262276329276336276416276511276689276778276790276952276954278880278912278968279169279259279279279284279345279515279598279685279813279867279928279932279984280231280273280319280368280423280464280500280520280614280673280753280853280862280950280977281070281074281075281317281385281411282625282631282712282784282992283074283155283270283429283608283780284006284154284213284285284420284427284484]-1Muon Channel Yield [Events/pb200250300350400450500550 Work In ProgressATLAS = 13 TeV, 2015 DatasetsDilepton Search SelectionD E F G H JRun297730298595298609298633298687298690298771298773298862298967299055299144299147299184299243299584300279300345300415300418300487300540300571300600300655300687300784300800300863300908301912301918301932301973302053302137302265302269302300302347302380302391302393302737302831302872302919302925302956303007303079303201303208303264303266303291303304303338303421303499303560303638303832303846303892303943304006304008304128304178304198304211304243304308304337304409304431304494305380305543305571305618305671305674305723305727305735305777305811305920306269306278306310306384306419306442306448306451307126307195307259307306307354307358307394307454307514307539307569307601307619307656307710307716307732307861307935308047308084309375309390309440309516309640309674309759310015310247310249310341310370310405310468310473310634310691310738310809310863310872310969311071311170311244311287311321311365311402311473311481]-1Muon Channel Yield [Events/pb200250300350400450500550 Work In ProgressATLAS = 13 TeV, 2016 DatasetsDilepton Search SelectionA B C D E F G I K LFigure 9.1: Number of events passing the event selection, normalized to theintegrated luminosity, as a function of run number during the 2015 (top)and 2016 (bottom) data-taking periods.1159.1. Event Selection9.1.1 Background ProcessesThe background processes for this analysis are modelled using MC simu-lations. The three main background contributions to this search are, inorder of importance, DY production, top quark production, and diboson(WW , WZ, ZZ) production. The multi-jet and W+ jets SM backgroundprocesses are found to be negligible and are not considered in this search. Asummary of the various properties of the background processes consideredis presented in Table 9.1. For each background sample, this table presentsthe MC generator used, the order in QCD at which the sample is generatedand corrected, the showering program employed, and the PDFs adopted. Inparticular, the DY and top quark backgrounds are generated and showeredusing Powheg [69] and Pythia [70, 71], respectively, while the dibosonbackground is generated and showered using Sherpa [68]. All backgroundprocesses are generated at NLO with the CT10 [83] PDFs. The DY and topquark backgrounds are corrected to Next-to-Next-to-Leading Order (NNLO)with the CT14NNLO [84] PDFs, while the diboson background is correctedto NLO. In order to gain statistics in regions of phase space of interest,the DY and diboson processes are generated in slices of dimuon invariantmass. Once the background processes are generated, the ATLAS detectorresponse is simulated with GEANT4 [85]. Momentum calibration and reso-lution smearing are applied to the muon objects in the MC samples, in orderto match the performance observed in data [53]. The background simula-tions then pass through the same event selection discussed in Section 9.1.Finally, data collected by ATLAS is compared with the sum of the simu-lated backgrounds, in order to look for possible data excesses, which wouldindicate the presence of new BSM physics.Process Generator Order Corrected Parton Shower PDFsqq¯ → ZR∗ → +− Powheg v2 [69] NLO NNLO Pythia 8.186 [71] CT10 [83]tt¯→ m, Wt→ m Powheg v2 [69] NLO NNLO Pythia 6.428 [70] CT10 [83]WWPWZPZZ → mR,R Sherpa 2.1.1 [68] NLO NLO Sherpa 2.1.1 [68] CT10 [83]Table 9.1: Summary of background processes considered in this search. Thecolumns from left to right give the process of interest, generator, matrixelement order, parton shower program, and PDFs adopted.9.1.2 Signal ProcessesVarious BSM signal processes are generated, in order to compare discrimi-nating variable distributions with collected data, in the hope of finding com-1169.1. Event Selectionpatibility between new physics and data. Signal samples for this analysisare obtained by reweighting a LO DY sample. This is validated by compar-ing the reweighted signal templates to dedicated signal samples generatedat specific pole masses. For CI signal samples, the DY background estimateis used below 300 GeV, as a negligible amount of new physics is expectedin this range. The simulated signal samples are fed into the same GEANT4program as the background processes, in order to simulate the ATLAS de-tector response. A summary of the various properties of the signal processesconsidered is presented in Table 9.2.Process Generator Order Corrected Parton Shower PDFsqq¯ → ZR∗ → +− Pythia 8.186 [71] LO NNLO Pythia 8.186 [71] NNPDF23LO [86]qq¯ → Z ′ → +− Pythia 8.186 [71] LO NNLO Pythia 8.186 [71] NNPDF23LO [86]CI: qq¯ → +− Pythia 8.186 [71] LO NNLO Pythia 8.186 [71] NNPDF23LO [86]Table 9.2: Summary of signal processes considered in this search. Thecolumns from left to right give the process of interest, generator, matrixelement order, parton shower program, and PDFs adopted.Figure 9.2 shows the dimuon invariant mass distribution for Z ′ signals ofvarying pole mass. A notable feature of these distributions is the increasingtails at lower invariant mass for higher Z ′ pole masses. This is due to thePDFs, hence the moniker parton luminosity tails. Indeed, for particles witha nonzero natural width generated at masses close to the collision energy,the PDFs favor lower-mass collisions. This leads to an increased fractionof off-shell production for signal events as the kinematic production limitis approached. The size of the parton luminosity tails increases with theresonance width. The parton luminosity tails produce a noticeable impacton cross-section limit values presented in Chapter 11 when at least 5− 10%of events are in the parton luminosity tail.1179.1. Event SelectionDimuon Invariant Mass [GeV]100 200 300 1000 2000-1Events / pb-810-710-610-510-410-310-210-1101 ATLAS Work In Progress = 13 TeVsχModel: Z’1 TeV2 TeV3 TeV4 TeV5 TeV6 TeVFigure 9.2: Invariant mass distribution of the dimuon system for various Z ′pole masses. As the pole masses get larger, the parton luminosity tails atlower invariant mass become more important.9.1.3 Higher-Order CorrectionsIn addition to the precise matrix element calculations provided by the MCgenerators, higher-order corrections to the main DY background process andthe various signal processes are desirable, to the extent that they are com-putationally feasible. In this analysis, mass-dependent K-factors are usedin order to obtain a better estimate of the cross-sections of the signal andbackground processes. In particular, higher-order QCD and EW correctionsare applied using K-factors defined asK(m) =best(m)MC(m)P (9.1)where “best” refers to an external NNLO QCD cross-section calculationusing the CT14NNLO PDF set, and including missing higher-order EWcorrections for the Powheg samples. The NLO EW corrections are omittedfor the Pythia samples, as they are not available. The nominal higher-order1189.1. Event SelectionPDFs used to compute the final K-factors are the CT14NNLO PDFs. Thereare four main sets of K-factors applied to the DY background and varioussignal processes in this analysis.First, K-factors are calculated in order to correct the DY backgroundand signal cross-sections from LO to NNLO in QCD with respect to theNNPDF23LO PDFs generated with Pythia 8. Second, to correct theDY cross-section from NLO to NNLO in QCD with respect to the CT10PDFs generated with Powheg + Pythia 8, K-factors are calculated us-ing VRAP0.9 [87]. Third, LO to NLO EW corrections are calculated usingMcsanc [88]. Finally, K-factors related to LO Photon-Induced (PI) cor-rections, computed using MRST2004QED [89], take into account that thegenerated DY samples do not include these QED effects. Figures 9.3 and 9.4illustrate the invariant mass dependence of the various higher-order correc-tions considered in this analysis.NNLO-to-NLO k-factors shown uses the proton parton distribution functions MSTW2008nnlo atNNLO QCD and CT10 at NLO QCD (a similar observation was obtained for CC DY but is notshown here) [299]. An updated version of DY NLO 1.4 is now available which shows for totalLO QCD NC DY cross sections in the mass range 60 to 5000 GeV an excellent agreement [299],however, more detailed cross checks are worthwhile also for CC DY production and specificphase space cuts also for the resonant region where the experimental precision is very high (lessthan a few percent). For example, the fiducial resonant W cross section predictions varied within1% between FEWZ and DYNNL (using the same SM and electroweak par meters for bothprograms) as reported by ATLAS [94] already in 2012.The QCD NNLO-to-NLO k-factor for LHC Run II a Ôs = 14 TeV are illustr ed for NCDrell Yan production in Fig. III.8 (right). The QCD k-factors show a wide spread for invariantmasses larger than about 4 TeV reflecting the lack of knowledge in the proton parton distributionfunctions at high Bjorken-x values. The corresponding spread in the predictions at NNLO QCDusing modern PDFs with respect to the CT10nnlo PDF is shown in Fig. III.8 (left).0.50.60.70.80.911.11.21.31.41.510 102 10 3 10 4CT10nnloHERAPDF15nnloJR09nnloABM11nnloMSTW08nnloNNPDF2.3nnlo (0.118)Mll (GeV)NNLO PDF/CT10 NNLOCT10nnloHERAPDF15nnloJR09nnloABM11nnloMSTW08nnloNNPDF2.3nnlo (0.118)Mll (GeV)NNLO PDF/CT10 NNLO00.511.522.5310 102 10 3 10 40.50.60.70.80.911.11.21.31.41.51000 2000 3000 4000 5000 6000 7000 8000 9000 10000CT10nnloHERAPDF15nnloMSTW08deutCPJR09nnloABM11nnloMSTW08nnloNNPDF2.3nnlo (0.118)Mll (GeV)NNLO PDF/CT10CT10nnloHERAPDF15nnloMSTW08deutCPJR09nnloABM11nnloMSTW08nnloNNPDF2.3nnlo (0.118)Mll (GeV)NNLO PDF/CT1000.511.522.531000 2000 3000 4000 5000 6000 7000 8000 9000 10000Fig. III.8: Invariant mass dependence of the total NC Drell Yan production cross section predictionsfor modern NNLO PDFs w.r.t. the CT10nnlo PDF (left plots) and the QCD NNLO-to-NLO QCD k-factors w.r.t. to CT10 NLO QCD (right plots). The lower and upper panels show the same quantitiesbut with dierent y-axis ranges from 0 to 3 and 0.5 to 1.5), respectively. The LHC energy is Ôs = 14TeV. Calculations are based on VRAP 0.9 and the NNLO (NLO) PDFs [276] as indicated in the legend.While the QCD k-factors are rather insensitive to the choice of the SM model inputs andthe electroweak parameter scheme, care has to be taken for the absolute cross section predictionsincluding those NLO electroweak corrections which are not addressed already in the unfolding ofthe experimental data. It is well know from the literature, see e.g. [126] for a brief introductioninto the most commonly used electroweak schemes, that the Gµ electroweak scheme is well suitedfor Drell Yan production.In the calculations presented here, the electroweak scheme is set to the Gµ scheme accord-ing to the details outlined in [126] and calculated by SANC [300]. A summary of the values isgiven in Tab. III.2.The CKM values are taken from electroweak fits based on all precision observables asreported in [301]. Here the values of the CKM fit [301] are used. The pseudo-rapidity ÷¸distribution of resonant single W± production is sensitive to the choice of the value of Vcs.Fig.III.9 illustrates the eect of changing the fitted Vcs to the currently best experimentally81Figure 9.3: Invariant mass dependence of the total DY production cross-se ion predictions for mode n NNLO PDFs with res ect to the CT10NNLOPDFs (left) and QCD NNLO-to-NLO K-factors with respect to theCT10NLO PDFs (right). The top and bottom panels show the same quan-tities, but with different y-axis ranges. The calculations are carried out as-suming a centre-of-m ss ene gy of √s = 14 TeV and ar bas d on VRAP0.9and the PDFs as indicated in the legend [90].1199.2. Dimuon Invariant Masseach invariant mass bin: The central value of the combined NNLO QCD and NLO EW exceptQED FSR prediction is taken from the additive approach while the dierence to the factorisedapproach results is taken as a double sided systematic uncertainty estimate. The resulting meanHO EW except QED FSR corrections with those symmetric uncertainties are shown in Fig.III.12(lower plot) for the expected LHC Run II at Ôs = 14 TeV. Also illustrated in Fig. III.12 (upperplot) is the rather weak energy dependence for the HO EW except QED FSR corrections.-30-25-20-15-10-500 2000 4000 6000 8000 100007 TeV NLO CT1014 TeV NLO CT107 TeV LO MSTWnnlo14 TeV LO MSTWnnloMll (GeV)δ miss (%)14 TeV EW systematicMll (GeV)δ miss (%)-30-25-20-15-10-500 2000 4000 6000 8000 10000Fig. III.12: HO EW except QED FSR (”miss in %) corrections for NC Drell Yan production. Theresults of the factorised (additive) approach based on LO QCD (NLO QCD) for Ôs = 7 TeV are shownin the upper plot with empty squares (empty circles) and for 14 TeV with full squares (full circles). Anestimate of the EW except QED FSR systematic uncertainty, see text, is shown in the lower plots forÔs = 14 TeV. All calculations are based on FEWZ 3.1.b2 and the PDFs as indicated in the legend.2.4 Matching Monte Carlo programs and external calculationsThe methodologies discussed in the previous chapter work reliably for total cross sections andwell defined variables like the invariant mass or the pseudo-rapidity of the final state leptons,but fail e.g for variables like the pT (¸) or pT (Z,W ) which rely on a modelling of soft gluonresummation and parton shower eects usually taken care of in Monte Carlo programs. Whilethe LHC Monte Carlo programs are powerful tools for the description of complex QCD processes,they are not very well defined w.r.t. the electroweak part and the EW parameter schemeused. Here, a study has been performed to understand the matching of a well-defined externalQCD calculation using the Gµ scheme with parameters according to Tab. III.2 and currentlyPDG guided EW parameter settings as used in LHC Monte Carlo generations. Fig. III.13shows the deviations between external NLO (LO) QCD predictions using FEWZ 3.1.b2 with86Figure 9.4: Higher-order EW corrections for DY production. The re-sults of the factored (additive) approach based on LO QCD (NLO QCD)for √s = 7 TeV are shown with empty squares (empty circles) and for√s = 14 TeV with full squares (full circles). All calculations are based onFEWZ 3.1.b2 and the PDFs as indicated in the legend [90].9.2 Dimuon Invariant MassThe discriminating variable used in this analysis is the invariant mass ofthe final state dimuon pair. The invariant mass is calculated by assigning afour-vector to each of the two muons in the final state and calculatingm2 = (p1 + p2)2P (9.2)where p1 and p2 are the four-vectors of the final state muons. FromSection 5.5.3, the error on m can be approximated asm = m√(p1Tp1T)2+(p2Tp2T)2O (9.3)Figure 9.5 shows the dimuon invariant mass distribution for the analysisdiscussed in this dissertation. A summary of the event yields in specific mranges s given in Table 9.3.1209.2. Dimuon Invariant MassEvents2−101−10110210310410510610710 Data*γZ/Top QuarksDiboson (3 TeV)χZ’ (4 TeV)χZ’ (5 TeV)χZ’ATLAS-1 = 13 TeV, 36.1 fbsDimuon Search SelectionData / Bkg0.60.811.21.4Dimuon Invariant Mass [GeV]100 200 300 1000 2000  (post-fit)Data / Bkg0.60.811.21.4Figure 9.5: Invariant mass distribution of the dimuon system. The data areshown as black markers, while the SM background processes are shown asfilled histograms. For illustration purposes, three different Z ′ signals areadded on top of the background distribution. The shaded band in the lowerpanels illustrates the total systematic uncertainty.1219.3. Kinematic Distributionsm [GeV ] 80–120 120–250 250–400 400–500 500–700DY 10 700 000 ± 600 000 177 900 ± 10 000 12 200 ± 700 1770 ± 120 1060 ± 80Top quarks 24 700 ± 1700 34 200 ± 2400 6100 ± 500 830 ± 70 401 ± 33Dibosons 26 000 ± 2800 5400 ± 600 910 ± 100 155 ± 17 93 ± 11Total SM 10 800 000 ± 600 000 218 000 ± 10 000 19 200 ± 900 2760 ± 140 1550 ± 90Data 11 321 561 224 703 19 239 2766 1532Z ′ (4 TeV) 0.00873 ± 0.00032 0.0334 ± 0.0015 0.0441 ± 0.0021 0.0246 ± 0.0014 0.052 ± 0.004Z ′ (5 TeV) 0.00347 ± 0.00014 0.0137 ± 0.0006 0.0151 ± 0.0007 0.0105 ± 0.0006 0.0176 ± 0.0012m [GeV ] 700–900 900–1200 1200–1800 1800–3000 3000–6000DY 263 ± 23 110 ± 11 37 ± 4 5.4 ± 0.8 0.30 ± 0.07Top quarks 68 ± 6 24.5 ± 3.0 5.3 ± 0.9 0.11 ± 0.08 Q 0.001Dibosons 24.3 ± 2.9 9.8 ± 1.2 3.2 ± 0.4 0.45 ± 0.07 0.0184 ± 0.0035Total SM 355 ± 24 144 ± 11 45 ± 4 6.0 ± 0.8 0.32 ± 0.07Data 322 141 48 4 0Z ′ (4 TeV) 0.0362 ± 0.0026 0.048 ± 0.004 0.067 ± 0.006 0.186 ± 0.022 1.24 ± 0.19Z ′ (5 TeV) 0.0153 ± 0.0011 0.0185 ± 0.0015 0.0233 ± 0.0021 0.0258 ± 0.0029 0.118 ± 0.020Table 9.3: Expected and observed event yields in different m intervals.The quoted errors correspond to the combined statistical, theoretical, andexperimental systematic uncertainties. Expected event yields are reportedfor the Z ′ model, for two values of the pole mass.9.3 Kinematic DistributionsOnce the event selection is defined, kinematic variables can be examined,in order to compare MC simulations of expected background processes withcollected data. Below are the main kinematic distributions used in theanalysis. In particular, Figures 9.6 to 9.11 show the kinematic distributionsused to validate that MC simulations are in agreement with data.1229.3. Kinematic DistributionsEvents2−101−10110210310410510610710 Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeV [GeV]TLeading Muon p30 40 100 200 300 1000 2000Data / Bkg0.60.811.21.4(a)Events2−101−10110210310410510610710 Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeV [GeV]TSubleading Muon p30 40 100 200 300 1000 2000Data / Bkg0.60.811.21.4(b)Figure 9.6: Reconstructed muon pT distribution for the leading (top) andsubleading (bottom) muon after event selection. The distributions are shownfor dimuon invariant masses greater than 120 GeV.The data are shown asblack markers, while the SM background processes are shown as filled his-tograms. For illustration purposes, three different Z ′ signals are added ontop of the background distribution. The shaded band in the lower panelsillustrates the total systematic uncertainty.1239.3. Kinematic DistributionsEvents2−101−10110210310410510610710 Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS-1 = 13 TeV, 36.1 fbsDilepton Search Selection > 120 GeVµµm [GeV]TLeading & Subleading Muon p30 40 100 200 300 1000 2000Data / Bkg0.60.811.21.4(a)Events2−101−10110210310410510610710Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeV [GeV]TDimuon pair p20 30 40 100 200 1000 2000Data / Bkg0.60.811.21.4(b)Figure 9.7: Reconstructed muon pT distribution for the sum of the leadingand subleading muons (top) and dimuon system (bottom) after event selec-tion. The distributions are shown for dimuon invariant masses greater than120 GeV.The data are shown as black markers, while the SM backgroundprocesses are shown as filled histograms. For illustration purposes, threedifferent Z ′ signals are added on top of the background distribution. Theshaded band in the lower panels illustrates the total systematic uncertainty.1249.3. Kinematic DistributionsEvents050001000015000200002500030000Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeVηLeading Muon 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(a)Events050001000015000200002500030000Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeVηSubleading Muon 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(b)Figure 9.8: Reconstructed muon  distribution for the leading (top) and sub-leading (bottom) muon after event selection. The distributions are shownfor dimuon invariant masses greater than 120 GeV.The data are shown asblack markers, while the SM background processes are shown as filled his-tograms. For illustration purposes, three different Z ′ signals are added ontop of the background distribution. The shaded band in the lower panelsillustrates the total systematic uncertainty.1259.3. Kinematic DistributionsEvents0100002000030000400005000060000Data*γZ/Top QuarksDibosonATLAS-1 = 13 TeV, 36.1 fbsDilepton Search Selection > 120 GeVµµmηLeading & Subleading Muon 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(a)Events020004000600080001000012000 Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeVηDimuon pair 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(b)Figure 9.9: Reconstructed muon  distribution for the sum of the leadingand subleading muons (top) and dimuon system (bottom) after event selec-tion. The distributions are shown for dimuon invariant masses greater than120 GeV.The data are shown as black markers, while the SM backgroundprocesses are shown as filled histograms. For illustration purposes, threedifferent Z ′ signals are added on top of the background distribution. Theshaded band in the lower panels illustrates the total systematic uncertainty.1269.3. Kinematic DistributionsEvents02000400060008000100001200014000160001800020000Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeVφLeading Muon 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(a)Events02000400060008000100001200014000160001800020000Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeVφSubleading Muon 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(b)Figure 9.10: Reconstructed muon ϕ distribution for the leading (top) andsubleading (bottom) muon after event selection. The distributions are shownfor dimuon invariant masses greater than 120 GeV.The data are shown asblack markers, while the SM background processes are shown as filled his-tograms. For illustration purposes, three different Z ′ signals are added ontop of the background distribution. The shaded band in the lower panelsillustrates the total systematic uncertainty.1279.3. Kinematic DistributionsEvents0500010000150002000025000300003500040000Data*γZ/Top QuarksDibosonATLAS-1 = 13 TeV, 36.1 fbsDilepton Search Selection > 120 GeVµµmφLeading & Subleading Muon 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(a)Events020004000600080001000012000140001600018000Data*γZ/Top QuarksDiboson (2 TeV)χZ’ (3 TeV)χZ’ (4 TeV)χZ’ATLAS Work In Progresss = 13 TeV, 36.1 fb-1 Dilepton Search Selection mµµ > 120 GeVφDimuon pair 3− 2− 1− 0 1 2 3Data / Bkg0.911.1(b)Figure 9.11: Reconstructed muon ϕ distribution for the sum of the leadingand subleading muons (top) and dimuon system (bottom) after event selec-tion. The distributions are shown for dimuon invariant masses greater than120 GeV.The data are shown as black markers, while the SM backgroundprocesses are shown as filled histograms. For illustration purposes, threedifferent Z ′ signals are added on top of the background distribution. Theshaded band in the lower panels illustrates the total systematic uncertainty.128Chapter 10Systematic UncertaintiesThere are three distinct types of systematic uncertainties considered in thisanalysis: those encapsulating experimental effects, those due to theoreticaleffects, and those pertaining to the PDFs of the incoming partons. Theexperimental systematic uncertainties are applied to both signal and back-ground processes, whereas the theoretical and PDF-related systematic un-certainties are applied to the background processes only. The systematicvariations are estimated as a function of m, and for each m bin theuncertainty applied is the larger between the up and down variations. Theoverall uncertainty related to each effect is the symmetric up/down variationenvelope, expressed as a function of dimuon invariant mass. In all cases, thenon-negligible systematic uncertainties are treated as nuisance parametersin the statistical analysis described in Chapter 11. This chapter describesall of the systematic uncertainties considered in the search for new BSMphysics presented in this dissertation. Section 10.1 outlines the experimen-tal systematic uncertainties, Section 10.2 presents the theoretical systematicuncertainties, and Section 10.3 discusses the systematic uncertainties relatedto the PDFs of the incoming partons. Section 10.4 gives a quantitative sum-mary of the systematic uncertainties considered in the analysis presented inthis dissertation.10.1 Experimental UncertaintiesThe experimental systematic uncertainties considered in this analysis areapplied to both signal and background simulation samples. They includethe beam energy uncertainty, the luminosity measurement uncertainty, thepile-up reweighting uncertainty, and the trigger efficiency uncertainty. Fur-thermore, the uncertainties on the muon momentum scale, the muon mo-mentum resolution (both in the ID and the MS), and the muon isolationefficiency are also evaluated. The uncertainty on the efficiency to reconstructand select muons is also taken into account.The dominant experimental systematic uncertainty in this search is dueto the reconstruction and selection efficiency of muons. In particular, the12910.1. Experimental Uncertaintiesuncertainty related to the high-pT WP selection is larger with increasingpT due to the cut on the relative qRp error. The uncertainty related to themuon isolation and trigger is estimated by varying the data-to-simulationSFs applied to simulation by their respective uncertainties. The trigger SFsand their uncertainties are presented in Chapter 7. The systematic uncer-tainties related to the scale and resolution of the ID and MS pT measure-ments are obtained by varying the parameters of the pT smearing describedin Section 5.5.2 by their appropriate uncertainties, and taking the relativedifference between the two estimates as the uncertainty. An uncertaintyon the beam energy of 0.65% is estimated and included. A flat systematicuncertainty of 3.2% is assessed due to the uncertainty on the luminositymeasurement. The uncertainty related to pile-up is estimated by varyingthe mean number of interactions per bunch crossing in simulation and tak-ing the relative difference between the nominal and varied simulation as theuncertainty.Figures 10.1 and 10.2 depict the magnitude of each experimental system-atic uncertainty source, expressed as a fraction of the signal or backgroundconsidered. The systematic uncertainty on the trigger efficiency, the muonmomentum scale, and the pile-up reweighting are neglected in the statisti-cal analysis, because of their negligible contribution. All other sources ofexperimental systematic uncertainty are used as nuisance parameters in thestatistical analysis described in Chapter 11.13010.1. Experimental UncertaintiesDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030Reco. UpReco. DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030Iso UpIso DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030Trig UpTrig DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030Scale UpScale DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030ResID UpResID DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030ResMS UpResMS DnATLAS Work In Progress = 13 TeVsFigure 10.1: Systematic uncertainties due to experimental sources relatedto muon performance. Shown are, from left to right and top to bottom, theuncertainty related to muon reconstruction and selection, muon isolation,muon trigger, muon momentum scale, muon momentum resolution in theID, and muon momentum resolution in the MS.13110.2. Theoretical UncertaintiesDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030Beam Energy UpBeam Energy DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030Luminosity UpLuminosity DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PRW UpPRW DnATLAS Work In Progress = 13 TeVsFigure 10.2: Systematic uncertainties due to experimental sources related toaccelerator performance. Shown are the uncertainty related to beam energy(top left), luminosity (top right), and pile-up (bottom).10.2 Theoretical UncertaintiesThe theoretical systematic uncertainties considered in this analysis are ap-plied to background simulation samples. They include the variations in thes strong coupling constant, the differences between the additive and fac-tored treatment of the electroweak corrections (the additive treatment isused as the nominal treatment in this search), and PI corrections. In addi-tion, the theoretical systematic uncertainties on the normalization of the tt¯and diboson background contributions are evaluated.The systematic uncertainty related to the strong coupling constant sis evaluated using the VRAP program, by varying the nominal input valueof s = 0O118 by ± 0O003. The uncertainty related to PI corrections isestimated by taking into account the uncertainties on the quark massesand on the photon PDF. This search nominally uses the additive treat-13210.2. Theoretical Uncertaintiesment when combining higher-order electroweak and QCD corrections, i.e.,(1 + EW + QCD). The systematic uncertainty resulting from electroweakcorrections is estimated by comparing the additive treatment to the mul-tiplicative treatment of this combination, i.e., ((1 + EW)(1 + QCD)),and taking the difference between the two treatments as the uncertainty.Additional theoretical systematic uncertainties are assigned to the estima-tion of the tt¯ and diboson backgrounds. They are derived following thePDF4LHC prescription [91]. In particular, the variation of the factorizationand renormalization scales are taken into account.Figure 10.3 depicts the contribution of each theoretical systematic un-certainty to the total systematic uncertainty used in the statistical analysisdescribed in Chapter 11. All theoretical systematic uncertainties are usedas nuisance parameters in the statistical analysis, except the diboson nor-malization systematic uncertainty, which is neglected.13310.2. Theoretical UncertaintiesDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030alphaS UpalphaS DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PI UpPI DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030EW UpEW DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030DB UpDB DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030TTBar UpTTBar DnATLAS Work In Progress = 13 TeVsFigure 10.3: Systematic uncertainties due to theoretical sources. Shown are,from left to right and top to bottom, the uncertainty related to the strongcoupling constant s, PI corrections, EW corrections, diboson backgroundestimation, and tt¯ background estimation.13410.3. Parton Distribution Function Uncertainties10.3 Parton Distribution Function UncertaintiesBecause varying the PDFs of the incoming partons changes the DY cross-section as a function of m, theoretical systematic uncertainties pertainingto the PDFs of the incoming partons are considered. In particular, thechoice of the PDFs used, the variations of the PDF eigenvector sets, and thevariations in the PDF scales are evaluated in this analysis.The uncertainty on the PDF scales is evaluated by using the VRAPprogram and varying the nominal CT14NNLO PDF renormalization andfactorization scales up or down simultaneously by a factor of 2. The result-ing maximum variations are taken as the PDF scale uncertainties. EachPDF has a set of independent parameters associated with it, the so-calledeigenvectors of the PDF, which can be varied in orthogonal directions toquantify the systematic uncertainties associated with the PDF variations.For eachm histogram bin, the asymmetric uncertainty on the cross-sectionis calculated using∆+ =√√√√ n∑i=1(max(+i − 0P −i − 0P 0))2P∆− =√√√√ n∑i=1(max(0 − +i P 0 − −i P 0))2P(10.1)where n is the number of PDF eigenvectors, +i (−i ) is the cross-sectionfor the higher (lower) value of the ith PDF eigenvector, and 0 is the cross-section for the central value PDF. A total of seven eigenvector variationsare considered [84]. These seven variations result from the bundling of the28 eigenvectors of the CT14 PDFs into seven bundles with similar mass de-pendency. The eigenvector bundles are provided by the CT14 authors, andare particularly useful when considering any future combination effort withother searches due to the orthogonality of the eigenvector bundles betweentheW and Z bosons. The systematic uncertainty due to the variation of thePDF eigenvectors is then taken as the larger of the positive and negative vari-ation on the cross-section calculated in Equation (10.1). The nominal PDFchoice used for the incoming partons in this analysis is the CT14NNLO PDFset [84]. The uncertainty related to this choice is evaluated by comparingthe central values of the CT14NNLO PDFs to similar PDFs. In particular,two alternatives for the nominal PDF choice are investigated: MMHT14 [92]and NNPDF3.0 [93]. When the difference between the nominal PDF set pre-13510.3. Parton Distribution Function Uncertaintiesdictions and an alternative choice is larger than the uncertainty related tothe PDF eigenvector variation, the maximum absolute deviation from theenvelope of these comparisons is used as the PDF choice uncertainty.Figures 10.4 and 10.5 depict the contribution of each systematic uncer-tainty pertaining to the PDFs of incoming partons to the total systematicuncertainty used in the statistical analysis described in Chapter 11. All sys-tematic uncertainties pertaining to the PDFs of the incoming partons areused as nuisance parameters in the statistical analysis.Dimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFReducedChoiceNNPDF UpPDFReducedChoiceNNPDF DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFScale UpPDFScale DnATLAS Work In Progress = 13 TeVsFigure 10.4: Systematic uncertainties pertaining to the choice (left) andscale (right) of the PDFs of the incoming partons.13610.3. Parton Distribution Function UncertaintiesDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFVar1 UpPDFVar1 DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFVar2 UpPDFVar2 DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFVar3 UpPDFVar3 DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFVar4 UpPDFVar4 DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFVar5 UpPDFVar5 DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFVar6 UpPDFVar6 DnATLAS Work In Progress = 13 TeVsDimuon Invariant Mass [GeV]100 200 300 1000 2000Systematic Variation [%]30−20−10−0102030PDFVar7 UpPDFVar7 DnATLAS Work In Progress = 13 TeVsFigure 10.5: Systematic uncertainties pertaining to the eigenvector varia-tions of the PDFs of the incoming partons. Shown are, from left to rightand top to bottom, the uncertainty related to the seven eigenvector bundlesprovided by the CT14 authors.13710.4. Summary10.4 SummaryTable 10.1 summarizes the various systematic uncertainties considered andtheir various contributions. The experimental systematic uncertainties aredominated by the muon reconstruction efficiency, which results in a relativesystematic uncertainty of ∼ 10% (∼ 17%) at m = 2 TeV (m = 4 TeV).The dominant theoretical systematic uncertainty is the DY background PDFeigenvector set variation in this analysis, resulting in a relative systematicuncertainty of ∼ 8% (∼ 13%) at m = 2 TeV (m = 4 TeV).Source Signal [%] Background [%]Luminosity 3.2 (3.2) 3.2 (3.2)MC statistical Q1O0 (Q1O0) Q1O0 (Q1O0)Beam energy 1.9 (3.1) 1.9 (3.1)Pile-up effects Q1O0 (Q1O0) Q1O0 (Q1O0)DY PDF choice N/A Q1O0 (1.9)DY PDF variation N/A 7.7 (13)DY PDF scales N/A Q1O0 (1.5)DY S N/A 1.4 (2.2)DY EW corrections N/A 2.1 (3.9)DY PI corrections N/A 3.0 (5.4)Top quarks theoretical N/A Q1O0 (Q1O0)Dibosons theoretical N/A Q1O0 (Q1O0)Reconstruction efficiency 10 (17) 10 (17)Isolation efficiency 1.8 (2.0) 1.8 (2.0)Trigger efficiency Q1O0 (Q1O0) Q1O0 (Q1O0)Muon momentum scale Q1O0 (Q1O0) Q1O0 (Q1O0)Muon momentum resolution 2.7 (2.7) Q1O0 (6.7)Total 11 (18) 14 (24)Table 10.1: Summary of the pre-marginalized relative systematic uncertain-ties in the expected number of events at dimuon masses of 2 TeV (4 TeV).The values quoted for the background represent the relative change in thetotal expected number of events in the corresponding m histogram bincontaining the reconstructed m mass of 2 TeV (4 TeV). For the signal un-certainties, the values were computed using a Z ′ signal model with a polemass of 2 TeV (4 TeV), by comparing yields in the core of the mass peak,within the full width at half maximum, between the distribution varied dueto a given uncertainty and the nominal distribution.138Chapter 11Statistical AnalysisThe comparisons between data and MC simulations presented in Chapter 9allow for the statistical analysis of the available dataset. In particular, thecompatibility between the data and the SM expectation can be quantified.Any excess of data above the SM expectation can be interpreted as a mani-festation of various BSM theories. In the case of an excess, the LHC has thepotential to measure the properties of the new phenomena. On the otherhand, if no significant excess is found, constraints on theoretical parame-ters of BSM theories are placed. In this chapter, Section 11.1 describes thestatistical methods used to quantify the agreement between the data andthe MC simulations, and Section 11.2 presents the various limits set on theBSM models presented in Chapter 3.11.1 Search ResultsIn order to quantify any potential excess of data compared with MC simula-tions, a search for a resonant signal is performed using the dimuon invariantmass distribution. Starting from Poisson statistics, the likelihood of observ-ing n events given an expected number of events  is given byL(n|) = nz−n!O (11.1)As this search uses the m distribution presented in Section 9.2, thegeneralization of this likelihood becomes the product of the Poisson likeli-hoods across the bins of the m histogram:L(n|) =cbin∏j=1njj z−jnj !P (11.2)where j represents the expected number of events in bin j and nj cor-responds to the observed number of events in bin j. The expected numberof events for this search depends on the number of background events from13911.1. Search ResultsSM processes and the number of signal events from the given BSM modelunder consideration:j = sj + bj P (11.3)where sj and bj are the expected number of signal and background eventsin bin j, respectively. The parameter  determines the strength of the signalprocess, with  = 0 corresponding to the background-only hypothesis and = 1 corresponding to the nominal signal hypothesis.The systematic uncertainties described in Chapter 10 are accounted forin the search by introducing nuisance parameters s, which parameterise allsources of systematic uncertainty, into the likelihood and by modifying theexpected number of events to allow for systematic error fluctuations:j → ˜j = j(1 +csys∑s=1s"sj), where "sj =(varsj − jj)O (11.4)In the above equation, varsj represents the number of background eventsin bin j for the systematically varied m distribution corresponding tothe systematic uncertainty s. Hence, "sj quantifies the relative shift in theexpected number of background events in bin j from the nominal numberof expected background events for the systematic uncertainty s. Addinga Gaussian prior probability density function constraint to the nuisanceparameters i, the likelihood of observing the m distribution obtained indata given a signal strength  and nuisance parameters  = (1P 2P O O O P csys)isL(n|P) =cbin∏j=1˜njj z−~jnj !csys∏s=1z−2sR2√2.O (11.5)From this expression, the maximum-likelihood estimators ˆ and ˆ fora given observed m distribution and signal hypothesis can be computedby maximizing the likelihood function. Likewise, the nuisance parametervalues that maximize the likelihood function under the background-onlyhypothesis, ˆ0, are computed for the observed data.From these quantities, the test statistic q0 can be constructed:q0 =+2 lnL(data|0;^0)L(data|^;^) for ˆ Q 0P−2 ln L(data|0;^0)L(data|^;^) for ˆ ≥ 0P(11.6)14011.1. Search Resultswhere a larger value of q0 corresponds to a larger incompatibility betweenthe data and the background-only hypothesis. Using the log-likelihood ratiotest described in [94], the probability of the background fluctuating in such away as to create a signal-like excess equal to or larger than what is observedin data, the so-called p-value p0, can be obtained:p0 =∫ ∞qobs0f(q0|0P ˆ0)yq0P (11.7)where f(q0|0P ˆ0) denotes the probability density function of q0 under theassumption of the background-only hypothesis. The value of p0 for ˆ Q 0 iscapped at 0.5 by setting q0 = 0 for Z ′ pole masses above 1.5 TeV, in order toavoid negative probabilities arising from the lack of statistics in this region.The significance, Z, defined such that a Gaussian distributed variablefound Z standard deviations () above its mean has an upper-tail probabilityequal to p0, is used to quantify any potential excess in data:Z = Φ−1(1− p0)P (11.8)where Φ−1 is the inverse of the cumulative distribution function of thestandard Gaussian distribution. Figure 11.1 depicts the cumulative distri-bution function of the standard Gaussian distribution and its inverse.4− 2− 0 2 4x00.10.20.30.40.50.60.70.80.91(x)Φ(a)0 0.2 0.4 0.6 0.8 1x5−4−3−2−1−012345(x)-1Φ(b)Figure 11.1: Cumulative distribution function (left) and inverse of the cu-mulative distribution function (right) of the standard Gaussian distribution.The generally accepted significance value required in order to claim evi-dence (discovery) of new physics is 3 (5).14111.1. Search Results11.1.1 Asymptotic ApproximationFigure 11.2 shows the q0 distribution for background-only pseudo-experiments,or toys, generated using the nuisance parameter values ˆ0 and event countsfollowing Poisson probabilities. In the limit where the number of observedevents in data is large, the distribution for q0 for background-only datasetsfollows a 2 distribution with one degree of freedom [95].0Test Statistic q0 5 10 15 20Number of toys110210310410510610 =0)µ|=0µf(qFigure 11.2: Distribution of the q0 test statistic for background-only toys.The solid blue line shows the 2 distribution with one degree of freedomscaled to the integral of the q0 distribution.Rather than generating the f(q0|0P ˆ0) distribution for each q0 calculated,the asymptotic approximation described in [94] is utilized in order to savecomputational resources. In particular, it has been shown thatp0 = 1− Φ(√q0) and Z = √q0P (11.9)where Φ is the cumulative distribution function of the standard Gaussiandistribution.14211.1. Search Results11.1.2 Look-Elsewhere EffectWhen considering p-values, the so-called “look-elsewhere effect” [96] mustbe taken into account. This effect states that an apparently statisticallysignificant observation may have actually arisen because of the size of theparameter space being searched. Because we are calculating the local p-valueover a large dimuon invariant mass range, the look-elsewhere effect cannotbe neglected. To account for this, a global p-value, i.e., the probability ofmeasuring a particular local p-value somewhere in the background invariantmass spectrum that is at least as significant as the one observed in data, iscalculated. The fluctuations in the background invariant mass distributionare modeled by running an ensemble of pseudo-experiments generated underthe background-only hypothesis. The largest local significance for each toyis then used as the means by which to measure the global p-value:pglobal =1ctoys∫ ∞z^0n(z0)yz0P (11.10)where n(z0) is the distribution of highest local significances observed inthe pseudo-experiments, and zˆ0 is the local significance observed in data.The global p-value represents the probability of obtaining a local signifi-cance larger than or equal to the local significance observed in data, underthe background-only hypothesis. In other words, the global p-value can beinterpreted as a p-value of local p-values.Figure 11.3 shows the p-values obtained from the collected dataset usingthe methodology described above. The binning used for this p-value scan isan optimized binning corresponding to the dimuon mass resolution, whichvaries from 60 GeV atm = 1 TeV to 200 GeV atm = 2 TeV and 420 GeVat m = 3 TeV.14311.2. Exclusion Limits [TeV]Z’M0.2 0.3 0.4 1 2 3 40Local p3−102−101−10110210σ0Local significanceσ1σ2σ3σ0Global significance for largest excessσ1ATLAS -1 = 13 TeV, 36.1 fbsµµ→χ, Z’0Observed pFigure 11.3: Local p-value as a function of pole mass assuming Z ′ signalshapes. Local (global) significance levels are shown as dashed grey (red)lines.11.2 Exclusion LimitsIf no significant excess is found, exclusion limits on parameters of interestfor various BSM scenarios described in Chapter 3 are set. The likelihoodfunction used for this procedure is the same as Equation (11.5), with theexpected number of events given byj = sj(ΘP) + bj()P (11.11)where  still represents the set of nuisance parameters, and sj(ΘP) isthe number of signal events expected from the BSM scenario under consid-eration, which depends on the model parameter Θ. For the resonant signallimits, Θ corresponds to a choice of the Z ′ pole mass, whereas in the CI sig-nal limits, Θ corresponds to a choice of the energy scale Λ and interferenceparameter ij .14411.2. Exclusion LimitsBayes’ theorem is used to relate the marginalized likelihood function tothe posterior probability for the parameter Θ given n observed events:P(Θ|n) = 1N LM(n|Θ)e (Θ)P (11.12)where N is a normalization constant and e (Θ) is the prior probabilitydensity function of the model parameter Θ. For resonant signals, a uniformand positive prior e (Θ) is assumed. For CI signals, two priors are con-sidered: 1RΛ2 and 1RΛ4. LM(n|Θ) is the marginalized likelihood, i.e., thelikelihood after all nuisance parameters have been integrated out:LM(n|Θ) =∫L(n|ΘP)csys∏s=1ysO (11.13)The 95% Confidence Level (CL) limit on Θ is then obtained by findingΘlim such that ∫ lim0P(Θ|n)yΘ = 0O95O (11.14)These calculations are performed using the Bayesian Analysis Toolkit [97],which uses a Markov Chain Monte Carlo technique to perform the integra-tion over the nuisance parameters. The observed limit on Θ is calculatedusing the data distribution n. The expected limit on Θ is obtained by tak-ing the median Θlim from a large sample of pseudo-experiments generatedunder the background-only hypothesis for the particular signal of interestunder consideration.11.2.1 Z ′ Cross-Section and Mass LimitsThe results presented in this section use the same m binning as theone presented in Figure 9.5, with the bins in the Z boson peak region80− 120 GeV summed together into a single bin in order to help constrainmass-independent components of systematic uncertainties. Upper limits areplaced on the product of the cross-section and the branching ratio (W) ofthe BSM scenario Z ′ boson as a function of the Z ′ pole mass. Lower masslimits can be set on the mass of the theoretical Z ′ boson using the upperlimits on W, by plotting the observed W as a function of Z ′ pole mass andfinding where the observed limit intersects the theoretical line. Figure 11.4gives the 95% CL upper limit on the product of cross-section and branchingratio as a function of Z ′ pole mass. Table 11.1 summarizes the observed and14511.2. Exclusion Limitsexpected lower limits on the mass of various Z ′ gauge boson models at the95% CL. [TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 B [pb]σ-510-410-310-210-1101 Expected limitσ 1±Expected σ 2±Expected Observed limitSSMZ’χZ’ψZ’ATLASµµ →Z’ -1 = 13 TeV, 36.1 fbsFigure 11.4: Expected (dashed black line) and observed (solid red line)upper 95% CL limits on the product of the Z ′ production cross-section andbranching ratio to two muons as a function of Z ′ pole mass. Theoreticaluncertainties related to the Z ′SSM signal are shown as a grey band aroundthe black line for illustration purposes, but are not included in the limitcalculation.14611.2. Exclusion LimitsModel Width [%] Z6 [rad]Lower limits on Mo′Observed [TeV] Expected [TeV]Z ′SSM 3.0 - 4.0 3.9Z ′ 1.2 0O50 . 3.6 3.6Z ′h 1.2 0O63 . 3.6 3.5Z ′I 1.1 0O71 . 3.5 3.4Z ′ 0.6 0O21 . 3.4 3.3Z ′c 0.6 −0O08 . 3.4 3.3Z ′ 0.5 0 . 3.3 3.2Table 11.1: Observed and expected 95% CL lower mass limits for various Z ′gauge boson models. The widths are quoted as a percentage of the resonancemass.11.2.2 Minimal Z ′ Model LimitsAs described in Section 3.1.3, minimal Z ′ models can be characterized by the′ and Min parameters, representing the strength of the Z ′ boson couplingrelative to that of the SM Z boson and the mixing between the generatorsof the (W − a) and weak hypercharge n gauge groups, respectively. The95% CL limits are placed on ′ as a function of the Z ′Min mass, and on′ as a function of Min. The results are shown in Figures 11.5 and 11.6,and summarized in Table 11.2. Limit curves in the ′ −Mo′Min parameterspace are shown for three representative values of the mixing angle, Min,between the generators of the (W − a) and the weak hypercharge n gaugegroups. These are: tan Min = 0, tan Min = −2, and tan Min = −0O8, whichcorrespond respectively to the Z ′W−a, Z ′3g, and Z ′ models at specific valuesof ′. The grey band envelops all observed limit curves, which depend onthe choice of Min ∈ [0P .]. The corresponding expected limit curves arewithin the area delimited by the two dotted lines. Limits in the ′ − Minparameter space are set for several representative values of the mass of theZ ′ boson in the minimal Z ′ model. In both cases, the region above each lineis excluded.14711.2. Exclusion Limits [TeV]MinZ’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5’γ2−101−10110 Exp. Obs.]pi [0, ∈ MinθLimit range for )χ(Z’Minθ)3R(Z’Minθ)B-L(Z’MinθATLAS-1 = 13 TeV, 36.1 fbsµµ → MinZ’Figure 11.5: Expected (dotted and dashed lines) and observed (filled areaand lines) 95% CL limits on the relative coupling strength ′ as a functionof the mass of the Z ′ boson in the minimal Z ′ model. Limit curves areshown for three representative values of the mixing angle, Min, between thegenerators of the (W−a) and the weak hypercharge n gauge groups. Theseare: tan Min = 0, tan Min = −2, and tan Min = −0O8, which correspondrespectively to the Z ′W−a, Z ′3g, and Z ′ models at specific values of ′. Theregion above each line is excluded. The grey band envelops all observedlimit curves, which depend on the choice of Min ∈ [0P .]. The correspondingexpected limit curves are within the area delimited by the two dotted lines.14811.2. Exclusion LimitsMinθ0 0.5 1 1.5 2 2.5 3 ’γ2−101−10110Exp.    Obs. = 5.0 TeVMinZ’M = 4.5 TeVMinZ’M = 4.0 TeVMinZ’M = 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-1 = 13 TeV, 36.1 fbsµµ → MinZ’Figure 11.6: Expected (empty markers and dashed lines) and observed (filledmarkers and lines) limits at 95% CL on ′ as a function of Min. The limitsare set for several representative values of the mass of the Z ′ boson in theminimal Z ′ model. The region above each line is excluded.Model ′ tan Min Lower limits on bo′MinObserved [TeV] Expected [TeV]Z ′√4124 sin Min −45 3.4 3.3Z ′3g√58 sin Min −2 3.6 3.6Z ′W−a√2512 sin Min 0 3.6 3.6Table 11.2: Observed and expected 95% CL lower mass limits for variousminimal Z ′ models.14911.2. Exclusion Limits11.2.3 Limits on Contact InteractionsThe binning used to set limits on CI models corresponds to eight bins abovem = 400 GeV of varying width from 100 GeV to 1500 GeV. The proceduredescribed in Section 11.2 is employed, with the parameter of interest Θrepresenting the energy scale, Λ, and the interference parameter, ij , ofthe CI. All permutations of the chiral structure of the CI are investigated.Two priors are considered: 1RΛ2 and 1RΛ4. Figures 11.7 and 11.8 present thelower limits on the CI scale Λ, and the results are summarized in Table 11.3.Chiral StructureLL Const LL Dest LR Const LR Dest RL Const RL Dest RR Const RR Dest [TeV]Λ1015202530354045ObservedExpectedσ 1 ±Expected σ 2 ±Expected ATLAS-1 = 13 TeV, 36.1 fbs2ΛPrior: 1/µµ →CI Figure 11.7: Expected (dashed black line) and observed (solid black line)lower limits on the energy scale Λ at 95% CL, for the CI model with con-structive (Const) and destructive (Dest) interference for all considered chiralstructures using a 1RΛ2 prior.15011.2. Exclusion LimitsChiral StructureLL Const LL Dest LR Const LR Dest RL Const RL Dest RR Const RR Dest [TeV]Λ1015202530354045ObservedExpectedσ 1 ±Expected σ 2 ±Expected ATLAS-1 = 13 TeV, 36.1 fbs4ΛPrior: 1/µµ →CI Figure 11.8: Expected (dashed black line) and observed (solid black line)lower limits on the energy scale Λ at 95% CL, for the CI model with con-structive (Const) and destructive (Dest) interference for all considered chiralstructures using a 1RΛ4 prior.Channel PriorLower limits on Λ [TeV]Left–Left Left–Right Right–Left Right–RightConst Dest Const Dest Const Dest Const DestObserved 1/Λ2 30 20 28 22 28 22 28 20Expected 26 20 24 21 24 21 24 20Observed 1/Λ4 27 19 25 21 25 21 25 19Expected 24 18 23 20 22 20 22 18Table 11.3: Observed and expected 95% CL lower limits on Λ for the LL,LR, RL, and RR chiral coupling scenarios, for both the constructive (Const)and destructive (Dest) interference cases using a uniform positive prior in1/Λ2 or 1/Λ4. The limits are rounded to the nearest 100 GeV.151Chapter 12Conclusion and OutlookThe work presented in this dissertation is centred around one commonthread: muons.In particular, the performance of the ATLAS detector with respect tohigh-pT muons is evaluated. A new selection WP allowing higher selectionefficiency with a modest increase in pT resolution is investigated. The per-formance of the muon trigger system of the ATLAS experiment is measuredusing W+ jets and tt¯ samples, and trigger SFs are provided for the entirecollaboration.With the expected upgrade of the NSW during LS2 in mind, the sTGCdetector technology is characterized through a series of test beam campaigns.An average spatial resolution of 45 µm is obtained, well below the 100 µmrequired by ATLAS for the NSW upgrade project. The operation of full-sized sTGC quadruplets with complete 4-layer VMM readout electronicsfrom both pads and strips is achieved.Finally, the main result of this dissertation describes a search for newhigh-mass phenomena in the dimuon final state. It is motivated by varioustheories of BSM physics. The search results are found to be consistent withthe SM prediction. Thus, lower limits on the mass of hypothetical newparticles are presented. The lower limits range from 4.0 TeV for the Z ′SSMmodel, to 3.3 TeV for the Z ′ model. In addition, lower limits on the CIscale Λ are set, ranging between 18 TeV and 30 TeV, depending on thechiral structure of the CI.Future work includes analyzing the entire dataset collected during Run 2of the LHC. This has been accomplished for the resonant search and hasbeen published in [98]. The next logical step for this search is thus toinvestigate non-resonant signals using the full Run 2 dataset in order toconstrain BSM scenarios predicting, e.g., CIs. This can be accomplishedby searching for a broad excess in the m spectrum, or by performing theanalysis of angular information of the dimuon system and examining theforward-backward asymmetry of dimuon systems. In addition, exclusivechannels could provide hints of new physics that would be buried withinthe inclusive search signal. These could include searching in final states152Chapter 12. Conclusion and Outlookcontaining two muons and ZmissT , or two muons and b-jets.Beyond the third run of data-taking at the LHC, up to 3000 fb−1 ofdata will be delivered by the HL-LHC. This vast dataset has the potentialto uncover extremely rare processes, such as the Higgs boson decaying intomuon pairs. Such an analysis would be the first measurement of the Higgscoupling to second generation fermions, allowing to probe whether or not theHiggs boson’s properties deviate from the SM prediction. This measurementhas the potential to uncover signs of new physics, which could manifest itselfvia contributions to the Higgs production and decay rates.153Bibliography[1] L. Evans and P. Bryant, LHC Machine, Journal of Instrumentation3, S08001–S08001 (2008). (Cited on page 1).[2] ATLAS Collaboration, The ATLAS Experiment at the CERN LargeHadron Collider, Journal of Instrumentation 3, S08003 (2008). (Citedon pages 1, 28, 30, 31, 33, 34, 36, 38–40, 43, 45).[3] CMS Collaboration, The CMS Experiment at the CERN LHC, Journalof Instrumentation 3, S08004 (2008). (Cited on page 1).[4] ATLAS Collaboration, Observation of a new particle in the search forthe Standard Model Higgs boson with the ATLAS detector at the LHC,Physics Letters B 716, pp. 1–29 (2012). (Cited on page 1).[5] CMS collaboration, Observation of a new boson with mass near 125GeV in pp collisions at √s = 7 and 8 TeV, Journal of High EnergyPhysics 2013, p. 81 (2013). (Cited on page 1).[6] S. L. Glashow, Partial-symmetries of weak interactions, Nuclear Physics22, pp. 579–588 (1961). (Cited on page 1).[7] S. Weinberg, A Model of Leptons, Phys. Rev. Lett. 19, pp. 1264–1266(1967). (Cited on page 1).[8] A. Salam, Weak and Electromagnetic Interactions, Conf. Proc.C680519,pp. 367–377 (1968). (Cited on page 1).[9] G. ’t Hooft and M. Veltman, Regularization and renormalization ofgauge fields, Nuclear Physics B 44, pp. 189–213 (1972). (Cited onpage 1).[10] J. J. Aubert et al., Experimental Observation of a Heavy Particle J ,Phys. Rev. Lett. 33, pp. 1404–1406 (1974). (Cited on page 1).[11] S. W. Herb et al., Observation of a Dimuon Resonance at 9.5 GeV in400-GeV Proton-Nucleus Collisions, Phys. Rev. Lett. 39, pp. 252–255(1977). (Cited on page 1).154BIBLIOGRAPHY[12] UA1 Collaboration, Experimental observation of lepton pairs of in-variant mass around 95 GeV/c2 at the CERN SPS collider, PhysicsLetters B 126, pp. 398–410 (1983). (Cited on page 1).[13] S. H. Neddermeyer and C. D. Anderson, Note on the Nature ofCosmic-Ray Particles, Phys. Rev. 51, pp. 884–886 (1937). (Cited onpage 1).[14] H. E. Logan, TASI 2013 lectures on Higgs physics within and beyondthe Standard Model, arXiv:1406.1786 (2014). (Cited on page 3).[15] Wikimedia Commons, Standard Model of Elementary Particles, Ac-cessed: 2019-04-16. (Cited on page 4).[16] Particle Data Group, Review of Particle Physics, Phys. Rev. D 98,p. 030001 (2018). (Cited on page 6).[17] F. Englert and R. Brout, Broken Symmetry and the Mass of GaugeVector Mesons, Phys. Rev. Lett. 13, pp. 321–323 (1964). (Cited onpage 8).[18] P. W. Higgs, Broken symmetries, massless particles and gauge fields,Physics Letters 12, pp. 132–133 (1964). (Cited on page 8).[19] P. W. Higgs, Broken Symmetries and the Masses of Gauge Bosons,Phys. Rev. Lett. 13, pp. 508–509 (1964). (Cited on page 8).[20] G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Global Conser-vation Laws and Massless Particles, Phys. Rev. Lett. 13, pp. 585–587(1964). (Cited on page 8).[21] P. W. Higgs, Spontaneous Symmetry Breakdown without MasslessBosons, Phys. Rev. 145, pp. 1156–1163 (1966). (Cited on page 8).[22] T. W. B. Kibble, Symmetry Breaking in Non-Abelian Gauge Theories,Phys. Rev. 155, pp. 1554–1561 (1967). (Cited on page 8).[23] DESY, Weighty insights with heavy quarks, Accessed: 2019-06-29.(Cited on page 11).[24] A. D. Martin et al., Parton distributions for the LHC, The EuropeanPhysical Journal C 63, pp. 189–285 (2009). (Cited on pages 11, 12).[25] ATLAS Collaboration, Standard Model Summary Plots Spring 2019,ATL-PHYS-PUB-2019-010 (2019). (Cited on page 13).[26] Super-Kamiokande Collaboration, Evidence for Oscillation of Atmo-spheric Neutrinos, Phys. Rev. Lett. 81, pp. 1562–1567 (1998). (Citedon page 15).155BIBLIOGRAPHY[27] SNO Collaboration, Measurement of the Rate of ,z+ d → p + p + e−Interactions Produced by 8W Solar Neutrinos at the Sudbury NeutrinoObservatory, Phys. Rev. Lett. 87, p. 071301 (2001). (Cited on page 15).[28] SNO Collaboration, Direct Evidence for Neutrino Flavor Transforma-tion from Neutral-Current Interactions in the Sudbury Neutrino Ob-servatory, Phys. Rev. Lett. 89, p. 011301 (2002). (Cited on page 15).[29] R. Massey, T. Kitching, and J. Richard, The dark matter of gravita-tional lensing, Reports on Progress in Physics 73, p. 086901 (2010).(Cited on page 16).[30] K. G. Begeman, A. H. Broeils, and R. H. Sanders, Extended rotationcurves of spiral galaxies: dark haloes and modified dynamics, MonthlyNotices of the Royal Astronomical Society 249, pp. 523–537 (1991).(Cited on page 16).[31] N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters,arXiv:1807.06209 (2018). (Cited on page 16).[32] P. Langacker, The physics of heavy Z ′ gauge bosons, Rev. Mod. Phys.81, pp. 1199–1228 (2009). (Cited on pages 17, 18).[33] CMS collaboration, Search for high-mass resonances in dilepton finalstates in proton-proton collisions at √s =13 TeV, Journal of HighEnergy Physics 2018, p. 120 (2018). (Cited on page 18).[34] CMS collaboration, Search for contact interactions and large extradimensions in the dilepton mass spectra from proton-proton collisionsat √s =13 TeV, Journal of High Energy Physics 2019, p. 114 (2019).(Cited on page 18).[35] D. London and J. L. Rosner, Extra gauge bosons in E6, Phys. Rev. D34, pp. 1530–1546 (1986). (Cited on page 18).[36] H. Georgi and S. L. Glashow, Unity of All Elementary-Particle Forces,Phys. Rev. Lett. 32, pp. 438–441 (1974). (Cited on page 18).[37] J. C. Pati and A. Salam, Lepton number as the fourth “color”, Phys.Rev. D 10, pp. 275–289 (1974). (Cited on page 19).[38] R. N. Mohapatra and J. C. Pati, Left-right gauge symmetry and an“isoconjugate” model of CP violation, Phys. Rev. D 11, pp. 566–571(1975). (Cited on page 19).[39] G. Senjanovic and R. N. Mohapatra, Exact left-right symmetry andspontaneous violation of parity, Phys. Rev. D 12, pp. 1502–1505 (1975).(Cited on page 19).156BIBLIOGRAPHY[40] L. Basso et al., Phenomenology of the minimal W−a extension of thestandard model: Z ′ and neutrinos, Phys. Rev. D 80, p. 055030 (2009).(Cited on page 19).[41] E. Salvioni, G. Villadoro, and F. Zwirner, Minimal Z-prime models:Present bounds and early LHC reach, Journal of High Energy Physics11, p. 068 (2009). (Cited on page 19).[42] E. J. Eichten, K. D. Lane, and M. E. Peskin, New Tests for Quark andLepton Substructure, Phys. Rev. Lett. 50, pp. 811–814 (1983). (Citedon page 21).[43] E. Eichten et al., Supercollider physics, Rev. Mod. Phys. 56, pp. 579–707 (1984). (Cited on page 21).[44] L. Randall and R. Sundrum, Large Mass Hierarchy from a SmallExtra Dimension, Phys. Rev. Lett. 83, pp. 3370–3373 (1999). (Citedon page 22).[45] H. Davoudiasl, J. L. Hewett, and T. G. Rizzo, Phenomenology ofthe Randall-Sundrum Gauge Hierarchy Model, Phys. Rev. Lett. 84,p. 2080 (2000). (Cited on page 22).[46] ALICE Collaboration, The ALICE experiment at the CERN LHC,Journal of Instrumentation 3, S08002 (2008). (Cited on page 23).[47] LHCb Collaboration, The LHCb Detector at the LHC, Journal ofInstrumentation 3, S08005 (2008). (Cited on page 23).[48] E. Mobs, The CERN accelerator complex - August 2018. Complexedes accélérateurs du CERN - Août 2018, OPEN-PHO-ACCEL-2018-005 (2018). (Cited on page 24).[49] ATLAS Collaboration, Luminosity Public Results, Accessed: 2019-06-23. (Cited on pages 25–27).[50] ATLAS Collaboration, Luminosity determination in pp collisions at√s = 8 TeV using the ATLAS detector at the LHC, The EuropeanPhysical Journal C 76, p. 653 (2016). (Cited on page 25).[51] ATLAS Collaboration, Luminosity determination in pp collisions at√s = 13 TeV using the ATLAS detector at the LHC, ATLAS-CONF-2019-021 (2019). (Cited on page 25).[52] J. Pequenao and P. Schaffner, How ATLAS detects particles: diagramof particle paths in the detector, CERN-EX-1301009 (2013). (Citedon page 29).157BIBLIOGRAPHY[53] ATLAS Collaboration, Muon reconstruction performance of the AT-LAS detector in proton–proton collision data at √s = 13 TeV, TheEuropean Physical Journal C 76, p. 292 (2016). (Cited on pages 37,52, 53, 57, 91, 116).[54] ATLAS Collaboration, Muon Spectrometer Eta-Meter, Accessed: 2019-06-23. (Cited on page 41).[55] ATLAS Collaboration, Muon Spectrometer Layout Sketch, Accessed:2019-06-23. (Cited on page 42).[56] R. Fruhwirth, Application of Kalman filtering to track and vertexfitting, Nuclear Instruments and Methods in Physics Research SectionA: Accelerators, Spectrometers, Detectors and Associated Equipment262, pp. 444–450 (1987). (Cited on page 46).[57] ATLAS Collaboration, Reconstruction of primary vertices at the AT-LAS experiment in Run 1 proton–proton collisions at the LHC, TheEuropean Physical Journal C 77, p. 332 (2017). (Cited on page 47).[58] M. Cacciari, G. P. Salam, and G. Soyez, The anti-kt jet clusteringalgorithm, Journal of High Energy Physics 2008, pp. 063–063 (2008).(Cited on page 48).[59] Wikimedia Commons, b-tagging, Accessed: 2019-05-13. (Cited on page 49).[60] ATLAS Collaboration, Performance of b-jet identification in the AT-LAS experiment, Journal of Instrumentation 11, P04008 (2016). (Citedon page 49).[61] ATLAS Collaboration, Optimisation and performance studies of theATLAS b-tagging algorithms for the 2017-18 LHC run, ATL-PHYS-PUB-2017-013 (2017). (Cited on page 49).[62] ATLAS Collaboration, Optimisation of the ATLAS b-tagging per-formance for the 2016 LHC Run, ATL-PHYS-PUB-2016-012 (2016).(Cited on page 49).[63] W. Lampl et al., Calorimeter Clustering Algorithms: Description andPerformance, ATL-LARG-PUB-2008-002 (2008). (Cited on page 50).[64] ATLAS Collaboration, Electron reconstruction and identification inthe ATLAS experiment using the 2015 and 2016 LHC proton–protoncollision data at √s = 13 TeV, The European Physical Journal C 79,p. 639 (2019). (Cited on page 51).[65] Wikimedia Commons, Sagitta, Accessed: 2019-05-30. (Cited on page 52).158BIBLIOGRAPHY[66] ATLAS Collaboration, ATLAS muon spectrometer: Technical De-sign Report, CERN-LHCC-97-022, ATLAS-TDR-010 (1997). (Citedon page 66).[67] E. Bothmann et al., Event Generation with Sherpa 2.2, SciPost Phys.7, p. 034 (2019). (Cited on page 89).[68] T. Gleisberg et al., Event generation with SHERPA 1.1, Journal ofHigh Energy Physics 2009, pp. 007–007 (2009). (Cited on pages 89,116).[69] S. Alioli et al., A general framework for implementing NLO calcula-tions in shower Monte Carlo programs: the POWHEG BOX, Journalof High Energy Physics 2010, p. 43 (2010). (Cited on pages 89, 116).[70] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 physics andmanual, Journal of High Energy Physics 2006, pp. 026–026 (2006).(Cited on pages 89, 116).[71] T. Sjöstrand, S. Mrenna, and P. Skands, A brief introduction toPYTHIA 8.1, Computer Physics Communications 178, pp. 852–867(2008). (Cited on pages 89, 116, 117).[72] J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to par-ton shower simulations, Journal of High Energy Physics 2014, p. 79(2014). (Cited on page 89).[73] ATLAS Collaboration, Technical Design Report for the ATLAS In-ner Tracker Strip Detector, CERN-LHCC-2017-05, ATLAS-TDR-025(2017). (Cited on page 95).[74] ATLAS Collaboration, Technical Design Report for the ATLAS In-ner Tracker Pixel Detector, CERN-LHCC-2017-021, ATLAS-TDR-030(2017). (Cited on page 95).[75] ATLAS Collaboration, Technical Design Report for the Phase-II Up-grade of the ATLAS LAr Calorimeter, CERN-LHCC-2017-018, ATLAS-TDR-027 (2017). (Cited on page 95).[76] ATLAS Collaboration, Technical Design Report for the Phase-II Up-grade of the ATLAS Muon Spectrometer, CERN-LHCC-2017-017, ATLAS-TDR-026 (2017). (Cited on page 95).[77] T. Kawamoto et al., New Small Wheel Technical Design Report,CERN-LHCC-2013-006, ATLAS-TDR-020 (2013). (Cited on pages 96,97, 99).159BIBLIOGRAPHY[78] sTGC Collaboration, Performance of a full-size small-strip thin gapchamber prototype for the ATLAS new small wheel muon upgrade,Nuclear Instruments and Methods in Physics Research Section A: Ac-celerators, Spectrometers, Detectors and Associated Equipment 817,pp. 85–92 (2016). (Cited on pages 98, 100–102, 105, 107).[79] L. Landau, On the energy loss of fast particles by ionization, J.Phys.(USSR) 8, pp. 201–205 (1944). (Cited on page 109).[80] R. O. Duda and P. E. Hart, Use of the Hough Transformation toDetect Lines and Curves in Pictures, Commun. ACM 15, pp. 11–15(1972). (Cited on page 110).[81] P. Hough, Method and means for recognizing complex patterns, UnitedStates Patent (1962). (Cited on page 110).[82] Wikimedia Commons, Hough Transform, Accessed: 2019-04-16. (Citedon page 111).[83] H.-L. Lai et al., New parton distributions for collider physics, Phys.Rev. D 82, p. 074024 (2010). (Cited on page 116).[84] S. Dulat et al., New parton distribution functions from a global anal-ysis of quantum chromodynamics, Phys. Rev. D 93, p. 033006 (2016).(Cited on pages 116, 135).[85] S. Agostinelli et al., GEANT4—a simulation toolkit, Nuclear In-struments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment 506, pp. 250–303(2003). (Cited on page 116).[86] R. D. Ball et al., Parton distributions with LHC data, Nuclear PhysicsB 867, pp. 244–289 (2013). (Cited on page 117).[87] C. Anastasiou et al., High-precision QCD at hadron colliders: Elec-troweak gauge boson rapidity distributions at next-to-next-to leadingorder, Phys. Rev. D 69, p. 094008 (2004). (Cited on page 119).[88] S. G. Bondarenko and A. A. Sapronov, NLO EW and QCD proton–proton cross section calculations with mcsanc-v1.01, Computer PhysicsCommunications 184, pp. 2343–2350 (2013). (Cited on page 119).[89] A. D. Martin et al., Parton distributions incorporating QED contri-butions, The European Physical Journal C - Particles and Fields 39,pp. 155–161 (2005). (Cited on page 119).160BIBLIOGRAPHY[90] J. R. Andersen et al., Standard Model Working Group Report, LesHouches 2013 Workshop Proceedings, pp. 80–90 (2014). (Cited onpages 119, 120).[91] J. Butterworth et al., PDF4LHC recommendations for LHC RunII, Journal of Physics G: Nuclear and Particle Physics 43, p. 023001(2016). (Cited on page 133).[92] P. Motylinski et al., Updates of PDFs for the 2nd LHC run, Nu-clear and Particle Physics Proceedings 273-275, pp. 2136–2141 (2016).(Cited on page 135).[93] NNPDF collaboration, Parton distributions for the LHC run II, Jour-nal of High Energy Physics 2015, p. 40 (2015). (Cited on page 135).[94] G. Cowan et al., Asymptotic formulae for likelihood-based tests of newphysics, The European Physical Journal C 71, p. 1554 (2011). (Citedon pages 141, 142).[95] S. S. Wilks, The Large-Sample Distribution of the Likelihood Ratiofor Testing Composite Hypotheses, Ann. Math. Statist. 9, pp. 60–62(1938). (Cited on page 142).[96] E. Gross and O. Vitells, Trial factors for the look elsewhere effect inhigh energy physics, The European Physical Journal C 70, pp. 525–530 (2010). (Cited on page 143).[97] A. Caldwell, D. Kollár, and K. Kröninger, BAT – The Bayesian anal-ysis toolkit, Computer Physics Communications 180, pp. 2197–2209(2009). (Cited on page 145).[98] ATLAS Collaboration, Search for high-mass dilepton resonances using139 fb−1 of pp collision data collected at √s =13 TeV with the ATLASdetector, Physics Letters B 796, pp. 68–87 (2019). (Cited on page 152).161

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