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Searches for new resonances decaying to top-antitop quark pairs with the ATLAS detector in sqrt(s) =… Swedish, Stephen 2014

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Searches for new resonances decaying to top-antitopquark pairs with the ATLAS detector in√s = 7 TeVproton-proton collisionsbyStephen SwedishB.Sc. Honors in Physics, First Class, University of Alberta, 2006M.Sc. Physics, University of Alberta, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)August 2014c© Stephen Swedish, 2014AbstractThis work presents the results of two analyses searching for massive resonancesdecaying to top-antitop quark pairs in the√s =7 TeV pp collisions measured withthe ATLAS detector located at the CERN Large Hadron Collider. The peculiarposition of the top-quark within the Standard Model, as the most massive particle,motivates many theories predicting the existence of new massive particles that cou-ple strongly to top-quarks. These particles may manifest themselves at the LHCas new massive resonances decaying to top-antitop quark pairs. An analysis con-ducted on the first 2.04 fb−1 of data collected in 2011 searched for resonances inthe subset of top-pair events where the W -boson from each top decay decays lep-tonically to a final state electron or muon. A second analysis conducted on the full4.7 fb−1 of 2011 data searched for resonances in the subset of top-quark pair eventswhere the W -boson from each top decay decays hadronically to a diquark pair. Theanalysis focused on the case where each top-quark is sufficiently boosted such thatthe resultant fully hadronic system is highly collimated, and each top-quark decayis reconstructable as a single hadronic jet with large angular separation. In eachanalysis, the leptophobic Z′ from topcolor assisted technicolor models, and theKK-gluon from Randall-Sundrum warped extra-dimension models were chosen asbenchmarks to test for the presence of narrow and wide resonances respectively.No significant deviation from the Standard Model was observed in either analysis.The results were interpreted as 95% C.L. upper limits on the cross-section timesbranching ratio to top-quark pairs, as a function of resonance mass for each bench-mark model. The existence of a Randall-Sundrum KK-gluon was excluded at the95% C.L. over the mass range 500 to 1620 GeV.iiPrefaceThe author made numerous contributions to the ATLAS experiment and the physicsanalyses presented herein under the supervision of Professor Colin Gay, and Pro-fessor Oliver Stelzer-Chilton. The ATLAS experiment is an effort carried out bya collaboration of more than 3000 members. The work is broadly subdivided intoservice tasks which contribute to the general running of the experiment, and con-tributions made to specific physics analyses.Service contributions were made in many 8 hour shifts by the author and con-sisted of:• Real-time monitoring of the ATLAS online data processing chain• Real-time monitoring of the operation and data acquisition of the ATLASTransition Radiation Tracker• Providing training for new TRT shifters• Serving as a global monitoring expertThe last role consisted of maintaining the real-time data quality monitoring soft-ware used by the ATLAS Data Quality Monitoring shifter, liaising with other mon-itoring experts to keep the system up-to-date and properly integrated within theATLAS monitoring, and providing on-call 24/7 support to the Data Quality desk tohelp resolve unexpected software and monitoring issues.The author made significant contributions to the analyses presented in this the-sis via the software development of an analysis framework in collaboration withDr. Michele Petteni and Professor Bernd Stelzer that was used to obtain all theresults presented herein. The author made contributions in terms of both codingiiiand design as the framework was developed between late 2010 and early 2012,including:• Developing general tools for calculating systematic uncertainties• Developing general code for reweighting events and properly handling theassociated uncertainty• Developing code for easy specification of analysis cuts• Developing code for histogram and yield table presentation• Introducing the use of a single ROOT file for persistent storage of informa-tion• Developing diagnostic tools to inspect the analysis data at any stage in theanalysis• Modularising and generalizing the framework for quick adaptation to futureanalysesIn 2012, the framework was rapidly and successfully deployed within a new anal-ysis team, and has since been used in at least two additional studies.The physics analyses presented in this thesis were conducted in communicationwith, and under the approval of the ATLAS ”top” and ”exotics” physics groups.Beginning in 2010 the author worked closely with Dr. Michele Petteni, ProfessorBernd Stelzer, Professor Oliver Stelzer-Chilton, Professor Ashutosh Kotwal, andChris Pollard on an analysis searching for new top-pair resonances in the dileptonchannel. In that analysis the author made the following contributions:• Developed data-driven corrections to the Drell-Yan prediction• Developed and verified the signal template reweighting procedure• Evaluated most of the systematic uncertainties• Ran the full analysis chain and generated the nominal Monte-Carlo predic-tionsiv• Produced output histograms and yield predictionsIn 2012, the author took a leading role as an ”analysis contact” in an analysissearching for top-pair resonances in the boosted fully hadronic channel (See section6) joining team members Dr. Trisha Farooque, Dr. Michele Petteni, Dr. AlexMartyniuk, Professor Pekka Sinervo, Professor Gilad Perez, Jeff Droor, and RyanUnderwood. In that analysis the author made the following contributions:• Implemented the official ATLAS object corrections and systematic uncer-tainty tools• Generated all Monte Carlo predictions• Performed the event selection study and optimization• Implemented and studied b-matching criteria• Developed the data-driven QCD background prediction• Interfaced top-tagging tool into analysis• Developed top-tagging visualization tools• Implemented and verified the PDF systematic uncertainty procedure• Evaluated all other systematic uncertainties• Developed and verified the signal template reweighting procedure• Ran the full analysis chain and generated the nominal Monte-Carlo predic-tions• Produced output histograms and yield predictions• Calculated the final cross-section limits and verified that the posterior prob-ability distributions for the nuisance parameters were not overconstrained• Generated final histograms and yield table for presentationvThe author also served as an analysis contact and was responsible for main-taining the analysis group’s TWiki, leading weekly analysis meetings, and liaisingwith the ATLAS physics groups and related analysis teams; these responsibilitiesincluded presenting the analysis to the ATLAS collaboration for status updates andapproval.The author was also responsible for generating the official KK-gluon cross-section predictions used by all ATLAS top-pair resonance analyses on the datacollected in 2011.The following publications and notes are associated with the previously de-scribed work:• Search for resonances decaying into top-quark pairs using fully hadronic de-cays in pp collisions with ATLAS at√s = 7 TeV, The ATLAS Collaboration,JHEP01 (2013) 116• A search for tt¯ resonances with the ATLAS detector in 2.05 fb−1 of proton-proton collisions at√s = 7 TeV, The ATLAS Collaboration, Eur. Phys. J. C(2012) 72:2083• A search for resonances in the dilepton channel in 1.04 fb−1 of pp collisionsat√s = 7 TeV with the ATLAS detector, EPJ Web of Conferences 28, 12020(2012)• A search for tt¯ resonances in the lepton plus jets final state using 4.66 fb−1of pp collisions at√s = 7 TeV, ATLAS-COM-CONF-2012-174• A Search for tt¯ Resonances in the Dilepton Channel in 1.04/fb of pp Colli-sions at√s = 7 TeV, ATLAS-COM-CONF-2012-174In addition, the author was invited to present the work presented in this thesis,and a summary of various related ATLAS analyses, in the following talk:• Searches for fourth generation vector-like quarks and tt¯ resonances with theATLAS detector, The 2013 Phenomenology Symposium, May 6-8, 2013;Pittsburgh, PennsylvaniaFinally, the work of this thesis was also presented in two additional conferencetalks:vi• Search for Resonances Decaying into Top Quark Pairs Using Fully HadronicDecays in pp Collisions with ATLAS at√s = 7 TeV, Canadian Associationof Physicists, May 27-31, 2013; Montreal, Canada• Search for Resonances Decaying into Top Quark Pairs Using Fully HadronicDecays in pp Collisions with ATLAS at√s = 7 TeV, North West APS Meet-ing 2012, October 18-20, 2012; Vancouver, British Columbia, CanadaviiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . xxivAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Theory and Background . . . . . . . . . . . . . . . . . . . . . . . 42.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . 42.1.1 Quantum Field Theory . . . . . . . . . . . . . . . . . 52.1.2 The Standard Model Lagrangian . . . . . . . . . . . . 62.1.3 The Perturbative Regime . . . . . . . . . . . . . . . . 122.1.4 The Parameters of the Standard Model . . . . . . . . . 182.2 Motivations for New Physics . . . . . . . . . . . . . . . . . . 192.2.1 The Top Quark and the Flavor Hierarchy . . . . . . . 192.2.2 Grand Unification . . . . . . . . . . . . . . . . . . . . 202.2.3 The Hierarchy Problem and Higgs Fine-Tuning . . . . 22viii2.2.4 Top-Down Predictions from String Theory . . . . . . 232.3 Benchmark Models . . . . . . . . . . . . . . . . . . . . . . . 242.3.1 The Randall-Sundrum Warped Extra-Dimension Model 242.3.2 Topcolor . . . . . . . . . . . . . . . . . . . . . . . . 272.4 Physics of Proton-Proton Interactions . . . . . . . . . . . . . 282.4.1 The Collision Coordinate System . . . . . . . . . . . 292.4.2 The Anatomy of the Proton-Proton Collision . . . . . 322.4.3 Event Generation . . . . . . . . . . . . . . . . . . . . 372.4.4 Top-Pair Events . . . . . . . . . . . . . . . . . . . . . 403 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.2 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . 493.2.1 Layout and Operation . . . . . . . . . . . . . . . . . 493.2.2 Beam Parameters . . . . . . . . . . . . . . . . . . . . 543.2.3 LHC Performance in 2011 . . . . . . . . . . . . . . . 553.3 The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . 573.3.1 Detection Strategy and Layout . . . . . . . . . . . . . 593.3.2 The Full Simulation . . . . . . . . . . . . . . . . . . 923.3.3 Reconstruction . . . . . . . . . . . . . . . . . . . . . 934 The Statistical Methods . . . . . . . . . . . . . . . . . . . . . . . 1094.1 An Overview of Bayesian Inference . . . . . . . . . . . . . . 1114.2 The Template Likelihood . . . . . . . . . . . . . . . . . . . . 1124.3 The Frequentist p-value . . . . . . . . . . . . . . . . . . . . . 1134.4 Numerical Implementation . . . . . . . . . . . . . . . . . . . 1145 Analysis I: The Search for Resonances in the Dilepton Channel 1165.1 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.1.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . 1195.1.2 Signals . . . . . . . . . . . . . . . . . . . . . . . . . 1225.1.3 Collision Data Samples . . . . . . . . . . . . . . . . . 1275.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . 1275.3 Control Region Validation and Data Driven Drell-Yan Corrections 129ix5.4 Signal Region Observation . . . . . . . . . . . . . . . . . . . 1385.5 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . 1435.5.1 Estimation of Systematic Uncertainty . . . . . . . . . 1435.5.2 Background-Only Consistency . . . . . . . . . . . . . 1505.5.3 Signal Exclusion Limits . . . . . . . . . . . . . . . . 1516 Analysis II: The Search for Resonances in the Fully Hadronic Chan-nel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1536.1 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . 1566.1.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . 1566.1.2 Signals . . . . . . . . . . . . . . . . . . . . . . . . . 1576.1.3 Collision . . . . . . . . . . . . . . . . . . . . . . . . 1586.2 Object and Event Selection . . . . . . . . . . . . . . . . . . . 1586.2.1 Top Jet Selection . . . . . . . . . . . . . . . . . . . . 1606.3 Data Driven Estimate for the QCD Background . . . . . . . . 1676.3.1 The ABCD Method . . . . . . . . . . . . . . . . . . . 1676.3.2 The Extended ABCD Method . . . . . . . . . . . . . 1696.4 Selection Efficiency Validations . . . . . . . . . . . . . . . . 1736.5 Signal Region Observation . . . . . . . . . . . . . . . . . . . 1766.6 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . 1786.6.1 Estimation of Systematic Uncertainty . . . . . . . . . 1796.6.2 Signal Exclusion Limits . . . . . . . . . . . . . . . . 1867 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . 189References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192xList of TablesTable 2.1 The gauge charge quantization of the fundamental Standard Modelmultiplets [1]. . . . . . . . . . . . . . . . . . . . . . . . . 9Table 2.2 KK-gluon-quark coupling strengths [g−1s ] . . . . . . . . . . 27Table 3.1 Performance parameters of the Inner Detector subsystems[2]. 72Table 3.2 Standalone resolutions of the ECAL and TILE calorimeters [3] 83Table 3.3 Intrinsic parameters of the Muon Spectrometer [2]. . . . . . 90Table 3.4 Tracking parameters and performance of the inner detector[2]. 96Table 5.1 Collision data samples . . . . . . . . . . . . . . . . . . . . 127Table 5.2 Predicted and observed event rates in the signal region . . . 138Table 5.3 Theoretical uncertainties on the background cross-sections 146Table 5.4 The systematic shifts to the overall predicted rate due to thevarious systematic sources [%]. . . . . . . . . . . . . . . . 147Table 5.5 The excluded mass range for the KK-gluon as predicted in thedefault RS1 model . . . . . . . . . . . . . . . . . . . . . . 151Table 6.1 The pT ranges of the various QCD dijet samples. . . . . . . 157Table 6.2 Benchmark Acceptance Times Efficiency . . . . . . . . . . 158Table 6.3 The template pT that was used to evaluate OV3 in various pTranges of candidate jets. . . . . . . . . . . . . . . . . . . . 163Table 6.4 Results of ABCD method control tests . . . . . . . . . . . 171Table 6.5 Overall rate predictions for Region P . . . . . . . . . . . . 172Table 6.6 Top-Quark selection efficiency . . . . . . . . . . . . . . . 176Table 6.7 Multijet background rate predictions . . . . . . . . . . . . 176xiTable 6.8 Expected and observed yield in the fully hadronic analysis . 176Table 6.9 The systematic shifts to the overall predicted rate for varioussystematic sources in %. . . . . . . . . . . . . . . . . . . . 185Table 6.10 The excluded mass range for the KK-gluon as predicted in thedefault RS1 model . . . . . . . . . . . . . . . . . . . . . . 186xiiList of FiguresFigure 2.1 The helicity of particles [4]. . . . . . . . . . . . . . . . . 6Figure 2.2 The Higgs potential [5]. . . . . . . . . . . . . . . . . . . 10Figure 2.3 (a) Lines representing particle states. (b) A fundamental fermionvertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 2.4 The Feynman diagram representation of the lowest order fermionscattering terms. Time flows from left-to-right along the hor-izontal axis; arrows running backward in time indicate anti-fermion states, and vertical lines represent both possible vertexorderings. Each diagram summarizes the transition of incom-ing fermion states on the left, into outgoing fermion states onthe right. From left to right the top diagrams depict t-, u-, ands- channel fermion-fermion scattering processes. The bottomdiagram depicts the three-body decay of a fermion. . . . . 14Figure 2.5 Electron charge screening due to the vacuum polarization ofthe photon field. [6] . . . . . . . . . . . . . . . . . . . . . 16Figure 2.6 The content of the Standard Model [7]. . . . . . . . . . . 18Figure 2.7 The Standard Model mass hierarchy[8]. . . . . . . . . . . 20Figure 2.8 The running of the coupling constants [9]. . . . . . . . . . 21Figure 2.9 Higgs fermion (left) and boson (right) virtual corrections. . 22Figure 2.10 A schematic representation of the warped anti-de Sitter space[10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.11 A schematic depiction of the 5th-dimensional components ofthe bulk SM wave-functions. . . . . . . . . . . . . . . . . 25xiiiFigure 2.12 (a) A vector representation and angular cones in Cartesian andcylindrical coordinates. (b) The relationship between pseudo-rapidity and polar angle. . . . . . . . . . . . . . . . . . . 30Figure 2.13 The collision coordinate system. The coloured ellipses corre-spond to the angular cones depicted in figure 2.12a; in the η-φsystem they occupy the same area. . . . . . . . . . . . . . 31Figure 2.14 A schematic diagram of a pp→ tt¯+jets events [11]. Partons(blue) from two collinear protons (large green ovals) inter-act via a hard collision ( large red circle) producing two top-quarks (small red circles) that subsequently decay. The partonsfrom the hard interaction (red) shower and hadronize (greenovals), the resulting hadrons then decay (green circles). Theevent contains electromagnetic interactions (yellow) and addi-tional parton collisions (purple). . . . . . . . . . . . . . . 33Figure 2.15 Parton splitting vertices. . . . . . . . . . . . . . . . . . . 33Figure 2.16 A schematic representation of the dependence of the proton’sstructural resolution on the 4-momentum of the mediating par-ticle. At lower energy, the valence quarks are most visible. Athigher energies, virtual sea-quarks are resolved. . . . . . . 34Figure 2.17 The MSTW 2008 NNLO parton distribution functions for eachspecies of parton, at Q2 = 10 GeV2 (left) and Q2 = 100002 GeV(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 2.18 The evolution of a parton emerging from the proton collisioninto a hadronic jet. . . . . . . . . . . . . . . . . . . . . . 37Figure 2.19 The three-body decay of the top-quark . . . . . . . . . . . 41Figure 2.20 Leading order Standard Model top-pair production diagrams. 41Figure 2.21 Feynman diagram for resonant top-pair production. . . . . 42Figure 2.22√s = 7 TeV pp→ tt¯ resonance shapes. left: The Pythia Z′ pre-diction. right: The MadGraph-Pythia KK-gluon prediction. 43Figure 2.23 Invariant mass distribution for Standard Model as predictedby MC@NLO+Herwig (black), and example resonant top-pairproduction for a 1 TeV KK-gluon (red) and a 1.6 TeV Z′ (blue). 43xivFigure 2.24 (a) Product of W -branching ratios. (b) Final state channelprobabilities for top-pair events . . . . . . . . . . . . . . 44Figure 2.25 A schematic diagram of a lepton+jets top-pair event, whereone top decays semileptonically, and the other top decays hadron-ically, in the resolved (a), and highly boosted (b) topologies. 45Figure 3.1 (a) A schematic diagram of a single RF-cavity and the instan-taneous electric and magnetic field configuration induced byan an AC current. (b) A schematic of an LHC accelerationchamber realized as a series of RF-cavities. . . . . . . . . 50Figure 3.2 A schematic diagram of the CERN accelerator complex show-ing the injection chain and the LHC [12]. ATLAS is one offour detector experiments located on the main LHC ring. . 52Figure 3.3 A cross-sectional diagram of an LHC arc cell. The separatedcounter-rotating beam-pipes are surrounded by superconduct-ing magnetic coils and housed in a common cryostat [13]. 53Figure 3.4 The coupled magnetic fields of a LHC dipole. The counter-rotating beams are supplied opposite vertical magnetic fieldssuch that each are simultaneously bent toward the centre of theLHC ring[14]. . . . . . . . . . . . . . . . . . . . . . . . . 54Figure 3.5 The total integrated LHC delivered and ATLAS recorded lu-minosities as a function of time for 2011. . . . . . . . . . 56Figure 3.6 The Poisson mean µ for the number of interactions occurringwithin the ATLAS Detector varies significantly over each data-taking period. The plot shows the amount of data collected asfunction of µ in 2011 [15] . . . . . . . . . . . . . . . . . 57Figure 3.7 A diagram of the ATLAS detector. A portion is cut away toreveal the concentric subsystem structure [2]. . . . . . . . 58Figure 3.8 The ATLAS strategy for identifying and measuring final ob-jects is based on making a ordered set of measurements us-ing a concentric series of enclosed subsystems. The schematicshows the different and distinguishable interactions of the var-ious particle types as they traverse the subsystems [16]. . . 63xvFigure 3.9 The main components of the magnet system. The exterior con-sists of air-core toroidal magnets, 8 large magnets over the bar-rel, capped by 8 smaller ones at each end-cap. In the centre ofthe toroid is a solenoid magnet surrounded by the steel of thehadron calorimeter [2]. . . . . . . . . . . . . . . . . . . . 65Figure 3.10 The layout of the barrel inner detector [2]. The detector sub-systems form concentric cylinders around the beam pipe. Thethree pixel layers lay closest to the beam-pipe, and are sur-rounded by four SCT layers that in turn are surrounded by theaxially oriented straw-tube matrix of the barrel TRT. . . . 66Figure 3.11 A schematic diagram of a simple silicon sensor [17]. . . . 67Figure 3.12 A diagram depicting the layout of a pixel module [2]. . . . 68Figure 3.13 An image of an SCT module (left). A diagram of the SCTmodule showing the mounting, and off-angle orientation of the4 strip sensor wafers (right) [2]. . . . . . . . . . . . . . . 70Figure 3.14 A schematic diagram depicting the interaction of an electronwith a series of straw-tubes in the barrel TRT. The electroninduces ionizations at random positions along its path withinthe drift-tubes. The electron induces transition radiation in theinter-tube material which induce additional ionizations in thetube [18]. . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure 3.15 The layout of the ATLAS calorimeter subsystems [2]. . . . 74Figure 3.16 A simulation of an electromagnetic shower within the accor-dion structure of the ECAL [19]. . . . . . . . . . . . . . . 76Figure 3.17 The segmentation of the barrel ECAL into three layers of cells[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 3.18 Azimuthal barrel HCAL module segmentation (left). Tile ar-rangement in a barrel HCAL module (right)[2]. . . . . . . 79Figure 3.19 The electrode structure and arrangement of FCAL1 [2]. thincylindrical LArg gaps are formed around thick anodes that alsoact as absorbers. . . . . . . . . . . . . . . . . . . . . . . 81xviFigure 3.20 A diagram of a the pulse structure of a typical calorimeter re-sponse. The triangular physics pulse is reshaped by the front-end electronics and sampled and digitized at 40 MHz [2]. . 82Figure 3.21 A schematic diagram of chamber arrangement in the muonspectrometer. left: A cross-sectional view of the barrel showsthe barrel MDT chamber arrangement. right: A side view ofthe barrel and end-cap transition regions shows the positions ofthe various chamber types: the MDTs in green and turquoise,the CSCs in yellow, the RPCs in white, and the TGCs in purple[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 3.22 A schematic cross-section of an MDT tube (left), and the typi-cal layout of a barrel MDT chamber (right) [2]. . . . . . . 86Figure 3.23 A cross-section diagram of a CSC gap. Wires are positionedequidistant from each other and the perpendicularly orientedcathodes on the edges of the gap[2]. . . . . . . . . . . . . 87Figure 3.24 A schematic diagram of the RPC arrangement[2]. . . . . . 89Figure 3.25 A schematic diagram of the TGC triplet module[2]. . . . . 90Figure 3.26 The ATLAS full simulation chain. The output of the chain aresimulated events in RDO format which can be treated iden-tically to the event RDO measured by ATLAS. The physicssimulation truth is also stored at stages in the simulation chain.[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 3.27 (a) A track passes near the primary vertex. The perigee is thepoint of closest approach with the primary vertex, from whichit is separated by transverse and longitudinal distances z0 andd0. (b) The projection of the track onto the bending plane. 95Figure 5.1 (a) A schematic diagram of the typical truth objects in a thedileptonic top-pair event. (b) Their associated truth 3-vectors.(c) The projection of the experimentally measured 3-vectorsonto the transverse plane. The neutrino information has beenreduced to a single two component vector in the transverseplane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117xviiFigure 5.2 The reconstructed HT + EmissT vs. truth mtt¯ . Each mtt¯ bin isnormalized to unity [20] . . . . . . . . . . . . . . . . . . 118Figure 5.3 The various tree-level diagrams for single top production. . 120Figure 5.4 The tree-level diagram for Drell-Yan production. Two leptonsare produced through qq¯ annihilation to either a virtual photonor a massive Z-boson. The rate of the process is significantlyenhanced at the Z-mass pole. . . . . . . . . . . . . . . . . 120Figure 5.5 The tree-level diagram for diboson production. . . . . . . 121Figure 5.6 (a) The reweighted KK-gluon resonance shapes. (b) The reweightedreconstructed KK-gluon HT +EmissT templates. The reconstructedSM tt¯ prediction is shown in grey. The red line-shape corre-sponds to a 700 GeV resonance. . . . . . . . . . . . . . . 124Figure 5.7 (a) The reweighted Z′ resonance shapes. (b) The reweightedreconstructed Z′ HT +EmissT templates. The reconstructed SMtt¯ prediction is shown in grey. The red line-shape correspondsto a 700 GeV resonance. . . . . . . . . . . . . . . . . . . 125Figure 5.8 The reweighted acceptance times efficiency for each bench-mark model. . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 5.9 The jet multiplicity distribution in the Z-peak control region:(a) before correction, and (b) after correction. The rate inMonte Carlo is normalized to the observed rate in data. Un-der each plot is shown the Data/MC rate ratio in each bin. 131Figure 5.10 The jet η (a) and pT (b) distributions for ee events in the Z-mass control region . . . . . . . . . . . . . . . . . . . . . 132Figure 5.11 The inclusive jet η (a) and pT (b) distributions for µµ eventsin the Z-mass control region . . . . . . . . . . . . . . . . 133Figure 5.12 The inclusive electron η (a) and pT (b) distributions for eeevents in the Z-mass control region . . . . . . . . . . . . 134Figure 5.13 The inclusive muon η (a) and pT (b) distributions for ee eventsin the Z-mass control region . . . . . . . . . . . . . . . . 135Figure 5.14 A comparison of the predicted and observed HT +EmissT distri-butions in the (a) ee and (b) µµ channels in the Z-mass controlregion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136xviiiFigure 5.15 The distribution of Z → ee (a) and Z → µµ (b) Monte Carloevents in the EmissT vs. Z-mass plane. Regions A and C corre-spond to the signal region [21]. . . . . . . . . . . . . . . . 137Figure 5.16 A candidate high HT +EmissT event. See text for details. . . 139Figure 5.17 The predicted and observed leading jet pT in the signal re-gion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Figure 5.18 The predicted and observed sub-leading jet pT in the signalregion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Figure 5.19 The predicted and observed leading jet η in the signal region. 141Figure 5.20 The predicted and observed sub-leading jet η in the signal re-gion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Figure 5.21 The predicted and observed EmissT distribution. . . . . . . . 142Figure 5.22 The HT + EmissT distribution used for the statistical analysis.The yield in each bin is normalized to 100 GeV, which variesacross the spectrum. The observation in data agrees within thebackground only prediction with the total statistical and sys-tematic uncertainty which is represented by the hatched bars. 143Figure 5.23 Top: the SM background prediction. Bottom: the SM pre-dicted template shape for a 700 GeV KK-gluon. The nominal(black) template prediction compared to predictions where theJES nuisance parameter is shifted in value positively (green)and negatively(blue) according to its parameterized one-sigmauncertainty band. . . . . . . . . . . . . . . . . . . . . . . 148Figure 5.24 The nominal (black) Standard Model background template pre-diction compared to predictions where the fakes rate was shiftedin value positively (green) and negatively (blue) according toits parameterized one-sigma uncertainty band. . . . . . . . 149Figure 5.25 The LLR spectrum determined from an ensemble of pseudo-experiments and the observed LLR, calculated as described insection 4. . . . . . . . . . . . . . . . . . . . . . . . . . . 150xixFigure 5.26 The expected and observed 95% C.L. upper limits on the σ ×BR(X → tt¯) for (a) Z′s and (b) KK-gluons. Superimposed oneach graph is the cross-section for the corresponding defaultbenchmark model described in section 2. The green and yel-low bands respectively correspond to the one and two sigmauncertainty on the expected limit. . . . . . . . . . . . . . 152Figure 6.1 (a) A schematic depiction of the jets in a boosted fully hadronicditop event. The top-decay, which is contained to a large cone,consists of three sub-jets, one for each of the three quarks inthe decay. (b) Each top-decay is reconstructed as a single jet.Each b-jet is also potentially identifiable and should lie withinthe radius of the larger top-decay jet. A schematic view of thetop-jet topocluster distribution in the η−φ is also shown. Thesubstructure is expected to have a three-prong energy distribu-tion consisted with the 3-body top-decay hypothesis. . . . 155Figure 6.2 The predicted mass distributions for QCD (blue) and SM tt¯(white) for the (a) leading and (b) sub-leading jets. . . . . 160Figure 6.3 The predicted number of b-tagged LCW jets found within ∆R<1.0 of the (a) leading and (b) sub-leading jets. . . . . . . 161Figure 6.4 The topocluster distribution (blue) of a simulated top jet rep-resented in an η − φ plane centred on the jet direction. Theheight of the clusters correspond to their pT . The same jet isshown (a) without, and (b) with, the minimum topocluster en-ergy cut of 2 GeV. Superimposed are the parton pT s (red) andtheir matching neighbourhoods (green) for the best matchedtemplate. . . . . . . . . . . . . . . . . . . . . . . . . . . 164xxFigure 6.5 The topocluster distribution (blue) of (a) low OV3, and (b) highOV3 valued QCD jets represented in an η − φ plane centredon the jet direction. The height of the clusters correspond totheir pT . The same jet is shown (a) without, and (b) with,the minimum topocluster energy cut of 2 GeV. Superimposedare the parton pT s (red) and their matching neighbourhoods(green) for the best matched template. . . . . . . . . . . . 165Figure 6.6 (a) The OV3 distribution for leading jets in passing the prese-lection, and their (b) selection efficiency as a function of lowercut on the OV3 value for data, and simulated 2 TeV Z′ andQCD. The data sample is expected to be dominated by QCDmultijet events . . . . . . . . . . . . . . . . . . . . . . . 166Figure 6.7 (a) The OV3 distribution for leading jets passing the preselec-tion and falling in the top-mass window, and their (b) selectionefficiency as a function of lower cut on the OV3 value for data,and simulated 2 TeV Z′ and QCD. The data sample is expectedto be dominated by QCD multijet events . . . . . . . . . . 167Figure 6.8 A schematic depiction of a sample of events distributed in aplane defined by two variables, X and Y , and partitioned onthe basis of passing (+) or failing (-) cuts on the variables. 168Figure 6.9 A schematic depiction of the orthogonal regions used in the ex-tended ABCD method. The preselection and top-mass windowcuts are applied to the entire sample, the X and Y axes corre-spond to the tagging state of each jet, each of which can takeon one of four value partitioning the sample into 16 orthogonalregions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Figure 6.10 The estimated multijet rate as a function of mtt¯ obtained formthe extended ABCD method. The variable bin width corre-sponds to the choice of binning used in the statistical analysis,and the yield in each bin is normalized to 100 GeV. The blackvertical lines correspond to the statistical uncertainty on themethod, and the red bars correspond to the maximum varia-tion among the five different estimates. . . . . . . . . . . 173xxiFigure 6.11 The leading jet mass distribution observed in data for the loos-ened L′+P′ selection where there is no jet mass or top-taggingrequirement on the jet. The rates of SM tt¯ and QCD eventsare estimated by fitting their expected shapes to the observeddistribution. . . . . . . . . . . . . . . . . . . . . . . . . 174Figure 6.12 The sub-leading jet mass distribution observed in data for theloosened N′+P′ selection where there is no jet mass or top-tagging requirement on the jet. The rates of SM tt¯ and QCDevents are estimated by fitting their expected shapes to the ob-served distribution. . . . . . . . . . . . . . . . . . . . . . 175Figure 6.13 A comparison between observation and prediction for the lead-ing (a) and sub-leading (b) jet mass distributions. The largecombined statistical and systematic uncertainty on the predic-tion is not depicted. . . . . . . . . . . . . . . . . . . . . . 177Figure 6.14 A comparison between observation and prediction for the lead-ing (a) and sub-leading (b) jet pT distributions. The large com-bined statistical and systematic uncertainty on the prediction isnot depicted. . . . . . . . . . . . . . . . . . . . . . . . . 177Figure 6.15 A comparison between observation and prediction for the lead-ing (a) and sub-leading (b) jet η distributions. The large com-bined statistical and systematic uncertainty on the prediction isnot depicted. . . . . . . . . . . . . . . . . . . . . . . . . 178Figure 6.16 The mtt¯ distribution used for the statistical analysis. The binwidth varies across the spectrum and the yield in each bin isnormalized to 100 GeV. The observation in data agrees withthe prediction within the sampling uncertainty estimated fromthe data. The large total systematic and statistical uncertaintyon the prediction is not represented. . . . . . . . . . . . . 179Figure 6.17 The nominal (black) template prediction compared to predic-tions where the b-tagging scale factor was shifted in value pos-itively (blue) and negatively (red) according to its parameter-ized one-sigma uncertainty band. (a) the SM tt¯ and (b) KK-gluon predictions are shown. . . . . . . . . . . . . . . . . 182xxiiFigure 6.18 The nominal template prediction (black) surrounded by the un-certainty enveloped formed from the combined Monte Carlostatistical and ISR/FSR systematic uncertainties. . . . . . 183Figure 6.19 The nominal template prediction (black) surrounded by thepositive (blue) and negative (red) one sigma total PDF uncer-tainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Figure 6.20 The expected and observed 95% C.L. upper limits on the σ ×BR(X → tt¯) for Z′s. Superimposed on the graph is the cross-section for the default benchmark model described in section2. The green and yellow bands respectively correspond to theone and two sigma uncertainty on the expected limit. . . . 187Figure 6.21 The expected and observed 95% C.L. upper limits on the σ ×BR(X → tt¯) for KK-gluons. Superimposed on the graph isthe cross-section for the default benchmark model describedin section 2. The green and yellow bands respectively corre-spond to the one and two sigma uncertainty on the expectedlimit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188xxiiiList of AbbreviationsADS5 Five dimensional anti-de Sitter spaceATLAS A toroidal LHC ApparatuSBSM Beyond the Standard ModelCellOut Refers to energy contribution to the ATLAS missing transverse energy measurementthat comes from calorimeter clusters not associated with any reconstructed object.CKM Cabibbo Kobayashi Maskawa (matrix)CSC Cathod Strip ChamberDAQ Data AquisitionDGLAP Dokshitzer Gribov Lipatov Altarelli Parisi (equation)ECAL Electromagnetic CalorimeterEF Event FilterEM Electromagnetic, in the context of jet algorithms this refers to jets that take EM scalecalibrated topoclusters as input.FCAL Forward CalorimeterFEB Front-End BoardsFSR Final State RadiationGUT Grand Unification TheoryHCAL Hadronic CalorimeterHEC Hadronic End-cap CalorimeterHLT High Level TriggerIR Infrared, following from De Broglie relation, refer to low energy, or low momentumtransfer.xxivIRC Infrared and collinear (safety)ISR Initial State RadiationJES Jet Energy Scale, the calibration factor applied to jets measured in data to correct themeasured energy to the inferred energy of the physical jet.KK Kaluza-KleinL1 Level 1 (Trigger)L2 Level 2 (Trigger)LArg Liquid ArgonLCW Refers to locally calibrated topoclusters, in the context of jet algorithms this refers tojets that take LCW topoclusters as input.LEP Large Eletron Positron ColliderLHC Large Hadron ColliderLO Leading order, refers to first perturbative correction to transition probabilities above thenon-interacting case.MC Monte CarloMDT Monitored Drift TubeMV1 The ATLAS standard b-tagging algorithmMWPC Multiwire Proportional ChamberNLO Next-to-leading order, refers to the second perturbative correction to transition proba-bilities above the non-interacting case.NNLO Next-to-Next-to-leading orderPDF Parton Distributon FunctionPOPOP 1,4-bis(5-phenyloxazol-2-yl) benzene, a scintillator and wavelength shifterPTP p-terphenyl, a scintillator.QCD Quantum ChromodynamicsQED Quantum ElectrodynamicsQFT Quantum Field TheoryRF Radio FrequencyRLC Refers to a circuit consisting of an resistor inductor and capacitor.xxvROD Readout DriversRPC Resistive Plate ChambersRS1 The Randall-Sundrum warped extra-dimension model with a single finite extra-dimensionin which non-Higgs particles can propagate through the bulk.SCT Silicon TrackerSM Standard ModelTGC Thin Gap ChamberTILE Hadronic scintillating tile calorimeterTRT Transition Radiation TrackerTTC Timing, Trigger, and Control (System)UV Ultraviolet, following from De Broglie relation, refers to high energy, or high momen-tum transfer.xxviAcknowledgementsThe completion of this thesis constitutes the end of a period of my life that was atonce a challenging stepping stone to future success and the realization of a child-hood dream to contribute to the particle physics endeavor at the high-energy fron-tier. The experience of being based at CERN during the candidate Higgs discovery,and being able to take part in the exciting search for new physics that constitutedmy PhD work, both with my Canadian colleagues within ATLAS Canada, but alsowith various international teams, is a life highlight that I don’t expect will everfade. I am especially grateful to my supervisors Prof. Colin Gay and Prof. OliverStelzer-Chilton who provided me with both incredible opportunities to learn andparticipate in the field of particle physics, but also the support, guidance, expertise,and encouragement required to take advantage of them. The nature of experimen-tal paricle physics means I am indebted to a large number of collaborators withoutwhom my work would itself not have lead to original and important contributionsto the field. I would like to thank in particular Dr. Michele Petteni, Dr. TrishaFarooque, and Prof. Pekka Sinervo. Not only were they major contributors to thestudies I participated in, but my practical education in research was significantlybolstered by learning from their own technical expertise with data analysis andexperimental particle physics.Finally, I thank my family for their constant support and encouragement, with-out them none of what I accomplished would be possible. In particular, I wouldlike to acknowledge my daughter Ember. She accompanied me at every stage ofthis adventure, bore its sacrifices, shared in its excitement, and even served herfather as a fully fluent French-English interpreter for the two years we both calledCERN our home. To you Ember, I say thank you.xxviiChapter 1IntroductionThe Standard Model of particle physics arose in the 20th century as the most com-prehensive and successful description of the fundamental nature of the universe. Itpostulates that all matter, and the forces it experiences, are describable entirely interms of interactions between fundamental particles propagating throughout space-time. The exertion of forces between matter is now understood as a special case ofgeneral particle interactions where mutual recoil is induced among two matter par-ticles by the emission and absorption of an intermediate force particle. The Stan-dard Model consists of a finite set of indistinguishable particles and a descriptionof their interactions with each other. The theory has incorporated all the observedmatter particles, and three of the known fundamental forces of nature: the electro-magnetic, weak nuclear, and strong nuclear forces; however, it does not presentlyaccommodate a description of the comparatively ultra-weak gravitational force.Particle interactions are understood as fundamentally probabilistic quantumstate transitions. Accordingly, the experimental study of fundamental physics hasconsisted of making statistically significant measurements of the differential ratesof processes, and comparing these measurements to the predictions derived fromvarious hypotheses. A significant experimental tool in this effort are so-called col-lider experiments. These experiments collide accelerated counter-rotating beams ofparticles at known energies such that they induce, in a well controlled manner, highenergy interactions between initial state particles. Surrounding these interactionsare placed detectors which measure and identify the final state particles emerging1from the interaction. The results of a series of collider experiments, combinedwith measurements made from numerous non-collider experiments, has led to thedefinition of the Standard Model of particle physics. Except for its description ofneutrinos as massless, the Standard Model has stood up to every experimental testof its validity. However, in spite of its success, the theory itself shows deep hintsthat it is an incomplete description of physics.Further statistical analysis at currently accessible energies may reveal new physics,by which we mean the existence of additional particles or interactions. A key as-pect of testing for the existence of the former are resonance searches at colliderexperiments. When two initial state particles transition to a final state via theirannihilation into a massive intermediate particle, the resultant final state probabil-ity distribution exhibits an excess peaked at the invariant mass of the intermediateparticle. The course of discovery in particle physics has been charted in signifi-cant part by the experimental observation of such resonances. Much of the hadronspectrum, whose categorizing led to the formulation of the quark model of hadronicmatter [22]; the massive bosons, associated with the weak nuclear force; and therecently discovered boson, tentatively identified as the long-sought Higgs particle;were all discovered or characterized by searching for resonances.The most exotic matter particle in the Standard Model is the top quark. It isthe most massive known particle, with mass close to the Higgs boson. Its peculiarposition is seen by some theorists as a hint that the top-quark has a special role inany new physics that may exist to address outstanding issues with Standard Model[23]. A key prediction of many beyond the Standard Model (BSM) theories isthe existence of a new massive boson that interacts preferentially with top quarks.These new particles may manifest themselves at collider experiments via new top-pair resonances.This thesis presents two searches for top-pair resonances at the Large HadronCollider (LHC) with the ATLAS experiment on data collected throughout 2011.Each search was conducted in the context of two benchmark models: Topcolor [24]and Randall-Sundrum warped extra-dimensions [25]. Topcolor proposes an ex-tended structure for the fundamental forces as the source of the high top mass, andpredicts the existence of a new Z′ boson, that couples strongly to top quarks whichwould manifest itself at the LHC via a narrow-width resonance. The Randall-2Sundrum extra-dimension model is a theory which explains both the relative weak-ness of gravity and the disparate fermion masses as geometric effects brought onby the existence of an additional small highly warped extra-spatial dimension. Thefirst extra-dimensional excitation of the gluon, the KK-gluon, dominantly couplesto top-quarks and would manifest itself at the LHC as a moderate width resonance.The first search was conducted in the dilepton channel, where each top itselfdecays to a final state containing one charged lepton, allowing for a relatively cleanselection of ditop events. In a second analysis, high mass resonances were searchedfor in the boosted fully hadronic channel. That search focused on the subset of highenergy top-pair decays where both tops are highly relativistic and decay entirelyinto highly collimated clusters of hadrons, each of which can be reconstructed assingle objects called jets. For the first time a new algorithm, the top templatetagger, was employed to distinguish top-jets from the multijet background on thebasis of jet substructure.The layout of this thesis is as follows. Section 2 will summarize the relevanttheory. Section 3 will provide a description of the Large Hadron Collider and AT-LAS detector experiments, including data acquisition, reconstruction techniques,and the general performance of the relevant variables in the analysis. Section 4will describe the statistical methods used to analyze the data and set limits. Section5 and 6 will describe the search strategy, techniques, and results for the dileptonchannel and the boosted fully hadronic channel respectively. The thesis will con-clude with a discussion of the significance of this work and future extensions of itwithin the field.3Chapter 2Theory and BackgroundThis chapter summarizes the theoretical bases for the fundamental particle phe-nomena that are analyzed in this thesis. In particular it outlines the connection ofthe model parameters of the underlying quantum field theory (QFT) of nature tothe observable outcomes of proton-proton collisions: the testable predictions at theLHC. Focus is given to production of top-quark pairs, and how the top-pair invari-ant mass distribution provides a mechanism for testing the fundamental structureof the QFT model of nature.The chapter is laid out as follows. First, the Standard Model of particle physicsis introduced. A following section then outlines the outstanding issues with theStandard Model that motivate BSM theories. That section is followed by the pre-sentation of two BSM models that serve as benchmark hypotheses for the reso-nance searches presented in this thesis. The final section gives an overview ofthe physics of proton-proton collisions, the generation of top-quark pairs, and howproton-proton collision hypotheses are simulated with Monte-Carlo computationaltechniques.2.1 The Standard ModelThis section describes the quantum field theory construction of the Standard Modeland the scheme for using the theory to predict the statistical properties of the ob-served particle spectrum, specifically scattering cross-sections. In this overview,4and throughout the rest of this thesis, the Heaviside-Lorentz system with naturalunits (h¯ = c = 1) is used to describe physical quantities, as is the standard conven-tion in particle physics [26].2.1.1 Quantum Field TheoryThe quantum field theoretic framework was developed in order to find a descrip-tion of the observed particle phenomena that was consistent with special relativityand quantum mechanics. Its first successful application was Quantum Electrody-namics (QED), a framework that placed matter and electromagnetic radiation onan equal footing - both were found to be describable by quantized fields whichexhibit particle epiphenomena - and eventually led to a model building schemefor describing all the forces. Weinberg gives a concise overview of the history ofQFT’s development in [27].Fundamental particles are understood only as indivisible structureless objectswhich transmit conserved quantities, such as momentum or charge, across space-time between point-like interactions with other particles. Within QFT, particles canbe modeled in a quantum mechanical fashion in a 3+ 1 dimensional Minkowskispace consisting of three space dimensions (x=(x1,x2,x3)), one time dimension(x0 ≡ t), and squared Lorentz invariant norm:ds2 ≡ dsµdsν = ηµνdxµdxν = dx20− (dx21 +dx22 +dx23), (2.1)as wave-packets of momentum eigenmodes of a field, ζ (x, t), denoted by theirwavenumber k:|ζ 〉=∑j∫d3kA(k)eikx√(2pi)3|χ j〉, (2.2)where A(k) is the normalization and χ is a state-vector encoding the coordinateindependent internal states of the field. Multi-particle dynamics are handled bymoving to a Fock space description where a multi-particle state is described by thenumber of quanta occupying each eigenmode, nk, of any number of different fields,j, such that a general state represented in momentum space has the form:|Ψ〉= |n11,n12, ...,n1k ,n1k+1, ...n21,n22, ...,n2k ,n2k+1, ...nj1,nj2, ...,njk,njk+1, ...〉. (2.3)5The most observationally relevant application of QFT is the determination oftransition amplitudes between multi-particle Fock states which, in keeping withquantum mechanics, are determined in the interaction picture by the overlap be-tween the time evolved initial state, Ψi, and a possible final state, Ψ f [28]:M = 〈Ψ f |Ψi(t = ∞)〉. (2.4)The dynamics of a specific theory are summarized in a Lorentz covariant way bythe Lagrangian (density) L for the fields, expressed in terms of the fields them-selves, which become operators on the field eigenstates. From the Lagrangianboth the equations of motion and the Hamiltonian (density), which define the fieldeigenstates and their time evolution, can be determined. A critical consequence ofthe QFT construction, which expressed itself in all attempts to construct relativis-tic quantum mechanical particle models, is the appearance of charge-conjugateanti-particle states associated to each particle state that possess otherwise equalbut opposite charges. The existence of anti-particles will be left implicit in thefollowing summary.2.1.2 The Standard Model LagrangianThe fields in the Standard Model are partially characterized by their intrinsic angu-lar momentum, or spin, S. The angular kinematics of particle interactions dependon the particle helicity: the projection of the particle’s spin onto its direction ofmotion (See figure 2.1).Figure 2.1: The helicity of particles [4].Spin also presents itself in the fundamental quantum statistical properties ofparticles. Half-odd-integer spin fermionic fields obey Fermi-Dirac statistics, whichforbid occupation of a field state by more than one quanta, and constitute matter;6their statistical behaviour is why the atomic model for matter does not collapse.In contrast, integer-spin bosonic fields obey Bose-Einstein statistics, which permitany number of quanta to occupy a field state, allowing bosonic phenomena, suchas electromagnetic radiation, to exhibit classical wave behavior in the macroscopicaggregate limit [27].Matter and the non-gravitational forces are described by gauge theories: QFTsthat satisfy the principle of local gauge invariance: the demand that two otherwiseidentical fields, that differ only by an unobservable coordinate dependent complexphase factor, should yield identical physical predictions. Local gauge invariancehas been adopted as a principle, and has its origin in the study of QED. It wasidentified as a symmetry of the theory [26], and was later realized to be generallycritical to the construction of stable predictive models [29]. Remarkably, imposinglocal gauge invariance on a theory for free fermions automatically manifests inter-action terms in the Lagrangian with bosonic fields whose general nature is dictatedby the symmetries among the internal states of the fermion Lagrangians. This prop-erty has driven the construction of the Standard Model as the identification of theminimal set of fields and fundamental symmetries that reproduce the experimen-tal observations in nature. The internal symmetries of the theory depend on thespin-related Lorentz invariant quantity chirality. Dirac-spinors can be expressedin a basis of left- and right-handed orthogonal chirality states; each invariant un-der Lorentz boost and spatial rotations, with distinct, and mirrored, transformationproperties:ψ = ψL +ψR, (2.5)where, using the gamma matrix algebra of the Dirac equation of motion for the freefermionic fields [28]:ψL =12(1− γ5)ψ and ψR =12(1+ γ5)ψ, (2.6)The fermionic fields manifest themselves in three identical generations, eachconsisting of two leptons and two quarks. In order of increasing generation theleptons consist of the electron and electron-neutrino (e,νe), the muon and muon-neutrino (µ ,νµ ), and the tauon and tau-neutrino (τ ,ντ ). Similarly, the quarks con-sist of the up and down quark (u, d), the charm and strange quark (c, s), and the7top and bottom quark (t, b). Critically, no right-handed neutrinos (left-handed anti-neutrinos) have been experimentally observed, indicating an apparent chiral asym-metry in nature. The fermionic fields can be grouped together into left- and right-handed multiplets with internal states corresponding to the distinct particle typesamong which transformations leave the Lagrangian unchanged. The Lagrangianfor a free massless fermion field ψ consists only of a kinetic term:L = iψ¯γµ∂µψ (2.7)Ensuring the gauge invariance of the Lagrangian under internal symmetry trans-formations necessitates the replacement of the standard derivative, ∂µ in the freefermionic Lagrangian by the gauge covariant derivative, Dµ which contains thecouplings to bosonic gauge fields.The internal symmetries are summarized by symmetry groups; each of theStandard Model multiplets posses some subset of the underlying symmetries SU(2)L×U(1)Y ×SU(3) which give rise to three sets of gauge fields that can be representedin the general covariant derivative:Dµ := δµ ig12Y Bµ − igs2σ jW jµ − ig32λαGαµ (2.8)where g1, g2, and g3 are the gauge coupling constants which determine the strengthof their respective interactions. The nature of a specific fermion’s gauge interac-tions are summarized by a set of conserved quantized charges, which are couplingfactors between the multiplets and the coupling constants for a given force.The quark fields themselves represent triplets of three coloured fields, whichpossess one of three colour charges: red, green, or blue, q = (qR,qG,qB), eachtaking a positive or negative value in analogy with electric charge. This symme-try gives rise to 8 massless bi-coloured self-interacting bosonic fields (Gα ) calledgluons, with colour dependent normalization factors λα ; the gauge theory for theirinteractions with quarks is referred to as Quantum Chromodynamics (QCD).The origin of the electromagnetic and weak forces are interconnected at thegauge level, and described by a unified electroweak sector generated by the chiralSU(2)L×U(1)Y symmetry. The hyperweak fields Wj couple only to multiplets8with non-zero weakisopin, I, proportionally to its projection, I3, whose two states(1/2,−1/2) represents the two different charges of the hyperweak force. Only thethe left-handed multiplets possess non-zero I. The hypercharge boson B0 couplesto all fermions proportionally to their weak hypercharge Y . The chiral multiplets,summarized by their quantized charges, are shown in table 2.1.Table 2.1: The gauge charge quantization of the fundamental Standard Modelmultiplets [1].r⊕b⊕g I I3 YquarksQiL =(uLdL) (cLsL) (tLbL)1 1/2(+1/2−1/2)1/3uiR = uR cR tR 1 0 0 4/3diR = dR sR bR 1 0 0 -2/3leptonsLiL =(νe,LeL) (νµ,LµL) (ντ,LτL)- 1/2(+1/2−1/2)-1eiR = eR µR τR - 0 0 -2Higgs φ =(φ+φ 0)- 1/2(+1/2−1/2)+1In the Standard Model the electroweak symmetry is broken, giving rise to parti-cle masses, via the Higgs mechanism, which extends the electroweak sector of thetheory by a complex scalar weak isospin doublet: the Higgs field, Φ. The generalLagrangian density for this field is:LH = (DµΦ)†(DµΦ)−V (Φ) (2.9)It permits a gauge invariant potential term:V (Φ) =−µ2Φ†Φ+ λ4(Φ†Φ)2. (2.10)Positive µ2 and λ terms locate the minimum value of the Lagrangian density at adegenerate configuration where the field is not in its ground state, giving the field anon-zero vacuum expectation value: its average expected value throughout space,v. This degeneracy can be visualized in two-dimensions by plotting the real andimaginary components of φ , which is shown in figure 2.2. Choosing the orientation9Figure 2.2: The Higgs potential [5].of the field to be:Φ(x) =1√2(0v+H(x)), (2.11)and expanding the covariant derivative for Φ in terms of the non-zero componentresults in a theory whose Fock space represents the physically observable particlestates and a single new physical field, H(x), corresponding to a neutral scalar bosonwith a gauge invariant mass term. The massless spin-1 gauge bosons translate intoobservable representations, the vector bosons, W+,W−,Z0, and A, the weak bosonsand photon respectively, related by:W± =1√2(W 1µ ±W2µ)(2.12)(ZµAµ)=(cosθW sinθW−sinθW cosθW)(ZµAµ)(2.13)which acquire mass terms through the first term in equation 2.9 given by:M2WW+µ W−µ +12(Zµ ,Aµ)(M2Z 00 0)(ZµAµ)(2.14)The weak mixing angle, θW , is related to the coupling strengths of the electroweaktheory, or the weak boson masses, by:cosθW =g2√g21 +g22=MWMZ(2.15)10The fermions can acquire mass in a gauge-invariant way via Yukawa couplingswith the scalar Higgs of the form [30]:−v√2∑i j(Y i j`¯`iL`jR +Yi jd d¯iLdjR +Yi ju u¯iLujR)(2.16)This general coupling permits mass eigenstates that are mixtures of the physicalquark flavor states. This mixing presents itself experimentally in the flavour viola-tion of charged weak interactions, but is otherwise transparent to the rest of the fun-damental theory. The mixing is represented in the Cabibbo-Kobayashi-Maskawamatrix which transforms the observable down-type flavour eigenstate (u,d,s) intotheir mass eigenstates, (u′,d′,s′):d′s′b′=VCKMdsb (2.17)where,VCKM ≡Vud Vus VubVcd Vcs VcbVtd Vts Vtb=0.973 0.225 0.0040.225 0.973 0.0410.009 0.040 0.999 (2.18)The charged weak bosons then couple to quark mass multiplets: (u,d′), (c,s′),(t,b′); the coupling between flavour states i and j is proportional to the CKM factor|Vi j|. The mass-mixing is small, especially for the 3rd generation. The matrix itselfcan be expressed in terms of 4 independent parameters, for more detail see [22].The Standard Model Lagrangian can be symbolically summarized as a col-lection of subcomponents. Kinetic terms can be added for the Higgs and gaugebosons without violating gauge invariance that together with the Higgs generatedmass terms define the free field Lagrangians for each field type,Lf reeSM =L f +LW +LEM +LQCD +LH , (2.19)from which the Dirac, Proca, and Klein-Gordon equations of motion can be derived11for the massive fermion, vector-boson, and Higgs field states respectively.The rest of the Standard Model Lagrangian consists of the interaction terms.Each fermionic interaction consists of a current, J: a quantized flow of charge be-tween two fermionic fields; and the bosonic field which couples to the current. Let-ting EM, CC, and NC denote the electromagnetic, charged weak and neutral weakinteractions respectively, the electroweak fermionic interaction terms are [30]:LF,EW =−JµemAµ − JµNCZµ − JµCCW+µ −(JµCC)†W−µ (2.20)where, defining gW ≡ g2, and making the identifications that e = g1 cosθW , and theelectric charge of a particle is Q f ≡ I3 +Y/2:Jµem = e∑fQ fψ f γµψ f ,JµNC = −gW2cosθW[∑fψ f ([I3 cos2 θw +Y sin2 θW ]γµ − I f3 γµγ5)ψ f],JµCC = −gW√2[∑iv¯iγµ 1− γ52`i +∑i ju¯iγµ 1− γ52V i jCKMdj]. (2.21)The QCD interaction terms among the quarks are more complicated as there arethree charges and 8 independent bi-colour states, defining gs ≡ g3 they are:LF,QCD =−∑qJa,µq Gaµ (2.22)withJa,µq =−gsq¯γmuλ a2q (2.23)Additionally, the gauge covariant kinetic terms of the non-abelian bosonic fieldscontain cubic and quartic self interaction terms, for more details see [30].2.1.3 The Perturbative RegimeThe Standard Model Lagrangian provides a framework that, in principle, allowsone to define arbitrary multi-particle Fock-states, and the transition amplitudes be-tween them by considering combinations of the 2↔ 1(2) interactions defined in the12interaction terms of the Lagrangian. In practice, such a calculation is only analyt-ically possible when the magnitude of the interaction terms are small with respectto the free field Lagrangians. In this so-called perturbative regime, the interactionterms can be treated as small corrections to the free-field interaction Hamiltonian,H0:Hˆ ′ =−eiHˆ0t′Linte−iHˆ0t ′ , (2.24)and the time evolution of states can be determined from perturbation theory [28]:|Ψ(t)〉= |Ψ(−∞)〉− i∫ t−∞dt ′∫spaced3xHˆ ′|Ψi(−∞)〉. (2.25)The transition amplitude can then be expressed as:M = 〈Ψ(∞) f |Ψ(∞)i〉= 〈Ψ(∞) f |Sˆ|Ψ(−∞)i〉, (2.26)where Sˆ is the Dyson expansion:Sˆ =∞∑n=0(−i)nn!∫...∫d4x1∫d4x2...d4xnT{Hˆ′(x1)Hˆ′(x2)...Hˆ′(xn)}, (2.27)and T denotes the enclosed operators are time-ordered.The terms in the perturbative expansion are given pictorial representation viaFeynman diagrams which encode the rules for their calculation. The prescriptionfor calculating transition amplitudes of interest is then reduced to drawing all pos-sible Feynman diagrams, and then calculating and summing the integral associatedwith each one. The symbolism of the Feynman diagrams also offers a conceptualmodel for particle interactions: the interaction terms in the Lagrangian are repre-sented by vertices where three or four lines intersect at a single point as shown infigure 2.3.Transitions between initial and final multi-particle external states are said tobe mediated by the exchange of intermediate virtual particles, which transfer mo-mentum and quantum numbers between two points in space-time, called vertices.The simplest physically relevant fermionic diagrams, involving the exchange ofa single virtual particle among four external free particle states, are the tree-leveldiagrams shown in figure, 2.4. They correspond to the generalized notion of the13f ermionγ/W/Zg(a) (b)Figure 2.3: (a) Lines representing particle states. (b) A fundamental fermionvertexexertion of force between two fermionic currents flowing arbitrarily in space-time;they include three different scattering processes and the three-body decay of a sin-gle particle.qD : p4C :−p2B :−p3A : p1qD : p4C :−p2B :−p3A : p1qD : p4C : p3B : p2A : p1q−p2p3p4p1Figure 2.4: The Feynman diagram representation of the lowest order fermionscattering terms. Time flows from left-to-right along the horizontal axis;arrows running backward in time indicate anti-fermion states, and ver-tical lines represent both possible vertex orderings. Each diagram sum-marizes the transition of incoming fermion states on the left, into out-going fermion states on the right. From left to right the top diagramsdepict t-, u-, and s- channel fermion-fermion scattering processes. Thebottom diagram depicts the three-body decay of a fermion.14Each diagram represents all time orderings of the vertices, as these are inte-grated over in the expansion, and, using the numeric labeling in figure 2.4, lead tothe following general expression - a scalar product of vectors - for the covarianttree-level fermionic transition amplitude:− iM = i(g′U1(p1)γµC1,2U2(p2))(−iTµνq2−m20)(g′U3(p3)γνC3,4U4(p4))(2.28)where here Ui denotes a diagram dependent Dirac-spinor for either a particle orantiparticle, g′ is the coupling constant of the mediating force, Ci, j is a mediatorand current dependent charge factor, T µν is a tensor representing the summationover internal spin-states of the mediator, and q is the 4-momentum of the media-tor. The equation is the result of a trivial integration over the the momentum statesof the virtual particle, that is fully constrained to a single momentum state by therequirement of conservation of momentum among the external states. As a con-sequence, the square of the virtual particle’s mass q2 differs from the square of itsrest-mass, m20. Q2 = m20−q2 is referred to as the virtuality, and the amplitudes ofhighly virtual processes are suppressed. The internal state dynamics are handled bythe vector algebra, and spin and colour blind calculations involve additional sum-mations over the initial and final state-spaces. Similar diagrams and amplitudesexist for processes with external bosons which can be mediated by either virtualfermions or bosons.Referring to the alphabetic labeling in figure 2.4, All the two-body scatteringprocesses correspond to the general process AB→ CD, and can be characterizedby their q2 according to the Mandelstam variables:s = (PA +PB)2t = (PA−PC)2u = (PA−PD)2, (2.29)with√s adopted as the symbol for the invariant mass of two colliding particles.This perturbative picture of particle dynamics permits a conceptualization wherethe probability of an interaction between a current at one point in space-time and15a current at another point is proportional to a product of the currents’ charges, andthe force coupling constants. For electromagnetism, the weak force, and QCD, thecoupling constants are reexpressed as the more experimentally relevant products:α = e2/4pi , αW = g2W/4pi , and αs = g2s/4pi respectively. In particular, α corre-sponds to the fine-structure constant, which appears in the Coulomb potential fortwo point charges separated by a distance r : |V (r)| = |α/r|. The classical no-tion of a force on a charged particle in an electromagnetic field is understood as astatistical averaging of virtual photon exchanges.Predictive perturbative theories must be renormalized so that they are express-ible as measurable particle states and not unobservable bare states in order to avoidultraviolet divergences in the calculation of diagrams in higher orders of αi, whereignorance of physics at arbitrary momentum scales leads to infinite transition am-plitudes. In the renormalized theory, the definition of a free particle under theinteraction of a given force depends on the momentum scale of the interaction.This characteristic can be conceptualized as the resolution with which the chargescreening of the bare particle, provided by the polarization of virtual pair produc-tion in the surrounding vacuum, is penetrated by the mediating particle. This isshown schematically in figure 2.5.Figure 2.5: Electron charge screening due to the vacuum polarization of thephoton field. [6]The momentum dependence enters the perturbative calculation as a runningof the force coupling constants with the momentum scale of the interaction. Theperturbative regime for a given force then corresponds to α  1. Critically, thenon-abelian nature of QCD is postulated to lead to an anti-screening, evidenced in16the theoretical property called asymptotic freedom, where αs → 0 as q2 → ∞ andαs → 1 as q2 → 0. This behaviour motivates the experimentally consistent pos-tulation of colour confinement, which forbids the existence of unbound colouredstates at distances larger than O(10−15)m and offers an explanation for why quarksappear in nature bound within net colourless hadrons: either as mesons (qq¯ pairs)or hadrons (qqq triplets).The full probability amplitude for a scattering process, calculated to the Nthperturbative order in g consists of a summation over all Feynman diagrams with ≤N vertices, beginning with the leading order (LO) two-vertex process:M (gN) =∑kMk(g2)+∑kMk(g3)+ ...+∑kMk(gNi ) (2.30)The probability amplitude contains all paths between the specified initial and fi-nal state, which in general allows different Feynman diagrams to constructivelyor destructively interfere with each other. The approximate probability amplitudecan then be used to predict decay or scattering rate probabilities, the measurementof which serves as the primary mechanism for testing the Standard Model. Forscattering processes the amplitude is used to predict final state probability distribu-tions differentiated in final state variables of interest, X , normalized to the initial-scattering-state flux, F , known as the differential scattering cross-section [31]:dσ = |M |2FdX , (2.31)which is expressed in units of area called barns(b), where b = 100 fm2. At present,experimental precision motivates calculations up to next-to-next-to-leading order(NNLO), or O(α3i ), in only a few cases.In particular, s-channel processes provide a means of detecting and measuringthe masses of fundamental particles. When the mediator has mass m0 these pro-cesses are characterized by resonant cross-sections that are peaked at s = m20, withcharacteristic mass width Γ, and shape given by a Breit-Wigner distribution withapproximate form [31]:dσds∝1(s−m20)2 +m20Γ2(2.32)172.1.4 The Parameters of the Standard ModelThe Standard Model is fixed by 19 independent parameters, which must be deter-mined experimentally via cross-section and decay rate measurements [22]. Fun-damentally, they can be expressed as the the Higgs potential terms µ and λ ; thegauge coupling constants g1, g2 and g3; the Yukawa couplings for the 9 massivefermions; the 4 independent parameters of the CKM matrix; and the QCD param-eter θ , which specifies the structure of the gluon self-interaction. Other than θ , thevariables can be reexpressed as the elements of the CKM matrix and 14 other ex-perimentally measurable variables: the non-neutrino particles masses, the electriccharge, and αs. The Standard Model is then fully defined by equation 2.18 and thetable of particle properties shown figure 2.6.Figure 2.6: The content of the Standard Model [7].At least one extension to the Standard Model is required since mixing betweenthe neutrino states has been experimentally observed. Such mixing indicates thatneutrinos aren’t massless, as is assumed by the Standard Model. The simplestextension to the Standard Model is obtained by the addition of a neutrino mixing18matrix, analogous to the CKM matrix, defined such that charged lepton flavourstates are identical to their mass states. At present, the parameters of the matrixare not fully constrained by experiment. Understanding the physics of the neutrinosector is one of the most important areas of study in particle physics. However,since the neutrino masses are constrained to be less than 18 MeV, the high massstudies presented in this thesis are blind to the details of neutrino mixing [22].2.2 Motivations for New PhysicsFor a variety of reasons the Standard Model is considered to be an incompletedescription of nature. The QFT framework itself is necessarily an effective de-scription valid only up to some momentum scale, ΛUV , evidenced in part by thenecessity of the renormalization procedure, but also due to the failure to properlyincorporate gravity and general relativity. In the absence of any new physics, theStandard Model is valid only up to the Planck scale ΛPlanck = 1.22× 1019 GeV,where the interaction energy itself becomes so large so as to generate strong grav-itational interactions. However, there are numerous reasons to believe that evenwithin its effective regime a more complete QFT formulation exists, which wouldconsist of adding new fermions, symmetries, or spatial dimensions. Each of thesecases will imply an extension of the Standard Model Lagrangian by new fieldsand interaction terms, either fundamental or effective, which can be tested viacross-section measurement in the same manner as the structure of the StandardLagrangian. Two specific models for extending the Lagrangian are discussed insection 2.3, in this section the outstanding issues with the Standard Model thatmotivate those models are reviewed.2.2.1 The Top Quark and the Flavor HierarchyThe development of particle physics has largely been characterized by reduction-ism, where simplifying laws or concepts are postulated as explanations for dis-parate observed phenomena. A notable reduction was the explanation of the plethoraof hadron species as bound states of the more fundamental quarks. Now thethree identical fermion generations manifesting themselves at successively highermasses motivate efforts at reduction. The lack of explanation for their vastly dis-19parate masses, summarized in table 2.7, is referred to as the fermion mass prob-lem [32]. The flavor mass hierarchy among the charged fermions alone begins atmasses on the order of O(10−4) GeV, and terminates with the top quark mass whichlies, remarkably, at the electroweak scale with mass 174 GeV ∼ v = 246 GeV.Figure 2.7: The Standard Model mass hierarchy[8].Within the Standard Model the top-quark has the strongest coupling to theHiggs-boson, and the natures of the two are closely related. For example, the Higgsboson interacts with massless bosons via virtual top-quark loops, and it follows thatthe top-quark necessarily plays an important role in the many new physical theoriesthat attempt to address its outstanding problems. In addition, as the most-massivefermion, the top-quark plays an important role in theories for augmented or alter-native mass generation mechanisms.2.2.2 Grand UnificationReductionism has also been fruitful in efforts to describe the fundamental forcesand now motivates the pursuit of a fully unified description of them. This pro-20cess began with Maxwell’s unification of electricity and magnetism, and was laterextended with the formulation of the unified electroweak sector of the Standardmodel. Now, formulations where the strong force and the electroweak force arethemselves manifestations of a unified gauge description are being sought in socalled Grand Unification Theories (GUTs). These theories attempt to reduce thenumber of free parameters in the Standard Model and so provide a theoretical ex-planation for some of the necessary, and yet unexplained relationships betweenthem [22].These theories make a specific set of predictions, one of which is gauge cou-pling unification. Remarkably, within the Standard Model alone, when the forcecoupling constants are run to higher energy, they appear to nearly converge at asingle value, known as the GUT scale, at ΛGUT ≈ 1016/GeV, as shown in figure2.8.Figure 2.8: The running of the coupling constants [9].If Grand Unification is assumed to be a physical reality the GUT scale repre-sents the maximum energy scale by where new physics must present itself [9].212.2.3 The Hierarchy Problem and Higgs Fine-TuningAn outstanding problem in particle physics is accommodating the apparent weak-ness of gravity. If the gauge theory description is an effective description of fun-damental physics then there should exist a spin-2 boson which mediates the gravi-tational force. However, including this particle in the Standard Model Lagrangianintroduces terms whose coupling constants are 10−16 times weaker than the elec-troweak scale. This hierarchy problem between the gauge forces has a severe im-plication for the Standard Model.Like all particles in the perturbative theory, the bare Higgs boson receives aninfinite series of quantum self corrections. The Higgs mass is constrained to beless than O(1) TeV in order to avoid unitary violation, and maintain conservationof probability. However, unlike the other particles in the theory, the Higgs massremains significantly dependent on the cut-off scale of the effective theory. Everymassive known field induces two point loop corrections to the Higgs mass, such asthose shown in figure 2.9.Figure 2.9: Higgs fermion (left) and boson (right) virtual corrections.The resultant Standard Model Higgs mass correction term at first order is dom-inated by the fermionic corrections and is of order Λ2UV . The observed mass isgiven by the equation [33]:(mH)2 = (m0H)2−116pi2 [∑fλ 2f ]Λ2UV + ..., (2.33)where f runs over the fermionic fields. If the Standard Model is complete, then22the cutoff scale of the theory, ΛUV , is the Planck scale, and in order to obtainan electroweak scale Higgs mass, the bare Higgs mass term and the correctionterm must cancel to the astonishing precision of O(10−34). If grand unification isassumed this can be marginally lowered to O(10−28). In either case, in the absenceof a mechanism to generate the required cancellation, the implication is that theYukawa couplings realized in nature necessarily belong to a narrow region of theYukawa coupling parameter space in order to yield the cancellation, and are thussaid to be fine-tuned. This aesthetic problem is seen as a hint that additional physicsmay exist that removes the fine-tuning requirement from the theory.2.2.4 Top-Down Predictions from String TheoryIf a complete description of nature is possible, QFT must be replaced by a theorythat ultimately incorporates general relativity and quantum mechanics at the Planckscale. The theoretical pursuit of such a framework has culminated in the formu-lation of M-theory, a generalization of various superstring descriptions of nature,the details of which are beyond the scope of this thesis. However, M-theory canbe thought of as an extrapolation of present understandings of physics to arbitrar-ily high energy scales, toward the most fundamental, or top-level physics. Thatprocess has yielded the following set of general predictions [34]:• Particles are not point-like, but correspond to different configurations ofO(10−35)m strings.• An internal symmetry exists between fermions and bosons, called supersym-metry.• There exists an additional 6 spatial dimensions.The string hypothesis is presently considered untestable, however the latter twocharacteristics may manifest themselves in nature such that they impact the effec-tive QFT description in testable ways leading to a so-called top-down approachto model building. Such models involve augmenting the Standard Model with cer-tain extra-dimensional or supersymmetric realizations in order to solve outstandingproblems with the lower-energy QFT description.232.3 Benchmark ModelsThis section summarizes the motivations and structure of the two BSM theoriesthat serve as benchmark models for the resonance searches for top-pair resonancesdescribed in this thesis.2.3.1 The Randall-Sundrum Warped Extra-Dimension ModelRandall-Sundrum warped extra-dimension models are top-down motivated modelsthat propose that the hierarchy problems of the Standard Model are only apparentproblems in an effective theory that fails to take account of an underlying aspect ofnature: the existence of a highly warped extra spatial dimension. A brief descrip-tion of the setup and general results of the model are given below.The Randall-Sundrum Model with a single finite warped extra-dimension (RS1)proposes that the standard Minkowski space is extended to a slice of (4+1) dimen-sional anti-de Sitter space (AdS5) [10]: a Lorentzian space whose 5th dimension isfinite with length pirc, where rc is referred to as the compactification radius [25].In realistic models the “radial” dimension, y, is small with normalized coordinateφ = y/rC; and bounded by two branes with different energy densities: a high energydensity UV brane located at φ = 0 and a low energy density IR brane located at±φ = pi . The energy differential gravitationally warps the bulk space such that theregular (3+1) Minkowski metric describing the space perpendicular to y dependson φ . The squared 4+1 dimensional norm is:ds2 = e−2krC|φ |ηµνxµxν − r2c dφ 2, (2.34)where k is a constant on the order of the Planck scale.From the quantum mechanical perspective, the gravitational warping corre-sponds to an exponential localization of the graviton wave function toward the UVbrane. By allowing the gauge bosons and fermion fields to propagate through thebulk the model can explain the fermion mass hierarchy and produce corrections tothe gauge coupling runnings that lead to gauge coupling unification. The geometryof the 5th dimension imposes boundary conditions on the 5th dimensional com-ponent of the bulk wave-functions such that only highly discretized towers of 5th-24Figure 2.10: A schematic representation of the warped anti-de Sitter space[10].dimensional momentum states are permitted, analogous to the quantum mechanicalparticle in a box model, though with non-trivial solutions for the eigenstates. Eachbulk particle species can occupy one of its tower states, with the ground state energylevel corresponding to the Standard Model. The ground state modes correspondingto the Standard Model are shown schematically in 2.11.Figure 2.11: A schematic depiction of the 5th-dimensional components of thebulk SM wave-functions.The 3+1 dimensional effective theory, which reproduces the Standard Model,is obtained by integrating over the 5th dimension. The effective Standard Modelhierarchy problem can be generated from the 5th dimensional warp factor and a25fundamental Planck scale, Λ5DPlanck, that is of the order of the electroweak scale:Λ2Planck =(Λ5DPlanck)3k[1− e−2krcpi]. (2.35)This offers an explanation for the gauge hierarchy problem as merely an apparenteffect. Critically, the exponential warp factor reduces the required tuning from aprecision of better than O(10−28), to only about O(10−2) [25].Integrating over the 5th dimension results in the SM Lagrangian augmentedby an infinite number of successively more massive copies of the bulk fields, socalled Kaluza-Klein modes, corresponding to the tower of 5th-dimensional states.The effective masses of the ground state particles depend on the overlap of theirwave-function with the Higgs at the IR brane, offering a geometric rationale for thefermion mass hierarchy. The extra-dimensional momentum dominantly contributesto the masses of the excited states; their values and spacing are nearly identicaland reflect the geometry of the bulk-space [35]. Choices of k and rC that providesatisfactory solutions to the gauge hierarchy problem predict the first excited stateswill have O(TeV) scale mass.A consequence of the warped geometry is that the 5th dimensional momen-tum is not a conserved quantity, and so the total number of excited KK-states canvary in time and complete decays of excited states to Standard Model particles areallowed. The phenomenology of the excited fields depends on their localizationand is constrained by experimental results. In particular, the first excitation of thegluon (the KK-gluon), gKK , is exponentially localized towards the IR brane, andwith dominant coupling to Standard Model top-quarks is a favoured search can-didate for the RS1 model. Electroweak measurements in the b-quark sector placeupper limits on the coupling of the KK-gluon to the left-handed third generationdoublet. In particular, the coupling must be small enough so as not to cause devia-tions in the observed Z→ bb¯ rate [35]. Thus, in this framework, tL is less localizedtowards the IR than tR , resulting in a chirally asymmetric coupling with the KK-gluon [25]. For simplicity the remaining quark states are assumed to have identicalprofiles; their low mass implies localization towards the UV brane.The relevant phenomenology of the model, which depends on the wave-functionlocalizations, the compactification radius, and the warp-factor can be specified by26the KK-gluon mass, and a set of coupling constants between the KK-gluon and thequark states [36]. Letting q denote the lightest two quark generations, and the sub-scripts R, and L, refer to the right and left handed states, the couplings expressedas a multiple of the SM strong coupling constant are summarized in table 2.2:Table 2.2: KK-gluon-quark coupling strengths [g−1s ]gKKtL gKKtR gKKbLgKKbR gKKqL gKKqR1.0 4.0 1.0 -0.2 -0.2 -0.2These default couplings predict that the KK-gluon has a mass width of ΓgKK/mgKK ≈15% and branching ratio to top-quarks of about 95%, though the exact value de-pends on the mass of the KK-gluon.2.3.2 TopcolorThe high mass of the top-quark suggests it plays a special role in theories for mass-generation, including the Standard Model Higgs mechanism, where it appears asthe dominant virtual contributor. This motivates the formulation of theories withseparate mass-generating mechanisms for the top-quark. Topcolor has emerged asa theory where the top-quark itself generates mass, especially its own, via the mani-festation of a composite top-pair particle, the top-quark condensate: a bosonic stateformed from a bound top-antitop pair [37]. Topcolor can been added to the Stan-dard Model Higgs Mechanism, with the Higgs generating fundamental masses forthe quark states and Topcolor generating the bulk of the third generation masses.It can also be added to supersymmetric theories to solve their so-called flavourchanging neutral current problem [38]. However, in the literature it is most com-monly associated with its inclusion in Extended Technicolour.Topcolor proposes that the Standard Model possesses additional broken gaugesymmetries that couple asymmetrically to the three fermion generations. The glu-ons, in analogy with the photon, are then realized as the massless remnants of anextended broken symmetry. Under Topcolor the symmetry and breaking of theStandard Model are extended to [39]:SU(3)1×SU(3)2×U(1)Y1×U(1)Y2×SU(2)L→ SU(3)QCD×U(1)EM (2.36)27The gauge fields associated with the symmetries denoted 1 and 2 couple preferen-tially to the third, and lightest two generations respectively. The extended symme-try breaking yields additional massive bosons: a sector of 8 massive top-gluons,and a Z′ boson that couples dominantly to quarks. The top-gluons are assumed tocouple preferentially to the third generation and cause the formation of bottom andtop-quark condensates, which in turn generate large and degenerate mass terms forthe bottom and top-quarks. To reproduce the observed particle spectrum, the Z′ isassumed to couple asymmetrically to top and bottom pairs, generating attractiveand repulsive forces between the former and latter respectively, breaking the bot-tom quark condensate and reproducing the observed masses of the third generation.The mass of the third generation quarks then consists of two components, a fun-damental mass term εm; and a larger contribution from the condensate: (1− ε)m.The fundamental term can be generated by the Higgs, or some other mechanism.An important phenomenological consequence of Topcolor, and a promisingmeans of its discovery, is the observation of a narrow top-pair resonance associ-ated with the Z′ boson. A leptophobic topphylic Z′ with highly suppressed lep-tonic coupling and enhanced top-quark coupling, is chosen as a benchmark modelfor generic narrow top-pair resonances that could occur in a variety of theorieswith an additional broken U(1) symmetry among top-quarks [40]. The parameterspace for the model consists of the strength of its interactions among the leptonsand different quarks. When the top-quark coupling is maximized, and all othercouplings minimized, the model is summarized completely in terms of the mass ofthe leptophobic Z′, which has width Γ/M = 1.2%.2.4 Physics of Proton-Proton InteractionsAt the LHC, perturbative processes are generated at high rate through the hardcollision of the partonic constituents of collinear and opposing beams of protons.However, these perturbative hard processes are embedded within maximally non-perturbative phenomena: the initial momentum structure of the protons and the fi-nal state evolution of scattered partons into collimated jets of hadrons. This sectionprovides an overview of the model of proton and jet physics which connects theanalytic predictions of QFT to predictions for the observable outcome of proton-28proton collision events at the LHC. Following the general description of the model,a summary of the simulation used to generate samples of collision events and pro-duction cross-sections is given. Finally, the specific resonant and non-resonanttop-pair hypotheses that are tested in the analyses presented in this thesis are de-scribed.2.4.1 The Collision Coordinate SystemThe phenomena studied in proton-proton collisions are highly relativistic within thelab-frame and generally boosted along a known direction of motion. The centre-of-mass frame of the partonic collision is boosted along the proton beam axis toa degree that varies event-by-event and is determined by the collinear momentumasymmetry between the colliding partons. Within the event itself, systems of de-caying particles are Lorentz boosted along the parent particle’s direction of motion.To efficiently handle the arbitrary boosting, and make meaningful event-by-eventcomparisons, a specialized coordinate system is used that allows 4-vectors to befully determined by 3-coordinates, and wherein angular separations and magni-tudes are Lorentz boost invariant.For particles involved in collision events the relativistic approximation E ≈ |p|holds to a precision below the resolution of experiment. Fundamental 4-vectorscan then be fully described in terms of their spatial 3-vector. Defining the boostdirection of the collision to be along the z-axis, spatial vectors are specified by theirpolar and azimuthal angles with respect to the z-direction, θ and φ respectively; andthe magnitude of their projection onto the transverse (x-y) plane, R; as depicted infigure 2.12a.R and φ are perpendicular to the z-direction, and thus invariant with respect toboosts in the z-direction. A system where the angular separation between vectorsis also Lorentz invariant is achieved by defining the pseudorapidity coordinate,η =− ln tan(θ/2). The relationship between θ and η is shown in figure 2.12b. Thepseudorapidity can be expressed in terms of particle momenta and, in the highlyrelativistic approximation, is nearly identical to rapidity, y:η ≡ 12ln(|p|+ pz|p|− pz)≈12ln(E + pzE− pz)≡ y. (2.37)29(a)(b)Figure 2.12: (a) A vector representation and angular cones in Cartesian andcylindrical coordinates. (b) The relationship between pseudorapidityand polar angle.An important property is that differences in rapidity are Lorentz invariant. Theexample angular cones, and space-vector depicted in the cylindrical coordinatesystem in figure 2.12a can be reexpressed in η-φ -R space as shown in figure 2.13.The angular space is now represented by a rectilinear system periodic in φ andperpendicular to the strictly positive transverse magnitude. Critically, two cones30φFigure 2.13: The collision coordinate system. The coloured ellipses corre-spond to the angular cones depicted in figure 2.12a; in the η-φ systemthey occupy the same area.characterized by the same rapidity separation will have the same angular separationin η-φ -space defined as:∆R≡√∆η2 +∆φ 2, (2.38)regardless of their boost along the z-direction.In summary, letting pT denote transverse momentum: the magnitude of theprojection of an object’s momentum onto the transverse plane; the relationshipbetween Cartesian and collision coordinate 4-momenta for massless particles isgiven in the following set of equations.px = pT cosφ (2.39)py = pT sinφpz = pT sinhηE = pT coshη312.4.2 The Anatomy of the Proton-Proton CollisionThe structure of the proton is described by the quark model [22] as three valencequarks, two up and one down, bound together within a fluctuating sea of virtualpartons. In most physics studies, the proton-proton collisions of interest are eventsin which a significant fraction of the proton momenta are exchanged between twopartons at high enough energies that the parton interaction is perturbatively calcu-lable. The final state of the hard partonic interaction is surrounded by the partonicremnants of the collided protons: the spectating partons which did not participatein the interaction, the initial state radiation (ISR) splitting off of the incident hardpartons, and additional scatterings between other partons. Some partons producedin this process, such as top-quarks, will immediately decay, and then the emergingpartonic system will continue to split via the spontaneous emission of additionalpartons. Some of the splittings may be hard and well separated, leading to so-calledfinal state radiation, but most will be relatively soft(low energy) and collinear withthe initiating parton [41]. The showering process accelerates as the energy of thepartons approaches O(1)GeV where QCD becomes strongly interacting [42]. Thesystem of parton showers then coalesces via non-perturbative processes into jetsof hadrons within 10−15 m of the collision point. Electromagnetic and weak inter-actions may also occur in either the hard-process, the parton decays, or additionalsplitting processes. This complicated collision process is represented schematicallyfor a top-pair event in the pseudo-Feynman diagram shown in 2.14.The perturbative structure of the Feynman diagram for a collision event canbe seen as consisting of a relatively low order core diagram for the hard process,that is preceded and followed by recursive series of splittings, the bulk of whichare the parton splittings shown in figure 2.15. In the so called soft and collinearapproximation the perturbative splitting probabilities can be factored out of the fullhigh-multiplicity vertex amplitude, such that their details do not affect the hard-process cross-section, and events can be built up by iteratively adding splittingsto the hard-process [41]. For a given splitting, the emitted particle carries a smallfraction, (1− f ), of the initial energy, and has transverse momentum kT definedwith respect to the direction of motion of its harder partner. The probability distri-32Figure 2.14: A schematic diagram of a pp→ tt¯+jets events [11]. Partons(blue) from two collinear protons (large green ovals) interact via ahard collision ( large red circle) producing two top-quarks (small redcircles) that subsequently decay. The partons from the hard interaction(red) shower and hadronize (green ovals), the resulting hadrons thendecay (green circles). The event contains electromagnetic interactions(yellow) and additional parton collisions (purple).Figure 2.15: Parton splitting vertices.butions for g→ gg, and q→ qg, splittings have a similar form [41]:dPA→B ∝αspid f1− fdk2Tk2T; (2.40)33and both suffer a divergence as kT → 0: a collinear, θ → 0, divergence in bothcases; and a soft, E → 0, divergence strictly in the latter [41]. The divergencesassociated with the non-perturbative regime are avoided by introducing a cutoff inperturbative calculations, of Q0 ≈ 1GeV .The proton has a time-dependent structure: each constituent parton can be con-ceptualized as lying on a partonic path, whose history consists of series of splittingsthat served to alter the parton’s virtuality, as shown schematically in figure 2.16.Figure 2.16: A schematic representation of the dependence of the proton’sstructural resolution on the 4-momentum of the mediating particle. Atlower energy, the valence quarks are most visible. At higher energies,virtual sea-quarks are resolved.According to the Heisenberg uncertainty principle, increasingly virtual fluctu-ations occur at shorter and shorter time-scales. As a consequence, the parton dis-tribution functions(PDFs), which describe the probability of finding a given partonspecies i carrying a fraction of the proton’s longitudinal momentum xi, depend onthe Q2 of the parton when it enters the hard interaction. The PDF evolution in Q2is describable by the DGLAP system of integro-differential equations based on thesplitting functions. The DGLAP equations relate the probability of finding a partonwith xi to the probability that it arose from the splitting of another less virtual par-ton down to the non-perturbative cutoff [41]. The PDFs themselves are determinedfrom global fits to various proton cross-section measurements carried out over arange of x and Q2 values. Various models, or PDF sets, consisting of around 10 to40 parameters exist, and yield similar results. The MSTW PDF set at various Q2 is34shown in figure 2.17.x­610 ­510 ­410 ­310 ­210 ­110)2xf(x,Q­1­0.500.511.522.533.54gd duuss,cc,2 = 2.5 GeV2Q)2xf(x,Qx­610 ­510 ­410 ­310 ­210 ­110)2xf(x,Q02468101214161820gbb,2 = 10 000 GeV2Q)2xf(x,QMSTW 2008 NNLO PDFs (68% C.L.)Figure 2.17: The MSTW 2008 NNLO parton distribution functions for eachspecies of parton, at Q2 = 10 GeV2 (left) and Q2 = 100002 GeV (right)..The convolution of the colliding proton PDFs yields the parton luminosity:the probability distribution for the initial two parton state entering into the hard-interaction. At the LHC the proton-proton initial state is at rest and uniquely deter-mined by the proton-proton collision energy√s, however, the parton-parton sys-tem has a smaller centre of mass energy√sˆ and is generally longitudinally boostedwith respect to the proton-proton collision.According to the QCD factorization theorem [43], inclusive proton-proton cross-sections can be calculated by convolving specific perturbative parton-parton cross-sections, σˆi j, with generic models for the PDFs of the colliding partons, fi(x1,µ)and f j(x2,µ), and summing over the possible parton initial state combinations iand j:dσpp = ∑i, j,k∫dx1dx2 fi(x1,µ f ) f j(x2,µ f )σˆi j(x1,x2,µ f ) (2.41)35The factorization scale, defines the resolution with which the hadron’s momentumstructure is probed and is taken to be equal to the QCD renormalization scale, andset to the momentum of the hard interaction of interest: µ ≡ µF = µr = Q. Anon-physical dependence on µ remains for calculations made to finite perturbativeorder. The exclusive event-by-event history of the incident partons, integrated overin the parton luminosity, includes initial state radiation of hard well separated par-tons; these originate from the unrecombinable splittings from the incident partons’histories within the virtual fluctuations of the protons [44].The splitting of the emerging partons from the proton-proton collision can alsobe approximated by a forwards evolution of DGLAP equations, unconstrained byPDFs, for kT > µ . The resulting partonic final state of the proton-proton collision isthen a multiplicity of parton showers with collimated energy flows that correspondto the 4-momenta of any initial-state-radiation, scattered partons from the hardinteraction, final-state-radiations, and the remnants of the protons. The degree ofshower collimation is related to the Lorentz boost of the initiating parton (p); it isroughly contained to an angular separation given by:∆R <2mppp, (2.42)where mp, and pp are the mass and momentum of the initiating parton.As the parton showers emerge from the interaction point, and their constituentpartons reach O(10−15)m separation distances, the partons begin to coalesce intobound states of colourless hadrons as a consequence of quark confinement. Thishadronization process is not perturbatively calculable, but, like the showering pro-cess, it is assumed to happen at distances far enough from the hard interaction sothat its unknown details do not impact the perturbative cross-section [43]. Con-ceptually the process is postulated to occur because of the spontaneous gener-ation of real qq¯ pairs from the energy stored in the collimated tube-like gluonfields that form between the separating partons. The spontaneous qq¯ pair gener-ation eventually permits (pseudo)stable colourless bound hadron states that mini-mize the energy stored in the gluon field. The observable result of the showeringand hadronization process for a parton is then an associated system of collimatedhadrons called a hadronic jet. The evolution of the jet system from an emergent36parton is summarized in figure 2.18.ΔRFigure 2.18: The evolution of a parton emerging from the proton collisioninto a hadronic jet.The jet system has a 4-momentum that is correlated to the initial parton andso can serve as a proxy through which partons can be measured and identified.The multiplicity of reconstructed jets depends on the jet definition, as the show-ering parton can be reconstructed as a single jet, or a number of smaller jets cor-responding to some level of the parton showering process. This flexibility in thedegree to which the partonic system is resolved has been referred to as jetography[45]. Critically, the dependence of jet variables on the approximated and incalcu-lable collinear and infrared details must be understood. Generally, infrared andcollinear(IRC) safe definitions, which are insensitive to IRC details, are sought[45].2.4.3 Event GenerationEvent-by-event variability: the kinematics, number, composition, and origin of jetsand other objects; renders continuous predictions for the final state distribution ofcollision processes impossible. Instead, the final states of proton-proton events aresimulated on an event-by-event basis by numerically sampling the “event-space”defined by the proton-proton collision model. Samples of events for a given hy-pothesis can be generated via Monte Carlo techniques for a variety of applications,their discrete construction mirroring the discrete collection of real data. Through-out the remainder of this thesis such samples are referred to as “Monte Carlo”37(MC).The general event generation strategy is to factorize the event structure intoa hard process with a specified number of particle emissions plus the additionalinitial and final state radiations. Efficient generation is then achieved by first sam-pling the parton-luminosity convolved hard-interaction (eq.2.41), over the helicity-,colour-, and phase-space given the fully calculated hard-process amplitude. Addi-tional perturbative radiations are then simulated by repeatedly sampling the split-ting probabilities, backwards in time for ISR, and forwards in time for FSR. In eachdirection the iteration continues until the virtuality of all particles reaches the non-perturbative cutoff. In particular, the final state showering of all resultant partonsemerging from the interaction point is assumed to be strongly ordered such thateach emission is less virtual than the emission that came before it: Q21 > Q22 > Q23...[42]. An ambiguity exists in the definition of Q2 and currently at least two orderingschemes are in use: angular ordering, and pT ordering.Non-perturbative hadronization models are employed to transfer the resultantperturbatively calculated parton-showers into hadronic jets. Two models in partic-ular are in wide use, they have been tuned to measurement in data and are found togive good effective descriptions of jets[42]:• The cluster model is based on a property of perturbative QCD called precon-finement, where at each stage of the parton showering process, phase-spaceadjacent partons are found to form colour singlet states. The model proceedsby non-perturbatively splitting gluons in the parton shower into qq¯ pairs,and then forming colour-singlet massive hadrons from the resulting systemof phase-space adjacent quarks• The string model is a more complicated attempt at simulating the hadroniza-tion process based on a model for colour confinement. The tube-like colourflux between separating partons is modelled by elastic strings with constantenergy density. The string can fragment, via the spontaneous production of anew qq¯ pair into two new strings according to a tunable fragmentation func-tion. Strings are assigned to the parton shower, and then evolved in time-steps until a series of stable non-fragmenting strings is obtained. Baryonformation is permitted by allowing strings to form between a single quark38and a bound di-quark system.Each model handles the flow of colour charge from the initial parton statethrough to the evolution of the hadronization process, and transfers the partonshower to an intermediate colourless state composed of hadrons. Simulations ofthe scattering of the remaining proton remnants are incorporated into the models.Finally, the potentially detectable pseudo-stable final state of the event is then ob-tained by sampling the well known decay probabilities for all unstable particles.Various general purpose event generators have been created that employ differ-ent implementation prescriptions for the complete proton-proton collision model-ing. In addition, a number of specialized event generators have also been developedfor modeling specific processes with improved accuracy; they must be interfacedwith a general purpose generator to obtain full predictions.The following three general purpose generators are used to derive predictionsin the studies described in this thesis:• Pythia [46, 47] is a LO generator consisting of a library of pre-calculated2→ 2 hard processes, which can be selected for generation and evolved to afinal state with a p⊥ parton showering ordering given by Q2 ≡ f (1− f )m2.The hadronization process is modelled by using the Lund string model.• Herwig [48] is a also LO order generator but uses angular ordered partonshowering given by Q2≡ E2θ 2≈m2/( f (1− f )). The hadronization processis modelled with cluster model.• Sherpa [11] uses a combination of the Herwig and Pythia techniques, em-ploying p⊥ ordering, but using the cluster hadronization scheme.The following set of specialized generators are used to derive predictions in thestudies described in this thesis:• MC@NLO [49] is an event generator based off the Herwig framework, whichseeks to better model QCD for a selection of important LHC processes bygenerating the hard-process at Next-to-Leading-Order. Its NLO library con-sists of a subset of Standard Model processes involving Higgs, heavy quarks,or diboson events. Its main function is matching the NLO hard-process to39the parton showers provided by one of the general purpose generators in amanner that avoids double counting between NLO and LO diagrams.• Alpgen [50] is a generator for modeling the additional jet multiplicity for cer-tain Standard Model processes, most notably single boson production withan additional n jets: Z/γ∗/W +n−jet events.• MadGraph [51] is a tool for calculating the amplitudes for arbitrary LOFeynman diagrams specified by the user, which can serve as input into thegeneration chain. It is particularly useful for calculating the matrix elementsassociated with new physics.2.4.4 Top-Pair EventsThis section provides an overview of the relevant theory for the production of top-pair events at the LHC. Such events are characterized by the decay modes of eachtop-quark and the invariant mass of the ditop system. This section is laid out asfollows. First the top-quark’s properties and decay are summarized. Then the non-resonant and resonant top-pair production predicted under the Standard Model andbenchmark BSM models are described. Finally, the characterization of the top-pairfinal state which motivates various search strategies, is discussed.The Top quarkThe top quark is the heaviest known particle in the Standard Model. It was discov-ered in 1995, but its existence was predicted by the observation of the b quark, some20 years prior, which had to be accompanied by a finite massed partner in order toensure the stability of the Standard Model. With a mass of 173.07±0.52 GeV, andwidth of 2.0±0.5 GeV, the top-quark has an associated short lifetime of 3.3±0.8×10−25 s. It mixes minimally with the lighter generations and so decays dominantlyto a W and a b-quark, with decay branching ratio: Λ(t→Wb)/Λ(t→W (b,s,d))=|V 2tb|= 0.91. The dominant top-quark decay mode is depicted in figure 2.19.A critical consequence of the top-quark’s short lifetime is that it decays per-turbatively prior to the showering and hadronization process, which opens up newavenues for study which are not possible with other quarks. In particular, a hadron-40W+tbq, `q′,ν`Figure 2.19: The three-body decay of the top-quarkically decaying top-quark will have a multicore hadronic structure potentially re-constructible as separate jets.Standard Model Top-Pair ProductionUnder the Standard Model, top-anti-top pairs are dominantly produced by gluon-fusion, supplemented by quark-annihilation. The lowest order Feynman diagramsfor these processes are shown in figure 2.20.gtt¯ggttt¯ggttt¯gggtt¯qq¯Figure 2.20: Leading order Standard Model top-pair production diagrams.Gluon-fusion dominates since no valence anti-quarks exist within the protonand the qq¯ initial state necessarily involves a virtual sea-quark whose PDFs aresuppressed, this characteristic is evidenced in figure 2.17.The parton-parton cross-sections for top-pair production have been calculatedto approximate NNLO for√s = 7 TeV, and the total theoretical inclusive cross-section, σ(pp→ tt¯X) has been estimated to be 165 pb. The ditop Standard Modelinvariant mass differentiated cross-section for top pair production is a non-trivialfunction, but has a roughly exponentially decreasing form over the accessible rangeat the LHC [52].41Resonant Top-Pair ProductionTop-pair production via a massive new mediating boson, of the types consideredin this thesis, would proceed via an s-channel process where the massless gluonmediator is replaced by a new massive particle. In each case a small coupling tolight-quarks provides an LHC relevant production mechanism, while the dominantcoupling to top-quarks provides a distinct final state to search for, as is shown forthe example of a KK-gluon in figure 2.21.gKKtt¯qq¯gKKqR gKKtRFigure 2.21: Feynman diagram for resonant top-pair production.The massive propagator gives a resonance line-shape that is proportional to theBreit-Wigner form for the hard-sub-process multiplied by a factor representing theconvolution with the parton luminosity f (sˆ):dσds∝ f (sˆ)1(sˆ−M2)2 +M2Γ2(2.43)Line-shapes for selected resonance masses are shown in figure 2.22.As the resonance mass increases, the overall rate suffers a kinematical suppres-sion due to the reduced initial-state phase-space at the resonant collision energy,and the line shape picks up significant contributions from highly virtual interac-tions proportional to the parton-luminosity. The result is a broadening and deform-ing of the resonance shape. The effect is most pronounced for the wider KK-gluonsthan for the narrow Z′ s. The broadening of the resonances at higher mass can yieldparadoxical behavior in the kinematic acceptance.In the models considered here, interference with Standard Model top-pair pro-duction is ignored and the resonances are predicted to manifest themselves at theLHC as enhancements of the top-pair production rate, directly proportional to theirtheoretical cross-sections. Figure 2.23 shows the invariant mass distribution forthe Standard Model background with two benchmark models stacked on top, all42 mass (GeV)ttruth t500 1000 1500 2000 250000. mass (GeV)ttruth t500 1000 1500 2000 250000. 2.22:√s = 7 TeV pp→ tt¯ resonance shapes. left: The Pythia Z′ pre-diction. right: The MadGraph-Pythia KK-gluon prediction.normalized to their relative cross-sections.Invariant Mass [GeV]500 1000 1500 2000Abritrary Yield­210­110110 tSM tKK­gluonZ’Figure 2.23: Invariant mass distribution for Standard Model as predicted byMC@NLO+Herwig (black), and example resonant top-pair productionfor a 1 TeV KK-gluon (red) and a 1.6 TeV Z′ (blue).43Decay Channels and TopologiesSearches for top-pair production at the LHC depend on the top-pair final state. Thenature of that state is characterizable by two aspects, the top-pair decay channel,and the kinematic topology of the decay. The combination of decay channels andtopologies that an analysis seeks to measure dictate the analysis strategy as theyimpact its signal sensitivity and susceptibility to other background processes.Since the top-quark dominantly decays to a W and b quark, its decay channelsare effectively determined by the product of the two W decays, as is shown infigure 2.24. This leads to three classes of decay channels. The fully-hadronicchannel consists of top-pair decays where both W s decay fully hadronically. Thelepton plus jets channel corresponds to the case where one of the Ws decays to afinal-state electron or muon. The dilepton channel is where both W s decay to afinal state electron or muon. A fourth classification, wherein tauonic decays arespecifically searched for is also possible in principle.(a) (b)Figure 2.24: (a) Product of W -branching ratios. (b) Final state channel prob-abilities for top-pair eventsThe kinematics of the top decay are largely determined by the Lorentz boostof the top quark in the lab frame. At moderate energies, each top quark’s decayproducts are well separated in the detector, and the final state consists of 6 wellseparated objects at the particle level: two b-quarks, and four additional fermions;this is referred to as the resolved topology. However, as the boost increases the44three decay products in each top-decay become highly collimated, with approxi-mate separation ∆R ≈ 2mtop/pT,top. When the top-quarks possess sufficient mo-menta the final state is characterized by the boosted topology wherein each top-decay can itself be treated as a single collimated system. These two topologies arerepresented schematically in figure 2.25 for the lepton plus jets channel, in order tosimultaneously demonstrate the effect on semileptonic and hadronically decayingtop-quarks.(a) (b)Figure 2.25: A schematic diagram of a lepton+jets top-pair event, where onetop decays semileptonically, and the other top decays hadronically, inthe resolved (a), and highly boosted (b) topologies.The two analyses presented here each focus on a different decay channel andtopology. The first analysis presented selected top-pair candidates using a resolvedselection in the dilepton channel. The second analysis selected top pair eventsin the boosted fully hadronic channel. As a result, each analysis was optimizedto search for resonances over different invariant mass ranges, and each employeddifferent analysis strategies. These analyses will be discussed in detail in chapters5 and 6, following a general description of the experiment and statistical methods.45Chapter 3Experiment3.1 OverviewThe experimental setup for the analyses considered here consists of two separateapparatii: the Large Hadron Collider, for generating the proton-proton collisions,and the detector experiments, for detecting events by measuring and identifyingthe particles emerging from them. Together they enable the measurement of differ-ential proton-proton cross-sections for various processes.The Large Hadron Collider is a synchrotron proton-proton collider. It gener-ates an instantaneous proton-proton collision flux or instantaneous luminosity, L ,measured in b−1/s, at multiple interaction points along its circumference. The pro-duction rate (dN/dt)prod for a process of interest at these points is proportional tothe luminosity: (dNdt)prod=L σ . (3.1)The collisions are generated by colliding bunches of counter-rotating protons. Sur-rounding one of the interaction points is the ATLAS detector, which detects andperforms measurements on the 1000s of detector-stable particles that emerge fromthe bunch crossing via a variety of measurements carried out by specialized detec-tion elements located throughout its volume. The experimental goal of ATLAS isto forensically reconstruct the structure of the final state of the collision event, atsome level in its partonic evolution. It produces a physics relevant summary of the46event in terms of a set of 4-vector physics-object representations of the distinguish-able final-state fundamental particles, and the vertex corresponding to the collisionpoint.The vast majority of the proton-proton collision events occurring within theATLAS detector are characterized by collisions with minimal momentum trans-fer between the colliding partons. Such minimum bias events are of little physicsvalue. Moreover, their rate far exceeds the rate at which data can be transmitted,stored, and analyzed. Thus a critical function of the ATLAS detector is to makeshort latency decisions as to whether an event should be stored for further analy-sis. This task is accomplished with a multi-stage trigger system that makes use ofspecialized algorithms and electronics.The predicted detection rate of a process of interest within ATLAS is then givenby: (dNdt)= AεL σ , (3.2)where A is the kinematic acceptance of the analysis, ε is the ATLAS efficiencyfor detecting events, and L is here the ATLAS luminosity estimate. The analysisdependent kinematic acceptance is often limited by the geometry of the precisiondetection systems within ATLAS. The detection efficiency depends on both triggerand reconstruction efficiencies.In principle, hypothesis testing proceeds by comparing the differential rates ofobserved data and predicted parton scattering processes. The practical realizationof a differential event count with respect to an observable X , derived from thephysics objects, is to count events in suitably grained bins of the observable, i.e.a histogram, over a finite number of collisions proportional to a certain integratedluminosity : L =∫∆t dtL . In this context, histograms amount to correlated series ofkinematically restricted independent counting experiments, each with a predictedrate dependent on the kinematic acceptance, Ai, and the detector efficiency, εi,for the ith bin’s range; and each directly proportional to the estimated recordedintegrated luminosity L, such that the expected number of events is given by:Ni = εiLAiσ . (3.3)47Equation 3.3 represents the general statistical model for the prediction of the fullcollision event and detection process as described in terms of a single variable.Hypothetical predictions for equation 3.3 are produced by propagating generatedevents for processes of interest through a detailed simulation of the ATLAS detec-tor. In general, multiple proton-proton collisions will occur within ATLAS, andwill be propagating through its detection systems simultaneously, a phenomenonknown as pile-up. The nature of pile-up depends on the luminosity conditions atthe interaction point, and realistic models of such conditions are also included inthe full simulation.The statistical significance of comparisons of experimental observation, and theprediction represented by equation 3.3, depend on various experimental limitationsThe performance of the detector is characterized by the reconstructed 4-momentaresolutions, and the reconstruction and identification efficiencies. A combinationof data and Monte-Carlo sample sizes and the detector performance place limitson the appropriate binning for a tested observable by introducing statistical uncer-tainty. Most critically, the uncertainties on the calibrations of the detector perfor-mance are a significant source of systematic uncertainty and must be incorporatedinto the statistical model for the prediction. That procedure will be discussed inChapter 4.Understanding the experimental performance and calibration motivates the restof this chapter which is devoted to summarizing the operation, design, and generalexperimental details of ATLAS and the LHC. First, section 3.2 briefly summa-rizes the LHC layout and the physics of the LHC proton beam. Next, section 3.3provides an overview of the ATLAS experiment and constitutes the bulk of thischapter. It begins with a general outline of the operating principles, design, andmethodologies of ATLAS, and is then followed by three sub-sections. Section3.3.1 summarizes the layout, and operation of each subsystem of the ATLAS de-tector. Following that, section 3.3.2 provides a brief overview of the full ATLASsimulation. Finally, section 3.3.3 summarizes the details and performance of thealgorithms used to reconstruct events.483.2 The Large Hadron ColliderThe LHC supplies the collision phenomena studied by the ATLAS detector. Itsperformance is characterized by the proton-proton collision energy, and the lumi-nosity conditions at the interaction point, which each depend on the details of itsdesign and operation. In this section a brief summary of the layout and basic op-erating principles are provided, in addition to the relationship between the beamparameters and the delivered luminosity. At the end of the section a summary ofthe LHC performance over the course of the 2011 data taking period is given.3.2.1 Layout and OperationThe LHC is the largest and most energetic synchrotron accelerator ever constructed[53]. It is situated inside a 26.7 km tunnel that formerly housed the Large ElectronPositron Collider (LEP) [54]. The tunnel is located between 40 m and 170 munderneath the Swiss-French border near Geneva, Switzerland. In order to probethe field theory structure of nature at the TeV scale, within the confines of theexisting tunnel, the LHC was designed to accelerate and collide counter-rotatingbeams of protons at centre of mass collision energies up to 14 TeV. The beamsconsist of trains of tightly packed bunches of protons that are created and primedfor ultimate acceleration within the LHC by a series of smaller accelerators, knownas the injection chain.The accelerators consist primarily of two basic components: radio frequency(RF) cavities, used to construct and accelerate the bunch trains; and super conduct-ing magnets, used to steer and focus the beams [55]. A typical RF cavity is depictedin figure 3.1a: it is a hollow conducting disk, or rounded pill-box, with aperturesalong the beam axis at the centre of each of its circular sides. When an appropriateoscillating voltage is applied in the direction of the beam axis, along the surface ofthe cell, energy is cyclically transferred between an oscillating longitudinal electricfield along the beam axis and an oscillating magnetic field running in the azimuthaldirection. The cavity acquires both capacitive and inductive properties similar toa simple RLC circuit [56]. The longitudinal electric field, E, obeys the travelling49wave equation, which defines the RF-field:E = E0 cos(ωt +φ) , (3.4)where E0 is the amplitude, ω is the oscillation frequency, and φ is a constant phase-shift.A typical acceleration chamber is shown in figure 3.1, it consists of a series ofcavities separated by focusing magnets placed along the beam axis with correlatedseparation distance and oscillation phase such that electric field maxima in a givendirection are generated in a synchronized sequence within successive cavities. Theoscillating maxima define RF buckets: travelling volumes within which protonswill only receive accelerations in a single direction.(a)Figure 3.1: (a) A schematic diagram of a single RF-cavity and the instanta-neous electric and magnetic field configuration induced by an an ACcurrent. (b) A schematic of an LHC acceleration chamber realized as aseries of RF-cavities.As accelerators, RF cavities provide several important benefits for particle ac-celeration: high duty cycle, or a high fraction of system operation time spent pro-viding acceleration; large aperture, or circular transverse clearance, for the beam;and the ability to focus and separate the beam of particles into tight bunches con-fined to the RF buckets [53]. For acceleration to proceed the beam of particles mustbe harmonically synchronized with the chamber oscillations, i.e. the beam must becomposed of bunches separated by integer multiples of the RF period and travel-ling in phase with RF wave crests. Letting d denote the cavity separation distance,50and β the beam velocity, the RF frequency synchronization criteria is:ω = k 2piβd, (3.5)where k is a positive integer [57]. Equation 3.5 indicates that the expected beamvelocity influences RF chamber design. However, once a highly relativistic beamis achieved the beam velocity becomes constant at β ≈ 1 and the same chamberdesign can be used to continually add energy to the beam. This principle of syn-chrotron acceleration allows a finite set of chambers arranged in a circuit to con-tinually accelerate a beam of highly-relativistic particles to higher energy so longas two criteria are met: the accelerating system supplies more energy than is lostper revolution due to synchrotron radiation, and the magnetic steering system canprovide enough bending power to keep the beam within the accelerating circuit. Atthe LHC, maximum achievable energies are limited by the latter consideration.The ultimate LHC design energy of 7 TeV counter-rotating beams necessitates∼ 8 T magnetic fields to keep the beam confined to the LHC ring. Achieving 8T with practical power consumption requires the ultra-low resistivities of state-of-the-art superconducting technology. The basic component of the LHC super-conducting magnets are solenoids constructed with NbTi Rutherford cables, calledcoils, cooled to 2K with superfluid helium [53]. Different magnetic field configu-rations are produced via different arrangements of these superconducting coils.The successive accelerators of the injection chain provide the variety of ma-chine operating ranges required to accelerate thermal protons to the highly rela-tivistic energies suitable for the main LHC ring; they also determine most of theparameters of the LHC beams. The beam generation begins with the Duoplas-motron which strips protons from hydrogen gas using an electric field to form theinitial proton source [58]. The first stage of acceleration begins with a 200 MHz ra-dio frequency (RF) quadrupole, which uses electric fields to simultaneously focusand accelerate the proton source into a beam of 750 keV proton bunches. Next theLINAC linear accelerator accelerates protons to 50 MeV, at which point the beamis injected into the Proton Synchrotron Booster (PSB), which is the first in a se-ries of proton synchrotrons. The PSB determines the normalized transverse beamemittance, εn, which is a measure of the phase-space occupied by the ensemble of51particles in the beam. The PSB accelerates the beam of protons to 1.4 GeV forinjection into the Proton Synchrotron, which generates the final bunch train struc-ture for the LHC beam: nominally 72 bunches shortened to less than 5 ns in length[53]. The Super Proton Synchrotron is the last stage of the injection chain. In twoconsecutive steps it accelerates and injects two LHC beams, in counter-rotating di-rections at 450 GeV. The injection chain and LHC are schematically represented infigure 3.2.Figure 3.2: A schematic diagram of the CERN accelerator complex showingthe injection chain and the LHC [12]. ATLAS is one of four detectorexperiments located on the main LHC ring.The main LHC tunnel is pseudo-circular, consisting of 8 2.45 km arcs and 8545 m straight segments [14]. Detector experiments are located on the straightsegments around interaction regions where the beams are housed in a commonpipe, tightly focused, and crossed at a shallow angle. The LHC uses two systemsof superconducting RF cavities, one for each beam. Each system consists of 4single cell 200 MHz RF cavities, and two quad cell 400 MHz cavities, to captureand then accelerate the beam respectively.Magnetic bending and focusing is achieved in each arc segment with 23 arccells. The standard arc cell consists of six dipoles, two quadrupoles, and someadditional multipole magnets [14]. In total there are 1232 dipole magnets, 39252quadrupole, and thousands of additional higher pole magnets for correcting andtuning the beam in the LHC ring [59]. Throughout the arc cells and most of thering two separate beam pipes are used to store the counter-rotating proton beams.Opposite magnetic fields are supplied to each beam by a coupled magnet sys-tem housed within a common cryostat. The magnetic coils lie in close proximity tothe 56 mm beam pipes, separated by a thin beam screen which shields and absorbssynchrotron energy, and prevents heating of the superconducting magnet. The coilconfiguration varies depending on the required magnetic field configuration. Across-sectional view of the LHC in figure 3.3 shows the characteristic twin boredesign [53].Figure 3.3: A cross-sectional diagram of an LHC arc cell. The separatedcounter-rotating beam-pipes are surrounded by superconducting mag-netic coils and housed in a common cryostat [13].The coupled dipole magnets bend the opposing beams through the arcs of theLHC rings generating opposing vertical uniform magnetic fields transverse to thebeam direction as shown in figure 3.4.Quadrupole magnets are used to focus the beam in the transverse plane perpen-dicular to the beam velocity using magnetic field gradients that accelerate diverg-ing protons toward the ideal transverse position. Additional multipole magnets areused to correct orbital deviations in the beam, and to suppress beam resonances:trajectory deviations that are driven in cycle with acceleration [53].53Figure 3.4: The coupled magnetic fields of a LHC dipole. The counter-rotating beams are supplied opposite vertical magnetic fields such thateach are simultaneously bent toward the centre of the LHC ring[14].3.2.2 Beam ParametersLuminosity is a measure of the proton-proton flux at the interaction point (IP)where the beams are focused and intersect each other with a finite crossing an-gle. L has units of counts per area, and was presented in equation 3.3 as a globalparameter that scales the predicted amount of data collected in analyses. The lu-minosity is related to the following set of parameters which describe the collidingbeams:• E - The beam energy• Nb - The number of particles per bunch• nb - The number of bunches per beam• frev - The revolution frequency• γr - The relativistic gamma factor• εn - The normalized beam emittance: an invariant measure of the transversephase-space area occupied by the beam [55].54The luminosity depends critically on the transverse radius of the beam, σ , whichvaries over the beam path, but is focused to O(1) mm at the interaction points. σ isrelated to the emittance by the betatron function, β ∗, which characterizes the shapeof the beam in transverse phase space, it is the ratio of the radius of the beam toits maximum divergence angle [55]. The beam area at any point can be expressedas piσ2 = piεn/γβ ∗. At the interaction point β ∗ is minimized, and the beams arefocused to narrow cross-sectional area. The finite crossing angle adds an additionalgeometric reduction factor, F , and is defined as [53]:L =N2b nb frevγr4piεnβ ∗F. (3.6)3.2.3 LHC Performance in 2011From the ATLAS detector vantage point the relevant aspects of the LHC perfor-mance are the number of interactions per bunch crossing, which determines thelevel of event pile-up within the detector, the luminosity, and the centre of masscollision energy. Data used in the analyses presented here was collected in 2011,during which time the LHC was operated at half its ultimate design energy. 3.5TeV proton beams were collided under various luminosity conditions achieving√s = 7 TeV.The data collection is partitioned into two periods. The first period lasted fromMarch until August, during which the beams had a bunch spacing of 75 ns and aβ ∗ = 1.0 m; a total of 2.04 fb−1 of good quality data was collected. Following atechnical stop for machine maintenance, a second higher luminosity period of datataking was performed from September to November where the bunch spacing wasreduced to 50 ns and the beam had a β ∗ = 1.5 m. In total 4.7 fb−1 of high qualitydata was collected in 2011.The luminosity recorded by the ATLAS detector is measured by a variety oftechniques. Differences in the live-time of the detector and the LHC running meanthat slightly less luminosity was measured in the ATLAS detector than was deliv-ered to it by the LHC. Furthermore, data is assessed for quality, and a small fractionof the sample is excluded due to intolerable detector malfunctions. The luminosity55delivered and recorded over the course of the 2011 run is shown in figure 3.5.Day in 2011­1 fbTotal Integrated Luminosity 01234561/3 1/5 1/7 1/9 1/11 = 7 TeVs                ATLASLHC DeliveredATLAS Recorded­1Total Delivered: 5.46 fb­1Total Recorded: 5.08 fbFigure 3.5: The total integrated LHC delivered and ATLAS recorded lumi-nosities as a function of time for 2011.The steeper increase after the technical stop is indicative of the higher instan-taneous luminosity, which was achieved at the price of a larger number of pile-upinteractions per bunch-crossing. The pile-up conditions at any time are charac-terized by the Poisson mean for the number of interactions per bunch-crossing,µ . The average µ for the first and second data taking periods where 6.3 and 11.6respectively. Figure 3.6 shows the collected luminosity as a function of µ .56Mean Number of Interactions per Crossing0 2 4 6 8 10 12 14 16 18 20 22 24 ]­1Recorded Luminosity [pb­310­210­110110210310410 =7 TeVsATLAS Online 2011, ­1 Ldt=5.2 fb∫> = 11.6µ * = 1.0 m, <β> =  6.3µ * = 1.5 m, <βFigure 3.6: The Poisson mean µ for the number of interactions occurringwithin the ATLAS Detector varies significantly over each data-takingperiod. The plot shows the amount of data collected as function of µ in2011 [15]3.3 The ATLAS DetectorThis section provides a general, non-exhaustive, overview of the ATLAS operatingprinciples and detector layout, it is largely based off of two comprehensive ATLASdesign and performance reports [2, 60], but also supplemented by subcomponentspecific material.ATLAS(A Toroidal LHC ApparatuS) is one of two general purpose detector ex-periments located at the LHC. It is designed to provide the most complete physicaldescription of the final-state of the proton-proton collision possible so as to facil-itate the full range of possible analyses, from tests of the Standard Model, to thediscovery of new physics. The ATLAS detector is described within the collisioncoordinate system, centred on the interaction point with the positive x-directionpointing towards the centre of the LHC ring (see section 2.4.1). It consists ofa strategic arrangement of concentric cylindrical subsystems which make variousmeasurements of detectable particles as they interact with the volume of the de-tector. ATLAS measures 44 m in length and 25 m in diameter, and is designed to57maximally cover the solid angle around the interaction point in order to captureas much of the event energy as possible, though 4pi coverage is made impossibleby the aperture required for the beam pipe. The layout of the ATLAS detector isshown in figure 3.7.Figure 3.7: A diagram of the ATLAS detector. A portion is cut away to revealthe concentric subsystem structure [2].During LHC operation the ATLAS detector is exposed to a continuous lumi-nosity and correspondingly intense particle flux that is roughly constant in η ; sur-viving the LHC luminosity while simultaneously making precision measurementsof collision events influences much of the design of ATLAS. The Cartesian an-gular separation for a constant ∆η decreases strongly with |η |, as was shown infigure 2.12b. Fine granularity precision detection systems are instrumented overa central region of |η | < 2.5, where they can survive the lower particle flux andmaintain good kinematic acceptance for events of interest. Beyond the precisionregion, increasingly coarser granularity detectors, capable of withstanding the highparticle flux are used.ATLAS is designed to unambiguously identify and measure the 4-vectors as-58sociated with the following set of physics objects:• Primary Vertices - 3D space-points associated with the initial proton-protoncollisions within a single bunch crossing.• Secondary Vertices - The decay positions of heavy particles such as b-quarks and taus, which can be used to tag their decay.• Jets - Clusters of reconstructed hadronic energy depositions, due to a hadronicjet.• Photons(γ) - Clusters of electromagnetic energy depositions, due to the ab-sorption of a photon.• Electrons(e) - Clusters of electromagnetic energy depositions, and measure-ments along the charged particle’s path.• Muons(µ) - Charged tracks traversing the detector due to a passing muon.• Transverse Energies - The total momentum imbalances in the x and y di-rection, Ex and Ey, the negative vectorial combination of which, the missingtransverse energy, ET , corresponds to the sum of the transverse momenta ofall undetected particles (e.g. neutrinos).Particle objects of interest, those reconstructable with tolerable resolution thatoriginate from a hard interaction, tend to have energies on the order of 10 GeV upto 1 TeV. Not only must hard events themselves be quickly identified and storedwithin an inter-event minimum bias background, on an event-by-event basis, objectreconstruction itself must occur within an intra-event minimum bias backgrounddue to the presence of pile-up interactions. At√s = 7 TeV, over |η | < 2.5 theaverage charged particle multiplicity for particles with pT > 100 MeV, due to asingle minimum bias event is O(6) per ∆η = 0.1 [61]3.3.1 Detection Strategy and LayoutThe general particle detection process that provides the raw data for physics objectreconstruction can happen in two steps:591. The particle interacts with and loses energy to the detector material generat-ing hits at various points in space and time.2. Hits within active elements of the detector are sensed by generating electricalsignals, which are read out as Raw Data Objects which represent the finestgrained data that is stored for analysis.Particle hits occur while the particle traverses and interacts with the moleculeswithin a material via either electromagnetic or strong interactions. When theseinteractions lead to the production of electrically charged particles, or photons,the material can be suitably instrumented to amplify that response into measurablesignals. This is the basis of particle detection in ATLAS.Electromagnetically interacting particles can lose energy to a material throughmultiple mechanisms. Charged particles can directly excite or ionize matter viaelectromagnetic interactions with atomic electrons, via collisions. The collisionenergy loss, E, with respect to the depth of material traversed, x, is given by theBethe-Bloch formula [62]:dEdx=4piN0z2α2mv2ZA{ln[2mv2I(1−β 2)]−β 2}, (3.7)where β is the Lorentz boost of the penetrating particle with velocity v and electriccharge z; Z and A are the average atomic number and mass of the atoms of thematerial; I is the effective ionization potential; m is the electron mass; α is the finestructure constant; and N0 is Avogadro’s number.Ultra-relativistic particles, such as electrons emerging from proton-proton col-lisions, predominantly lose energy via bremsstrahlung radiation of gamma rays,induced by deceleration within the electric field of nuclei. The total radiation lossfor electrons is given by [62]:(dEdx)rad=−EX0(3.8)where X0 is the material dependent radiation length which defines the materialthickness required to reduce the energy of a beam of electrons by a factor of 1/e.60The expected energy loss of an electron in a thickness of material, x is:〈E〉= E0e−x/X0 (3.9)Sufficiently energetic photons can pair-produce within a medium into a detectableelectron-positron pair by interacting with the Coulomb field of an electron or nu-cleus. The pair production probability for a photon traversing a material of thick-ness x is also related to the radiation length:P(γ → e−e+) = e−7x/9X0 . (3.10)Hadrons interact strongly, and can also be detected by nuclear collisions that lead todetectable ionization signals. Their interaction with matter is characterized by thenuclear interaction length, λint , the hadronic analogue of radiation length, or themean free path between inelastic nuclear collisions which result in the destructionof the incident hadron and the production of secondary hadrons.The propensity for electrons, photons, and hadrons to rapidly lose energy inmatter means that they can be fully stopped and absorbed within a practical amountof material. However, λint >> X0, and thus more radiation lengths are required tostop hadrons than to stop electrons and photons. Muons stand out as a specialcase. At collider relevant energies they lose energy primarily through ionization,and minimally so, and cannot be stopped with practical amounts of material.Two types of composite measurements based off of the aforementioned mate-rial interactions are used to facilitate two types of measurements:• Tracking measurements consist of determining the curved trajectories ofcharged particles as they traverse magnetic fields by performing non-destructivemeasurements along their paths. Tracking allows for the determination ofboth charge and momentum by measuring the curvature of particle trajecto-ries.• Energy measurements consist of destructively absorbing the energy of aparticle within a volume of material, and sampling the energy loss to inferthe incident particle’s position and energy.61The differing material stopping relationships among the detectable final stateparticles, and the ability of charged particles to be non-destructively tracked, moti-vates a specific detection strategy at ATLAS that allows, in principle, for the unam-biguous measurement and identification of the physics objects. Moving outwardfrom the interaction point the strategy consists of a series of steps:1. Tracking of the trajectory of charged particles.2. Distinguishing pions from electrons.3. Initiating energy measurements of photons, electrons, and hadrons.4. Fully absorbing photons and electrons.5. Fully absorbing and completing the measurement of hadrons.6. Tracking of muons as they emerge from the calorimeters.This detection strategy is summarized in figure 3.8, which shows the interactionsof the various final state particles traversing the detector subsystems.Starting from the beam pipe, tracking and electron identification is conductedusing the inner detector (ID) which consists of three subsystems: two precisionsemiconductor trackers, the Pixel and Semiconductor Tracker (SCT), surroundedby the Transition Radiation Tracker (TRT). The ID is immersed in a solenoid mag-netic field which provides the magnetic bending for the ID tracking. Surroundingthe solenoid is the electromagnetic calorimeter (ECAL), which provides the ini-tial energy measurement for all interacting particles and fully absorbs photons andelectrons. Surrounding the ECAL is the hadronic calorimeter, which completesthe measurement and full absorption of hadronic particles that escape the ECAL.Finally, the calorimetry is surrounded by the largest subsystem, the Muon Spec-trometer, which consists of an array of tracking planes, immersed in a magneticfield generated by air-core toroid magnets, that track and identify muons as theyleave the detector.The cylindrical subsystems are partitioned into barrel and end-cap components.In the most forward regions of the detector the cylindrical design is interrupted byforward calorimeters which extend the coverage of the calorimetry to |η | < 4.9.62Figure 3.8: The ATLAS strategy for identifying and measuring final objectsis based on making a ordered set of measurements using a concentricseries of enclosed subsystems. The schematic shows the different anddistinguishable interactions of the various particle types as they traversethe subsystems [16].Additionally, located furthest in |η | is the ATLAS luminosity detector, LUCID,which provides a precision measurement of the instantaneous luminosity.Each detector subsystem can be seen as being located at the front end of auniversally organized and structured Data Acquisition System. Each subsystemconsists of a multitude of detection elements, that are grouped together into mod-ules instrumented with front-end (FE) electronics. The modules provide read-outof the raw data objects, the information is transiently stored by the front-end elec-tronics in 2.5 µs pipelined memory buffers which set the maximum latency for thefirst level of the trigger system to render a data accept decision.63In the following subsections an overview of the layout and operation of eachsubsystem will be provided which will include a summary of the subdetector di-mensions, its main detection element, and its intrinsic performance parameters.Those sections are followed by a summary of the triggering and data acquisitionsystem.Magnet SystemThe ATLAS detector subsystems are embedded within a multicomponent mag-net system consisting of superconducting coils. The magnets provide the requiredmagnetic bending throughout the tracking volumes. The layout of the magnet sys-tem is shown in figure 3.9.The solenoid magnet is a cylinder of super-cooled Al-stabilized NbTi wind-ings laying between the inner detector and the barrel ECAL and supplies an axialmagnetic field pointing in the z-direction, which provides bending in the transverseR-φ plane. The solenoid is centred within the ATLAS coordinate system with axiallength of 5.8 m and occupies the volume between 2.46 m < r < 2.56 m, whichcorresponds to a radial material thickness of .66 X0 [2]. Steel plates in the hadroniccalorimeter system provide enough ferromagnetic material to act as a magnetic fluxreturn yoke, which confines the returning magnetic flux within the calorimetry.Magnetic bending in the muon system is supplied by an air-core toroid mag-net system consisting of barrel and end-cap subsystems composed of Al-stabilizedNb/Ti/Cu windings. These systems generate an inhomogeneous field in the φ di-rection, roughly circling the ATLAS calorimeters, throughout the open volume ofthe muon system. The barrel toroid consists of 8 independently housed and cooledrectangular coils 25 m in length. The coils are equidistant from each other, formingan 8-fold symmetry, with the combined array having inner and outer diameters of9.4 m and 20.1 m respectively.The toroid end-caps each consist of 8 smaller rectangular coils housed in acommon cryostat with axial length 5 m that are positioned within the barrel toroid,one on either side of the barrel solenoid. Again the field direction is parallel to theφ -direction. The end-cap coils are oriented offset by ∆φ = pi/8 rad with respect tothe toroid arrangement.64Figure 3.9: The main components of the magnet system. The exterior con-sists of air-core toroidal magnets, 8 large magnets over the barrel,capped by 8 smaller ones at each end-cap. In the centre of the toroidis a solenoid magnet surrounded by the steel of the hadron calorimeter[2].In the barrel solenoid, the magnetic field strength is highest in the centre of thedetector, about 2.0 T and rapidly drops near the end of the barrel where the fieldlines begin to spread out and exit the interior, there the strength is 0.9 T. The toroidsystem has an average field strength of 0.5 T, in the barrel region, and 0.2 to 3.5 Tin the end-cap region; its field value varies strongly with φ and R [2].Inner DetectorThe role of the inner detector is to measure charged particle tracks. There are 4main functions associated with this:• Primary and secondary vertex reconstruction• Charge identification over |η |< 2.5• Momentum measurement over |η |< 2.565• Electron/pion identification over |η |< 2.0The layout of the barrel inner detector subsystems is shown in figures 3.10.Figure 3.10: The layout of the barrel inner detector [2]. The detector subsys-tems form concentric cylinders around the beam pipe. The three pixellayers lay closest to the beam-pipe, and are surrounded by four SCTlayers that in turn are surrounded by the axially oriented straw-tubematrix of the barrel TRT.Precise vertex identification is based on 3D measurements of the charged par-ticle trajectory performed by the precision trackers: the Pixel and SCT systems.Both systems are based on semiconductor technology. Surrounding the precisiondetectors is the TRT which makes up the bulk of the inner detector volume. It iscomposed of a dense array of straw-tubes: single sensing wires encased in gas-filled tubes. The straw tubes of the TRT provide 2D measurements and can distin-guish electrons from pions.Precision Trackers66Both precision tracker systems use the same basic sensing silicon chip build-ing block: a reversed biased pn-junction characterized by a bulk n-doped siliconregion, with a shallow large area p-implant. A simplified silicon sensor is schemat-ically depicted in fig 3.11 [17]. In the p-doped material the majority free chargeFigure 3.11: A schematic diagram of a simple silicon sensor [17].carrier is an electron hole while in the n-doped material the majority free chargecarrier is the electron. At the pn-junction charge carriers thermally diffuse acrossthe boundary until the voltage due to the charge differential across the boundary,Vd pl , inhibits net charge flow. At that point a depletion zone is setup inside thebulk material where electrons and holes have combined and are immobilized. Thedevices are further overdepleted and reverse-biased by applying an external volt-age opposite the built-in voltage, V > Vd pl , inducing a net non-zero electric field(V −Vd pl)/d throughout the depletion zone of depth d.When a charged particle interacts in the depletion zone it generates electron-hole pairs. The re-mobilized charge carriers are then accelerated in opposite direc-tions, generating a detectable pulse current which can be read out on either sideby metalically bonded readout electronics that amplify and transmit the signal forprocessing and storage.The Pixel detector is the first active sensing component of the ATLAS detector.It is contained in a cylindrical volume roughly 12 cm in radius and 30 cm in length,and typically provides three precision 3D space-point measurements along the pathof charged particles over |η | < 2.5. Its design is influenced by the dual demands67of providing precision measurement, and surviving in the concentrated radiationflux at small R. Two n-type materials are used: a material with lower charge car-rier density (n), and a material with a higher charger carrier density (n+). Thebasic detection element is the pixel sensor: an n+-implant, with high charger car-rier density, nominal area 50× 400 µm2, placed at the surface of a 250 µm thickn-type bulk, with large p-implants on the opposite side that provide the depletion.This n+-in-n design deviates from the classic p-in-n design described above, butis necessary for maintaining performance over the life of the detector. Eventually,the high fluence of particles through the detector will induce type-inversion trans-forming the n-bulk into an effectively p-type material. The operating principlesare generally the same as described above for the classic design, the pn-junctioncreates a depletion zone, but the pulse current caused by the passage of a chargedparticle is readout by the n+implants instead of the pn-junction itself. After type-inversion, a depletion zone will be generated from the n+ contacts and the sensorwill continue to function.Each pixel module measures 2× 6 cm and contains 47,268 n+-pixels that areindividually bump-bonded to 16 front-end readout chips. Figure 3.12 shows aschematic image of an ATLAS pixel module.Figure 3.12: A diagram depicting the layout of a pixel module [2].68When a particle interacts in the common depletion zone, analog signals can beread out from multiple pixel sensors. The position measurement is calculated asthe centroid of the pixel cluster response, which has a resolution smaller than thepixel dimensions themselves. The third dimensional measurement perpendicularto the module plane is determined by the precision positioning of the module itself(see Table 3.1).In total the pixel detector is composed of 1744 identical pixel modules and hasapproximately 80.4 million readout channels. The barrel component consists ofthree concentric cylindrical layers of pixel sensors, oriented parallel to the beampipe. A first vertexing layer is located at R = 5 cm, it is surrounded by two addi-tional layers at 9, and 12 cm; each layer 80 cm in length. In each end-cap the pixelsensors are arranged in three successive disks, centred around the beam pipe, withinner and outer radii 9 cm and 15 cm respectively, located at z = 50, 58, 65 cm.Operating at larger distance from the interaction point is the Silicon Tracker,which is not required to be as radiation resistant as the pixel detector. Its functionis to provide an additional 4 precision space-point measurements over |η |< 2.5.The basic sensing unit of the SCT is the strip sensor, which is a classic p-in-n silicon sensor, consisting of a p+-implant electrode 80 µm ×6 cm in area. Inthe barrel region, sensor layers are formed by one-sided implantation of 768 stripsensors at 80 µm pitch into a 285 µm thick 6× 6 cm silicon wafers. Four wafersare combined together, first paired to create two 6×12 cm layers, then one layer ismounted underneath the other with a rotation angle of 40 mrad. In the end-caps, asimilar, but radially symmetric, design is used, where the strip sensor pitch varieswith R, leading to trapezoidal layers. Figure 3.13 shows the design of a barrel SCTmodule. The small stereo-angle between the layers enables each module to provide2D measurements within the plane, with a third dimensional measurement deter-mined by precision module positioning. As with the pixel detector, the passage ofa particle is read out as analog signals from multiple sensors, yielding an intrinsicmodule accuracy smaller than the sensor dimensions (see Table 3.1).The SCT detector contains 4088 modules and about 6.3 million readout chan-nels. In the barrel they are arrayed in 4 concentric cylindrical layers in the barrel,1.5 m long, at r = 30, 37, 44 and 51 cm. Modules are positioned such that theirlongest dimension is parallel with the z-direction, and their normal direction forms69Figure 3.13: An image of an SCT module (left). A diagram of the SCT mod-ule showing the mounting, and off-angle orientation of the 4 strip sen-sor wafers (right) [2].a small angle with the R-direction allowing for slight overlaps among the modulesso as to ensure full coverage in φ . In the end-caps, the modules are arrayed in 9consecutive disks with inner radii varying between 27 cm and 44 cm, and outerradii of 56 cm. The disks are located between 85 cm and 272 cm along |z|.The Transition Radiation TrackerThe third component of the ATLAS inner detector tracking system is the Tran-sition Radiation Tracker (TRT). It is the largest inner detector component by vol-ume and has two important tasks: providing 2-dimensional measurements of chargedparticle trajectories up to |η | < 2.0, and discriminating electrons from pions. TheTRT induces and measures transition radiation, the magnitude of which can be usedto discriminate the typically ultra-relativistic electrons from the more moderatelyboosted pions.The basic sensing unit of the TRT is a straw tube: a single wire cylindricaldrift chamber consisting of a 4 mm diameter hollow conducting tube, acting as acathode, surrounding a central 35 µm gold plated tungsten anode wire, filled with aXe/CO2/O2 (70/27/3) gas mixture. A radial electric field is created by applying avoltage to the cathodes of -1530 V. The TRT straw-tube wall is constructed by glu-ing two multi-layer films together back-to-back [63]. Each film contains 4 layersin the following order, 25 µm polyimide, 0.2 µm aluminum, 5 µm graphite, and70heat activated adhesive 5 µm polyurethane. The two layers are bonded togetherwith polyurethane, which also makes the tube air tight.Charged particles traversing the tube initiate ionization of the gas and the freedelectrons are accelerated toward the anode wire, eventually acquiring enough en-ergy to cause secondary ionizations in the gas leading to a chain reaction avalanchethat collides with the anode wire and amplifies the initial ionization signal. In thebarrel region, straws are embedded in a matrix of polypropylene fibres which pro-vide a volume permeated by many material boundaries; when a particle passesthrough these boundaries, Transition radiation (TR) x-rays are generated by theelectric field reconfiguration of the particle in the media [64]. The total radiatedenergy is proportional to the γ factor of the traversing particle. As pions are farmore massive than electrons with mpi ≈ 300me, γe = 300γpi and electrons will emit300 times more transition radiation. A schematic of an electron traversing TRTstraw-tubes is shown in figure 3.14.Figure 3.14: A schematic diagram depicting the interaction of an electronwith a series of straw-tubes in the barrel TRT. The electron induces ion-izations at random positions along its path within the drift-tubes. Theelectron induces transition radiation in the inter-tube material whichinduce additional ionizations in the tube [18].When a charged particle passes through a straw tube, a pulse signal is readout.The time-dependent structure of the pulse is digitized into bits by partitioning thesignal into time increments and testing two pulse thresholds: low, and high, definedto distinguish general charged particle hits from those that also include significantadditional ionization due to transition radiation. Additionally, the length of thelow-threshold pulse is used to estimate the dE/dX of the particle and aid in particle71identification [18]. The minimum distance of the charged track from the anode isestimated based on the timing of the leading edge of the of the pulse, correspondingto the drift-time for the arrival of the closed ionization seed.In the barrel the straws are oriented parallel to the beam pipe, in order to pro-vide 2D measurements in the R-φ plane. The active anode length for barrel strawsis 72 cm, but the anode itself consists of two segments joined in the centre of thetube by a glass bead. This provides support for the straw, and reduces occupancy,since each segment can be readout independently. There are up to 73 radial layersof straws in the barrel. organized into modules, which fill the volume 55<R< 108,cm and |z|< 71 cm. In the end-cap regions 37 cm straws are oriented in the radialdirection and organized into single straw layers separated by 15 µm radiator foil.The end-caps provide 2D track measurements in the z-φ plane. In total there areabout 351000 TRT readout channels.Summary of the Inner Detector PerformanceThe performance parameters of the inner detector modules are summarized intable 3.1.Table 3.1: Performance parameters of the Inner Detector subsystems[2].SystemMeasurementsLayerIntrinsic Alignment Tolerancesper Accuracy Radial Axial AzimuthTrack (µm) (R) (z) (R-φ )Pixel ≥ 3Layer-0 10 (R-φ ) 115(z) 10 20 7Layer-1 and -2 10 (R-φ ) 115(z) 20 20 7Disks 10 (R-φ ) 115(R) 20 100 7SCT ≥ 4Barrel 17(R-φ )580(z) 100 50 12Disks 17(R-φ )580(z) 100 50 200TRT ≈ 36 all 130 - - 30CalorimetryThe calorimeter subsystems are located around the solenoid magnet and TRT, cov-ering |η |< 4.9, and work together to measure and identify particles, and completethe energy measurement. The calorimetry also acts as a background shield for the72muon system, by fully absorbing electrons, photons and hadrons, and reducing totolerable levels the chance that non-muons can punch through in to the muon sys-tem. Thus the calorimeters are essential for measuring or identifying every finalstate object at ATLAS.Calorimeters operate by inducing showering, the conversion of a single highenergy particle into a cascade of lower energy particles via repeated interactions ina volume with high material thickness. When a particle showers within a materialit deposits its energy over a macroscopic volume. The shower process proceedsdifferently for electrons and photons than it does for hadrons, the latter of whichincludes both electromagnetic and nuclear sub-showers. The magnitude and shapeof the shower energy distribution are used to reconstruct the incident particle en-ergy, trajectory, and type.Within ATLAS, sampling calorimeters are employed, which consist of alter-nating layers of shower inducing absorber and active sensors, which sample theionization energy loss of the shower. The sensors are read out in 3-dimensionalgrids of cells, which provide a granulated measurement of shower energy distribu-tions.The calorimetry can be grouped into four broad subsystems. The finely grainedelectromagnetic calorimeter (ECAL), is primarily responsible for measuring elec-trons and photons. The more coarsely grained hadronic calorimeter (HCAL) sur-rounds the ECAL and completes jet measurements and stops hadronic particles,it consists of two subsystems: the Tile Calorimeter (TILE) in the barrel region,and the Hadronic End-cap Calorimeters (HEC). Both the HCAL and the ECALcover the range |η | < 3.2. A series of specially optimized electromagnetic andhadronic forward calorimeters operate in the most forward regions of the detectorat 3.2 < |η |< 4.9, allowing the near complete measurement of transverse energy.The layout of the calorimeter subsystems is shown in figure 3.15Calorimeter measurements are achieved by calibrating the response of cellclusters to real and simulated data, that reconstruction performance will be sum-marized in section 3.3.3. In the following subsections, the showering process, andthe operation and layout of each subsystem is provided. Those sub-sections arefollowed by a summary of the overall calorimeter system cell granularity and per-formance.73Figure 3.15: The layout of the ATLAS calorimeter subsystems [2].ShoweringThe shower process proceeds differently for electrons and photons, than it doesfor hadrons, the latter of which includes both electromagnetic and nuclear sub-showers. Critically, since λint > X0, hadronic showers are larger, and require morematerial to be full absorbed.Electron initiated electromagnetic showers begin when the incident electronemits brehmstrahlung photons, which in turn pair produce into more electrons.The resulting electrons and photon continue radiating and pair-producing. Incidentphotons, produce a similar shower, only the process starts with an initial pair pro-duction. The cascade continues until particle energies drop below a critical valueεC, where the ionization energy loss dominates and particles are absorbed by thematerial. The cascade process is fundamentally stochastic, and is governed by theenergy loss equations 3.9 and 3.10.The total energy deposited by a particle is proportional to the total path lengthof all the particles in the shower, T . The energy of incident particles are theninferred by sampling the ionization energy loss of their associated shower. Thestochastic nature of the shower development leads to a stochastic variance on the74path length, and thus the intrinsic resolutions of shower energy measurements:σ(E) ∝√E ∝√T . (3.11)The magnitude of the stochastic uncertainty is dependent on the sampling fre-quency [64].Showers induced by hadronic particles, and their energy measurement, are sim-ilar in principle, but more complicated. The hadronic showering is initiated via thestrong interaction with an atomic nuclei, which includes both elastic and inelasticcollisions. The outcome of these collisions is highly variable, giving rise to nu-clear fragments such as protons, neutrons, lighter nuclei, and, pi0 and η mesons.The pi0 and η mesons then proceed to decay and shower electromagnetically. Asfor EM showers, the hadronic portion of the shower will evolve multiplicatively solong as the nuclear scattered products have enough energy to break up successivenuclei. The variability of hadronic interactions means the fraction of undetectableenergy is different for each showering event. Moreover, the initial pi0 and η frac-tion, which largely determines the fraction of energy going into the EM cascadealso varies from event to event. These two characteristics place limits on the res-olution of hadronic showers, resulting in lower energy resolutions for hadrons vs.leptons.The Electromagnetic CalorimeterThe electromagnetic calorimeter (ECAL) is the innermost of the calorimetersubsystems optimized to induce, measure, and fully contain electromagnetic show-ers. Both hadronic and electromagnetic showers will begin in the ECAL, thoughthe latter will typically be fully contained. The projective depth of the ECAL, itsmaterial thickness along a ray extending outward from the interaction point, variesfrom 22 X0 at |η |= 0, to 38 X0 at the extent of its coverage, |η |= 2.5.The ECAL consists of accordion shaped absorber plates separated by thin sens-ing gaps. The absorber plates consist of lead sandwiched between two sheets of0.2 mm steel and have thickness between 1.1 mm to 2.2 mm throughout the ECAL,varied in |η | to meet performance requirements. The sensor gaps are 4.2 mm in thebarrel, and vary between 1.8 mm and 6.2 mm in the end-caps. A multi-layer cop-75per electrode is held in the centre of each gap by a polymer honeycomb structure.The rest of the gap is filled with liquid argon (LArg). The electrode itself consistsof three copper layers separated by polyimide and glue. The outer two layers areheld at high voltage and provide the accelerating field for ionization electrons. Themiddle electrode layer, conductively isolated, reads out the charge collection sig-nal via capacitive coupling [2]. The high voltage is set to 2 kV in the barrels, andvaried between 0.9 and 2.5 kV in the end-caps. The signal collection time in theLArg gaps is determined by the total time for the electrons to drift to the collectionelectrode, which is about 450 ns [2]. The accordion arrangement allows for readoutat the inner and outer faces of the ECAL while maintaining full coverage over therequired |η | range.Figure 3.16: A simulation of an electromagnetic shower within the accordionstructure of the ECAL [19].Figure 3.16 shows a simulation of an electromagnetic shower propagating throughthe typical accordion design of the calorimeter. Signal readout from the calorime-ter electrodes is segmented in non-Cartesian 3D layers of η × φ cells, with theinnermost barrel layer finely segmented in η as shown in figure 3.17.At collider relevant energies, electrons lose a substantial amount of their en-ergy while traversing the upstream material which has a radiation length of 2 to5 X0 over |η | < 1.8 [2]. The energy loss depends on any initial showering that76Figure 3.17: The segmentation of the barrel ECAL into three layers of cells[2].occurred, which is subject to large statistical fluctuations for the moderately thickinner detector. An additional thick preshower sampling layer, located upstream ofthe bulk of the detector, covering |η | < 1.8, enables event-by-event correction forthe upstream energy loss by effectively counting the particle multiplicity of the pre-shower electron system via a non-destructive ionization energy loss measurement.In the barrel the presampler is 1.1 cm thick, covers up to |η |< 1.47, and con-sists of two half-barrels of 32 rectangular sectors, each 310× 29 cm. Each sectoris composed of a series of modules, arranged end to end, with the electrode lengthperpendicular to η and plane orientation perpendicular to the projective direction.77Each module contains between 56 and 128 electrodes. All barrel electrodes are28 cm long with width varying in η . The electrodes have a similar layered designto those used in the accordion bulk, where two anodes ares held at 2 kV and anionization signal is readout through a capacitively coupled central cathode. Theend-cap presamplers are disks consisting of 32 trapezoidal modules covering 1.5< |η |< 1.8. Each module consists of two 2 mm LArg gaps parallel to the z direc-tion, formed by three electrode planes, perpendicular to the beam pipe. In total theECAL has 173,312 readout channels.The Hadronic CalorimeterThe hadronic calorimeter surrounds the ECAL, and covers |η | < 3.2. Twodifferent sampling calorimeter technologies are employed in the barrel and end-capregions. Roughly 10 λint of material thickness is provided by the sampling bulk,plus an additional 1 λint of outer support material, which is sufficient to containhadronic jets, and suppress punch through into the muon system.The barrel HCAL, or Tile Calorimeter (TILE), consists of interleaved steelabsorber plates and plastic scintillating tiles. Each tile is composed of polystyrenedoped with 1.5% PTP and 0.0044% POPOP [2]. Ionization induced by the chargedparticles in the shower ultimately excite the electronic states of the doping molecules,which subsequently emit photons as they de-excite. The signal photons are read-out by wave-shifting optical fibre, and amplified and digitized by photo-multipliertubes downstream.The TILE extends from 2.28 m < R < 4.25 m and is subdivided into threecomponents: a 5.8 m long central barrel covering |η | < 1.0 and two 2.6 m longextended barrels covering 0.8 < |η | < 1.7. Each subcomponent consists of trape-zoidal plates and tiles oriented perpendicular to the beam line. Each scintillatingtile is 3 mm thick, with azimuthal and radial dimensions that vary with radius be-tween 200 mm and 400 mm, and 97 mm and 187 mm respectively. The scintillatingtiles are interspersed with steel plates, 5 mm and 4 mm thick, to form the staggeredarrangement shown in shown in figure 3.18.The scintillation light is collected along the azimuthal edges of each tile andgrouped into readout bundles which define 3 layers of pseudo-projective cells, anal-ogous to the ECAL. In total the TILE has 10010 readout channels.78Figure 3.18: Azimuthal barrel HCAL module segmentation (left). Tile ar-rangement in a barrel HCAL module (right)[2].The Hadronic End-cap Calorimeter (HEC) is a sampling LArg calorimeter sim-ilar to the ECAL, but with different geometry and absorber material. The HECconsists of four wheels, one inner and one outer wheel on each end-cap, and cov-ers 1.5 < |η | < 3.2. In contrast to the rest of the calorimetry, the HEC can beused to detect muons [2]. The inner and outer wheels are 816 cm and 961 cm longin the z-direction respectively. The sampling planes are formed by placing elec-trodes in argon filled gaps between trapezoidal absorber plates and are orientedperpendicular to the beam pipe. Each LArg gap is 8.5 mm and instrumented withthree electrode planes oriented perpendicular to the beam pipe. The electrodes areequidistant and separated by honeycomb spacers. The outer two electrodes arecomposed of highly resistive kapton, and held at 2 kV. The central readout elec-trode consists of a conductive readout insulated on either side by kapton layers.Series of alternating sampling and absorbing planes are grouped together into32 wedge modules. In the inner wheel, wedges consist of a 12.5 mm front copperplate, followed by an additional 24 copper plates, each 25 mm thick. In the outerwheel, a 25 mm front copper plane is followed by 16 50 mm plates. The wheelshave outer radii of 2030 mm, and inner radii of 475 mm, except for the first 9plates, which have a smaller inner radius of 372 mm. In total the HEC has 5632readout channels.79The Forward CalorimetersThe FCAL is a LArg calorimeter designed to operate in the high flux envi-ronment of the forward region covering 3.1 < |η | < 4.9. It is divided in the z-direction into three cylindrical subcomponents, roughly equal in size. FCAL1 is anelectromagnetic calorimeter with front-face positioned at 4.7 m, it is immediatelyfollowed by the hadronic calorimeters FCALs 2 and 3.The high fluence of the forward region poses challenges for measurement, read-out, and heat dissipation, and motivates a sampling geometry that significantly dif-fers from the previously discussed calorimeter subsystems. Each FCAL is about45 cm long in the z-direction, and composed of tubular electrodes embedded inabsorber material that run the length of the subcomponent oriented parallel to thebeam direction. LArg gaps have a straw-like shape, and are formed between a thincylindrical copper anode layer, and a coaxial cathode rod slightly smaller in radius.The gap separation itself is maintained by a plastic fibre winding around the innercathode.The FCAL electrode structure is shown in figure 3.19. The thick cathode rodsact as part of the absorber matrix. The LArg gap size is chosen to be about 1/8the standard 2 mm gap size used in the other LArg calorimeters in order to avoidionization buildup due to the high occupancy in the forward region [65].In FCAL1 the electrode tubes are 5.6 mm in diameter, and the nearest neigh-bour centre-to-centre separation between the tubes, the electrode spacing, is about7.5 mm. Copper is used for the absorber material as it provides necessary heatdissipation. In total there are 12,260 electrode tubes in the FCAL1.FCAL2 and FCAL3 use an electrode spacing of 8.2 mm and 9 mm respec-tively. The tube diameter is also slightly larger at 6.2 mm in FCAL2 and 7.0 mmin FCAL3. FCAL2 and FCAL3 use tungsten for the absorber material, chosen forits large nuclear interaction length which is required to contain hadronic showers.FCAL2 and FCAL3 consist of 10200 and 8224 electrodes respectively.Summary of Calorimeter PerformanceThe response of a calorimeter cell is a current pulse either due to the collec-tion of LArg ionization, or the photomultiplier output from the collection of scin-tillation light, over the sampling gaps within the cell’s volume. The cell granu-80Figure 3.19: The electrode structure and arrangement of FCAL1 [2]. thincylindrical LArg gaps are formed around thick anodes that also act asabsorbers.larity varies depending on layer and η range, it is finest in the barrel ECAL, at0.025×0.025, coarser in the HCAL, and coarsest in the forward calorimeters. Thecell-granularity, and layer depth, of the calorimeter system are summarized in [2].For LArg calorimetry the significant drift time of the charges in the gap leadsto a long triangular pulse time structure that is much longer than the LHC bunchcrossing rate. As a result, superimposed on the calorimeter signals for an event ofinterest are the effects of many additional pile-up events. The calorimeter responseis reshaped and digitized by front-end electronics, in order to narrow the signalresponse and mediate the effects of pileup. An example of the shaped output of a460 ns long barrel pulse is shown in figure 3.20.The structure of the TILE signal is narrower, and uses a simpler shaping func-tion, however, for both the TILE and LArg calorimetry the pulse shapes are sam-pled at 25 ns. Cell energy measurements, E, are obtained from the sampled pulse81Figure 3.20: A diagram of a the pulse structure of a typical calorimeter re-sponse. The triangular physics pulse is reshaped by the front-end elec-tronics and sampled and digitized at 40 MHz [2].amplitudes, si, via [2]:E =n∑i=1ai(si), (3.12)where ai are determined from test signals of known energy. Similar methods areused to estimate the shower arrival time.Physics object energy measurement is made by considering clusters of calorime-ter cells. The energy resolution of the calorimeters can be parameterized as:σ(E)E=a√E(GeV )⊕bE(GeV )⊕ c, (3.13)where a, b, and c, are η dependent constants that are determined for each physicsobject, respectively they are the stochastic term, the noise term, due to pile-up andelectronics, and a constant term due to detector response inhomogeneities [3]. Thedesign resolutions for the calorimeters are summarized in table 3.282Table 3.2: Standalone resolutions of the ECAL and TILE calorimeters [3]Calorimeter a b cECAL 10% 170 MeV 0.7%TILE 52.9% - 5.7%Muon SystemThe muon spectrometer is the outermost subsystem located in the toroidal magneticfield, and constitutes the bulk of the ATLAS detector volume. The spectrometerfunctions analogously to the inner detector, sampling the paths of muons as theyescape the ATLAS detector and traverse the magnetic field. The muon spectrom-eter is required to measure the momentum of 1 TeV muons with a precision of atleast 10% in the region |η |< 2.7 and to trigger on muons over the range |η |< 2.4.This requires precisely locating the muon interactions over a large volume such thata path sagitta at 1 TeV, a curve depth on the order of 500 µm, can be measured to aprecision of 10% [2]. Muon paths are sampled with planar detector arrays, calledchambers, that are arranged into layers. As with the inner detector each chamberprovides up to two intrinsic measurements with an additional measurement com-ing from the location of the detection plane itself. The chambers are approximatelyarranged so that they provide a measurement in a bending plane, orthogonal to thetoroidal field direction at the chamber’s centre, or in an orthogonal non-bendingplane where the magnetic field lies parallel to the plane.The chambers are arranged in concentric pseudo-cylindrical layers, conform-ing to the 8 fold symmetry of the toroid system. In the barrel, the chambers arearranged on three layers located at r = 5 m, 7.5 m, and 10 m, each extending outto |η | < 1.04. Viewed in the transverse plane, each layer consists of two types ofrectangular chambers, distinguished by their width in the R-φ plane. The largerrectangular chambers are located at the centre of each octant, while the smallerchambers are located between each large chamber, offset in R, so as to providefull coverage in φ . The system coverage is extended out to |η | < 2.7 by end-capwheels. At each end, trapezoidal chambers are arranged to form three large wheelsat |z| =7.4 m, 10.8 m, and 21.5 m. Similar to the barrel arrangement, each wheelconsists of axial series of large trapezoidal chambers complemented by overlap-83ping smaller trapezoidal chambers, offset in z, providing complete φ coverage.Detection response times make it impractical to achieve efficient triggering andprecision bending plane measurements with the same detector technology: the for-mer requires ultra low-latency, while the latter entails longer readout times. More-over, the increase in muon flux at higher η necessitates different detection strate-gies between the central and forward regions of the muon system. As a result, overthe full η range four different chamber technologies are employed, two precisionchamber technologies: monitored drift tubes (MDTs) and cathode strip chambers(CSCs), to perform measurements in the bending plane; and two trigger chambertechnologies: resistive plate chambers (RPCs) and thin gap chambers (TGCs) toprovide orthogonal non-bending plane and fast trigger measurements. The layoutof the different chamber types within the muon system is shown schematically infigure 3.21.Figure 3.21: A schematic diagram of chamber arrangement in the muon spec-trometer. left: A cross-sectional view of the barrel shows the bar-rel MDT chamber arrangement. right: A side view of the barrel andend-cap transition regions shows the positions of the various chambertypes: the MDTs in green and turquoise, the CSCs in yellow, the RPCsin white, and the TGCs in purple [2].Each of the four chamber types and their layout within the Muon spectrometerare summarized in the following subsections. Those overviews are followed by asummary of the performance parameters of the muon system.Precision Chambers84The precision chambers provide precise sampling of the muon path in the bend-ing plane over the full η-range. The bulk of the precision system is instrumentedwith Monitored Drift Tube chambers (MDTs). The muon flux is highest in thesmall region of the inner most end-cap wheel at 2.0 < |η |< 2.7, where drift cham-ber response time is too slow to provide effective single particle measurement.There the region is instrumented with Cathode Strip Chambers, which are special-ized multiwire proportional chambers[66] that simultaneously readout both coor-dinates with low latency. Each chamber type is described below.The basic sensing unit of the MDTs is a 3 cm diameter aluminum drift tube,coaxial to a 50 µm diameter tungsten-rhenium wire held at 3080 V, filled withAr/CO2 gas (93/7) at 3 bar. The drift tube operates analogously to the straw-tubetrackers described in section 3.3.1, providing precision measurements in the coor-dinate perpendicular to the wire direction. However the larger mechanical structureof the MDTs, and the measurement precision requirements over the large volume ofthe muon spectrometer, introduce unique design and operational challenges. Eachdrift tube must be precisely located in 3D space, and within each tube the cen-tricity of the anode wire must be maintained. The required mechanical stability isachieved with the aid of optical laser monitoring systems that measure alignmentsand deformations both within and among the MDT chambers. The monitoring sys-tem feeds back into mechanical systems which can adjust chamber position, andapply corrective deformative forces to the drift-tubes. This monitoring feedbacksystem is critical for reducing the accuracy of a single in situ MDT drift tube to 20µm.MDT chambers consist of two multilayers of straw tubes, each multi-layer con-sisting of two to four layers of closely packed drift tubes. Spacing between multi-layers is used to house support structure and the optical alignment system, whichconsists of lenses, LEDs and CCD sensors [2]. The design of a typical barrel MDTchamber is shown in 3.22.Barrel MDT modules are rectangular with identical length drift tubes arrangedparallel to each other. In the end-cap, similar trapezoidal MDT chambers are con-structed by arranging tubes of varying length parallel to the trapezoid bases. MDTsare deployed over the entirety of the barrel layers, and all of the end-caps layersexcept for the first end-cap wheels, in the range 2.0 < |η | < 2.7, where the muon85(a) (b)Figure 3.22: A schematic cross-section of an MDT tube (left), and the typicallayout of a barrel MDT chamber (right) [2].flux exceeds the safe drift-tube hit rate of 150 Hz/cm2. In total, the MDTs cover asurface area of 5500 m2.Over 2.0 < |η | < 2.7 in the first end-cap wheels, an area corresponding to 65m2, Cathode Strip Chambers (CSCs) are employed to complete the precision cov-erage in the high flux environment. Cathode Strip Chambers are layers of gas filledplanar gaps with parallel anode wires spanning the centre of the gap, and cathodereadout strips instrumented on the interior surfaces of the gap. CSCs offer goodperformance for the high flux environment: 7 ns timing resolution, two orthogonalprecision measurements, low neutron sensitivity, single layer resolution of 60 µm,and simultaneous two track resolution.CSC planes have a gap thickness of 5 mm, and are filled with Ar/CO2 gas.Gold plated 30 µm diameter tungsten/rhenium wires are arrayed at a pitch of 2.5mm, within the centre of the gap, equidistant from nearest neighbour cathode stripsand anode wires. The surrounding cathode planes are lithographically segmentedinto strips; on one surface the strips are oriented orthogonal to the wires, and onthe opposing surface they are oriented parallel to the wires. A schematic of a CSCplane with cathode strips instrumented perpendicular to the wire direction is shownin figure 3.23.Both large and small chamber types use an identical number of readouts; the86Figure 3.23: A cross-section diagram of a CSC gap. Wires are positionedequidistant from each other and the perpendicularly oriented cathodeson the edges of the gap[2].larger chamber types have slightly larger strip dimensions. In the large (small)chambers, anode-perpendicular cathode strips are spaced 0.25 mm apart with widthsof 1.6 (1.5) mm and anode-parallel strips are placed 21 (12.5) mm apart.CSCs achieve position measurements in a manner different from drift tubes.The anode wires are used only to generate strong electric field gradients in thegas which amplify the initial ionization seed generated by a passing charged parti-cle into a macroscopic ion avalanche. The ionization pulse is then sensed via thecurrent induced in the cathode strips, due to its movement towards the wire. Thecurrent distribution in the cathode plane depends on the avalanche position, andcan be sampled by the cathode strips. Measurements in two cathode strips canunambiguously locate the avalanche position, with additional measurements fur-ther enhancing the resolution [66]. Sufficient performance in CSCs is achieved byreading out every third cathode strip corresponding to a readout pitch of 5.31 mmor 5.56 mm for small and large chamber types respectively [67].A CSC chamber is formed by combining 4 CSC planes oriented with anodewires running perpendicular to R at the centres of the chambers. Thus, each cham-ber provides 4 2D measurements. The bending plane measurements are determinedby the anode-perpendicular cathode strips while the non-bending plane measure-ments are provided by the anode-parallel cathode strips. Tracking resolution isminimized when incident particles impact the chamber at normal incidence. Thusthe chambers are angled projectively towards the interaction point to minimize the87off nominal crossing angle of particles.Triggering ChambersThe trigger chambers provide fast muon momentum measurements for the trig-ger system, in addition to precision measurement in the non-bending plane. Theneed for fast readout places stringent requirements on trigger chamber design. Thebarrel region (|η | < 1.05) is instrumented with Resistive Plate Chambers, whichare cathode and anode plates separated by a thin gas gap. In the end-caps, RPCscannot provide adequate performance in the high muon flux. Instead the end-capsare instrumented with Thin Gap Chambers which are specialized MWPCs.The basic sensor of a resistive plate chamber is called a detector layer. Eachdetector layer is a thin gas filled gap, with a longitudinal electric field appliedacross the gap thickness by planar anodes, which are insulated from the gap andreadout-cathodes by highly resistive materials. The central gap is filled with a94.7% C2H2F4 / 5% Iso-C4H10 0.3% SF6 gas mixture. Moving outward from the2 mm gas gap a detector layer consists of two plastic laminate resistive plates,each 2 mm thick with graphite electrode layers that generate the electric fieldpainted on their exterior. The outer electrode layers are coated with Polyethylene-terephthalate films which insulate them from the surrounding cathode readout layerwhich consists of 25 mm to 35 mm wide readout strips bound to polystyrene plates.Finally, a layer of copper covers the exterior of each polystyrene plane. The twosurrounding cathode strip layers are oriented orthogonal to each other. The RPCdetector plane operates similar to CSCs. The seed ionization from a passing par-ticle leads to an ionization avalanche that drifts toward the anode plane and thedrifting charge induces currents in the electrically isolated readout strips.Two detector layers are sandwiched together to form a unit, and an RPC con-sists of two partially overlapped units: an arrangement which provides coveragefor edge effects. The detector layers are held in position by paper honeycomb andan aluminum frame. A cross-section of the typical RPC layout is shown in figure3.24.RPCs vary in size, but are about 10 cm thick throughout the ATLAS detector.All barrel MDTs are assembled together with RPCs of equal size mounted on theirexterior sides. Additional stand-alone RPCs are mounted around the magnetic coils88Figure 3.24: A schematic diagram of the RPC arrangement[2].and ATLAS feet region.Thin Gap Chambers (TGCs) provide fast readout at high granularity and canoperate in the high flux environment of the end-cap muon-spectrometer. TGCsare built from classical single MWPC layers, where one coordinate measurementis provided by pickup from the anode wires, and an orthogonal measurement isprovided by one of the two cathode planes on either side of the gap that has beensegmented into readout strips.A TGC layer consists of two copper cathode planes, separated by a 2.8 mm CO2and n-C5H12 gas filled gap. The cathode-anode separation of 1.4 mm is narrowerthan the anode wire pitch of 1.8 mm. The anode lines are held at 2900 V. TGClayers are combined to form triplet and doublet TGC units. Both modules consistof two fully instrumented TGC layers, while the triplet module consists of a thirdlayer with two copper readout plates that serve as coincidence counters, but do notprovide position measurements. A schematic of the triplet module arrangement isshown in figure 3.25.TGC units are arranged with the anode wires laying perpendicular to the radialdirection, providing the muon measurement in the bending plane. The non-bendingcoordinate is provided by the cathode readout strips. The innermost wheel consistsof 7 TGC layers, while the middle wheel consist of 5 TGC layers.89Figure 3.25: A schematic diagram of the TGC triplet module[2].Summary of the Muon System PerformanceThe intrinsic performance of the chamber types across the coverage of themuon system is summarized in table 3.3.Measurements/trackChamber Bending PlaneResolution Alignment(RMS) in ToleranceType Barrel End-cap z/R φ time (µm)MDT 20 20 35 µm (z) - - 30CSC - 4 40 µm (R) 5 mm 7 ns 30RPC 6 - 10 mm (R) 10 mm 1.5 ns -TGC - 9 2-6 mm (R) 3-7 mm 4 ns -Table 3.3: Intrinsic parameters of the Muon Spectrometer [2].Trigger and Data AcquisitionSelecting and storing event data from the ATLAS detector presents a significanttechnical challenge. The vast majority of collision events will not contain a hardscattering process, and constitute a background in which hard processes must be90identified. Moreover, the maximum data readout and storage rate is limited bytechnological and economic feasibility in terms of the required electronics hard-ware capabilities, available space, and cost. This applies both to bandwidth andpersistent storage space. The information of a single ATLAS event correspondsto about 1MB of data. Thus, operating at design luminosity, storing every AT-LAS event would require a readout system with a PB/s transfer rate, and would fillO(100) EB1 of storage space after running for 24 hours [68]. Critical to operatinga sensible physics program is the recording of the largest possible subset of datathat contains the interesting hard scattering events.The ATLAS trigger and DAQ system is made up of a set of interconnectedcomponents. The trigger system is designed to be capable of reducing an inputevent rate of 40 MHz down, associated with the design bunch spacing of 25 ns,to a final data acquisition rate at O(100) Hz. This is accomplished with a tieredtrigger system consisting of level 1 (L1), and level 2 (L2) triggers, and the eventfilter (EF). The latter two levels are together referred to as the high level trigger(HLT).The trigger and readout chain proceeds as follows. Each FE board stores thedata for its component in 2.5 µs long pipeline memories. Signals from calorimetertrigger towers (coarse ∆η ×∆φ readout cells), and the muon trigger system aresent immediately to the level 1 trigger. The level 1 trigger uses dedicated purposebuilt programmable electronics located on the detector and in a nearby countingroom, to compute the L1 trigger decision based on the coarse measurements andreconstruction of high pT objects in the muon and calorimeter systems. It com-municates the decision to detector specific Readout Drivers (RODs) which retrievethe event data from the pipeline buffers for the HLT/DAQ system at a maximumrate of 75 kHz, within the 2.5 µs window. The HLT/DAQ stream begins withthe RODs of each subsystem, retrieving and temporarily storing the event data inreadout buffers, while the successive L2 and EF decisions are made. By focusingon regions of interest (RoIs) identified by the L1 trigger, the L2 trigger can ren-der refined decisions with a latency of less than 40 ms, using full reconstructionalgorithms, and provide an additional rejection factor of 30. At the highest level,11 EB = 1×1018 bytes.91the EF applies full reconstruction algorithms to the full event, and renders the finaldecision on whether events will be written to storage with a nominal output rate ofO(100)Hz3.3.2 The Full SimulationIn order to generate predictions for the interaction of LHC events with the ATLASdetector a detailed full computer simulation is employed. The goal of the simula-tion process is to produce, on an event-by-event basis, a prediction for the RDOresponse that would result if the hypothetical event occurred within ATLAS. Thesimulated RDO output can then be treated identically and directly compared to thereal RDO output collected in the experiment. A schematic of the simulation chainfrom generator to reconstruction is shown below; in principle the input into thereconstruction stage is indistinguishable in form from real data.Figure 3.26: The ATLAS full simulation chain. The output of the chain aresimulated events in RDO format which can be treated identically to theevent RDO measured by ATLAS. The physics simulation truth is alsostored at stages in the simulation chain. [12].For a single event, the simulation proceeds in a series of steps. Detector stableparticles from the generated event are output in a standardized universal format,HEPMC, upon which kinematic or particle filters can be applied to narrow the92pool of incoming events. The filtered generator level data is then read into detailedGEANT 4 [69] Monte Carlo simulation which time-step propagates each particlein the event through a detailed model of the ATLAS material layout and simulatesthe stochastic particle interactions and energy loss processes: the showering andionization hits. In a second digitization step, the hits are converted into simulatedelectrical signals. Digits are then sent to ROD emulators which produce the simu-lated RDOs.The effects of pile-up are simulated at the digitization stage by adding the ef-fects of additional interactions from a pool of pre-digitized minimum-bias events.Associated with each simulated event is the Poisson mean µ of the pile-up eventpool from which its simulated pile-up response was drawn. The luminosity con-ditions represented in full samples of Monte Carlo events can then be matched todata by reweighting each event so that the µ profile of the sample matches thedistribution in data (See figure 3.6).For each event, two sets of information are associated with the simulation pro-cess, the description of the simulated physics processes, called Monte-Carlo truth,and the simulation of the observable detector responses. Monte-Carlo truth playsimportant roles in assessing simulated detector performance, and in optimizationand characterization studies.3.3.3 ReconstructionThe methods and performance of ATLAS reconstruction are discussed in this sec-tion. In general, reconstructing objects with the ATLAS detector involves a numberof tasks:• pattern recognition, to identify candidate objects• quality cuts, to reject fake candidates while maintaining selection efficiency• 4-momentum estimationThe performance is quantified by the selection efficiency, background rejection,and 4-momentum resolution. As mentioned in section 2.4.1, the relativistic ap-proximation m ≈ 0 is accurate to a level well below the precision of the ATLASexperiment. Thus, 4-momentum measurements are achieved by measuring at least93three coordinates: either an object’s 3-momentum, or some projection of its mo-mentum and energy and two directional measurements.Physics object reconstruction is based on a combination of tracking and energymeasurements. Of all the measured physics objects, jets stand out for a variety ofreasons. First, there is an inherent arbitrariness in the definition of jets, reflect-ing the precision with which the pre-hadronization parton showering is resolved(See Section 2.4). Additionally, since leptons and photons can appear within thejet cascade, especially due to the decay of hadrons in the resulting hadronic jet,the terms isolated and non-isolated are used to distinguish reconstructed particleswhich originate from the initial hard-interaction from those that arise from jet cas-cades.This overview begins with a description of track reconstruction in the inner de-tector. That section is then followed by a series of subsections outlining the meth-ods and performance for each physics object. There are numerous reconstructionprescriptions available for each type of object. In this section, only the techniquesused in the analyses presented in this thesis are described.Inner Detector Tracking and VertexingThe tracks identified and measured by the inner detector are used in most of theobject reconstruction algorithms. The inner detector can reconstruct tracks withpT > 0.5 GeV with trajectories falling within |η | < 2.5, setting an absolute kine-matic acceptance on analyses that require inner detector tracking. Inner detectortracking consists of the following steps [2]:1. Track seeds are formed from combinations of hits in the 3 pixel layers andthe first SCT layer.2. Track candidates are formed by extrapolating seeds to match additional hitsthrough the SCT.3. Track candidates are then extended to find matching drift circle hits in theTRT.4. A track is fit to the candidate hits, outliers are removed, and fakes are rejectedbased on quality cuts.945. Primary and secondary vertices, in addition to photon conversions are searchedfor with dedicated algorithms.The reconstructed track can be characterized by the five parameters shown intable 3.4 and summarized in figure 3.27, that are determined at the track perigee,or point of closest approach to the primary vertex.Figure 3.27: (a) A track passes near the primary vertex. The perigee is thepoint of closest approach with the primary vertex, from which it isseparated by transverse and longitudinal distances z0 and d0. (b) Theprojection of the track onto the bending plane.The pT resolution of the track depends on the ability to reconstruct the tracksagitta, which is shown schematically in 3.4. The finite geometry of the inner de-tector limits the sampled chord-length of the transverse projection of the helicalpath to O(1)m depending on the η trajectory of the particle. Thus the sagitta, themaximum perpendicular distance from the path to the chord, is inversely propor-tional to the momentum in the bending plane pT ; typical sagitta measurements forO(100) GeV particles are O(1) mm. As a result, the resolution on the reconstructed95Table 3.4: Tracking parameters and performance of the inner detector[2].Track Parameter0.25< |η |< 0.50 1.50< |η |< 1.75σX(∞) pX (GeV) σX(∞) pX (GeV)Inverse transverse 0.34 TeV−1 44 0.41 TeV−1 80Momentum (1/pT )Azimuth angle (φ ) 70 µrad 39 92 µrad 49Polar angle (cotθ ) 0.7 ×10−3 5.0 1.2×10−3 10Transverse impact 10 µm 14 12 µm 20parameter (d0)Longitudinal impact 91 µm 2.3 71 µm 3.7parameter (z0× sinθ )track momentum is inversely proportional to track momentum.In general track measurement resolution can be summarized by the approxima-tion:σX(pT ) = σX(∞)(1⊕ pX/pT ). (3.14)Due to the inverse relationship between reconstructed pT , and the measured tracksagitta, the track pT resolution is proportional to the track resolution, this is incontrast with the track position and trajectory measurement resolution. In order tosummarize all resolutions by the same form, the momentum resolution is summa-rized as σ 1pT. The terms σX(∞) and pX for each variable are also summarized intable 3.27, for two representative regions of the detector corresponding to minimaland maximal material thickness [2].Various methods are used to reconstruct the primary vertex of the event that relyon a combination of identifying vertices as clusters of nearly intersecting tracks,track-refitting, and vertex fit quality assessment. The resolution on the vertex re-construction varies with track multiplicity. The typical resolutions on the Cartesiancoordinates are less than 1 mm, and O(.1) mm for vertices with ≥ 10 tracks [70].Precisely locating the primary vertex is not a critical aspect of this analysis and willnot be discussed further, for more details see [71]. Secondary vertex reconstructionis an important input into jet flavour tagging algorithms which will be summarizedlater in this section.96MuonsThe ATLAS detector is designed to identify and precisely measure muons over theenergy range 3 GeV to 3 TeV, up to |η | < 2.5. In ATLAS muons originate fromthe following 3 sources:• isolated muons - muons originating at the interaction not associated with ajet• heavy flavor decays - muons produced as part of b- and c-decays that areassociated with the resultant quark jet• cosmic rays - muons originating from interactions in the upper atmospherethat do not point toward the interaction point in generalFake muon tracks arise primarily from two sources:• cavern backgrounds - latent radioactivity in the cavern and ATLAS materialsthat generates energetic neutrons and other particles• punch through hadrons - hadrons originating from the interaction point thatescape the detector and subsequently interact with chambers or decay to pho-ton or leptonsThe general principle of muon reconstruction is that a real muon emerging fromthe event of interest will produce a track in the muon system that points back tothe interaction point. In the analyses presented here, muons are reconstructed us-ing the Combined Muon Algorithm which matches stand-alone muon spectrometertracks to inner detector tracks. This combination enhances stand-alone efficiencyover some regions of the solid angle coverage, improves momentum resolution formuons with pT < 100 GeV, and helps reject fake muons.Stand-alone muons are reconstructed using the MuonBoy[72] pattern recogni-tion algorithm which consists of four steps:1. ∆η×∆φ = 0.4×0.4 regions of interest (ROAs) are defined on any 2-coordinatetrigger hit.2. Local straight track segments are reconstructed by χ2 fits to the collection ofhits in each layer of the muon system.973. A muon track candidate is fit to the track segments.4. A global track refit is performed to the total set of hits.Muonboy outputs the best fit set of track parameters at perigee and the stand-alone muon track is paired with each inner detector track that shows reasonableagreement in (η ,φ). A full statistical combination of the track parameters atperigee is attempted for each pair, and the combination that minimizes the com-bined χ2 is accepted [60].The reconstructed muon design resolution varies throughout (η ,φ) space, butis less than 3% over a wide pT range. For central muons, the momentum resolu-tion varies from 2% at 4 GeV up to around 10% at 1 TeV, for more forward goingmuons, the resolution varies between 4 and 8%. Comparisons of the parameteri-zations between simulation and real data were performed, and a corrective randomGaussian smearing is applied to simulated muons in order to match Monte-Carloperformance to observations in data [73].The reconstruction efficiency is nearly 100% across |η | < 2.5 beyond whichthe combined efficiency drops off rapidly corresponding to the end of the inner de-tector. The reconstruction efficiency also drops to 0 at |η | < 0.1 where the activelayers of the muon system are interrupted to allow for inner detector and calorime-ter services [2]. Small drops in efficiency are also evident near |η |=1.0, whichcorresponds to the transition between the barrel and endcap components of theMuon spectrometer.Electrons and PhotonsElectrons and photons are reconstructed with similar, complementary techniques,together referred to as e/γ reconstruction, that consist of distinguishing and mea-suring the following three objects:• electrons and positrons• unconverted photons: those photons which do not pair produce before im-pacting the front face of the calorimetry.• converted photons: those photons which do pair produce to an electron/-positron pair within the inner detector.98The calorimeter is used for 4-momentum measurement and the inner detector isused for particle and charge identification.The main backgrounds to e/γ reconstruction are pions and jets. Charged pi-ons are light detector stable objects and can mimic electrons, while neutral pionscan decay to produce two collinear photons faking a photon signal. While jetsof hadrons are significantly different objects than electrons, their manifestation asthe overwhelmingly dominant object at the LHC means that even a small rate formisidentifying jets as electrons could potentially swamp real electron signals. Toreject these backgrounds and maintain e/γ signal efficiency, pattern recognitiontechniques have been developed based on the shower shape and composition ofcalorimeter clusters associated with candidate objects. Additionally, transition ra-diation measurements within the TRT are used to distinguish charged pions fromelectrons.The reconstruction begins by searching for electromagnetic showers in theECAL, by first identifying seed clusters in its second layer, using 5×5 cell slidingwindows, and then searching for a loosely matching track and associated photonconversion vertex. Electrons are identified as being associated with a single trackand no conversion vertex, converted photons are identified as being associated witha conversion vertex, and unconverted photons have no associated track. Candidateclusters are built by summing energy in 3×7 and 3×5 cell windows built aroundthe seed for electron and photon candidates respectively. As the analyses describedwithin this paper do not rely directly on reconstructing photons, the reader is re-ferred to [2] for further details.The energy of electrons is reconstructed by taking a linearly independent com-bination of the energy measured in the presampler (ps), strip layer (str), first twoaccordion layers (mid), and the third accordion layer (w3). The electron energyis reconstructed by computing a weighted average between the calorimeter clus-ter energy and the track momentum [74]. The η- and φ -direction of the electronis then determined from its track. The reconstructed calorimeter energy can bewritten as:Etot = s(η) [c(η)+w0(η)Eps +Estr +Emid +w3(η)Eback] . (3.15)99Overall 4 momentum resolution and subsequent calculations are dominated en-tirely by the energy resolution which is better than 2% for ET > 25 GeV over|η | < 0.6, and exceeds 3% only around the transition region [75]. The resolutionperformance was evaluated in simulation and real data. Corrective smearing fac-tors were determined in order to match Monte-Carlo performance to observationsin data.The analyses presented in this thesis uses tight electron selection criteria whichoffered maximum background rejection while maintaining reasonable efficiency.The tight selection consists of comparing and applying cuts on both tracking andshowering criteria [74]:1. Difference between observed and expected number of TRT hits ≤ 152. ≥ 1 hit in the pixel vertexing layer3. d0 < 1 mm4. A high ratio of high threshold to low threshold TRT hits to reject pions.5. A ratio of ECAL measured energy to track momentum, E/p, close to unity,indicative of a primarily electromagnetically interacting object.6. Angular differences between track position at the front face of the ECAL,and the impact point measured in the strip layer of ∆φ < .02 and ∆η < .0057. A low ratio of energy deposited in the first layer of the HCAL to the energydeposited in ECAL8. A high ratio of the second layer cluster energy between the standard electronwindow and an extended 7×7 cell window9. High ratio of difference of two highest energy cells to their sum10. A narrow shower widthThe cut values are optimized to maximize the purity of the electron selection. Thetight selection offers a background jet rejection of O(105) for electrons with 20GeV < ET < 50 GeV, and an overall selection efficiency better than 70%.100Topological ClustersHadronic clusters are calorimetric energy deposits associated with hadrons, analo-gous to e/γ clusters. However, they are primarily a sub-object that serve as inputinto the EmissT calculation and jet reconstruction algorithms. They are an attemptto reconstruct individual hadrons with the calorimeter. However, a complete de-scription of hadrons within jets is complicated by IRC effects, and often hadronsmay appear nearly collinear with multiple truth level hadrons reconstructed as asingle cluster. Thus, cluster multiplicity is in general lower than the truth hadronmultiplicity, but since the invariant mass of effectively massless collinear objectsis also effectively massless, this experimental limitation does not impact the EmissTor suitably defined jet measurements in a significant way.The topological clustering algorithm reconstructs the showers due to hadrons asvariable shaped 3D “blobs” of energy [60] and proceeds as follows. To distinguishhadronic signals from the calorimeter noise, seed cells are identified as those cellsthat have |Ecell|> 6σcell , where σcell represents noise fluctuations due to electron-ics and pile-up [2]. Next, proto-clusters are built by adding 3D nearest neighbours,with |Ecell|> 3σcell above a minimum threshold, to each seed cell, and adding thecell to a new seed list for the following iteration. If the candidate cell is also sharedbetween two proto-clusters, the two clusters are merged. Once the nearest neigh-bours have been evaluated for all initial seeds, the same procedure is applied to thenewly identified neighbour seeds. The process is repeated until no new neighboursare identified. In this way, proto-clusters are grown, and merged together, from thecalorimeter energy deposits. Next, if proto-clusters contain multiple maxima theyare split along the minima between them to form the final clusters.The ATLAS calorimeter system is a non-compensating calorimeter: the energyresponse ratio between electromagnetic and hadronic showers differs from unityand is around 1.4 [3]. This complicates the energy calibration of hadronic parti-cles since in general they contain a variable amount of electromagnetic, hadronic,and invisible energy. Moreover, the hadronic shower fraction of an incident hadronis itself energy dependent, leading to a non-linear energy response. By default,topoclusters are calibrated to the electromagnetic scale, which means they pro-vide the proper response for EM showers. To overcome the non-compensation,101topoclusters can be locally calibrated to the hadronic scale. In which case, theclusters are first classified as being primarily hadronic or electromagnetic, and thenweights are applied based on cluster energy, shape, and pseudorapidity [76]. Inspite of the correction, the energy resolution for topological clusters remains largerthan e/γ objects; for single pions, the energy resolution also improves with energybut is only about 8% at 100 GeV [77].JetsJet reconstruction is summarized by three characteristics:1. the jet finding algorithm2. the jet distance parameter R, in (η ,φ) space, which sets the angular size ofthe jet3. the inputs to the jet algorithmAll the jets considered in this thesis use the anti-kT algorithm, which will bedescribed in the following section. Various jet sizes and inputs were considereddepending on what level of the top-decay the analysis focused on, the various typesof jets that were used in the analyses presented in this thesis are described in thesections that follow.The anti-kT algorithmThe goal of jet reconstruction is to properly associate together systems of ob-jects descendent from common partons, and determine those system’s 4-momenta.These objects must be identified in the final state of the collision in the midst of ahigh-multiplicity event. A key criteria for useful jet definitions, a corollary of therequirement of IRC safety, is that a given jet algorithm must consistently recon-struct the parton descendent system as the same jet at any stage in the evolution ofthat system from parton through to hadronic jet, on an event-by-event basis: thisensures that the reconstructed jet is a good proxy for the initiating parton. Thisleads to the definition of various jets based on what entities are input into the jetalgorithm. Most notably particle jets use Monte Carlo particle truth as input.102All the jets used in the analyses described in this thesis use the seedless IRCsafe sequential recombination anti-kT algorithm [78]. The algorithm reconstructsjets with a roughly conical shape in (η ,φ) space with radii corresponding to thealgorithm’s distance parameter R. Entities are associated together by consideringtwo distance parameters: di, j, the distance between two entities i and j; and di,Bthe distance between entity i and the beam. The distance parameters are defined interms of the transverse momentum, kT , and the entity separation ∆Ri j[78]:di j = min(k−2T,i ,k−2T, j)∆R2i jR2(3.16)diB = k−2T,i (3.17)The algorithm proceeds by considering one entity at a time, in arbitrary order. Twoentities, i and j, are combined into a new entity i, if di j < diB, then j is removedfrom the list of entities. The procedure continues until there are no new entities jfor which di j < diB, at which point entity i is labelled a jet and removed from thelist of entities. The algorithm is repeatedly applied to the remaining entities untilall have been classified into jets.The final jet object is a system of N entities each with their own 4 momentum.The 4-momentum of the jet is calculated as the 4-momentum of the system ofassociated entities:(E,~p) =(N∑iEi,N∑i~pi)(3.18)A result of this treatment is that even when the entities are assumed massless,such as the case of topological clusters, reconstructed jets will generally have massarising from the angular distribution of the entities, i.e:m2jet =(N∑iEi)2−(N∑i~pi)2≥ 0 (3.19)Standard JetsStandard jets at ATLAS are reconstructed with distance parameters of R=0.4or R=0.6, both of which offer similar performance. In the analysis presented here103anti-kT jets with R=0.4 are used to reconstruct b-jets and additional light jets. Thestandard jet prescription has evolved over the first years of ATLAS running. Ini-tially, jets were formed from uncalibrated topoclusters, these are called EM jets.More recently, locally calibrated topoclusters were used as inputs. The resultingjets are referred to as LCW jets. In both cases, measured jet 4-momentum must becorrected for various effects [79]:1. Pile-up energy offset correction: Monte Carlo derived corrections to jet en-ergy based on the pile-up µ distribution, which subtract additional energydue to in-time and out-of-time pile-up.2. Jet Direction Correction: The naive jet direction, computed assuming a jetorigin at the centre of the detector coordinate system, is corrected to pre-cisely point back towards the reconstructed primary vertex associated withthe event.3. Jet Energy Scale Calibration: A parameterized scale factor is derived fromMonte Carlo that corrects reconstructed energy to the particle level energyin order to remove dependence on simulated detector effects.4. Residual Jet Energy Scale Calibration: A final calibration is applied to jetsin data using in situ techniques.The jet energy scale (JES) calibration corrects measured jets back to the particlejet level for the following detector effects:1. calorimeter non-compensation (EM jets only)2. dead material3. particle deflection out of cone by the magnetic field4. cluster reconstruction efficiencyThe JES calibration consists of determining a jet pT and η dependent scalefactor from simulation to calibrate simulated jets, and a residual JES correctiondetermined for jets in data in order to account for differences between simulationand experiment [79]. The uncertainty on the residual JES calibration is a major104source of systematic uncertainty in most analyses. It varies from 1% in the centralregion of the detector up to 6% in the forward regions. The final calibrated jets thatserve as input into the analyses are referred to as EM+JES or LCW+JES, dependingon the topocluster calibration.The jet selection efficiency rises from 96% for jets with pT > 40 GeV in thebarrel region up to 100% for high pT jets across all detector regions. Overall4 momentum resolution is dominated by the jet energy resolution which has thesame energy dependence as the calorimeter energy measurement. For EM+JESjets the resolution decreases from roughly 15%, at pT = 30 GeV, to better than 8%for pT > 300 GeV. The performance is slightly better for LCW+JES jets whoseresolution drops from roughly 14% to better than 6% over the same range.Fake jets can arise in data from non-collision sources such as beam phenom-ena, hadron calorimeter noise bursts, or rare EM calorimeter coherent fluctuations.However, their rate is suppressed to negligible levels by a set of quality cuts basedon jet shapes, cell energy distributions, jet timing, and the presence of associatedcharged tracks.Fat-Jet Calibration and PerformanceIn the fully hadronic analysis presented in this thesis, single jets correspondingto collimated decays from top quarks with pT 500 GeV were searched for. Tolocate these top-jets, LCW+JES R=1.0 jets, referred to as fat jets due to their largedistance parameter, were reconstructed identically to standard jets. However, fat-jets were calibrated differently: they do not receive an explicit pile-up correction,and they have a distinct JES and associated uncertainty.By default the jet mass is determined for fat-jets as the invariant mass of thesystem of massless topoclusters of which the jet is composed. However, unlikestandard jets no explicit pile-up correction was applied prior to this mass calcula-tion. In the analysis presented here the complementary cone technique was used toderive a data driven correction parameterized in terms of the number of collisionvertices in the event, NPV , and jet pT , from data events [80].105Flavour Tagging Jets originating from b-quarks can be distinguished from otherjets using methods that search for signs of the displaced decay of the b− quarkwithin the jet. Candidate jets are classified as b-jets using a multivariate analysiscalled MV 1[81]: an artificial neural network based on a combination of the outputweights from three tagging algorithms designed to search for displaced hadronicdecays. Each of these algorithms is introduced below [82]:• SV1: Explicitly reconstructs the displaced decay vertex of the b-hadron [82].• IP3D: Performs a b-jet hypothesis test based on the transverse and longitu-dinal impact parameter significance (d0/σd0 , z0/σz0) of tracks• JetFitter: Uses a Kalman fitter to reconstruct the flight length from the pri-mary vertex to the displaced vertex, which allows c-jets, b-jets, and light jetsto be distinguished.An operating point of 70% b-tagging selection efficiency is chosen for the b-tagging criteria in this analysisTransverse Energy Calibration and PerformanceThe missing transverse energy is reconstructed as a two component vector in the(x,y) plane, determined from the summations of the energy projections of all can-didate calorimeter cells and the reconstructed muons, Ex and Ey respectively. Onlycells associated with reconstructed calorimeter clusters, either eγ or topoclusters,are used in the summation. Calorimeter cells associated with reconstructed objectsreceive the energy calibration associated to their reconstructed object. The summa-tion over each object type contributes a term to the transverse energy measurement,denoted by the object type. Cells from non-jet-associated LCW topoclusters aresummed together with pT measurements from soft tracks in the inner detector thatfailed to impact the calorimeter. In the event that a soft cluster matches a track, thetrack measurement is used. This contribution to the transverse energy calculationis referred to as the CellOut term. For each cluster type the calorimeter contribu-tion to the missing transverse energy, Emissx(y) is merely the negative of the transverse106energy sum:Emissx(y) =−∑cellsEx(y) (3.20)The contribution from muons is computed directly from the reconstructed muontracks, and may also contain calorimeter deposits associated with the muons. Thetotal missing energy components can be written as:Emissx(y) = Emiss,ex(y) +Emiss,γx(y) +Emiss,topox(y) +Emiss,topox(y) +Emiss, jetsx(y) (3.21)+ Emiss,so f t− jetsx(y) +Emiss,µx(y) +Emiss,CellOutx(y)Which can be simplified to two components:Emissx(y) = Emiss,calox(y) +Emiss,µx(y) (3.22)Where the CellOut term has been absorbed into the calo term. EmissT is then calcu-lated as:EmissT =√(EmissX )2 +(EmissY )2 (3.23)Transverse energy measurements are dependent on object reconstruction andthus have correlated performance with the performance of each object type de-scribed thus far. The EmissT resolution has been estimated in data by studyingZ → ``, QCD dijet, and minimum bias events. These processes do not containany invisible energy and can be isolated with high purity. The resolution is foundto roughly obey the following formula:σEmissx,y = k√∑ET (3.24)where k is an empirically determined constant that depends on the process beingstudied, but is on the order of 0.5.Each term in the transverse energy calculation contributes its own source ofsystematic uncertainty. While the contribution depends on the value of EmissT andthe structure of the event, the dominant contributions come from the jet and CellOut107terms [83].108Chapter 4The Statistical MethodsThis chapter describes the common methods and procedure used to test hypothesesand quantify the results in each of the analyses presented in this thesis. The resultsof the analyses presented here are conclusions about a set of benchmark hypothesesthat are tested by comparing statistical models for the hypothetical predictions toactual observations in data using statistical inference. In general tested hypothesesfall into two classes. The background only, or null hypothesis prediction is com-posed of all known Standard Model processes. The null hypothesis is tested againsta space of signal plus background hypotheses by considering their correspondingpredictions, each consisting of the standard model prediction plus one of the spe-cific predictions associated with the new physics hypotheses. Each hypothesis istested by evaluating the agreement of its prediction with the observed event countin data for some selection of events.The analyses consisted of applying a set of acceptance and identification cutson a subset of events collected in data, and counting the number of accepted events.For each modelled sub-process in a given prediction, the predicted acceptance×efficiency,Aε , was determined by considering the fractions of events in Monte Carlo that passor fail the selection. The events in the MC sample are weighted relative to eachother by a product of various correction factors, such that each possesses a numer-ical weight wi. Letting ∑+ and ∑− refer to summations restricted to the acceptedand rejected sub-sets of events respectively, the predicted Aε and its uncertainty109δAε were determined as [84]:Aε = ∑+ wi∑wi, (4.1)andδAε =√∑+ w2i (∑−wi)2 +∑−w2i (∑+ wi)2(∑wi)2 . (4.2)The nominal Monte-Carlo prediction for a given process is related to the Aεprediction according to equation 3.3, and is an estimate of the Poisson mean eventcount, µ , given by:µ±δµ = L∑pσp[Aε]p±L√∑p(σpδ [Aε]p)2, (4.3)where the index p runs over all relevant processes that compose the hypothesis.That prediction must be compared to the actual observed number of events in data,N, which itself has a characteristic sampling uncertainty:N±δN = N±√N. (4.4)Meaningful comparisons must consider both the above statistical uncertaintiesand the systematic uncertainties on the statistical physics and experimental modelsused to derive the nominal prediction. The conclusions drawn from such compar-isons are necessarily a set of probabilistic statements about the consistency of theobservation in data with the tested hypothesis space. At least two different sta-tistical inference methodologies are widely used. Bayesian inference defines theconsistency as the probability of a hypotheses being true given the data, while theFrequentist method determines the probability of observing the data given a hy-pothesis.In the analyses presented here Bayesian probabilities for hypotheses are deter-mined from data, and form the foundation of the statistical method. The poten-tial signal significance in data is assessed with a hybridized frequentist p-value,which uses a test-statistic constructed from the Bayesian probabilities. Finally, theBayesian posterior probability distributions are used to determine exclusion limits110on model parameters.4.1 An Overview of Bayesian InferenceBayesian inference is an application of Bayes’ theorem which views knowledge ingeneral as probabilistic due to its basis in observations that are finite in scope andmeasured to a finite uncertainty [85]. The Bayesian approach to statistical analysisoffers two main advantages. Firstly, it is an easily comprehensible extension oflogic into a probabilistic framework. Secondly, it allows for systematic uncertain-ties to be incorporated in a straightforward way.Bayes’ theorem offers a prescription for determining the probability of a hy-pothesis, represented by a set of model parameters Φi, which have a prior proba-bility distribution P(Φi|I) based on current knowledge I, given a set of data D. Thenon-normalized posterior probability distribution for a set of parameters, P(ΦI|D, I),is then related to the probability of observing the data assuming the hypothesis istrue, P(D|Φi, I), or the likelihood (L ) according to[85]:P(ΦI|D, I) = P(D|Φi, I)P(Φi|I). (4.5)In words, equation 4.5 states that the non-normalized probability distribution for aset of model parameters, given a set of data, is equal to the likelihood of the dataassuming the model parameters times the prior probabilities for each parameter ofthe model.A hypothetical prediction is summarized by two sets of parameters: the funda-mental model parameters which the experiment seeks to test, Hi, and a set of nui-sance parameters, θ , for the aspects of the model that have a significant enough de-gree of systematic uncertainty that they impact the model prediction. The Bayesianmodel acknowledges that the nuisance parameters are not precisely known and en-codes their systematic uncertainty as prior probability distributions for their un-known true value as Gaussians about their nominal measured or assumed values.A probability distribution for only the parameters of interest, Hi, can then be deter-mined by marginalizing (integrating) over the nuisance parameter-space:P(Hi|D, I) =∫dθP(Hi,θ |D, I). (4.6)111The marginalized equation 4.6 is referred to as the reduced posterior probabilitydistribution.4.2 The Template LikelihoodBayes’ theorem is applied in the analyses presented here using a procedure calledtemplate fitting, whereby the likelihood in equation 4.5 is calculated from a his-togram for an observable measured in data. Hypothesis predictions are then sum-marized as fully simulated histograms for the observable, called templates, whichconsist of an Aε prediction for each bin. The nominal predicted Poisson meanin the kth bin of the distribution is then equal to the sum of the nominal templatepredictions, Tpk, associated with each process in the hypothesis. The effects ofpositive (+) and negative (-) one-sigma shifts due to the jth source of systematicuncertainty, ε±p jk, are determined by applying the estimated one-sigma shifts tothe corresponding parameters within the simulation, and re-deriving systematicallyshifted template predictions T±p jk:ε±p jk = T±p jk−Tp j (4.7)The nominal and shifted templates are then used to construct the Bayesian proba-bility as follows. First, the likelihood function for a hypothesis is formed by takingthe product of the Poisson probabilities, µk, to observe the data measured in eachbin, nk. µk depends on both the model parameters and the set of nuisance pa-rameters θi, according to ε±p jk. The unnormalized posterior PDF is then given byBayes’ Theorem by multiplying the likelihood function by the unit Gaussian priorprobabilities, G(θi,1), for the nuisance parameters:P(H,ΦI|D, I) =Nbins∏k=1µnkk e−µknkNsys∏j=1G(θi,1), (4.8)withµk = LNproc∑p=1σpTpk(1+θi[H(θi)ε+p jk +H(1−θ j)ε−p jk]),where G and H are unit Gaussian and unit Heaviside step functions respectively.112The null hypothesis is controlled only by the nuisance parameters, in that caseH is a null set. The signal hypothesis space is a two dimensional space consistingof a finite set of mass hypotheses {M}, and a continuous parameter for the numberof signal events {NM}. These parameters are assigned uniform prior probabilitieswhose explicit inclusion in the unnormalized posterior would be redundant.4.3 The Frequentist p-valueThe first step in a search for new physics is to determine whether the observed datais inconsistent with the background only hypotheses. A purely Bayesian approachto this problem necessitates the use of normalized PDFs, which in turn necessi-tates specifying the absolute prior probabilities for all new physical theories. Thespecification of relative priors can present a challenge for interpretation. For hy-pothesis rejection, it is more straightforward to use a Frequentist p-value, whichcan be constructed from any scalar measurement of the data, called a test statistic.The null hypothesis yields a specific distribution for the test statistic. The ob-servation in data can then be said to be consistent or inconsistent with the nullhypotheses based on the position, xD, of the observed test statistic within the pre-dicted distribution. This leads to two types of possible errors:• Type I: Incorrectly reject the null hypothesis• Type II: Incorrectly accept the null hypothesisA p-value is a statement of the likelihood of a type I error, or the significanceof a result. It must be defined in a model dependent way. In discovery analy-ses test statistics are chosen such that values tending towards one extremum ofthe distribution, EA, represent increasing compatibility with the alternative (back-ground+signal) hypothesis. In these cases one-sided p-values are precisely definedas the probability of obtaining a result that is more consistent with the alternativehypothesis than the observed statistic xD. If the statistic has probability distributionPH(x), this is formally given by:p =∫ EAxDPH(x)dx (4.9)113The optimal choice of such a statistic is the maximum likelihood ratio, often ex-pressed as a log-likelihood-ratio (LLR)[21]:LLR =−2lnL (data|NM ,M , θˆ)L (data|NM = 0,ˆˆθ), (4.10)whereˆˆθ and θˆ are the best fit values for the nuisance parameters in the backgroundand signal plus background cases respectively. According to the Neyman-Pearsonlemma, LLR has the property that at any significance level, it minimizes the prob-ability of a Type II error [21].In the analyses presented here the LLR is calculated in data and compared tothe distribution predicted from Monte Carlo. The Monte Carlo distribution is gen-erated by calculating the LLR for a large ensemble of Poisson fluctuated pseudo-experiments for a set of models that have their nuisance parameters randomly var-ied according to their priors. This procedure propagates both the statistical and sys-tematic uncertainty through the LLR distribution, and represents a hybrid Bayesianapproach via the dependence on the nuisance priors. A common problem in theapplication of this method is the so called look-elsewhere effect, which is a type Ierror enhancement caused by repeatedly testing a single dataset against indepen-dent alternative hypotheses. This is avoided in the hybrid approach by determiningthe maximum alternative likelihood, the numerator in the LLR, against the entiresignal hypothesis space simultaneously[21].4.4 Numerical ImplementationThe Bayesian Analysis Toolkit (BAT) [86], was used to derive the likelihood func-tion and incorporate systematic uncertainties using the nominal and systemati-cally shifted template predictions as input. It was also used to generate pseudo-experiments by randomly varying the mean prediction within the nuisance param-eter space according to the priors, and then randomly generating a simulated ob-servation by sampling the prediction’s Poissonian probability distribution. Mostcritically, it was used to perform the numerical integration required to determinethe posterior probability distributions for parameters of interest, and maximizationcalculations to determine best fit parameters based on Markov Chain Monte Carlo114sampling.115Chapter 5Analysis I: The Search forResonances in the DileptonChannelThis section presents an analysis that searched for top-pair resonances in the dilep-ton channel that was performed on the first 2.04 fb−1 of ATLAS data collected in2011 at√s = 7 TeV. That analysis was the first of its kind performed at ATLAS,and its results were published in The European Physical Journal C [20], in May2012. Several conference contributions and ATLAS internal documents describethe analysis at various stages in its progression [21, 87, 88]. The material in thissection is taken from some or all of these sources, but is consistent with the pub-lished results.The search in the dilepton channel was motivated by the presence of two lep-tons in the final state which allowed for strong suppression of the QCD multijetbackground, and a generally well understood background prediction. The analy-sis strategy was fairly straight-forward. A candidate pool of events was selectedfrom data using a set of data quality and kinematic cuts optimized to maximize thetop-pair signal significance against the non-top background. Events were selectedby searching for physics objects consistent with the observable dileptonic tt¯ final116state, corresponding to the process:pp→ tt¯→ bW+b¯W−→ b`+ν b¯`−ν¯ . (5.1)The anatomy of a typical dileptonic top-pair event is shown in figure 5.1. Theselection was optimized for selecting resolved decays where the lepton and jetdaughters of the top-decay are well separated. The focus on the resolved topologyoptimized the search sensitivity toward moderate mass, m < 1 TeV, resonances.In terms of reconstructable physics objects, the final state corresponds to 2 jets,two oppositely signed leptons (here restricted to either electrons or muons), andmissing transverse energy.yxz(a)yxzb-jetℓℓνν+-b-jet(b)yxETmisspT,j1pT,j2pT,ℓ1pT,ℓ2(c)Figure 5.1: (a) A schematic diagram of the typical truth objects in a the dilep-tonic top-pair event. (b) Their associated truth 3-vectors. (c) The projec-tion of the experimentally measured 3-vectors onto the transverse plane.The neutrino information has been reduced to a single two componentvector in the transverse plane.The presence of two neutrinos in the final state means the measurement indata alone cannot be used to infer the ditop invariant mass. While kinematic fitterapproaches that rely on the W and top mass are possible, this analysis used a simplevariable highly correlated to the ditop mass called HT +EmissT where HT is the scalarsum of the pT s of the two leading (highest pT ) jets, and two leading leptons i.e.:HT +EmissT = pT, jet1 + pT, jet2 + pT,`1 + pT,`2 +EmissT . (5.2)117The reconstructed physics object representation, and the quantities input into theHT +EmissT calculation are shown schematically in figure 5.1The reconstruction performance for the HT + EmissT variable depends on theresolutions of the 4-momenta entering into equation 5.2, and also the validity ofthe assumption that the b-jets from the top-decays tend to be the most energetic jetswithin the event. That performance is summarized by considering the correlationbetween the reconstructed HT +EmissT and the truth ditop invariant mass in figure5.2, which shows the normalized reconstructed HT +EmissT distribution as a functionof mtt¯ . mass [GeV]tTrue t0 500 1000 1500 2000 2500 3000 [GeV]missT + E TH050010001500200025003000A. U.-310-210-110ATLAS SimulationFigure 5.2: The reconstructed HT +EmissT vs. truth mtt¯ . Each mtt¯ bin is nor-malized to unity [20]5.1 Data SamplesThe collision and Monte Carlo data samples used in the analysis are summarizedin this section. The Monte Carlo samples used represent the tested signal andbackground hypothesis space. The background only hypothesis for this analysis isintroduced by summarizing the samples used.1185.1.1 BackgroundsThe Standard Model background can be partitioned into two classes: the irre-ducible Standard Model top-pair background, which forms the majority of thebackground estimate in the signal region and is selected because its final state gen-uinely matches the final state of signal candidates; and the reducible backgrounds,which the event selection attempts to suppress. The reducible backgrounds are se-lected accidentally by their propensity to generate final states that mimic genuinetop-pairs. An accurate modeling of such processes is essential to making meaning-ful inferences from the measurement in data.Standard Model Top-PairStandard Model top-pair production was discussed in detail in section 2.4.4.For this analysis, a sample generated with MC@NLO interfaced to Herwig thatused the CTEQ6.6[89] parton distribution function was used. The NLO generatorpredicted cross-section is corrected to the approximate NNLO prediction [90].The Non-Top-Pair BackgroundsSingle Top ProductionEvents containing the production of a single top quark can mimic the dileptonand ditop final state via associated jet production and possible misreconstructions.Single top production can proceed through either the s- or t-channel. A specialclass of processes containing an associated W in the final state are referred to asthe Wt channel. When a top quark is produced in association with a W boson, thedileptonic ditop final state is genuinely mimicked due to the presence of additionalradiated jets in the event. Figure 5.3 shows the two tree-level Wt diagrams, and theadditional s- and t-channel single top production diagrams.Single top production is simulated at NLO with MC@NLO, where special careis taken to prevent double-counting an NLO Wt event as an LO ditop event. Thesample is normalized to the cross-section predicted by MC@NLO [91].119WtqgWtqbbtqq¯qtbqFigure 5.3: The various tree-level diagrams for single top production.Drell-Yan ProductionThe electroweak pair production of fermion-anti-fermion pairs, via an intermediateγ or Z boson, known as Drell-Yan production, is a major top-pair background.The Z/γ∗→ f f¯ process is shown in figure 5.4. When it results in the productionof two final state leptons its occurrence with associated jets genuinely mimic thedileptonic ditop final state.Z/γ∗`¯`qqFigure 5.4: The tree-level diagram for Drell-Yan production. Two leptons areproduced through qq¯ annihilation to either a virtual photon or a massiveZ-boson. The rate of the process is significantly enhanced at the Z-masspole.However, the massive and narrow Z-boson propagator expresses a characteris-tic Breit-Wigner line shape for the process, sharply peaked at the Z mass. Further-more, the absence of neutrinos means that such events generally contain low EmissT .These characteristics allow some kinematic suppression, but also the ability to iso-late Z→ ` ¯` control regions that are particularly useful for validation and correctionpurposes.Modeling of the associated final state jets is performed with Alpgen Z/γ∗+N jets Monte Carlo, using a set of samples covering the kinematic range 10 GeV< m`` < 2000 GeV. Prior to the application of data-driven correction methods, the120W,ZW,ZqqFigure 5.5: The tree-level diagram for diboson production.rate for these processes is initially normalized to the NNLO prediction.Diboson ProductionThe diboson production process, pp→ (ZZ,ZW,WW ) with associated jets, mimicsthe ditop final state which is also characterized by two bosons and additional jets.At leading order these processes arise from t-channel quark-quark interactions asis shown in figure 5.5, where the bosonic combination in the final state depends onthe flavor transformation of the quark lines.As with Drell-Yan production accurate predictions of the associate jets andtheir multiplicity are attempted with Alpgen. The associated sets of Alpgen sam-ples are normalized such that their rate agrees with the NLO QCD calculations.Fake EventsThe high-rate of hadronic activity at the LHC means that even though object re-construction provides excellent fake rate suppression, there is usually a signifi-cant background contribution from events where jets are misreconstructed as otherphysics objects. Jets misidentified as leptons are referred to as fake leptons, andarise either through misreconstruction of the hadronic shower or the misidentifi-cation of a lepton arising from the semileptonic decay of a quark as an isolatedlepton.Fake dileptonic ditop events are dominated by W+jets events which containone real lepton. A subdominant contribution arises from QCD multijet events thatcontain two fake leptons.Modeling the rate of such ”fake” events is extremely difficult. First, the lowfake-rate for physics objects would entail a prohibitively inefficient simulation pro-cess in order to achieve a sample with reasonable statistics. Secondly, the fake-rateitself is not something well determined from Monte Carlo as it potentially relies121on poorly simulated details of jet phenomena and detector performance. Instead,a data-driven approach called the Matrix Method was used to arrive at an estimateof the fake rate from measurements in data. The procedure was carried out by theATLAS top-cross-section analysis team, which employed the same event selectionused in this analysis[92].5.1.2 SignalsBoth benchmark signal samples were generated using MADGRAPH interfaced toPythia. The samples were used to determine the predicted template shapes for theHT +EmissT distribution.For a given model, benchmark mass points differ only by the pole mass depen-dent portions of their Breit-Wigner distributions, i.e. the resonance mass alters onlythe invariant mass probability distribution of a sample; but, on an event-by-eventbasis, events from two different benchmark masses are indistinguishable. Thisproperty is taken advantage of in order to minimize the computational overheadfor simulation while producing a pseudo-continuous mass hypothesis space.For the KK-gluon hypotheses a single source sample corresponding to a genericKK-gluon with Msource = 2 TeV, Γsource = 500 GeV was generated with high statis-tics. Initially, each event in that sample is assumed to occur with equal probabil-ity, i.e. each event has a weight of 1. A target mass hypothesis was obtained byreweighting the events of the source sample, based on their truth mtt¯ , such thatthe reweighted probability distribution matches the target mass hypothesis. Thiswas achieved by assigning an invariant mass dependent weight to each event thatfactored out the source Breit-Wigner weight and applied the target Breit-Wignerweight:w(Mtarget ,mtt¯) =(m2tt¯ −M2source)2 +(M2sourceΓ2source)2(m2tt¯ −M2target)2 +(M2targetΓ2target)2(5.3)For the Z′ hypotheses, the source distribution was deliberately flattened by re-moving the Breit-Wigner dependence entirely. In that case the mass-dependentreweighting factor was given by:w(Mtarget ,mtt¯) =e−0.00195mtt¯(m2tt¯ −M2target)2 +(M2targetΓ2target)2(5.4)122The reweighting procedure was verified by comparing reweighted predictions toavailable dedicated samples that were generated at specific benchmark masses;statistical agreement at the truth level was found for all kinematic distributions.A series of reweighted target invariant mass distributions, and reconstructed,unit area normalized, HT + EmissT signal templates are shown in figures 5.6 and5.7. The reweighted overall Aε , multiplied by the theoretically predicted resonantbranching ratio to top-quark pairs, for each mass hypothesis is shown in figure 5.8.123mass [GeV]400 600 800 1000 1200 1400 1600 180000. ATLASwork in progresst t →KKg = 7 TeVssimulationUnit Area Reweighted Resonance Shapes(a) [GeV]missT+ETH200 400 600 800 1000 120000. ATLASwork in progresst t →KKg = 7 TeVssimulationUnit Area Reweighted Templates(b)Figure 5.6: (a) The reweighted KK-gluon resonance shapes. (b) Thereweighted reconstructed KK-gluon HT +EmissT templates. The recon-structed SM tt¯ prediction is shown in grey. The red line-shape corre-sponds to a 700 GeV resonance.124mass [GeV]400 600 800 1000 1200 1400 1600 180000. ATLASwork in progresst t →Z’ = 7 TeVssimulationUnit Area Reweighted Resonance Shapes [GeV]missT+ETH200 400 600 800 1000 120000. ATLASwork in progresst t →Z’ = 7 TeVssimulationUnit Area Reweighted TemplatesFigure 5.7: (a) The reweighted Z′ resonance shapes. (b) The reweighted re-constructed Z′ HT +EmissT templates. The reconstructed SM tt¯ predic-tion is shown in grey. The red line-shape corresponds to a 700 GeVresonance.125KKgluonM600 800 1000 1200 1400 1600 1800 2000 2200 240000.0050.010.0150.020.0250.030.0350.04 Acceptance ATLASwork in progressb bν­lν+ l→t t →KKg = 7 TeVssimulationZ’M600 800 1000 1200 1400 1600 1800 2000 220000.0050.010.0150.020.0250.030.0350.04 Acceptance ATLASwork in progressb bν­lν+ l→t t →Z’ = 7 TeVssimulationFigure 5.8: The reweighted acceptance times efficiency for each benchmarkmodel.1265.1.3 Collision Data SamplesThis analysis used the first 2.05 fb−1 of data collected by the ATLAS detector in2011. The superset of collision events containing two reconstructed leptons in thefinal state are reliably selected by using data samples which passed at least oneelectron or muon trigger that was maximally efficient for the kinematic cuts usedin the event selection. Two partially overlapping data streams corresponding toevents that passed an electron or muon trigger were used. In each case the triggerapplies a looser object selection than what is used in the event selection. The detailsof the data samples are summarized in the table below.Table 5.1: Collision data samplesL [fb−1] Muon Trigger Electron Trigger1.34 EF mu18 EF e20 medium0.21 EF mu18 medium EF e20 medium0.50 EF mu18 medium EF e22 medium5.2 Event SelectionThe analysis used an event selection that was optimized by the ATLAS top cross-section group to maximize the significance for top-pair events. The event selectioncan be broken down into two groups of cuts: a preselection, designed to selectgood dilepton events with multiple jets; and a kinematically restricted signal re-gion designed to maximize the ratio of top-pair events to the non-top background.Additional control regions were defined by omitting or inverting some of the kine-matic cuts.The preselection consists of the following cuts:• Good Runs Lists (Collision Data Only)ATLAS data is analyzed for quality on a run by run basis, and a set of goodruns lists are determined which identify data that is suitable for use in theanalysis. Only events specified in the good runs lists were used.• Pile-up Reweighting (Monte Carlo Only)127A reweighting procedure was applied to the Monte Carlo samples to matchthe simulated conditions to those observed in data. For periods B-K it wassufficient to match the distribution for the number of primary vertices Nvtx,to the distribution observed in data.• TriggerEvents are required to pass a lepton trigger associated with their triggerstream.• Bad Jet VetoEnergy deposits not associated with real jet production can be reconstructedas fake jets. Such depositions can occur due to numerous factors includinghardware problems, cosmic rays, and LHC beam conditions [93]. A set ofquality cuts are defined to reject such jets, any events containing bad jets arerejected.• Good Primary VertexTo reject background coming from the coincidental intersection of two cos-mic ray muons misreconstructed as a primary vertex, the primary vertex isrequired to have at least 5 charged tracks associated with it.• Two Good LeptonsThe event is required to have exactly two good leptons. In the µµ channelcuts are placed to reject events where a single cosmic ray muon may be re-constructed as two muons. Events are rejected if a muon pair exists withopposite signed impact parameters, both muons have |d0|> 0.5 mm or if themuons appear back-to-back in the transverse place: ∆φ > 3.1. Additionally,MC events are given a product of weights associated with each electron de-pending on its reconstructed position in the calorimeter that reflect propor-tionally the fraction of time certain regions of the calorimeter where deaddue to hardware failures.128• Two or More JetsThe event is required to contain at least two EM+JES jets with pT > 25 GeVand |η |< 2.5. In order to suppress the effects from pile-up at least 75% of thesum pT of the jet’s inner detector tracks must be associated with the hard-scattered primary vertex [94]. Fake jets due to misreconstructed electronsare rejected by removing from the event the closest jet within ∆R < 0.2 of anelectron.• Minimum Dilepton Invariant massA lower cut on the reconstructed invariant mass of the dilepton pair of m`` >10 GeV is applied to avoid J/ψ production.The signal region selection cuts depend on the dilepton channel which havediffering bosonic background content. In the ee and µµ channels the cuts aredefined to reject Drell-Yan events:• Reject Drell-Yan events by excluding the Z-mass pole:|m``−mZ|> 10 GeV• Neutrino selection: EmissT >40 GeVIn the eµ channel a cut is placed on the event HT , which unlike the observable’sdefinition includes the pT s of all good jets in the scalar summation. It is requiredthat HeventT > 130 GeV in the eµ channel.5.3 Control Region Validation and Data DrivenDrell-Yan CorrectionsA Drell-Yan enriched controlled region was defined in order to verify the simulatedreconstruction performance against data, and to correct the predicted Drell-YanMonte Carlo rate. A Z-peak control region, restricted to the ee and µµ channels,is defined by removing the two-jet requirement and inverting the Z-mass veto fromthe signal region selection.Initial comparisons between the nominal Monte Carlo prediction and data inthe Z-peak control region revealed a discrepancy in the jet multiplicity distribu-129tions. The data to Monte Carlo rate ratio is shown in 5.9 and indicates a clear sys-tematic deviation between the predicted and observed distributions. Since both thesignal region acceptance and the HT +EmissT observable depend on the jet content,the observation in data was used to correct this discrepancy. In the combined eeand µµ sample, the non-Z+jets background prediction was subtracted from the jetmultiplicity distributions for both data and Monte Carlo. Scale-factors normalizedto the overall rate were then determined in each jet multiplicity bin that would re-produce the observed shape while preserving the predicted overall rate. The resultsof this shape correction are shown in figure 5.9.Kinematic distributions of the corrected Drell-Yan Monte Carlo were comparedto the observation in data. For these comparisons, the overall Monte Carlo rate wasnormalized to data so as to suppress any deviation due to the overall rate uncertaintyin the control region.The inclusive jet and lepton pT and η distributions, composed of both the lead-ing and sub-leading objects in each event, are sensitive to the Monte Carlo mod-eling of both the truth level kinematics and the simulated reconstruction. Figures5.10, 5.11, 5.12, and 5.13 show the kinematic distributions for the reconstructedjets and leptons respectively, in the ee and µµ channels.Good agreement between data and Monte Carlo for the observable HT +EmissTis also observed, as shown in figure 5.14The Drell-Yan contribution in the signal region is attributable to the high EmissTand mll tails of the distribution. The Monte Carlo uncertainty on that rate is ac-cordingly rather high, and the rate in that tail region likely mismodelled. In orderto reduce that uncertainty, a data-driven scale factor for the Drell-Yan rate is deter-mined.130Events­110110210310410510610710810 ll→* γZ/FakesDibosontt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000 Number of Jets0 1 2 3 4 5 6 7 8 9 10Data/MC00.× ll→* γZ/FakesDibosontt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.6760 Number of Jets0 1 2 3 4 5 6 7 8 9 10Data/MC00. 5.9: The jet multiplicity distribution in the Z-peak control region: (a)before correction, and (b) after correction. The rate in Monte Carlo isnormalized to the observed rate in data. Under each plot is shown theData/MC rate ratio in each bin.131ee ­ Channel  Events­110110210310410510  ll→* γZ/FakesDibosontt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000 ηInclusive Jet ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5Data/MC00. ­ Channel  Events­110110210310410510610 ll→* γZ/FakesDibosontt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000  (GeV)TInclusive Jet p50 100 150 200 250 300 350 400Data/MC00. 5.10: The jet η (a) and pT (b) distributions for ee events in the Z-masscontrol region132 ­ Channel  Eventsµµ­110110210310410510  ll→* γZ/DibosonFakestt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000 ηInclusive Jet ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5Data/MC00. ­ Channel  Eventsµµ­110110210310410510610  ll→* γZ/DibosonFakestt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000  (GeV)TInclusive Jet p50 100 150 200 250 300 350 400Data/MC00. 5.11: The inclusive jet η (a) and pT (b) distributions for µµ events inthe Z-mass control region133ee ­ Channel  Events­110110210310410510  ll→* γZ/FakesDibosontt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000 ηInclusive Lepton ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5Data/MC00. ­ Channel  Events­110110210310410510610 ll→* γZ/FakesDibosontt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000  (GeV)TInclusive Lepton p50 100 150 200 250Data/MC00. 5.12: The inclusive electron η (a) and pT (b) distributions for eeevents in the Z-mass control region134 ­ Channel  Eventsµµ­110110210310410510  ll→* γZ/DibosonFakestt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0040 ηInclusive Lepton ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5Data/MC00. ­ Channel  Eventsµµ­110110210310410510610  ll→* γZ/DibosonFakestt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000  (GeV)TInclusive Lepton p50 100 150 200 250Data/MC00. 5.13: The inclusive muon η (a) and pT (b) distributions for ee eventsin the Z-mass control region135ee ­ Channel  Events­110110210310410510 ll→* γZ/FakesDibosontt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000  (GeV)missT+ETH200 400 600 800 1000 1200Data/MC00. ­ Channel  Eventsµµ­110110210310410510610 ll→* γZ/DibosonFakestt Single topData 2011 work in progressATLAS = 7 TeVsData Normalized KS Prob : 0.0000  (GeV)missT+ETH200 400 600 800 1000 1200Data/MC00. 5.14: A comparison of the predicted and observed HT +EmissT distri-butions in the (a) ee and (b) µµ channels in the Z-mass control region.136A control region B was defined by inverting the Z-mass veto in the signal selec-tion. The signal region itself consists of two disconnected selections on the lowerand upper sides of the excluded mZ window, denoted A and C respectively. Thesethree regions are represented in the (m``, EmissT ) plane shown in figure 5.15.Dielectron Mass (GeV)0 20 40 60 80 100 120 140 160 180 200 (GeV)missTE020406080100120140­110110A B C# Events A : 125# Events B : 1127# Events C : 62 work in progressATLASsimulation ­1 L dt =  2.05 fb∫ = 7 TeVsee ChannelDimuon Mass (GeV)0 20 40 60 80 100 120 140 160 180 200 (GeV)missTE020406080100120140110210A B C# Events A : 281# Events B : 1895# Events C : 133 work in progressATLASsimulation ­1 L dt =  2.05 fb∫ = 7 TeVs ChannelµµFigure 5.15: The distribution of Z → ee (a) and Z → µµ (b) Monte Carloevents in the EmissT vs. Z-mass plane. Regions A and C correspond tothe signal region [21].The Drell-Yan rate in the high EmissT region is orders of magnitude smaller thanin the peak and is susceptible to a higher modeling uncertainty than the overall rateprediction. Within region B, the non-Drell-Yan prediction, Nnon−DYMC (B), is sub-tracted from the observation in data, NData(B), which is then divided by the uncor-rected Drell-Yan prediction, NDYMC(B), to determine a scale factor in each channelR`` to correct the overall rate in the EmissT tail. The scale factor is then applied137to the predicted Drell-Yan rate in the orthogonal signal region, NDYMC(A+C), as isrepresented in equation 5.5.NDYMC(A+C) =NData(B)−Nnon−DYMC (B)NDYMCNDYMC(A+C) = R``NDYMC(A+C). (5.5)The resultant scale-factors and their statistical uncertainty in the ee- and µµ-channelsare Ree = 0.69±0.02 and Rµµ = 0.64±0.02 respectively.5.4 Signal Region ObservationThe overall observed rate in the signal region was compared to the total predictionfrom Monte Carlo. Table 5.2 presents the predicted rate, broken down by process,for the overall dilepton channel. The predicted rate agrees with observation withinthe total statistical and systematic uncertainties. A summary of the latter is givenin section 5.5.Table 5.2: Predicted and observed event rates in the signal regiontt¯ 4018+463−469SingleTop 209+32−31Z/γ∗→ `` 568+71−66Di-Boson 185+27−29Fakes 190+186−102Total Expected 5170+542−527Data 5304A candidate signal event from the signal region observed in data, with highHT +EmissT is shown in figure 5.16, which displays the energy of calorimeter clus-ters in the (η ,φ) plane, and a transverse view of both the tracking system and thecalorimetry. In the transverse view, two clusters of tracks leading to energy depo-sitions in both the electromagnetic and hadronic calorimeters indicate the presenceof two hadronic jets. In the hemisphere opposing the jets are two high pT tracksleading to energy deposition in the electromagetic calorimeter alone, and no tracksin the muon spectrometer, indicating the presence of two isolated electrons. Ared-dashed line indicates the direction of the reconstructed EmissT .138Figure 5.16: A candidate high HT +EmissT event. See text for details.Various kinematic distributions were reconstructed in the signal region andcompared to prediction to check for any significant deviation. Figures 5.17, 5.18,5.19, and 5.20 show the leading and subleading jet pT and and η . Figure 5.21shows the EmissT distribution. In all cases good agreement with the SM predictionwas observed within the total statistical and systematic uncertainty, represented inthe plots by hatched bands.139Events0200400600800100012001400 tt  ll→* γZ/Single topFakesDibosonData 2011 work in progressATLAS = 7 TeVs ­1 L dt =  2.05  fb∫  KS Prob : 0.7020  (GeV)TLeading Jet p50 100 150 200 250 300 350 400Data/MC00. 5.17: The predicted and observed leading jet pT in the signal region.Events02004006008001000120014001600180020002200 tt  ll→* γZ/Single topFakesDibosonData 2011 work in progressATLAS = 7 TeVs ­1 L dt =  2.05  fb∫  KS Prob : 0.2240  (GeV)TSub­Leading Jet p50 100 150 200 250 300 350 400Data/MC00. 5.18: The predicted and observed sub-leading jet pT in the signal re-gion.140Events0100200300400500600700800 tt  ll→* γZ/Single topFakesDibosonData 2011 work in progressATLAS = 7 TeVs ­1 L dt =  2.05  fb∫  KS Prob : 0.0560  (GeV)ηLeading Jet ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5Data/MC00. 5.19: The predicted and observed leading jet η in the signal region.Events0100200300400500600700800 tt  ll→* γZ/Single topFakesDibosonData 2011 work in progressATLAS = 7 TeVs ­1 L dt =  2.05  fb∫  KS Prob : 0.3870  (GeV)ηSub­Leading Jet ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5Data/MC00. 5.20: The predicted and observed sub-leading jet η in the signal re-gion.141Events02004006008001000 tt  ll→* γZ/Single topFakesDibosonData 2011 work in progressATLAS = 7 TeVs ­1 L dt =  2.05  fb∫  KS Prob : 0.2110  (GeV)missTE0 50 100 150 200 250Data/MC00. 5.21: The predicted and observed EmissT distribution.1425.5 Statistical AnalysisThe statistical analysis was performed on the HT +EmissT distribution that was ob-served in the signal region. A comparison between the Monte Carlo predictionsand the observation in data is shown in figure 5.22. For the statistical analysis,a variable-width binning was chosen in order to reduce the sampling and MonteCarlo statistical uncertainty in each bin; for presentation the yield in each bin isthen normalized to 1 GeV. As an example, a hypothetical 1 TeV KK-gluon predic-tion is superimposed on-top of the background only prediction in order to demon-strate the expected deviation from observation in the signal hypothesis case. [GeV]missT+E TH20040060080010001200Events / GeV-3 10-2 10-1 101102 10 [GeV]missT+E TH20040060080010001200-3 10-2 10-1 101102 10datatt Z+jetsOther BackgroundsUncertainties (1100 GeV)KKgATLAS=7TeV s -1Ldt=2.05  fb ∫ [GeV]missT+E TH20040060080010001200-3 10-2 10-1 101102 10Figure 5.22: The HT +EmissT distribution used for the statistical analysis. Theyield in each bin is normalized to 100 GeV, which varies across thespectrum. The observation in data agrees within the background onlyprediction with the total statistical and systematic uncertainty which isrepresented by the hatched bars.5.5.1 Estimation of Systematic UncertaintyFollowing the general description of the statistical methods given in section 4 thesystematic uncertainties were characterized and incorporated into the analysis byestimating the effect on the HT +EmissT distribution of positive and negative one-143sigma shifts of various model parameters. The estimated effect was obtained bypropagating the impact of the systematic shifts through the entire analysis chain, in-cluding the data-driven correction procedures, through to the final rate and observ-able distribution. The marginalized posterior probability distributions for each nui-sance parameter were inspected in order to ensure they showed reasonable agree-ment with the prior probability distributions and so were not overconstrained bythe fit. The overall uncertainty is determined by summing the uncertainty from alluncorrelated sources in quadrature, a property that renders subdominant sources ofuncertainty negligible to the statistical analysis. This analysis was performed incoordination with a related analysis searching for top-pair resonances in the lep-ton+jets channel. For consistency, each analysis used all sources of systematicuncertainty that were found to be non-negligible in at least one of the analyses.The following common set of systematic uncertainties was identified:• Physics Object Uncertainties1. Lepton identification and triggering efficiency2. Jet Energy Scale uncertainty3. Jet Energy Resolution uncertainty4. Cell-out term uncertainty in EmissT calculation• Uncertainty on Fakes Estimation• Beam Related Uncertainties1. Luminosity2. Pile-up• Theoretical Uncertainties1. Cross-section uncertainty2. PDF uncertainty3. ISR/FSR for SM tt¯4. Parton Showering for SM tt¯144The physics object performance systematic uncertainties arise due to uncertain-ties on the experimental calibration and performance estimates that were describedin section 3.3.3. In each case the uncertainty was kinematically parameterized. Toestimate the impact of the systematic uncertainty on the variable the correspondingparameterized positive and negative one-sigma shifts were applied to each object ineach Monte Carlo event. For the lepton efficiencies, weights were applied to eachevent based on the kinematics of each reconstructed lepton in order to produce thefinal effect on the observable. For jet modeling two uncertainties were considered:the uncertainty on the jet energy scale calibration, and an uncertainty on the jetenergy resolution. For the former case, the reconstructed energy of all jets in eachevent were shifted higher or lower according to the JES uncertainty, which was onthe order of 2.5% over 60 GeV < pT < 800 GeV. For the jet energy resolution, aGaussian smearing was applied that randomly shifted each jet’s energy in MonteCarlo simulating a one sigma increase in jet energy resolution. The resultant onesided shift to the HT +EmissT distribution was then symmetrized about the nominalprediction to estimate the effect of the one-sigma reduction in the resolution. Ineach case the shift in the jet measurement was propagated to the EmissT calculation.Kinematically parameterized positive and negative one-sigma shifts on the fakesestimate were applied as weights to the events in the fakes sample.There are two sources of uncertainty associated with the LHC beam itself. Theuncertainty in the pile-up model lead to a non-negligible correlated uncertainty onJES and the EmissT calculation. Their correlated positive and negative one sigmaeffects were evaluated with tools that alter their nominal energies in Monte Carloaccordingly. Additionally, correlated overall positive and negative 3.7% shifts tothe rates of all processes are incorporated into the model to account for the lumi-nosity uncertainty.Various sources of theoretical uncertainty exist. For each non-corrected back-ground process an overall rate shift associated with an uncertainty on the cross-section was considered. The cross-section uncertainties are summarized in table5.3The theoretical uncertainties on the background cross-sections include uncer-tainty due to the PDF modeling. However, the kinematics of the final state alsodepend on the PDF model. A separate PDF systematic was evaluated to assess the145Table 5.3: Theoretical uncertainties on the background cross-sectionsProcess UncertaintySM tt¯ 9%Diboson 5%Single Top 10%acceptance uncertainty on the final distributions for SM tt¯ and the signal samples.The systematic shifts for three different PDF sets, NNPDF, CTEQ, and MSTW,were determined by allowing each of their parameters to vary independently in aseries of trials. The shifts due to those parameters were then combined accordingto prescriptions provided by the PDF groups in order to determine the uncertaintyenvelope for each set [95]. Then the maximum predicted shift among the threePDF set uncertainties was chosen for the overall PDF uncertainty. The result wasan additional 3.7% uncertainty on the analysis acceptance and little impact on theshape of the observable.Three additional systematic uncertainties on the SM tt¯ prediction alone wereconsidered. The effect of the uncertainty on the model for the initial and final stateradiation was evaluated by determining the relative difference in the observableprediction for a set of dedicated ACERMC samples where the ISR/FSR parame-ters where varied within their one sigma uncertainties. The uncertainty on the par-ton showering process was estimated by considering the relative difference in theobservable prediction between two SM tt¯ samples simulated with different show-ering models, each generated with PowHeg but one interfaced to Pythia and oneinterfaced to Herwig for calculating the showering process. Finally, a generator un-certainty was estimated by considering the relative difference between the defaultMC@NLO generated Herwig interfaced sample and a PowHeg generated Herwiginterfaced sample with the half-difference between the predictions used to estimatethe one sigma uncertainty.In addition to the listed systematic uncertainties, the statistical uncertainty onthe Monte Carlo predictions was also incorporated as fully uncorrelated uncertain-ties among each sample prediction within each bin of the observable. Otherwise,the effect of each source of systematic uncertainty was modeled as fully correlatedacross the bins of the observable and among the various signal and background146samples. The effects of each source on the overall rate prediction for the back-ground and a 1 TeV KK-gluon are shown in table 6.9. The largest impact on thetemplate shapes was observed for the JES, Fakes, and ISR/FSR systematic uncer-tainties. As an example, the positive and negatives shifts for the former two casesare shown, along with nominal prediction in figures 5.23 and 5.24.Table 5.4: The systematic shifts to the overall predicted rate due to the varioussystematic sources [%].SM background mKK=1000 GeVLepton ID / Trigger 1.9 2.2Jet / EmissT 2.4 3.0ISR/FSR 0.9 5.1Parton Shower 1.0 -Generator 1.1 -PDF 3.7 0.6Fakes 2.6 -Top X-Section 6.9 -Total Systematic 9.7 6.3147(GeV)missT+ETH200 400 600 800 1000 1200normalizedcounts/100(GeV)020040060080010001200 positivenominalnegative(GeV)missT+ETH200 400 600 800 1000 1200counts/100(GeV)01020304050 positivenominalnegativeFigure 5.23: Top: the SM background prediction. Bottom: the SM predictedtemplate shape for a 700 GeV KK-gluon. The nominal (black) tem-plate prediction compared to predictions where the JES nuisance pa-rameter is shifted in value positively (green) and negatively(blue) ac-cording to its parameterized one-sigma uncertainty band.148(GeV)missT+ETH200 400 600 800 1000 1200normalizedcounts/100(GeV)020040060080010001200 positivenominalnegativeFigure 5.24: The nominal (black) Standard Model background template pre-diction compared to predictions where the fakes rate was shifted invalue positively (green) and negatively (blue) according to its parame-terized one-sigma uncertainty band.1495.5.2 Background-Only ConsistencyTo test the consistency of the null hypothesis with the observation in data, an LLRdistribution was generated according to the prescription outlined in section 4. TheLLR was calculated with respect to the KK-gluon model. The spectrum and theposition of the LLR observed in data are shown in figure 5.25.LLR­18 ­16 ­14 ­12 ­10 ­8 ­6 ­4 ­2 0Pseudo­Experiments110210310Pseudo­ExperimentsObserved value in DataATLAS work in progresst t →KKg = 7 TeVs­1 L dt = 2.05 fb∫Figure 5.25: The LLR spectrum determined from an ensemble of pseudo-experiments and the observed LLR, calculated as described in section4.The p-value obtained for the background-only hypotheses, i.e. the probabilityof obtaining a result at least as signal-like as what was observed in data, was 22%,indicating statistical consistency between the observation and the null hypothesis.Thus, it was concluded that no evidence of resonant top-pair production was foundby the analysis.1505.5.3 Signal Exclusion LimitsIn the absence of evidence to indicate the presence of new resonant top-pair produc-tion the results of the analysis were used to infer upper-limits on the cross-sectiontimes branching ratio for resonant tt¯ production for each of the two signal models(X), σ ×BR(X → tt¯) . In each model, the Bayesian posterior PDF for the numberof possible signal events was determined for a series of mass hypotheses and usedto determine 95% C.L. upper limits on the number of signal events present in theobservation. Those limits where then expressed as limits on σ ×BR(X → tt¯) byconsidering the predicted signal acceptance and rearranging the rate equation 3.3.Additionally, an expected limit at each mass point was determined by repeating theBayesian analysis on a set of 500 pseudo-experiments (PEs). The mean pseudo-experiment (PE) value was taken as the expected limit, and one and two sigmauncertainty bands on the expectation were estimated by considering the distribu-tion of the PE results. The observed limits were found to be consistent with theexpected limits. The observed and expected σ ×BR(X → tt¯) limits as a functionof mass for the two models are shown in figure 5.26.The σ ×BR(X → tt¯) limits can be interpreted as mass limits for the specificbenchmark models outlined in section 2. Those cross-sections are superimposedonto the observed limits in figure 5.26. Mass ranges where the default benchmarkcross-section is larger than the observed upper limit on the cross-section for res-onances of that type are considered to be excluded. The Z′ limit, which barelycrosses the benchmark model is considered to be too marginal to warrant a for-mal mass limit statement. The observed and expected excluded mass range for theKK-gluon are summarized table 5.5.Table 5.5: The excluded mass range for the KK-gluon as predicted in the de-fault RS1 modelExpected [GeV] Observed [GeV]500 < mgKK < 1080 500 < mgKK < 1070151 [TeV]Z’m0.5 0.6 0.7 0.8 0.9 1 B [pb]σ­110110210 Expected limitσ 1±Expected σ 2±Expected Observed limit BZ’σ BZ’σNLO  work in progressATLASt t →Z’ = 7 TeVs­1 L dt = 2.05 fb∫ B [pb]σ(a) mass [GeV]KKg60080010001200140016001800) [pb] t  t → KK  BR(g × σ-1 101102 10DileptonObs. 95% CL upper limitExp. 95% CL upper limit uncertaintyσExp. 1 uncertaintyσExp. 2Kaluza-Klein gluon = 7 TeVs-1 = 2.05 fbdt L  ∫ ATLAS(b)Figure 5.26: The expected and observed 95% C.L. upper limits on the σ ×BR(X → tt¯) for (a) Z′s and (b) KK-gluons. Superimposed on eachgraph is the cross-section for the corresponding default benchmarkmodel described in section 2. The green and yellow bands respectivelycorrespond to the one and two sigma uncertainty on the expected limit.152Chapter 6Analysis II: The Search forResonances in the Fully HadronicChannelThis section presents an analysis that searched for high mass, m > 1 TeV, top-pair resonances in the fully-hadronic channel. The fully hadronic channel is thehighest rate ditop channel. However, in the context of resonance searches it si-multaneously suffers from a high QCD background rate and challenges in properlyidentifying each top-decay within the intra-event jet background. As mentionedin section 2.4.4, the kinematics of the fully hadronic final state are partitionableinto various topological regimes. Top quark pairs produced at moderate invariantmasses, below 1 TeV, will manifest a final state consisting of 6 standard jets withincreasing proportion as the invariant mass decreases. As the invariant mass is in-creased above 1 TeV an increasing fraction of top-quarks will be highly boosted,possessing pT > 2mtop, and the resulting jets associated with their decay will be-gin to merge. Thus, in high mass resonance searches, the standard 6-jet resolvedselection increasingly suffers losses in acceptance as higher massed resonances areconsidered.The analysis presented here sought to overcome the traditional challenges ofthe fully hadronic channel by selecting ditop events in the highly boosted regimewhere each collimated top-quark decay is reconstructible as a single fat-jet. This153reconstruction strategy effectively focuses the analysis on an intermediate state ofthe event where the unique properties of the top-quark allow the multijet back-ground to be efficiently suppressed, provide unambiguous 4-momentum recon-struction, and ensure high selection efficiency for high invariant mass events. Theanalysis was conducted on the full 2011 dataset, comprising 4.7 fb−1 of data. Theresults were published in January 2013, in the Journal of High Energy Physics [96].The material presented in this section is either taken from, or is consistent with thatpaper.The analysis consists of selecting the simple process:pp→ tt¯→ j j, (6.1)where here j corresponds to a fat-jet, as described in section 3.3.3, is selected witha simple event selection that requires that the leading and subleading jets possesspTj,1 > 500 and pTj,2 > 450 GeV. At that momentum, the decay products of the top-quark should be fully contained within an R=1.0 jet cone, as is shown schematicallyin figure 6.1. QCD multijet events, that happen to possess two high-pT fat-jets arethe dominant source of fake top-pair events. However, fat-jets associated withreal collimated top-quark decays are distinguished from the multijet backgroundusing a specialized object selection based on three characteristic features of top-jets, shown schematically in figure 6.1 and summarized below:• Jet Mass - The distribution of reconstructed masses for top-jets is peaked atthe top mass. QCD jets will possess a non-peaked mass distribution associ-ated with the virtuality of the parton emerging from the hard-process.• b-quark-jet - The collimated top-jet should always contain a sub-jet associ-ated with the b-quark in its decay.• Jet Substructure - The energy flow and deposition of the reconstructed top-jetshould be consistent with the three-parton decay of the top-quark.The most sophisticated aspect of the analysis was the development and verificationof the top-jet selection techniques, based on jet mass, b-tagging, and most notably,the use of a new algorithm for tagging top-jets on the basis of their sub-structure,154ZYx(a)ZYxη-φ space(b)Figure 6.1: (a) A schematic depiction of the jets in a boosted fully hadronicditop event. The top-decay, which is contained to a large cone, consistsof three sub-jets, one for each of the three quarks in the decay. (b) Eachtop-decay is reconstructed as a single jet. Each b-jet is also potentiallyidentifiable and should lie within the radius of the larger top-decay jet.A schematic view of the top-jet topocluster distribution in the η −φ isalso shown. The substructure is expected to have a three-prong energydistribution consisted with the 3-body top-decay hypothesis.called top template tagging. Since the 4-momentum of each top-jet candidate couldbe unambiguously reconstructed, the reconstructed tt¯ invariant mass of the two can-didate top-jets, mrecott¯ was chosen as the observable that would yield the greatest dis-criminating power between a new resonance and the Standard Model background:mrecott¯ =√(Pj,1 +Pj,2)µ(Pj,1 +Pj,2)µ =√(E1 +E2)2− (~p1 +~p2)2, (6.2)where P, E, and ~p denote respectively the 4-momentum, energy, and 3-momentumof the leading (1) and subleading (2) jets.The other main challenges to the analysis were obtaining and verifying accurateStandard Model predictions in the high-pT fat-jet regime. A partially novel data-driven method for estimating the QCD background was developed to estimate therate at which multijet events could fake top-jets. A cross-check method, that relied155on reconstructing the top-jet mass peak of the leading and sub-leading jets, wasalso employed to measure the top-template tagging efficiency observed in data,and verify the multijet prediction.6.1 Data SamplesThe collision and Monte Carlo data samples used in the analysis are summarizedin this section.6.1.1 BackgroundsThe Standard Model background in this analysis consists of two dominant pro-cesses, SM tt¯ production, and QCD dijet production. The latter of which wasultimately estimated from data, but Monte Carlo was used in initial studies.Standard Model Top-Pair Production Standard Model top-pair production wasdiscussed in detail in section 2. For this analysis, a sample generated with MC@NLOinterfaced to Herwig/Jimmy that used the CT10 parton distribution function wasused for the SM tt¯ hypothesis. The generator predicted cross-section is correctedto the approximate NNLO prediction that was the best estimate of SM tt¯ cross-section at the time of the analysis [90].QCD Dijets The dominant component of the multijet background is composed ofQCD dijets events: the dominant hard scattering process at the LHC characterizedby a two parton final state. These events arise from the parton processes: qq→ qq,qq¯→ qq¯, gg→ gg, qg→ qg, gg→ qq¯ and qq¯→ gg, for which there are numerousdiagrams [97].QCD dijets could fake the ditop final state by producing jets which satisfy thetop-jet criteria. Such massive jets would necessarily originate from highly virtualpartons, contain a real or fake b-jet, and have an energy flow that, due to showeringand fragmentation, manages to mimic top-jet energy flow.The prediction for QCD used in the analysis needed to be derived from data fortwo reasons. The first was an absence of high statistics Monte Carlo QCD samplesin general, especially in the dijet invariant mass range m > 1 TeV. More crucially,156there is significant uncertainty in the details of QCD jet physics upon which thetop-tagging methods used in the analysis may depend. However, some truth-levelstudies were conducted using QCD Monte Carlo to help design and optimize theobject and event selection, and to complement investigations that were carried outin data. Those samples were generated with Pythia in various bins of final stateparton pT , denoted JX: the binning is summarized in table 6.1.Table 6.1: The pT ranges of the various QCD dijet samples.Sample Min. pT [GeV] Max. pT [GeV]J5 280 560J6 560 1120J7 1120 2240J8 2240 -Only J6 and J7 were found to have a significant contribution to the signal re-gion.6.1.2 SignalsBoth signal models were generated using MADGRAPH interfaced to Pythia. Thesamples were used to determine the acceptance times efficiencies for the object andevent selection and the mrecott¯ templates for a set of benchmark samples where thetop-quarks were allowed to decay via all channels. The acceptance times efficiencyfor each benchmark point in the analysis are listed in table 6.2.157Table 6.2: Benchmark Acceptance Times EfficiencyBenchmark Mass Point [TeV] Aε [%]Z′1.00 0.21±0.021.30 2.94±0.061.60 3.74±0.062.00 2.87±0.062.50 1.83±0.113.00 1.23±0.04KK-gluon1.00 0.34±0.041.15 1.15±0.091.30 2.30±0.111.60 2.96±0.131.80 2.85±0.132.00 2.40± CollisionThe analysis used all the data collected by ATLAS in 2011, corresponding to 4.7fb−1. Collision events containing at least one fat-jet in the final state were reliablyselected using data samples which passed a fat-jet trigger with threshold pT > 240GeV. The details of the data sample are summarized in the table below.Signal L [fb−1] TriggerAll 4.7 EF J240 A10TC6.2 Object and Event SelectionHighly boosted fully-hadronic ditop events were searched for by selecting eventsthat have two fat-jets with sufficient pT . The accordingly simple preselection isoutlined below:• Good Runs Lists (Collision Data Only)ATLAS data is analyzed for quality on a run by run basis, only the highquality data corresponding to the good runs lists were used in the analysis.• Pile-up Reweighting (Monte Carlo Only)158Monte Carlo samples were generated with an assumed pile-up-distribution.However, the actual pile-up distribution observed in data was different andvaried over time. Part way through 2011, the instantaneous luminosity of theLHC was increased, by increasing the proton bunch density while maintain-ing the 50 ns bunch spacing. To model these more intense pile-up conditions,Monte Carlo samples were generated where the number of vertices in theevent was randomly drawn from Poisson distributions with some mean µ .The pile-up in Monte Carlo was then tuned to match data by reweighting theevents on the basis of the mean of the Poisson distribution used to initiallygenerate the event.• TriggerEvents are required to pass the R=1.0 anti-kT LCTopo jet trigger.• Bad Jet VetoEnergy deposits not associated with real jet production can be reconstructedas fake jets. Such depositions can occur due to numerous factors includinghardware problems, cosmic rays, and LHC beam conditions [93]. A set ofquality cuts are defined to reject such jets. Any events containing bad jetsare rejected.• Lepton VetoIn order to maintain orthogonality with other ditop search channels, and toensure fully hadronic selection, a cut is applied to reject mini-isolated lep-tons.• Two high pT Jets1. The leading jet is required to have pT > 500 GeV.2. The sub-leading jet is required to have pT > 450 GeV.The remainder of the event selection consists of requiring that the leading andsub-leading jets are good top candidates, and that each pass the top jet selectioncriteria. The procedure for selecting top-jets is outlined below.1596.2.1 Top Jet SelectionTop Mass RequirementThe simplest means of selecting top-jets while rejecting the QCD background isto place a requirement on the jet mass. A cut is applied to select jets with recon-structed mass falling within a top-jet window defined as: |m jet − 172 GeV| < 50GeV. Figure 6.2 shows the jet mass distributions of the leading and recoil jets withall other selections applied.Leading Jet Mass [GeV]0100200300400Arbitrary Units / 10 GeV MultijetATLAS SimulationTop Template Tagger = 7 TeVs(a)Recoil Jet Mass [GeV]0100200300400Arbitrary Units / 10 GeV MultijetATLAS SimulationTop Template Tagger = 7 TeVs(b)Figure 6.2: The predicted mass distributions for QCD (blue) and SM tt¯(white) for the (a) leading and (b) sub-leading jets.b-jet MatchingTo further suppress the QCD background a b-tagged jet associated with the b-quarkin the top-decay is searched for. At least one good b-tagged R=0.4 LCW+JES jetis required to be found within ∆R < 1.0. The expected rate of such b-matchingwas investigated with Monte Carlo. Figure 6.3 shows the expected number ofb-matches for the leading and sub-leading jets for truth top-jets and QCD dijets.Applying the b-jet matching yields the greatest suppression of QCD jets of thethree top-tagging criteria.160Number of b-Matches in Leading Jet 01234Arbitrary Units / 10 GeV MultijetATLAS SimulationTop Template Tagger = 7 TeVsNumber of b-Matches in Sub-Leading Jet 01234Arbitrary Units / 10 GeV MultijetATLAS SimulationTop Template Tagger = 7 TeVsFigure 6.3: The predicted number of b-tagged LCW jets found within ∆R <1.0 of the (a) leading and (b) sub-leading jets.Top Template TaggingThe final and most sophisticated aspect of the top-jet selection is the attempt to tagjets as originating from a top-decay via their jet substructure, using top-templatetagging [98]. The scheme is based on the premise that the partonic energy flow ofa decaying top-quark should be consistent with the energy flow of its associatedexperimentally measured jet; specifically it is expected to exhibit a three-prongstructure corresponding to each hard parton in the top-decay.As described in section 3.3.3, the structure of a jet consists of a system of as-sociated topoclusters, each represented by massless 4-vectors. The top-templatetagger evaluates the consistency of the candidate jet structure with the three-partontop-decay hypothesis by directly comparing the jet topoclusters against a libraryof three body parton level energy flow predictions, called templates, that in princi-ple cover the top-decay phase-space that could have given rise to the candidate jet.Each template consists of three 4-vectors, that predict a specific trajectory, (ηi,φi)and energy, Ei, for each parton, i, within a frame where the η ,φ plane is centredon the trajectory of the jet. For each predicted parton, a matching neighbourhoodis defined as a ∆R < 0.2 cone about the parton trajectory. For each parton, the en-ergy difference between the predicted parton energy, and the sum of the observedjet topocluster energies, Etopo, found within its matching neighbourhood is deter-161mined.The level of agreement between the candidate jet and each template in thelibrary is quantified by a three dimensional Gaussian overlap function, with thethree dimensions corresponding to each of the calculated energy differences forthe three template partons. The width of each Gaussian depends on the energy ofthe predicted parton: σ = Ei/3. One template within the library will maximize theoverlap value, this maximum overlap value is referred to as OV3 and is representedmathematically as:OV3 = maxτnexp−3∑i=112σ2i(Ei− ∑∆R(topo,i)<0.2Etopo)2 (6.3)In order to suppress backgrounds due to pile-up and reduce the pile-up dependenceon OV3 a minimum cut of Etopo > 2 GeV is placed on the topocluster energy usedin the summation.The OV3 parameter serves simultaneously as a means of identifying top-jetsand rejecting QCD jets, since in principle only true top-decays should always beclosely represented in a suitably populated template library. Agreement with thelibrary indicates that not only is the energy distribution three prong in structure butthat the 4-vector combination is consistent with the top-quark decay hypothesis.Such a feature is not generally the case for massive QCD jets where the energyflow will tend to be consistent with that of a single fragmenting parton.The templates that compose the library, τn, were generated as a series of sub-libraries at specific top-quark pT s. A candidate jet was then pointed to a givensub-library on the basis of its measured pT . The template binning is summarizedin table 6.3, and was chosen to maximize the discrimination of the OV3 variablewhile minimizing the computational overhead.The anatomy of the overlap function in equation 6.3 is shown in figure 6.4where the maximum overlap template for a simulated jet from a true top-quarkis represented simultaneously with the topoclusters of the jet. Also shown is theeffect of applying the topocluster energy cut. In the top-jet case, the topoclusterdistribution shows the characteristic three-prong structure expected from the decayof a top-quark. The maximum template matches well to the distribution, with the162Table 6.3: The template pT that was used to evaluate OV3 in various pT rangesof candidate jets.Candidate Jet pT Range [GeV] Matching Template pT [GeV]400 - 500 400500 - 600 500600 - 700 650700 - 800 750> 800 850parton matching cones capturing most of the jet energy, and the best match templateyielding OV3 = 0.94.In order to demonstrate how the OV3 variable responds to QCD jets, figure 6.5shows the best template match for two simulated QCD jets: a typical low OV3valued jet, and a rarer high OV3 valued jet that would pass the selection and fakea top-jet. The distributions do not show the typical three-prong structure; in thelow OV3 case the best matched template corresponds to the three matching conesclustering around what is clearly a single prong structure. Much of the jet energyis not included in the summations, and the resulting difference between matchedand predicted energies are large. The high OV3 case shows that there is sometimesgood enough overlap between the template phase-space and the QCD jet configu-rations to achieve a high OV3 value, such as cases where the third template partonis relatively soft.Figure 6.6 shows a comparison of the OV3 distributions for samples of simu-lated jets originating from truth top-quarks, simulated QCD jets, and a QCD en-riched data sample. The OV3 distribution is strongly peaked at a value of 1 for top-quarks while it is peaked towards 0 in data and simulated QCD jets, demonstratingthe discrimination power of the variable. A minimum cut to select good top-jetcandidates was determined by considering the selection efficiencies for QCD andtruth top-jets as a function of the OV3 cut value. Those efficiencies are shown infigure 6.6. A cut value of 0.7 was chosen, corresponding to an operating point ofabout 70% acceptance for top-jets and 80% rejection for QCD jets, in a samplewhere the jet mass cut had not yet been applied.The jet mass itself depends on the jet structure as it is the angular separation163η-1 -0.50 0.51φ-1-0.500.51=0.943OV topoclusterstemplatepartonspartonmatchingconesη-1 -0.50 0.51φ-1-0.500.51=0.943OV topoclusterstemplatepartonspartonmatchingconesFigure 6.4: The topocluster distribution (blue) of a simulated top jet repre-sented in an η−φ plane centred on the jet direction. The height of theclusters correspond to their pT . The same jet is shown (a) without, and(b) with, the minimum topocluster energy cut of 2 GeV. Superimposedare the parton pT s (red) and their matching neighbourhoods (green) forthe best matched template.164η-1 -0.50 0.51φ-1-0.500.51=0.073OV topoclusterstemplatepartonspartonmatchingconesη-1 -0.50 0.51φ-1-0.500.51=0.883OV topoclusterstemplatepartonspartonmatchingconesFigure 6.5: The topocluster distribution (blue) of (a) low OV3, and (b) highOV3 valued QCD jets represented in an η − φ plane centred on the jetdirection. The height of the clusters correspond to their pT . The samejet is shown (a) without, and (b) with, the minimum topocluster energycut of 2 GeV. Superimposed are the parton pT s (red) and their matchingneighbourhoods (green) for the best matched template.1653Leading Jet OV00. Units -2 10-1 10Data 2011Multijet (2.0 TeV)tZ'->t > 450 GeVrecoil Tp > 500 GeVlead Tp = 7 TeVs-1 L dt = 4.7 fb ∫ATLAS(a) Requirement3Leading Jet OV00. 2011Multijet (2.0 TeV)tZ'->t > 500 GeVTLeading Jet p > 500 GeVlead TpATLAS = 7 TeVs-1 L dt = 4.7 fb ∫(b)Figure 6.6: (a) The OV3 distribution for leading jets in passing the preselec-tion, and their (b) selection efficiency as a function of lower cut on theOV3 value for data, and simulated 2 TeV Z′ and QCD. The data sampleis expected to be dominated by QCD multijet eventsbetween significantly energetic clusters that generates a non-zero jet mass. Thus,in the case of QCD, the more massive the jet, the more jet structure is necessarilypresent, and the chance of matching well to a top-decay template is increased. Thecorrelation between the OV3 value and jet mass is evident in figure 6.7. When asample with masses inside the top-mass window is considered, the efficiency fortop-quarks increases to about 75%, while the efficiency for QCD jets more thandoubles to roughly 40%. Also evident in the plot is a divergence between theMonte Carlo QCD prediction and the observation in data for the QCD efficiency,supporting the decision to use data-driven methods for the multijet backgroundestimate.1663Leading J etOV0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1ArbitraryUnits-210-110 Data 2011Multijet(2.0 TeV)tZ'->t|<50GeVtop- mj|m >450GeVrecoilTp>500GeVleadTp Requirement3Leading Jet OV00. 2011Multijet (2.0 TeV)tZ'->t| < 50 GeVtop-Mjet|M > 500 GeVTLeading Jet p| < 50 GeVtop - m j|m > 500 GeVlead TpATLAS = 7 TeVs-1 L dt = 4.7 fb ∫Figure 6.7: (a) The OV3 distribution for leading jets passing the preselectionand falling in the top-mass window, and their (b) selection efficiency asa function of lower cut on the OV3 value for data, and simulated 2 TeVZ′ and QCD. The data sample is expected to be dominated by QCDmultijet events6.3 Data Driven Estimate for the QCD BackgroundTo estimate the background in the signal region from QCD multijet events withtwo fake top-jets an extended version of a common procedure known as the ABCDmethod was employed. The extended method was developed out of a necessityto overcome shortcomings of the standard ABCD method. In this section first thestandard method is introduced and then the extended method is presented.6.3.1 The ABCD MethodAn internal document was released by the ATLAS statistics group summarizing theproper implementation of the ABCD method and several important criteria whichshould be met to ensure its accuracy [99]. That document forms the basis for thissummary.The rate of a process in a signal region can be estimated by taking measure-ments within a broader preselection of events defined in terms of two variables, Xand Y that are cut on in order to select the signal region. The signal region cuts par-tition the plane formed by the extended ranges of the two considered variables into167four regions. The signal region, D, passes both cut criteria, (X+,Y+). Two otherregions: B and C, each pass exclusively one cut criteria but fall within anotherselection for the cut that they fail: (X+,Y−) and (X−,Y+) respectively. Finally,region A, corresponds to the product of the failed selections of B and C, (X−,Y−).The regions are orthogonal to each other but are in general not connected. More-over, multiple ABCD relationships can be defined within the plane for the samesignal region, if numerous mutually orthogonal selections that fail the signal selec-tion are defined. The partitioning is represented schematically for the simplest casein figure 6.8.ABCD+YX-- +Figure 6.8: A schematic depiction of a sample of events distributed in a planedefined by two variables, X and Y , and partitioned on the basis of pass-ing (+) or failing (-) cuts on the variables.The rate in each region is proportional to the product of the two selection ef-ficiencies of that region’s cuts, ε±X and ε±Y . So long as the selection efficienciesbetween the two cuts are uncorrelated it is possible to estimate the rate of a processin one region by measuring the rates in the other three and solving for the productof efficiencies in the region of interest. This algebra is made explicit for the casewhere the rate in the signal region D is estimated from the other regions in the168following equation, where Ni and NTot denote rates for a process in region i and theoverall rate in the combined preselected region A+B+C+D, respectively:ND =[NTotε+X ε+Y]=[NTotε+X ε+Y][NTotε−X ε−YNTotε−X ε−Y]=[NTotε−X ε+Y][NTotε+X ε−Y][NTotε−X ε−Y]= NBNCNA(6.4)The procedure can be applied within each bin of any observable, so as toachieve shape and rate predictions. The validity of the procedure rests on the set ofcriteria outlined below:1. There is no correlation between the selection efficiencies in the ABCD plane.2. There are sufficient statistics for reasonable propagation of uncertainty to thesignal region estimate.3. The rates of other Standard Model background process can be reliably sub-tracted from the preselection.4. There is no significant potential BSM signal leakage outside of region D,since such a priori unknown contributions are unsubtractable from the ob-servation in data.6.3.2 The Extended ABCD MethodInitial attempts at applying the ABCD method to this analysis resulted in violationsof the validity criteria. In order to better understand the problem a preselection thatincluded the signal region was defined by considering the b-matching and top-tagging state of each jet within the sample of events that otherwise passed the restof the event selection. The preselection can be partitioned based on the four taggingstates of each, summarized below:169• t+b - top-tagged and b-matched• t - top-tagged and no b-match• b - not top-tagged and b-matched• no-tag - not top-tagged and no b-matchThe preselection is then partitioned into 16 regions defined on a grid wherethe tagging state of the leading and sub-leading jets are represented on the verticaland horizontal axes respectively, as shown schematically in figure 6.9. As thetagging criteria outlined above are mutually exclusive, each of the leading/sub-leading tagging combinations denote fully orthogonal regions, that can in principlebe used to carry out ABCD predictions.t + bbno-tagtno-tag bt t + bSub-leading JetLead JetJ K L PB D H NE F G MA C I OFigure 6.9: A schematic depiction of the orthogonal regions used in the ex-tended ABCD method. The preselection and top-mass window cuts areapplied to the entire sample, the X and Y axes correspond to the taggingstate of each jet, each of which can take on one of four value partitioningthe sample into 16 orthogonal regions.Region P, where both jets are fully tagged, corresponds to the signal region.The coloration in the schematic indicates the severity of the potential BSM back-170ground contamination, with green representing negligible contamination while theregions in red, K, L, M, and N, are predicted to contain roughly 10% or more frac-tional rate from the default benchmark models and are considered to be unsafe foruse in the analysis.The remaining regions were used to predict the QCD rate in region P and con-duct control tests of the extended method via the definition of various ABCD testscorresponding to four regions within the plane that do not include the signal orforbidden regions. A series of control tests, where the predicted rate could be di-rectly compared to to the observation in data were tested. The control regions fortesting are chosen to be the three safe regions closest to the signal region: D, G,and H. The results of the control tests for the overall rate are shown in table. 6.4Three tests failed, each of which required varying the top-tagging state of both jetsTable 6.4: Results of ABCD method control testsTest Control Region Prediction Observation AgreementC×B/AD711±22 721 YesC×H/I 770±61 YesB×F/E 873±32 NoE× I/AG485±16 495 YesE×H/B 526±42 YesF× I/C 596±22 NoB× I/AH172±7 186 YesB×G/E 174±8 YesD×G/F 145±9 Noat the same time, indicating a significant correlation in the top-tagging efficiencybetween the leading and sub-leading QCD jets that must be avoided. On the otherhand, those rules which only vary the top-tagging state of one of the jets at a timeall agree within statistical uncertainty leading to two specific requirements for validABCD equations:1. The equation cannot use data from regions K, L, M , or N.2. The equation can only vary the top-tagging state of one jet at a time.A consequence of these restrictions is that there is no valid direct ABCD methodfor P since the only equation that avoids the forbidden regions, P = J×O/P, is171susceptible to the top-tagging correlation. In order to arrive at a valid predictionfor region P, a tiered ABCD method was proposed, consisting of two steps:1. Use valid ABCD rules to safely predict the QCD rate in the forbidden regions2. Substitute those safe predictions into correlation safe rules for region PThere are four correlation safe methods for region P that depend on regions K, L,M and N: J×M/E, K×O/C, L×N/G, and K×N/D. These lead to five differ-ent tiered rules that arise from substituting K, L, M, and N by other valid ABCDpredictions. The resulting tiered formulae and their predictions are summarized intable 6.5.Table 6.5: Overall rate predictions for Region PFormula Prediction(J×F×O)/(E×C) 51±3(J×F×H×O)/(E×D× I) 56±6(J×F×H×O)/(B×C×G) 54±6(J×F× I×O)/(A×C×G) 51±4(J×F×B×O)/(A×E×D) 52±4Average 53±4All five predictions agree with each other within statistical uncertainty givingincreased confidence in the method. The final prediction is determined by takingthe average prediction of the five methods. The overall rate and its correlated sta-tistical uncertainty determined from the five methods is 53±4 events. Figure 6.10shows the estimated QCD contribution to the mtt¯ distribution, also shown is themaximum deviation in the prediction among the five methods.The extended ABCD method possesses an internal consistency, as evidencedby the agreement between the signal region predictions for the five methods. Theagreement between the observations of the QCD rate in data, and the predictionsconducted in the control regions reveal no evidence that significant correlationsexist among the the directly testable b-tagging efficiency combinations. As a finalcross-check on the method, the QCD rate in the signal region was estimated witha complementary method and found to be consistent with the extended ABCDprediction. The details of the cross-check are outlined in the following section.172 Mass [GeV]tt10001500200025003000Events / 100 GeV 24681012nm_minvjj_dat_regP_avgexp_hist_errEntries  11Mean     1367RMS     228.8Average PredictionMaximum EnvelopeATLAS   = 7 TeVs-1 L dt = 4.7 fb ∫Figure 6.10: The estimated multijet rate as a function of mtt¯ obtained formthe extended ABCD method. The variable bin width corresponds tothe choice of binning used in the statistical analysis, and the yield ineach bin is normalized to 100 GeV. The black vertical lines correspondto the statistical uncertainty on the method, and the red bars correspondto the maximum variation among the five different estimates.6.4 Selection Efficiency ValidationsIn order to cross-check the Monte Carlo prediction for the top-template tagging per-formance for top-quarks, and perform a consistency check for the predicted QCDbackground rate, an analysis of the jet mass distributions of the leading and sub-leading jets was performed where the top-quark and non-top-quark contributionswere estimated with two parameter χ2 fits. Such a procedure is viable in top-richregions, since the jet mass distribution is unaffected by the presence of a resonance,and can be used to extract the top-quark and QCD contributions regardless of theBSM content of the sample.To estimate the lead jet top-tagging efficiency for top quarks in real data thefollowing procedure was applied. Using ’′’ to denote regions where the leadingjet mass cut was removed but that are otherwise defined as they appeared in thestandard ABCD plane, figure 6.9, the shape of the top-quark contribution to the173jet mass distribution in region L′+P′ was determined by fitting the sum of threeGaussians to the Monte Carlo prediction for these regions. The QCD shape predic-tion was obtained by directly measuring the shape of data in the QCD dominatedregion G′+M′, which differs only by the absence of a b-tag on the sub-leadingjet. The actual QCD and top-quark contributions in the region L′+P′ can then beestimated by fitting the predicted shapes to each process to the observation in dataas is shown for the leading jet in figures 6.11.Leading Jet Mass [GeV]050100150200250300350400Events / 15 GeV 0102030405060708090Data 2011Combined Fittt MultijetATLAS-1 L dt = 4.7 fb∫  = 7 TeVs > 500 GeVlead Tp > 450 GeVrecoil Tp| < 50 GeVtop - mrecoil j|mFigure 6.11: The leading jet mass distribution observed in data for the loos-ened L′+P′ selection where there is no jet mass or top-tagging require-ment on the jet. The rates of SM tt¯ and QCD events are estimated byfitting their expected shapes to the observed distribution.The lead jet top-tagging efficiency for QCD in the top-mass window was di-rectly measured in the QCD enriched region as εq = NM/NG+M. Then the QCDcontribution to signal region was determined by multiplying the efficiency by the174integral of the QCD fitted function in L′+P′ over the top-window:NQCD = εq×∫ 222GeV122GeVf L′+P′QCD (m)dm (6.5)The rate of true top events in the signal region was then inferred by subtracting thepredicted QCD rate from the signal region. An analogous procedure was appliedusing the sub-leading jet, and the corresponding jet mass fit is shown in figure 6.12.Recoil Jet Mass [GeV]050100150200250300350400Events / 15 GeV 0102030405060708090100Data 2011Combined Fittt MultijetATLAS-1 L dt = 4.7 fb∫  = 7 TeVs > 500 GeVlead Tp > 450 GeVrecoil Tp| < 50 GeVtop - mlead j|mFigure 6.12: The sub-leading jet mass distribution observed in data for theloosened N′+P′ selection where there is no jet mass or top-taggingrequirement on the jet. The rates of SM tt¯ and QCD events are esti-mated by fitting their expected shapes to the observed distribution.The results of the fits were two cross-check estimates for the QCD rate in thesignal region and an estimate of top-tagging efficiency for leading and sub-leadingtruth top-jets. The top-quark efficiency results are summarized in table 6.6. The175uncertainty on the estimate is dominated by statistical uncertainties. Propagationof major systematic uncertainties to the top-quark prediction resulted in negligibleeffects on the final result.Table 6.6: Top-Quark selection efficiencyJet Class Data MCLeading 0.81±0.22±0.07 0.75±0.07Sub-Leading 0.62±0.17±0.06 0.62±0.05Excellent agreement was found between the QCD estimate and the cross-checks.As is shown in table 6.7, giving full confidence in the extended ABCD method.Table 6.7: Multijet background rate predictionsMethod DataLead Jet 53±5Sub-Leading Jet 60±5Extended ABCD 53±66.5 Signal Region ObservationThe predicted and observed rate in the signal region is summarized in table 6.8. 123events are observed in data which agrees with the background only expectation of112± 27 events within the total uncertainty. The uncertainty on the backgroundprediction is dominated by the total systematic uncertainty on the SM tt¯ predictionwhich was on the order of 50%.For the leading and sub-leading jets, the predictions for various kinematic vari-ables were compared to the observation in data and found to be in good agreement.Table 6.8: Expected and observed yield in the fully hadronic analysisProcess Yieldtt¯ 59±26Multijet 53±6Total Expected 112±27Data 123176The jet mass, pT , and η distributions for the leading and sub-leading jets are shownin figures 6.13, 6.14, and 6.15. The large systematic uncertainty is not representedin the images, however, their agreement with data is clear as there is already 1 to2 σ agreement by considering the sampling uncertainty on the data observationalone.Leading Jet Mass [GeV]120140160180200220240Events / 20 GeV 010203040506070Data 2011tt MultijetATLAS  = 7 TeVs-1 L dt = 4.7 fb ∫(a)Recoil Jet Mass [GeV]120140160180200220240Events / 20 GeV 10203040506070Data 2011tt MultijetATLAS  = 7 TeVs-1 L dt = 4.7 fb ∫(b)Figure 6.13: A comparison between observation and prediction for the lead-ing (a) and sub-leading (b) jet mass distributions. The large combinedstatistical and systematic uncertainty on the prediction is not depicted. [GeV] TLeading Jet p4005006007008009001000Events / 50 GeV 1020304050Data 2011tt MultijetATLAS  = 7 TeVs-1 L dt = 4.7 fb ∫(a) [GeV] TRecoil Jet p4005006007008009001000Events / 50 GeV 1020304050Data 2011tt MultijetATLAS  = 7 TeVs-1 L dt = 4.7 fb ∫(b)Figure 6.14: A comparison between observation and prediction for the lead-ing (a) and sub-leading (b) jet pT distributions. The large combinedstatistical and systematic uncertainty on the prediction is not depicted.177ηLeading Jet -2.5-2-1.5-1-0.500.511.522.5Events 5101520253035404550Data 2011tt MultijetATLAS   = 7 TeVs-1 L dt = 4.7 fb ∫(a)ηRecoil Jet -2.5-2-1.5-1-0.500.511.522.5Events 5101520253035404550Data 2011tt MultijetATLAS  = 7 TeVs-1 L dt = 4.7 fb ∫(b)Figure 6.15: A comparison between observation and prediction for the lead-ing (a) and sub-leading (b) jet η distributions. The large combinedstatistical and systematic uncertainty on the prediction is not depicted.6.6 Statistical AnalysisThe statistical analysis has been performed on the mtt¯ distribution that was ob-served in the signal region. A comparison between the Monte Carlo predictionand the observation in data is shown in figure 6.16. For the statistical analysis,a variable binning was chosen in order to reduce the sampling and Monte Carlostatistical uncertainty in each bin. For presentation the yield in each bin is nor-malized to 100 GeV. As an example, a hypothetical 1.6 TeV KK-gluon predictionis stacked on-top of the background only prediction in order to demonstrate theexpected deviation from the observation in the signal hypothesis case.178 Mass [GeV]tt10001500200025003000Events / 100 GeV 5101520253035Data 2011 = 0.35 pbσ (1.6 TeV) KKg tt Multijet ATLAS  = 7 TeVs-1 L dt = 4.7 fb∫ Top Template TaggerFigure 6.16: The mtt¯ distribution used for the statistical analysis. The binwidth varies across the spectrum and the yield in each bin is normal-ized to 100 GeV. The observation in data agrees with the predictionwithin the sampling uncertainty estimated from the data. The largetotal systematic and statistical uncertainty on the prediction is not rep-resented.6.6.1 Estimation of Systematic UncertaintyFollowing the general description of the statistical methods given in section 4 thesystematic uncertainties are incorporated into BAT by estimating the effect on theobservable of positive and negative one-sigma shifts of the corresponding modelparameters.A major source of uncertainty on the SM tt¯ prediction was the Monte Carlostatistical uncertainty, due to a lack of simulated data at high mtt¯ . This also lead tonoisy systematic estimates that, in some cases, were smoothed via averaging overadjacent bins. This analysis was performed in coordination with a related analysis179searching for top-pair resonances in the boosted fully hadronic channel using dif-ferent top-tagging techniques optimized to select moderately boosted top-quarkswith pT >200 GeV. For consistency, each analysis used all sources of systematicuncertainty that were found to be non-negligible in at least one of the two analyses.The marginalized posterior probability distributions for each nuisance parameterwere inspected in order to ensure they showed reasonable agreement with the priorprobability distributions and so were not overconstrained by the fit. The followingcommon set of systematic uncertainties was identified:• Jet Systematic Uncertainties1. LCW+JES b-tagging uncertainty2. Jet Energy Resolution uncertainty3. LCW+JES Jet Energy Scale uncertainty4. Fat Jet Mass Correction uncertainty5. Fat Jet Energy Scale uncertainty• Uncertainty on Fakes Estimation• Beam-Related Uncertainties1. Luminosity2. Pile-up• Theoretical Uncertainties1. Cross-section uncertainty2. PDF uncertainty3. QCD Renormalization and Factorization scale4. Electroweak virtual corrections5. Parton ShoweringThere were five sources of systematic uncertainty related to jet performanceand calibration. The dominant source was the LCW+JES flavour-tagging efficiency180scale factor uncertainty, for which there are three uncorrelated uncertainties for b-tagging, c-tagging, and light-jet-tagging. In each tagging case, an event weightwas calculated as the product of scale factors systematically shifted according tothe fully correlated kinematically parameterized scale factor uncertainty, for eachtagged jet in the event. The uncertainty on the rate of both the SM tt¯ and resonanceprocesses due to b-tagging was found to be on the order of 20% for all samples.Figure 6.17 shows the b-tagging systematic for the SM tt¯ and 1.6 TeV KK-gluonpredictions.The uncertainty on the jet energy scales for both LCW+JES and fat-jets wereconsidered. The latter had the potential to impact events by altering the acceptancefor b-tagged jets within the top-jet candidate. However it was found to have atmost a 1% effect on the rate predictions. Fat jets in the sample belong to a widekinematical range, across which the calibration is not expected to be correlated; ac-cordingly, the fat-jet JES uncertainty, shown in section 3.3.3, was treated in threeuncorrelated ranges of jet pT :< 500 GeV, 500 GeV - 800 GeV , and > 800 GeV.The total systematic uncertainty on the rate prediction due to the boosted jet cal-ibration was highest for the narrow 1 TeV Z′ resonance at 50%, and was on theorder of 20% for the higher mass resonances and Standard Model production. Theboosted jet energy resolution uncertainty was also propagated through to the finalobservable using the same approach as was described in section 5, and was foundto have only a 1% effect on the rate predictions.The complementary cone mass correction used to calibrate the fat-jet mass hadtwo sources of uncertainty. The effect of the statistical uncertainty associated withthe NPV parameterization was estimated by reprocessing the analysis after shiftingthe mass correction parameterization by its positive and negative one σ uncertain-ties. The complementary cone correction for R = 1.0 jets was inferred from aparameterization determined in data for R = 0.6 jets; the correction is expected toscale as R4. The effect of the uncertainty on this scaling rule was estimated byreprocessing the analysis using jet mass corrections derived with an R3.5 scalingand taking the difference of that result with the nominal prediction. The impact ofboth of these systematic uncertainties were found to be negligible when comparedto other systematic uncertainties.There are two sources of uncertainty associated with the LHC beam itself. The181Di-J etMass [GeV]1000 1500 2000 2500 3000024681012141618 bScale UptDefault tbScale Down(a)Di-J etMass [GeV]1000 1500 2000 2500 30000510152025303540bScale Up(m=1.6 TeV)KKDefault gbScale DownATLASwork in progress(b)Figure 6.17: The nominal (black) template prediction compared to predic-tions where the b-tagging scale factor was shifted in value positively(blue) and negatively (red) according to its parameterized one-sigmauncertainty band. (a) the SM tt¯ and (b) KK-gluon predictions areshown.182uncertainty on the pile-up model could potentially propagate through to the finalobservable by impacting the OV3 value. A 2% flat uncertainty was estimated for thepile-up effect by considering the residual pile-up-dependence of the OV3 variable.The value was estimated by determining the maximum difference in the taggingrate in three Nvtx bins: (≤ 6), (7,9) and (≥ 9). Additionally, correlated overallpositive and negative 3.7% shifts to the rates of all processes were incorporatedinto the model to account for the luminosity uncertainty.There were various sources of theoretical uncertainty. Two sources were con-sidered for the Standard Model top-pair production alone: ISR/FSR modeling andparton showering. The lack of high statistics Monte Carlo for Standard Model top-pair events meant that the prediction in the signal region suffered from a high de-gree of statistical uncertainty. At the high invariant mass considered, the ISR/FSRuncertainty was treated as uncorrelated between bins and added in quadrature tothe Monte Carlo statistical uncertainty; the combined effect dominated the system-atic uncertainty on the shape of the distribution, and is represented in figure 6.18.Di-J etMass [GeV]1000 1500 2000 2500 3000024681012141618202224 Stats UptDefault tStats DownFigure 6.18: The nominal template prediction (black) surrounded by the un-certainty enveloped formed from the combined Monte Carlo statisticaland ISR/FSR systematic uncertainties.The uncertainty on the parton showering process was estimated as described in183section 5.5.1, and was split into two uncorrelated regimes: mtt¯ < 1500 and mtt¯ >1500, and lead to a rate uncertainty of 18%The PDF and cross-section uncertainties were evaluated in the same manneras was described in 5.5.1. The uncertainty on the PDF systematic increased withresonance mass, varying from 3% for 1 TeV KK-gluons and rising to 20% for 2.5TeV Z′s, the effect on the latter is shown in figure 6.19.Di-J etMass [GeV]1000 1500 2000 2500 300002468101214 PartDF UptDefault tPartDF DownDi-J etMass [GeV]1000 1500 2000 2500 30000102030405060PartDF UpDefaultZ’ (m=2.0TeV)PartDF DownFigure 6.19: The nominal template prediction (black) surrounded by the pos-itive (blue) and negative (red) one sigma total PDF uncertainty.184Systematic uncertainties were assigned due to the QCD renormalization andfactorization scale uncertainty, and uncertainties in the higher order ElectroweakSudukov corrections[100]. The uncertainty on the QCD calculations was deter-mined in an internal ATLAS study where the SM tt¯ process was resimulated withµ varied by factors of 2 and 2−1. The rate difference between the two sampleswas parameterized in terms of mtt¯ and applied to the nominal prediction. At highinvariant mass electroweak virtual corrections contribute significantly to the top-pair production cross-section. The correction and its uncertainty, parameterized interms of mtt¯ , were calculated in [100]. For each of the preceding sources, the effecton the observable was determined by applying mtt¯-parameterized one-sigma accep-tance scale-factor shifts to the nominal predictions. The effects of these QCD andelectroweak uncertainties on the overall rate-predictions varied from 15%-20% and6%−11%, respectively, from the SM tt¯ to the highest mass resonances predictions.The effects of the dominant sources of systematic uncertainty, and the totalsystematic uncertainty for all sources considered, are summarized for the StandardModel background and the 1.6 TeV KK-gluon rate predictions in table 6.9.Table 6.9: The systematic shifts to the overall predicted rate for various sys-tematic sources in %.SM tt¯ mKK=1.6 TeVMonte Carlo 10 4ISR/FSR 14 -Parton Shower 18 -b-tagging 20 22Fat JES 19 19PDF 5 4Renormalization/Factorization 17 20EW Sudokov 7 8Total Systematic 44 36The uncertainty on the multijet prediction was estimated as a flat rate uncer-tainty. A systematic uncertainty was estimated on the method itself by consider-ing the maximum difference among the five distinct rate predictions in the tieredABCD method. That uncertainty was added in quadrature with the correlated sta-tistical uncertainty yielding a total systematic rate uncertainty of 11%.1856.6.2 Signal Exclusion LimitsIn the absence of evidence to indicate the presence of new resonant top-pair produc-tion the results of the analysis were used to infer upper-limits on σ ×BR(X → tt¯)as a function of resonance mass for the two signal (X) models. In each model, theBayesian posterior probability distribution for the number of possible signal eventswas determined for a series of mass hypotheses and used to determine 95% C.L.upper limits on the number of signal events present in the observation. Those limitswere then expressed as limits on the σ ×BR(X → tt¯) by considering the predictedsignal acceptance and inverting the experimental rate equation 3.3.At each mass point evaluated, an expected limit was calculated by determiningthe mean result of the Bayesian analysis applied to a set of 500 pseudo-experiments.The expected limit and its uncertainty were estimated, as described in section 5.5.3.The observed limits were found to be consistent with the expected limits. The ob-served and expected σ×BR(X→ tt¯) limits as a function of mass for the two modelsare shown in figures 6.20 and 6.21.The σ ×BR(X → tt¯) limits can be summarized as mass limits for the defaultparameter set for each benchmark model 2. The default predicted cross-sectiontimes branching ratios to top-quark pairs are superimposed onto the observed limitsin figure ??. The mass range where the hypothetical cross-section is larger thanthe observed upper limit on the cross-section for that model are considered to beexcluded. The Z′ limit, which barely crosses the benchmark model is consideredto be too marginal to warrant a formal mass limit statement. The observed andexpected KK-gluon lower mass limits are shown in table 6.10.Table 6.10: The excluded mass range for the KK-gluon as predicted in thedefault RS1 modelExpected [GeV] Observed [TeV]1.08 < mgKK < 1.62 1.02 < mgKK < 1.62186Z' Boson Mass [TeV]1 1.2 1.4 1.6 1.8 2) [pb]t t→ BR(Z' × σ-210-110110210Obs. 95% CL upper limitExp. 95% CL upper limit uncertaintyσExp. 1 uncertaintyσExp. 2Leptophobic Z' (LOx1.3)ATLAS Top Template Tagger = 7 TeVs-1 L dt = 4.7 fb∫Figure 6.20: The expected and observed 95% C.L. upper limits on the σ ×BR(X → tt¯) for Z′s. Superimposed on the graph is the cross-sectionfor the default benchmark model described in section 2. The greenand yellow bands respectively correspond to the one and two sigmauncertainty on the expected limit.187 Mass [TeV]KKg1 1.2 1.4 1.6 1.8 2) [pb]t t→ KK BR(g× σ-110110 Obs. 95% CL upper limitExp. 95% CL upper limit uncertaintyσExp. 1 uncertaintyσExp. 2KK gluon (LO)ATLAS Top Template Tagger = 7 TeVs-1 L dt = 4.7 fb∫Figure 6.21: The expected and observed 95% C.L. upper limits on the σ ×BR(X → tt¯) for KK-gluons. Superimposed on the graph is the cross-section for the default benchmark model described in section 2. Thegreen and yellow bands respectively correspond to the one and twosigma uncertainty on the expected limit.188Chapter 7Summary and ConclusionIn this thesis two analyses searching for new massive top-antitop quark resonanceswere presented, each a first of its kind at ATLAS. Each analysis was conductedon data collected in 2011 at a proton-proton collision energy of√s =7 TeV. Asearch for top-quark pair resonances in the dilepton channel sought to use the clearsignal of two oppositely signed leptons, EmissT , and additional jets to separate top-quark pair events from the non-top-quark pair background, in the first 2.04 fb−1of data. A second search for top-quark pair resonances with masses above 1 TeVwas conducted in the boosted fully hadronic channel over the full 4.7 fb−1 of data.That analysis implemented new techniques to identify large unconventional jets asoriginating from top-quark decays in order to separate top-quark pair events fromthe multijet background. Both analyses performed a statistical analysis on the can-didate events based on resonance mass correlated variables: the dilepton analysisconsidered the reconstructed HT +EmissT distribution, and the fully hadronic anal-ysis considered the reconstructed mtt¯ distribution. The two searches are currentlylimited by the available data sample size, and thus sensitivity to new resonant topproduction will continue to increase as more LHC data is collected and analyzed.The results of the analyses indicated no significant discrepancy from the Stan-dard Model prediction in either case. The observations were used to set limits onthe cross-section times branching ratio to top-antitop quark pairs for resonances forwith Breit-Wigner line-shapes as predicted by two new physics models: the lep-tophobic topcolor Z′, and the KK-gluon from the Randall-Sundrum model with a189single finite warped extra-dimension. Generic 95% C.L. upper limits on the cross-section times branching ratio to top-quarks for Z′-like resonance production rang-ing from 20 pb to 0.2 pb over the mass range 500 GeV< mZ′ <2 TeV, were set. Inaddition, generic 95% C.L. upper limits on the cross-section times branching ratioto top-quarks for KK-gluon-like production ranging from 20 pb to 0.3 pb over themass range 500 GeV< mZ′ <2 TeV were set. In the case of the KK-gluon, thecross-section limit can be summarized as a 95% C.L. exclusion limit on the KK-gluon mass for the default benchmark hypothesis; in the dilepton analysis the massrange 500 to 1070 GeV was excluded, and in the fully hadronic channel the massrange 1.03 to 1.62 TeV was excluded.The sensitivity of the dilepton analysis based on the HT +EmissT observable wassubstantially less than that achieved in similar lepton+jets analyses. However theresult is still encouraging. It is possible that by further optimizing the event selec-tion, especially for boosted top-quark decays, signal sensitivity can be enhanced.Moreover, using a kinematic fitter to reconstruct the top-quark pair invariant mass,or employing advanced statistical techniques, such as a neural network, could fur-ther enhance sensitivity. In spite of the apparently reduced sensitivity with respectto other top-quark pair decay channels, searches in the dilepton channel will con-tinue to be important for two reasons. First, the LHC’s discovery potential is max-imized by maintaining sensitivity to unexpected phenomena, and it remains possi-ble that new physics signals may present themselves exclusively in the dileptonicchannel. Moreover, in the case that a resonance decaying to Standard Model top-quarks is discovered, the dilepton channel will be important for characterizationas it will provide a means to measure the polarization of each top-quark. Finally,while not pursued in this thesis, the HT +EmissT distribution is also an importantvariable for searching for non-resonant new physics, and the analysis presentedhere could influence future work in that area.The results of the fully-hadronic search are particularly promising. The anal-ysis presented here set the most stringent limit at high mass in the fully-hadronicchannel at the LHC in the 2011 data. The analysis also demonstrated the viabil-ity of various specialized techniques to select samples of boosted fully hadroniccandidate decays against the overwhelming multijet background at the LHC. Inparticular, the analysis has shown that the challenges of fully hadronic analyses190that exist in resolved channels are manageable or disappear in the boosted regime.Additionally, the analyses demonstrated the usefulness of a partially novel data-driven method for estimating the QCD background.The boosted jet analysis techniques employed by this analysis have wide ap-plicability, and are potentially of critical importance to future analyses at the LHCand beyond. With the tentative discovery of the Higgs-like boson, the course ofresearch at the LHC will increasingly turn to focusing on searches for new massiveparticles, via their decay to Standard Model particles. The LHC collision energywill eventually be increased to its ultimate design value of 14 TeV and thus themass reach for new particle searches continues to be pushed higher. As a result,many future analyses will have a focus on events with highly boosted top-quarks,W s, Zs, or Higgs bosons in their decay chain, and thus topological regimes wherethe final state is characterized by one or more boosted jets will present themselvesas critical selection channels. Such analyses will necessarily rely on the use oftechniques like those pioneered in this work. In particular, the implementation ofthe top-template tagging technique in the analysis presented here can be seen aspart of a larger effort at the LHC to develop techniques to tag collimated hadronicdecays. The results presented here will have an important impact on the futuredevelopment and evaluation of the top-template tagging technique and other com-plementary methods.In closing, this thesis presented two orthogonal searches for the same phe-nomena in different decay channels and kinematic topologies. 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