A Search for Supersymmetry and Universal ExtraDimensions in Final States with Three Leptonsand Missing Transverse Momentum in 20.7 fb−1 of√s =8 TeV pp Collisions with the ATLAS DetectorbySamuel KingBSc, McGill University, 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)April 2014c© Samuel King, 2014AbstractThis dissertation presents a search for direct production of charginos andneutralinos in final states with three leptons and missing transverse mo-mentum in 20.7 fb−1 of√s =8 TeV proton-proton collisions delivered bythe Large Hadron Collider and collected with the ATLAS detector. TheStandard Model augmented with the minimal formulation of universal extradimensions (MUED) is phenomenologically similar to supersymmetry. Thissearch is also sensitive to MUED cascades characterized by the presence ofn =1 Kaluza-Klein excitations of Standard Model W and Z bosons. No sig-nificant excess over Standard Model predictions is observed. The results areinterpreted in the context of simplified supersymmetric models and MUED.New limits are set at the 95% confidence level on the parameter spaces ofthese models.iiPrefaceBecause of the immense complexity of the Large Hadron Collider (LHC) andA Toroidal LHC Apparatus (ATLAS), it is necessary that all ATLAS physicsanalyses are collaborative endeavors. This includes the analysis presentedherein. The author played a key role in almost all aspects of the analysis:signal region optimization, Monte Carlo-based background estimation, cal-culation of uncertainties, and the statistical interpretation of the results.The work would not have been possible, however, without major contribu-tions from colleagues and advisors. The present iteration of the analysis wasled by Zoltan Gecse (UBC) and Tina Potter (Sussex). Steve Farrell (UCI)provided the reducible background estimate and was largely responsible forimplementing the SUSYNT framework used for data analysis. Sigve Haug,Basil Schneider, and Lukas Marti (Bern) were instrumental in writing use-ful scripts for performing limit calculations using the HistFitter software.Stewart Martin-Haugh (Sussex) provided help with systematics computa-tions as well as final signal region plots with full systematics. All other workpresented herein has been primarily performed by the author.Earlier iterations of the analysis were performed with smaller datasets [1] [2][3], and the author contributed to all of these. A public report on the presentanalysis exists as an ATLAS conference note [4]. The minimal universalextra dimensions interpretation is entirely the work of the author and is notfound in any publication, although a smaller dataset interpretation in thismodel was performed by the author for an ATLAS conference note [5].iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . xix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Theoretical Preliminaries . . . . . . . . . . . . . . . . . . . . 42.1 The Standard Model of Particle Physics . . . . . . . . . . . . 42.2 Minimal Universal Extra Dimensions . . . . . . . . . . . . . . 92.2.1 TeV Scale Extra Dimensions . . . . . . . . . . . . . . 92.2.2 Features of MUED . . . . . . . . . . . . . . . . . . . . 132.3 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3.1 Features of the MSSM . . . . . . . . . . . . . . . . . . 232.3.2 Simplified Models . . . . . . . . . . . . . . . . . . . . 352.4 The LHC Inverse Problem . . . . . . . . . . . . . . . . . . . . 36iv3 Overview of ATLAS . . . . . . . . . . . . . . . . . . . . . . . 403.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . 403.2 ATLAS Coordinate System . . . . . . . . . . . . . . . . . . . 443.3 Inner Detector and Solenoid . . . . . . . . . . . . . . . . . . . 453.3.1 Pixel Detector . . . . . . . . . . . . . . . . . . . . . . 453.3.2 Semiconductor Tracker . . . . . . . . . . . . . . . . . . 463.3.3 Transition Radiation Tracker . . . . . . . . . . . . . . 463.4 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.4.1 Electromagnetic . . . . . . . . . . . . . . . . . . . . . 493.4.2 Hadronic . . . . . . . . . . . . . . . . . . . . . . . . . 503.5 Muon Spectrometer and Toroidal Magnets . . . . . . . . . . . 523.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 Reconstruction and Identification of Physics Objects . . . 584.1 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.1.1 Reconstruction and Identification . . . . . . . . . . . . 594.1.2 Additional Selection Cuts . . . . . . . . . . . . . . . . 614.2 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2.1 Reconstruction and Identification . . . . . . . . . . . . 624.2.2 Additional Selection Cuts . . . . . . . . . . . . . . . . 644.3 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.4 Overlap Removal Scheme . . . . . . . . . . . . . . . . . . . . 674.5 Missing Transverse Momentum . . . . . . . . . . . . . . . . . 675 Monte Carlo Simulated Samples . . . . . . . . . . . . . . . . 715.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.3 Correction Factors for Simulated Samples . . . . . . . . . . . 736 Signal Region Definitions . . . . . . . . . . . . . . . . . . . . 746.1 Baseline Event Selection . . . . . . . . . . . . . . . . . . . . . 746.2 Event Selection Optimization . . . . . . . . . . . . . . . . . . 766.2.1 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 766.2.2 Threshold Determination . . . . . . . . . . . . . . . . 79v6.3 Event Selection Summary . . . . . . . . . . . . . . . . . . . . 926.4 Approximate Expected Sensitivity . . . . . . . . . . . . . . . 927 Standard Model Background Estimate . . . . . . . . . . . . 987.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987.2 Reducible Background Estimate: The Matrix Method . . . . 997.2.1 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . 1027.2.2 Fake Rate Scale Factors . . . . . . . . . . . . . . . . . 1027.3 Sources of Uncertainty . . . . . . . . . . . . . . . . . . . . . . 1077.3.1 Uncertainties on Irreducible Backgrounds . . . . . . . 1077.3.2 Uncertainties on Reducible Backgrounds . . . . . . . . 1107.4 Background Estimate Validation . . . . . . . . . . . . . . . . 1168 Results and Interpretation . . . . . . . . . . . . . . . . . . . 1198.1 Signal Region Observations . . . . . . . . . . . . . . . . . . . 1198.2 Methodology for Statistical Interpretation of Results . . . . . 1238.3 Visible Cross Section Limits . . . . . . . . . . . . . . . . . . . 1268.4 MUED Interpretation . . . . . . . . . . . . . . . . . . . . . . 1288.5 SUSY Interpretations . . . . . . . . . . . . . . . . . . . . . . 1289 Looking Ahead . . . . . . . . . . . . . . . . . . . . . . . . . . 13110 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136A Monte Carlo-Based Background Estimate . . . . . . . . . . 147B Complete CLs Maps . . . . . . . . . . . . . . . . . . . . . . . 153viList of TablesTable 2.1 Approximate LO MUED parton level cross sections (106events,√s = 7 TeV) for the point (R−1,ΛR) = (500 GeV, 20)computed with PYTHIA. The cross sections are shown indescending order. Here Q (S) refers to doublet (singlet)quarks, ∗ denotes the n = 1 excitation, and i, j are quarkflavors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Table 2.2 The particle spectrum of SUSY. All SM fields and theircorresponding superpartners are tabulated. Note that i =1, 2 and j = 1, ..., 4. Both interaction and mass eigenstatesare shown for the SUSY fields. . . . . . . . . . . . . . . . . 24Table 2.3 Parameters are tabulated for both varieties of SIM consid-ered in this analysis. All masses are listed in GeV. Param-eters given as a range are varied to generate grids of signalpoints. Note also that mass degeneracy is assumed for allslepton flavors: me˜ = mµ˜ = mτ˜ . The term “heavy” heremeans that a particle is made sufficiently heavy so as tokinematically remove it from cascades. . . . . . . . . . . . 38Table 6.1 Trigger chains used in this analysis. The explicit technicalnames and the offline pT thresholds are provided. . . . . . 75Table 6.2 Summary of the signal region definitions. All regions re-quire the baseline selection (notably `+SFOC) and a b-veto. Note that SRnoZc events are removed from all otherSRnoZ-type regions to ensure orthogonality. . . . . . . . . 92viiTable 7.1 Uncertainties on irreducible SM yields in SRnoZa, b, and c. 112Table 7.2 Uncertainties on irreducible SM yields in SRnoZd. . . . . 113Table 7.3 Uncertainties on irreducible SM yields in all SRZ-type re-gions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Table 7.4 WZ generator systematics have been computed in each sig-nal region as shown here. All yields are scaled to 20.7 fb−1and all uncertainties are statistical. The POWHEG yieldshave been scaled to SHERPA at the three lepton stagewith a scale factor of 1.07. . . . . . . . . . . . . . . . . . . 115Table 7.5 Uncertainties on the reducible BG estimate in all relevantSRs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Table 7.6 Validation region definitions. . . . . . . . . . . . . . . . . 116Table 7.7 Predictions and observations in all validation regions. Un-certainties are systematic and statistical. . . . . . . . . . 117Table 8.1 Full BG estimate compared to data in all SRs. Errors arestatistical and systematic. . . . . . . . . . . . . . . . . . . 120Table 8.2 Expected and observed 95% CL upper limits on the visi-ble cross section and equivalent limits on signal yields areshown in each SR. . . . . . . . . . . . . . . . . . . . . . . 127Table A.1 MC yield estimates and statistical uncertainties for re-ducible and irreducible SM backgrounds at all stages ofthe SRnoZa,b,c cutflows. Note that the small overlap ofSRnoZa,b with SRnoZc has not been removed here. . . . 149Table A.2 MC yield estimates and statistical uncertainties for re-ducible and irreducible SM backgrounds at all stages ofthe SRnoZd cutflow. . . . . . . . . . . . . . . . . . . . . . 150Table A.3 MC yield estimates and statistical uncertainties for re-ducible and irreducible SM backgrounds at all stages ofthe SRZ-type cutflows. . . . . . . . . . . . . . . . . . . . . 151Table A.4 Validation region predictions compared to data observa-tions. Errors are statistical and systematic. . . . . . . . . 152viiiList of FiguresFigure 2.1 A schematic illustrating the fundamental particle contentof the SM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 2.2 Schematic illustrating the topology of the S1/Z2 orbifold. 14Figure 2.3 The MUED γ1 relic abundance is computed and comparedwith 7 year average WMAP results for two values of ΛR.The preferred scale is R−1 .1.4 TeV. “FS level 2” refersto the inclusion of n = 2 KK tower states in the calculations. 17Figure 2.4 The relative size of MUED radiative mass corrections asa function of ΛR (R = 1/500 GeV−1) for various n = 1modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 2.5 One loop corrections (right) break the approximate treelevel mass degeneracy (left) of the n = 1 tower states. Themasses shown here correspond to the point (R−1,ΛR,mh) =(500 GeV, 20, 120 GeV) . . . . . . . . . . . . . . . . . . . 21Figure 2.6 A cascade qq → q1q1 → 3` + /ET involving n = 1 MUEDexcitations. As shown in table 2.1, this diagram is theleading contribution to the final state of interest in thisthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.7 NLO cross sections for various SUSY processes at the8 TeV LHC as computed and plotted by the PROSPINOteam. The left-most pink curve shows the direct produc-tion mode considered here. . . . . . . . . . . . . . . . . . 32ixFigure 2.8 Running of SM couplings at two loop level. The dashedlines have been computed in the SM and the coloredlines in the MSSM. The MSSM GUT scale is seen to beQ ∼ 1016 GeV. The red (blue) line has been computedunder the assumption that the sparticle masses are at acommon scale of 0.5 (1.5) TeV. . . . . . . . . . . . . . . . 34Figure 2.9 The direct production cross section for χ˜±1 χ˜02 is largestamong all direct weak gaugino modes. The next largestmode χ˜±1 χ˜∓1 is shown here for comparison. . . . . . . . . . 37Figure 2.10 Feynman diagrams showing cascades of interest in SIMvia sleptons (a) and via WZ (b). Note the similarity tofigure 2.6. . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 2.11 Parton-level jet opening angle distributions for dijet pro-duction in simulated SUSY and UED events at√s =14 TeV with a sample mass spectrum taken from a mini-mal supergravity benchmark point. . . . . . . . . . . . . . 39Figure 3.1 A schematic of the LHC which shows the locations of allmajor detector experiments. . . . . . . . . . . . . . . . . . 42Figure 3.2 Integrated luminosity delivered by the LHC (green) andrecorded by ATLAS (yellow) throughout 2012 (a) and av-erage number of interactions per bunch crossing for thefull 2012 dataset (b). . . . . . . . . . . . . . . . . . . . . . 43Figure 3.3 A schematic of the ATLAS detector. . . . . . . . . . . . . 44Figure 3.4 A schematic showing various dimensions of the three IDsubdetectors (a), and a plot of the z- and r-componentsof the solenoidal magnetic field (b). . . . . . . . . . . . . 48Figure 3.5 A schematic showing the EM and hadronic calorimeters(a), and a stacked histogram of the amount of calorimet-ric material in units of the relevant materials’ interactionlengths (b). The unlabeled brown (blue) histogram in(b) corresponds to the pre-sampler (material between thecalorimeters and MS). . . . . . . . . . . . . . . . . . . . . 51xFigure 3.6 A photograph showing the orientation of the barrel toroids(a). The ID, solenoid, calorimeters, and MS are notpresent in this photo. Subfigure (b) shows a schematicof the major MS components and the toroid system. . . 54Figure 3.7 ATLAS cross section measurements compared to theoryat 7 and 8 TeV for various SM production modes of inter-est. Note that these are much smaller than the inelasticcross section 60.3 mb. . . . . . . . . . . . . . . . . . . . . 56Figure 4.1 Full η-dependence of the ATLAS electron reconstructionefficiency as measured in Z → ee decays in both data andsimulation. The average value is 0.987. . . . . . . . . . . . 60Figure 4.2 η-dependence of the ATLAS muon reconstruction effi-ciency as measured in Z → µµ decays in both data andsimulation. The efficiency is shown for both combined(CB) and tagged (ST) muons. . . . . . . . . . . . . . . . . 64Figure 4.3 Comparison of data and MC simulated missing transversemomentum distributions in Z → µµ decays. The variousMC contributions have been weighted by their cross sec-tions and the total number of events was then normalizedto data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 6.1 The approximate significance as a function of the lowerjet multiplicity Nj threshold is shown for several MUEDmodel points. It is seen that requiring Nj ≥ 3 maximizesthe significance. . . . . . . . . . . . . . . . . . . . . . . . 79Figure 6.2 The b-jet multiplicity distribution is shown for the BG andrepresentative signal points. All backgrounds are stackedand the uncertainties indicated are statistical only. Theplots include all events passing the baseline selection. . . 80Figure 6.3 Values of mSFOC nearest to mZ are plotted after the base-line selection and b-veto. . . . . . . . . . . . . . . . . . . 81xiFigure 6.4 The /ET distributions for events passing baseline, b-veto,and 10 GeV Z-veto (a), and baseline, b-veto, and Z-request (b). . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 6.5 The mSFOC distribution for events passing the baseline,b-veto, 10 GeV Z-veto, and /ET > 50 GeV (a) or /ET >75 GeV (b). . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 6.6 The mT distribution for events satisfying the baseline, b-veto, 10 GeV Z-veto, and /ET > 75 GeV. . . . . . . . . . 86Figure 6.7 The mT distributions the baseline, b-veto, 10 GeV Z re-quest, and 75 < /ET < 120 GeV (a), or /ET > 120 GeV(b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure 6.8 The p3T distribution for events satisfying the baseline, b-veto, 10 GeV Z-veto, /ET > 75 GeV, and mT > 110 GeV. 88Figure 6.9 The mSFOC distribution for events passing the baseline,b-veto, 10 GeV Z-veto, and /ET > 75 GeV. . . . . . . . . 89Figure 6.10 The Nj distribution for events passing the baseline, b-veto, 20 < mSFOC < 81.2 GeV, and /ET > 75 GeV. Thesignificance scan corresponding to this distribution wasshown in figure 6.1. . . . . . . . . . . . . . . . . . . . . . 90Figure 6.11 A significance scan at the baseline, b-veto, 20< mSFOC <81.2 GeV,and Nj ≥ 3 stage. . . . . . . . . . . . . . . . . . . . . . . 91Figure 6.12 Expected signal yields (left) and corresponding approx-imate significances (right) are shown for SIM via ˜` inSRnoZa (top) and SRnoZc (bottom). All yields have beenscaled to 20.7 fb−1. . . . . . . . . . . . . . . . . . . . . . 94Figure 6.13 Expected signal yields (left) and corresponding approxi-mate significances (right) are shown for SIM via WZ inSRnoZa (top), and SRnoZb (bottom). All yields havebeen scaled to 20.7 fb−1. . . . . . . . . . . . . . . . . . . 95Figure 6.14 Expected signal yields (left) and corresponding approxi-mate significances (right) are shown for SIM via WZ inSRZa (top), SRZb (middle), and SRZc (bottom). Allyields have been scaled to 20.7 fb−1. . . . . . . . . . . . 96xiiFigure 6.15 Expected signal yields (a) and corresponding approximatesignificances (b) are shown for MUED in SRnoZd. Allyields have been scaled to 20.7 fb−1. . . . . . . . . . . . 97Figure 7.1 Feynman diagram examples of the two leading BGs inthis analysis: s-channel WZ (a) and gluon fusion tt (b). 99Figure 7.2 The leading lepton real–fake composition in SRnoZa (a)and SRZc (b). . . . . . . . . . . . . . . . . . . . . . . . . 104Figure 7.3 Muon baseline→signal identification efficiency (a) and scalefactor (b). Both are binned in pT . . . . . . . . . . . . . . 105Figure 7.4 Fake rates (left) and scale factors (right) for electrons fromHF (top) and conversions (bottom). The HF plots arebinned in electron pT , and the conversion plots are binnedin electron |η| with peT > 15 GeV. . . . . . . . . . . . . . 106Figure 7.5 Unscaled (a) and Powheg-scaled (b) WZ /ET distributionsat the baseline stage. . . . . . . . . . . . . . . . . . . . . 109Figure 7.6 Distributions of p2T (a), /ET (b), M``` (c), and Nb (d) fordata and the full BG estimate are overlaid in the indicatedvalidation regions. Uncertainties on the BG are statisticaland systematic.√N statistical error bars are included onthe data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Figure 8.1 Distributions of /ET (a), p3T (b), and p2T (c) for data andthe full BG estimate are overlaid in the indicated SRnoZ-type regions. Uncertainties on the BG are statistical andsystematic.√N statistical error bars are included on thedata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure 8.2 Distributions of p1T (a), mT (b), and /ET (c) for data andthe full BG estimate are overlaid in the indicated SRZ-type regions. Uncertainties on the BG are statistical andsystematic.√N statistical error bars are included on thedata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122xiiiFigure 8.3 The non-normalized distribution of the profile log-likelihoodratio test statistic is shown for S+BG (µ = 1) and BG-only (µ = 0) hypotheses. The signal here is a SIM gridpoint with CLs ∼ 5%. 1.5 × 104 toy experiments havebeen used, and a value q˜ obs1 = 1.79 was seen in data. . . . 125Figure 8.4 95% CL exclusion limit placed on the MUED parameterspace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 8.5 95% CL exclusion limits placed on the SIM via ˜` (a) andvia WZ (b) parameter spaces. . . . . . . . . . . . . . . . 130Figure 9.1 LO Herwig++ cross section comparison for MUED at 8and 14 TeV. Note that a trilepton generator filter effi-ciency ∼5% has not been applied here. . . . . . . . . . . 132Figure 9.2 Approximate expected sensitivity to MUED with 20.7 fb−1of 14 TeV collisions. The black contour indicates the 95%CL limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Figure B.1 Observed CLs values across both SIM grids. . . . . . . . 154Figure B.2 Observed CLs values across the MUED grid. . . . . . . . 155xivGlossaryADD Arkani-Hamed–Dimopoulos–DvaliATLAS A Toroidal LHC ApparatusBG backgroundBKT brane kinetic termBSM beyond the Standard ModelCDF cumulative distribution functionCERN The European Organization for Nuclear ResearchCL confidence levelCM center of massCMS Compact Muon SolenoidCSC cathode strip chambersDGP Dvali-Gabadadze-PorratiECal electromagnetic calorimeterEF event filterEFE Einstein field equationsEW electroweakxvEWSB electroweak symmetry breakingFCal forward calorimeterGR General RelativityGRL good runs listHCal hadronic calorimeterHEC hadronic endcapHF heavy flavorID inner detectorIP interaction pointISR initial state radiationJVF jet vertex fractionKK Kaluza-KleinLAr liquid argonLEP Large Electron-Positron ColliderLF light flavorLHC Large Hadron ColliderLKP lightest Kaluza-Klein particleLO leading orderLSP lightest supersymmetric particleMC Monte CarloMDT monitored drift tubesMLE maximum likelihood estimatorxviMSSM minimal supersymmetric Standard ModelMUED minimal universal extra dimensionsNLO next-to-leading orderNNLO next-to-next-to-leading orderPDF parton distribution function or probability density functionPV primary vertexQCD quantum chromodynamicsQFT quantum field theoryRF radio frequencyROI region of interestRPC R-parity conserving supersymmetry or resistive plate chambersRS Randall-SundrumSCT semiconductor trackerSFOC same flavor—opposite chargeSIM simplified modelSM Standard ModelSSB spontaneous symmetry breakingSTM space-time-matterSPS Super Proton SynchrotronSR signal regionSUSY supersymmetryTDAQ trigger and data acquisitionxviiTGC thin gap chambersTRT transition radiation trackerVEV vacuum expectation valueVR validation regionWIMP weakly interacting massive particleWMAP Wilkinson Microwave Anisotropy ProbeXD extra dimensionsxviiiAcknowledgmentsWorking within the ATLAS Collaboration has been a rewarding and eye-opening experience. There are so many collaborators worthy of thanks thatit would be impractical to list them all here. I must first thank my advi-sors, Colin and Anadi, for their tireless help and guidance. I also extend ahearty thanks to Zoltan and Tina for their countless words of wisdom andenlightening discussions (often at 4:30 am on Skype).I am endlessly indebted to my family, Mark, Laura, and Hannah, withoutwhom this thesis would not exist. I thank the beautiful Karly for putting upwith the then-seemingly endless nights featuring yours truly hunched over alaptop, and my best bro Josh for being a great, robust pal.I would be remiss if I didn’t mention the friends I’ve made in the UBC AT-LAS lab: Stephen Swedish, Bill Mills, Simon Viel, Chang Wei Loh, ArashKhazraie, Matt Gignac, and Ricardo Cha´vez-Gonza´lez. All of you guysplayed a key role in shaping my “Ph.D. experience” and you will not soonbe forgotten.Finally, I’d like to thank Klaus Kinski, The Stone Roses, Brian De Palma,Teenage Fanclub, Slowdive, Dario Argento, Be´la Tarr, The Jesus and MaryChain, Andrei Tarkovsky, Claudio Simonetti, Small Black, John Carpenter,Hash Jar Tempo, Lilys, and Ian “Shotgun” Jones for helping to make lifemore palatable.xixChapter 1IntroductionIt is an exciting era for particle physics. The 2009 turn-on of the LHCat the European Organization for Nuclear Research (CERN) has enabledproton-proton (pp) collisions with center of mass (CM) energies as high as√s = 8 TeV. By 2015, this is expected to increase to almost 14 TeV. Thisunprecedented energy scale has enabled particle physicists working withinthe ATLAS and Compact Muon Solenoid (CMS) collaborations to discovera new boson which, at the time of this writing, is in agreement with theStandard Model (SM) Higgs hypothesis [6] [7].While discovery of a Higgs boson is surely the triumph of these early daysof the LHC, it is possible that discovery of phenomena beyond the Stan-dard Model (BSM) is imminent. There has been much speculation fromthe theory community since the 1970s as to what shape this “new physics”may take. The work in this dissertation is focused on particular instances oftwo of the most popular classes of BSM physics hypotheses: supersymmetry(SUSY) and extra dimensions (XD). Of course, a wide range of other BSMscenarios have been proposed. These include, but are not limited to, com-positeness (e.g. technicolor), little Higgs models, heavy exotic resonances,and hidden sector models. A detailed theoretical overview summarizing thestate of the field has been compiled by Morrissey et al. [8].1Both ATLAS and CMS, as well as the other LHC-based detector collab-orations and many other notable worldwide particle physics experiments,have devised and implemented sophisticated programs to facilitate poten-tial BSM discoveries. Indeed, with so much effort from so many involvedparties, discovering phenomena for which the Standard Model cannot ac-count has become the holy grail of experimental particle physics.To this end, the present work will elucidate a search for new physics in finalstates characterized by three light, charged leptons (e±, µ±) and missingtransverse momentum (/ET ). This final state has been chosen principallybecause multilepton production is a rare process at hadron colliders andthe SM backgrounds are therefore small. The analysis, performed on 20.7fb−1 of 8 TeV pp collisions collected by ATLAS, is optimized for and subse-quently interpreted in electroweak (EW) SUSY and minimal universal extradimensions (MUED). In the SUSY case, the desired final state is producedby cascade decays of directly produced charginos and neutralinos. MUEDproduces this final state via cascades involving excited states of SM W andZ bosons. Motivation for this work, as well as further details clarifying theexact models under consideration, will be provided in the next chapter.This thesis constitutes a re-optimized, higher energy or luminosity updateof three previous ATLAS searches to which the author contributed sub-stantially [1] [2] [3]; supporting documentation can be found in an ATLASconference note [4]. It should also be emphasized that this thesis presentsthe first search for MUED in the trilepton final state with 8 TeV LHC data.Previous collider searches for MUED have been performed at both the Teva-tron [9] and LHC [10]. The most stringent of these is a 2013 ATLAS dileptonsearch [11] which has placed a 95% CL lower bound on the inverse length ofthe extra dimension R−1 & 900 GeV. Cosmic microwave background datacollected by the Wilkinson Microwave Anisotropy Probe (WMAP) have beenused to set an upper bound R−1 . 1.4 TeV [12]. These existing limitsstrongly constrain the available MUED parameter space.2Many previous searches for EW SUSY have been performed both in thetrilepton [13] [14] and various other channels [15] [16] [17]. Of these searches,the 2013 iteration of the trilepton analysis performed by CMS is directlycomparable to (and most competitive with) the work in this thesis. A muchweaker but less model–dependent limit was also set by various collaborationspreviously working with the precision electroweak data delivered by theLarge Electron-Positron Collider (LEP) mχ˜±1& 103.5 GeV [18]. Note that afurther optimized trilepton search using 20.7 fb−1 is currently in preparationby ATLAS.3Chapter 2Theoretical PreliminariesThis chapter will provide a basic overview of qualitative theoretical concepts.The Standard Model is the keystone for all contemporary particle physics;this will be reviewed first. MUED is then presented as a straightforwardextension of the SM. Finally, a discussion of SUSY will be provided. Eachof these topics are associated with vast literatures, so the focus will beon details relevant for the present search. Motivation for studying bothaforementioned BSM scenarios will be recounted.2.1 The Standard Model of Particle PhysicsThe Standard Model arose from the work of theorists in the 1960s [19] [20].This model describes the strong and EW interactions as a non-Abelian gaugetheory with gauge group SU(3)c×SU(2)L×U(1)Y . Here “c” refers to quan-tum chromodynamics (QCD), “L” indicates the chirality of the weak force,and “Y ” is a reminder that this U(1) factor is associated with weak hyper-charge rather than electric charge. The SM describes a universe wherein thefundamental interactions of fermionic matter fields are mediated by gaugebosons. A schematic [21] outlining the particle content of the SM is shownin figure 2.1.In the many years since its conception, the predictive power of the SM has4Figure 2.1: A schematic illustrating the fundamental particle contentof the SM.been subjected to myriad experimental tests. With the noteworthy excep-tion of neutrino oscillations (see, e.g., recent T2K νµ − νe results [22]), thetheory has proven to be remarkably robust. Indeed, the history of exper-imental particle physics in the latter half of the twentieth century is sum-marized by recalling the most famous of these experiments. Deep inelasticscattering experiments at SLAC in the late 1960s [23] provided evidencefor hadronic substructure in the form of light flavor quarks. Gluons andthe W/Z bosons were discovered and characterized in the 1970s and ’80s atDESY [24] and CERN [25], respectively. In 1995, the top quark was dis-covered at Fermilab’s Tevatron [26]. Most recently, a particle which so faragrees with the SM Higgs boson hypothesis was discovered by ATLAS [6]and CMS [7], thereby completing the spectrum of figure 2.1.5It is clear that these experimental triumphs would be meaningless withouta corresponding theoretical framework in which to understand them. Aswith any gauge theory, the first concrete step towards such a framework iswriting down a Lagrangian. The pre-spontaneous symmetry breaking (SSB)SM Lagrangian density can be written in the following highly condensed butconvenient form [27]:LSM = −14FiµνFµνi + iψ¯ /Dψ + ψiyijψjφ+ h.c.+ |Dµφ|2 − V (φ) (2.1)This Lagrangian, symmetric under local SU(3)c × SU(2)L × U(1)Y gaugetransformations, is most easily understood by considering each term in turn.First note that Fµνi with gauge index i = 1, 2, 3 are the gauge boson fieldstrengths. In the second operator (understood implicitly as a sum of similaroperators), the gauge covariant derivatives Dµ are used to describe fermonic(ψ) and scalar (φ) kinetic terms and interactions via gauge bosons. Eachyij with generational indices i, j ∈ {1, 2, 3} is a Yukawa coupling encodingthe interactions between fermions and the scalar Higgs field φ. Note thatthe convention of using Weyl fermions has been adopted here; more will besaid about this below. The final two terms encapsulate Higgs—gauge bosonand Higgs self-interactions, respectively.Since it will be useful later, it is a convenient time to recall the generaldefinition of a gauge covariant derivative in quantum field theory:Dµ ≡ ∂µ − igAaµTa, (2.2)where g is the coupling constant associated with the vector Aaµ and thegenerator T a of the relevant Lie algebra. The SM gauge group, and thereforeLie algebra, is 8 + 3 + 1 = 12-dimensional, and the T aSM can convenientlybe taken to be the tensor products of the generators λb (σc, s) of SU(3)6(SU(2), U(1)):T aSM ∈ {λ1,...,8 ⊗ ISU(2) ⊗ 1, ISU(3) ⊗ σ9,10,11 ⊗ 1, ISU(3) ⊗ ISU(2) ⊗ s}. (2.3)While its precision is appealing, thinking in terms of this sort of languagerequires usage of many indices or tensor products when it comes time towrite invariant Lagrangian terms like those in equation 2.1. Flavor, gauge,spinor, generation, and Lorentz indices will therefore be suppressed in thisthesis whenever it is possible to do so without sacrificing clarity.In its simplest formulation, the Higgs mechanism is a process by whichSU(2)L × U(1)Y EW symmetry is spontaneously broken to U(1). Thisbreaking occurs because the vacuum state of the Higgs potential V (φ) doesnot share the symmetry of the Lagrangian. In this way the W± and Z areimbued with mass, while the photon remains massless [28] [29]. It’s impor-tant to note that the fermions in equation 2.1 are massless. Inserting typicalfermionic mass terms of the form −mψψ¯ψ would violate gauge invariance.In particular, such an operator mixes L and R fermion chiralities in a waywhich does not respect SU(2)L symmetry [27]. It turns out [30] that theHiggs mechanism allows desired mass terms of this form to emerge, wherethe masses are proportional to the Higgs vacuum expectation value (VEV)mψ ∝ VEV. The constants of proportionality are yij . With the renormal-izable [31] SM Lagrangian in place, it is then a straightforward endeavor toperturbatively derive a computationally useful set of associated Feynmanrules.This formulation of the SM (with modifications to accommodate small neu-trino masses [32]) has proven to be sufficiently robust so as to account forthe results of all subatomic physics experiments to date. Although this is animpressive theoretical achievement, the SM provides no answers to a num-ber of difficult open questions; those which are most relevant to the presentanalysis will now be mentioned.7It was Zwicky [33] who first postulated the existence of unseen dark matter(DM) based upon then–anomalous galactic rotation curve behavior. Ac-cording to the latest Planck results [34], the universe is comprised of 26.8%DM. It is therefore no surprise that characterizing DM is one of the key openproblems in both particle physics and cosmology. A wide variety of candi-dates have emerged from the theory community, but the most commonlyaccepted hypothesis classifies DM as a weakly interacting massive particle(WIMP). Although the SM offers no suitable WIMPs, it will be shown be-low that both SUSY and MUED do.The ultimate project of fundamental physics is to write down a naturaltheory which explains all known interactions. Unfortunately, when the SMcouplings are run up to large energies, nowhere do they converge to a single,“grand unified” value. Prediction of grand unification is a necessary (butnot sufficient) condition for a candidate fundamental theory.Perhaps the most glaring reminder that the SM is indeed not a theory ofeverything is its failure to model gravitation. Attempts to quantize GeneralRelativity (GR) via a spin-2 boson, the graviton, lead to a classic exampleof non-renormalizability in QFT. Several approaches to rectifying this situ-ation (e.g. string theory) are under investigation by theorists.One of the most intriguing open questions in high energy physics is thehierarchy problem [35]. This pertains to the poorly understood 15-order-of-magnitude discrepancy between the EW and Planck scales. As a problemwhich threatens naturalness, its solution is of particular importance for aes-thetically pleasing BSM scenarios. Naturalness is the idea that a maximallybeautiful physics theory is one wherein a minimum amount of “fine-tuning”has been performed on its parameters. This means that aesthete physicistsshould be skeptical of a model whose parameters require arbitrary, extremelyspecific values to give agreement with experiments—or, worse still, to evenmake sense at all. Potential solutions to all of these problems will be dis-cussed in the context of SUSY and MUED below.82.2 Minimal Universal Extra DimensionsThis section begins with an overview of TeV scale extra dimensions in par-ticle physics. Pertinent features (mass spectrum, loop structure, etc.) ofMUED will then be explored in some detail.2.2.1 TeV Scale Extra DimensionsIn most areas of physics it is usually assumed that our universe is (3+1)-dimensional. Certainly this is the case in the SM and GR. Nearly a centuryago this assumption was notably challenged by the seminal work of Nord-stro¨m [36], Kaluza [37], and Klein [38]. The famous contribution of theseauthors was a unification of two classical field theories, GR and classicalelectrodynamics, via an extra spatial dimension. Details of this are ex-plored below. After a period of dormancy, interest in extra dimensions wasrenewed towards the end of the twentieth century when string theory beganits rise to prominence. Additional dimensions in stringy models, however,are highly compactified and therefore impractical for discovery at LHC en-ergies.For completeness, it is worth mentioning in passing that theories incorpo-rating extra timelike dimensions have been explored in the literature [39].These exotic models will not be considered in this thesis, and the word “di-mension” should be understood to mean “spacelike dimension” in all thatfollows.It is natural at this stage to wonder what benefits may be obtained by con-sidering extra dimensions. It turns out [40] that model builders have beenable to address a surprisingly large number of important questions in thisway. Perhaps the most important motivation is that XD scenarios oftenprovide natural dark matter candidates. Many models also suggest elegantsolutions to the hierarchy problem. These considerations will be explored9further below.Kaluza-Klein TheoryAs mentioned above, the first fruitful attempt to employ XD as a unificationmechanism dates back to the work of Kaluza and Klein in the 1920s. Sincethe terminology and philosophy of this work remain useful today, its basicprinciples will be outlined before turning to modern developments.Recall that in GR a line element is defined asds2 ≡ gµν(x)dxµdxν , (2.4)where gµν is the metric tensor (a field on the 4D spacetime manifold) andxµ are the spacetime coordinates. Kaluza’s physical insight was to extendthis definition by allowing spacetime to be 5-dimensional:dsˆ2 ≡ gˆMN (x)dxMdxN , (2.5)where the coordinates now specify points on a 5D manifold (M,N ∈ {0, ..., 4}),and the new metric gˆMN is given in terms of gµν , the electromagnetic 4-potential Aµ, a scalar radion field Φ, and Newton’s constant G:gˆMN =(gµν + 16piGΦ2AµAν 4√piGΦ2Aµ4√piGΦ2Aν Φ2). (2.6)As with any XD scenario, an explanation as to why all previous experiments—and day-to-day human perceptions—agree with the hypothesis that the uni-verse is (3+1)-dimensional is in order. Kaluza’s only recourse was simplyto assume that the 5th dimension differential operator ∂4 annihilates all ofthe fields appearing in equation 2.6, so that physics is effectively 4D. Thisframework provides a unified description of classical electrodynamics andGR in the sense that the Einstein field equations (EFE) and the Maxwellequations can be recovered if the 5-dimensional EFE are assumed to take a10source-free formRˆMN −Rˆ2gˆMN = 0, (2.7)where RˆMN is the 5D Ricci tensor, and Rˆ is the 5D Ricci scalar.This framework was later quantized by Klein, who realized that the 5thdimension could be “hidden” by compactifying it on a sufficiently smalltopology. His proposal was a spacetime which factorizes as R4 × S1, whereR4 is a 4D manifold and S1 is a circle of radius R. Denote the coordinates onR4×S1 by (xµ, α) ≡ (x, α). It is reasonable to demand that physical tensorfields fµ...ν(x, α) satisfy a periodic boundary condition: fµ...ν(x, α+ 2piR) =fµ...ν(x, α). Fields on such a spacetime then admit Fourier mode expansions:fµ...ν(x, α) =∑n∈Zeinα/Rf (n)µ...ν(x). (2.8)The infinite set of R4-dependent Fourier modes are said to comprise a so-called Kaluza-Klein (KK) tower of states. Much like a quantum mechanicalparticle on a ring, the α-component of momentum is discretized in multiplesof R−1. Effectively 4D physics can be recovered if R is small enough, be-cause then even the n = 1 KK tower states will have α-momenta too largeto be produced at the LHC.To make all of this more explicit, it is convenient to consider the simplestcase of a complex scalar field φ of mass m0. The full 5-dimensional action isS5 =∫ 2piR0dα∫d4x(∂Mφ∗(x, α)∂Mφ(x, α)−m20|φ(x, α)|2). (2.9)11Expanding φ in a Fourier series then givesS5 =12piR∫ 2piR0dα ei(n−m)α/R∫d4x(∑m,n∂µφ(m)∗(x)∂µφ(n)(x)+∑m,nimRinRφ(m)∗(x)φ(n)(x)−m20∑m,nφ(m)∗(x)φ(n)(x))=∑n∫d4x(∂µφ(n)∗(x)∂µφ(n)(x)−[m20 +n2R2]|φ(n)(x)|2)(2.10)Thus, the effective 4D action for a single 5D scalar field corresponds to aKK tower of increasingly heavy 4D scalars with masses m0 ⊕ n/R. Noticethat each tower state is labeled by a number n ∈ N. Larger n correspondsto larger 5th dimension momentum; this is manifested as a larger mass in 4dimensions.KK theory is obviously no longer viewed as a viable theory of the universe.For instance, it has nothing to say about the strong and weak interactions.It also turns out that the extra dimensions of KK theory have a very large( TeV) compactification scale. However, the idea of using XD as a meansof answering difficult questions in physics has persisted.Widespread interest in TeV scale extra dimensions began in 1998 with thework of Arkani-Hamed et al. [41]. These authors hypothesized the existenceof so-called large extra dimensions, and such models are now eponymouslyreferred to as ADD. ADD addresses the constraint of apparently-4D physicsby confining SM fields to a 3-brane, and addresses the hierarchy problem byallowing gravity to spread through n ≥ 1 extra dimensions.Several new physics scenarios incorporate so-called warped extra dimensions.Such theories are often referred to as Randall-Sundrum (RS) models aftertheir originators [42]. In the most basic type of RS model, the topology ofspacetime is that of two 3-branes separated by a single extra dimension. Themetric changes rapidly along the extra dimension (spacetime is “warped”)12which suppresses the graviton wave function on the SM brane.2.2.2 Features of MUEDSeveral XD scenarios were briefly introduced in the previous section. Thepresent section serves as a more in-depth presentation of the scenario withwhich this dissertation is concerned: universal extra dimensions. A briefoverview will be presented first. It will then be possible to show some sampleMUED KK towers, characterize the mass spectrum, and illustrate explicitlythe cascade processes which contribute to the three lepton final state ofinterest.OverviewModels with extra dimensions in which all SM fields are free to propagateare said to possess universal extra dimensions. The idea was first proposedby Dobrescu et al. in 2001 [43]. It is a radical idea, because it impliesthat all SM fields are associated with KK towers (unlike, say, in ADD stylemodels where the SM is brane-localized). UED therefore has an intricatemass spectrum. Each SM particle has access to states of increasingly largeeffective mass labeled by natural numbers n. It will be shown below thatonly the n = 1 tower states are practical for LHC discovery. Apparently-4Dphysics is then recovered by compactifying the dimensions at a sufficientlysmall length scale R ∼ TeV−1 ∼ 10−19 m. Notice that this picture of“SM+partner fields” is reminiscent of supersymmetric models. Phenomeno-logically, the two models turn out to be quite similar; this will be a recurringtheme in this chapter.The simplest and most extensively studied UED scenario is called minimalUED. It is characterized by three parameters: R, a cutoff scale Λ > R−1,and the Higgs mass (which will always be set to mh = 125 GeV here). Anexplicit cutoff Λ is needed because the theory, like many extra dimensionsscenarios, is non-renormalizable [44]. This implies that UED should be un-derstood as an effective low energy theory which is embedded in a complete13higher energy theory. A single extra dimension which is compactified ona S1/Z2 orbifold is the defining characteristic of MUED. As shown in fig-ure 2.2, this modular structure can be roughly conceptualized as a circlewith diametrical identifications so that it becomes a line segment with well-defined endpoints. The fundamental domain of this structure can then betaken to be [0, piR] [45]. With this topology in place, a set of Feynman ruleshas been derived and used to compute leading order (LO) cross sectionsfor various collider-relevant processes [46] [47]. At the time of this writing,next-to-LO (NLO) cross sections have not been computed for MUED.Figure 2.2: Schematic illustrating the topology of the S1/Z2 orbifold.Naively, it could be argued that momentum should be conserved in universalXDs because all fields propagate in them. Recalling the discussion of KKtheory in section 2.2.1, conservation of momentum in the extra dimensionimplies that the KK (mode) number n is an exactly conserved quantity attree level in 4D. This means that the aforementioned Feynman rules do notinclude vertices involving a single KK tower state. The tree level masses ofthese states are therefore almost degenerate (dominated by R−1) and givenby:mn = m0 ⊕nR, (2.11)where m0 is the mass of the SM field in question.However, complications arise when quantum corrections are considered. Tosee this, note that translational symmetry is manifestly broken by the ex-14istence of the fixed points α = 0, piR of S1/Z2. More precisely, boundary-localized terms known as brane kinetic terms (BKTs) must be introducedinto the Lagrangian in order to allow renormalization of the fields in thebulk [45]. These terms have a simple form; for example [48]:LUED ⊃δ(α) + δ(α− piR)Λ(G3(Fµν)2 + iF3ψ¯ /Dψ + iF4ψ¯Γ4∂4ψ), (2.12)where the couplings G3 and F3,4 are arbitrary field–specific parameters ofthe theory. Since these new couplings are localized to the boundaries, theirassociated corrections are volume-suppressed. It turns out that their effectsare roughly the same size as corrections due to loops, and both effects endup breaking the mass degeneracy of equation 2.11. More details are givenbelow.This explicit violation of translational invariance means that n is not a con-served quantity in MUED. In the next subsection it will be shown that use oforbifolds in UED models is necessary to replicate the SM’s 4D chirality. Fornow it is enough to note that this orbifolding, along with the assumption—built into equation 2.12—that the BKTs are invariant under a swap of thefixed points (an additional Z2 symmetry), implies that the so-called KK-parity PKK ≡ (−1)n is conserved. This fact is of particular importance forcollider searches. It immediately implies that n = 1 states cannot be singlyproduced, and also that the lightest n = 1 KK particle (LKP) is stable. Theanalogy to R-parity conserving (RPC) SUSY is again seen to arise naturally.In MUED, the LKP is usually the excited photon γ1 [49]. The γ1 mass islarge (∼ R−1), and the cross section for EM interaction with the detectoris therefore small. Since this field is also stable, it can generate large /ETin the final state. It will be seen below that large mass splittings betweenvarious n = 1 states create the necessary phase space for production of hightransverse momentum (pT ) leptons.Before presenting further details, it is worthwhile to pause and make a few15motivating comments. Since the LKP is stable, heavy, and neutral, it is aWIMP DM candidate [50]. This property, coupled with the theory’s sim-plicity and predictive power, is the most important motivating factor forthe MUED search presented in this thesis. UED’s other important featuresinclude an explanation of the number of fermion generations [51], insightsinto neutrino oscillations [52], and a natural way to understand the existenceof the scalar Higgs doublet [53].Because the LKP is a DM candidate, its relic abundance can be computedand compared with cosmological observations. This computation has beenperformed for ΛR =20 and 50, and the results were compared with WMAPdata [12]. An illustrative plot from this work is reproduced in figure 2.3. Thecontours in this figure are drawn through the WMAP 7 year average physi-cal dark matter density parameter Ωch2 = 0.1120±0.0056, where h ∼ 0.719is the reduced Hubble constant. These results suggest that R−1 ∼1.4 TeVis the preferred scale when n ≤2 KK tower states are included. The goal forcollider searches is therefore—barring discovery—to push the lower boundon R−1 past 1.4 TeV. Note that the scale 1.4 TeV is obtained assuming thatDM is entirely γ1 and should therefore be treated as an upper bound.Several other flavors of UED have been studied extensively in the litera-ture [54]. Of particular experimental interest is a scenario wherein the SMand a single UED are embedded in a higher dimensional space where thebulk is only accessible to gravitons G. A KK-parity violating LKP decay isallowed γ1 → γ +G, and the corresponding signature is 2 photons and /ET .Stringent limits have been set on this scenario by ATLAS [55].Mass SpectrumNow that a general overview of MUED has been given, the next project isto write down the explicit KK towers and understand their quantum cor-rections. In particular, it is important to understand the mass spectrum ofthe theory and its implications for collider phenomenology.16Figure 2.3: The MUED γ1 relic abundance is computed and comparedwith 7 year average WMAP results for two values of ΛR. The preferredscale is R−1 .1.4 TeV. “FS level 2” refers to the inclusion of n = 2 KKtower states in the calculations.It is helpful to begin by writing down the effective 4D MUED Lagrangian.As usual, this is obtained by integrating the full Lagrangian LMUED overthe extra dimension. The form of the Lagrangian is a straightforward gen-eralization of equation 2.1:LeffMUED =∫ piR0dα[−14Fiµν(x, α)Fµνi (x, α) + iψ¯(x, α)ΓMDMψ(x, α)+ ψi(x, α)yijψj(x, α)φ(x, α) + h.c.+ |DMφ(x, α)|2 − V (φ)],(2.13)where M ∈ {0, 1, 2, 3, 4}, and ΓM are a set of Dirac matrices satisfying the5-dimensional Clifford algebra {ΓM ,ΓN} = 2ηMN [43].Recall that the KK tower emerges explicitly when the α integral in equa-tion 2.13 is performed by exploiting the periodicity of the XD to performFourier expansions of the fields along the orbifold. The next task is then towrite out these expansions in such a way that it is possible to recover theSM with the various zero modes. In particular, it must be decided whether17each field is even or odd under the α → −α Z2 symmetry of the orbifold(i.e. boundary conditions must be chosen to describe 5D parity). FollowingCheng et al. [56], note that odd fields are subject to Dirichlet boundaryconditions Φ|α=0,piR = 0 and even fields are subject to Neumann boundaryconditions ∂4Φ|α=0,piR = 0. For general even (+) or odd (−) fields Φ±(x, α),the Fourier expansions are thenΦ+(x, α) =1√piRφ(0)+ (x) +√2piR∞∑n=1cos(nαR)φ(n)+ (x), (2.14)Φ−(x, α) =√2piR∞∑n=1sin(nαR)φ(n)− (x).It is seen that zero modes of odd fields are projected out; this fact allowsrecovery of SM fermion chirality. Solutions of the 5D Dirac equation onR1,3 × (S1/Z2) can be written as Dirac spinors ψ = (ψL, ψR). Only oneof ψL or ψR can consistently be assigned a zero mode [9], which gives thedesired chiral 4D fermion structure. The zero mode of the vector’s 5th com-ponent A4 must also be odd (projected out) to remove the possibility of amassless adjoint scalar which is not part of the SM [56] [46]. The 0, ..., 3vector components Aµ are even.In summary, each field must be KK decomposed in such a way that thezero modes are the SM, and the topology of the orbifold makes it possibleto do this in a self-consistent way via boundary conditions. As an explicitexample of equation 2.14, the MUED quark fields Q (SU(2) doublets), U ,18and D (SU(2) singlets) can be written asQ(x, α) =1√piR[(u(x)d(x))L+√2∞∑n=1(QnL(x) cosnαR+QnR(x) sinnαR)],U(x, α) =1√piR[uR(x) +√2∞∑n=1(UnR(x) cosnαR+ UnL(x) sinnαR)],D(x, α) =1√piR[dR(x) +√2∞∑n=1(DnR(x) cosnαR+DnL(x) sinnαR)],(2.15)where u and d are the corresponding zero mode SM quarks. Notice thatthe right(left)-handed zero mode of Q (U , D) has been projected out, buthigher tower states contain both L and R.When all of the SM expansions analogous to equation 2.15 are used to per-form the integral in equation 2.13, KK towers with masses given by equa-tion 2.11 emerge. An example of this procedure was shown in equation 2.10.As was discussed above, though, the masses receive important quantum cor-rections beyond tree level. The form of these corrections has been computedby Cheng et al. [56] and will now be discussed.One loop bulk δBu and boundary δBo mass corrections for a general field φat KK tower level n > 0 take the formδBu(m2φn) =∆(φ)16pi4R2, (2.16)δBo(m2φn) = mnξ(φ) ln(Λµ),where ∆ and ξ are field-specific constants, and µ is the renormalization scale(set to R−1 for this analysis). δBo are assumed to vanish past the cutoff scaleΛ. Cheng et al. [48] have created a convenient visualization of the size ofthe radiative corrections as a function of the cutoff. This is displayed infigure 2.4. Note from the form of δBo that, for a given R, the mass split-19tings grow logarithmically with ΛR. It therefore is convenient to use thedimensionless product ΛR as a MUED parameter instead of Λ. The afore-mentioned authors have created another useful figure which illustrates thedegeneracy breaking effect of the one loop corrections. It is reproduced herein figure 2.5.Figure 2.4: The relative size of MUED radiative mass corrections asa function of ΛR (R = 1/500 GeV−1) for various n = 1 modes.The next natural question concerns the collider implications of the largerphase space now accessible in light of the widened MUED mass spectrum.Of particular importance to this thesis is the question of how a 3`+ /ET finalstate may be obtained from pp collisions. Approximate LO parton1–levelcross sections for all MUED strong production modes at√s = 7 TeV havebeen computed using the PYTHIA [58] Monte Carlo (MC) event generator.The results are shown in table 2.1. This table gives an idea of which partonlevel processes are important, and a Feynman diagram illustrating a cascadeof the most important such processes to 3` + /ET is shown in figure 2.6. It1In modern high energy physics, the generic term “parton” collectively describes quarksand gluons. The term has its origins in work by Feynman [57].20Figure 2.5: One loop corrections (right) break the approxi-mate tree level mass degeneracy (left) of the n = 1 tower states.The masses shown here correspond to the point (R−1,ΛR,mh) =(500 GeV, 20, 120 GeV)is seen that the cascades of interest are those involving W1/Z1.qqg qqqqZWLLL111111 111Figure 2.6: A cascade qq → q1q1 → 3`+ /ET involving n = 1 MUEDexcitations. As shown in table 2.1, this diagram is the leading contri-bution to the final state of interest in this thesis.21Table 2.1: Approximate LO MUED parton level cross sections (106events,√s = 7 TeV) for the point (R−1,ΛR) = (500 GeV, 20) computedwith PYTHIA. The cross sections are shown in descending order. HereQ (S) refers to doublet (singlet) quarks, ∗ denotes the n = 1 excitation,and i, j are quark flavors.Subprocess Approximate σ (mb)qi + qj → Q∗i +Q∗j 5.5×10−11qi + qj → Q∗i + S∗j 3.8×10−11q + g → Q∗ + g∗ 2.9×10−11q + q¯ → Q∗ +Q∗3.9×10−12qi + q¯i → Q∗j +Q∗j 2.8×10−12qi + q¯j → Q∗i +Q∗j 2.4×10−12qi + q¯j → Q∗i + S∗j 2.0×10−12g + g → g∗ + g∗ 5.7×10−13g + g → Q∗ +Q∗8.3×10−14Total 1.3×10−10222.3 SupersymmetrySince its theoretical origins in the early 1970s [59] [60] [61], supersymmetryhas remained at the forefront of research in both theoretical and experimen-tal subatomic physics. Confirming or excluding its predictions is one of themain components of the LHC physics program [62].SUSY predicts that, corresponding to each SM field, a so-called superpartnerfield exists whose spin differs by a half unit. Table 2.2, adapted from Bertoneet al. [63], gives a general sense of this construction. The nomenclature inthis table is standard. Matter field superpartners are prepended with an“s,” while the superpartners of the gauge bosons receive an “ino” suffix.It turns out that this idea can be used as a tool to solve several of theopen SM problems discussed above. This section serves as a basic reviewof the cardinal elements of SUSY. For simplicity, the essential character ofthe SUSY formalism will be discussed mostly in the context of the minimalsupersymmetric SM (MSSM). The discussion will then be specialized to the“simplified models” considered in this analysis. A much more comprehensiveintroduction can be found in, e.g., Martin’s classic primer [64].2.3.1 Features of the MSSMAlthough the key ideas of SUSY were written down in the early 1970s, itwasn’t until 1981 that these ideas began to coalesce into a model still widelyused today [65] [66] [67]. This important model, now understood to be thesimplest supersymmetric SM extension, came to be known in ensuing yearsas the MSSM; the present section will examine its key tenets. The discussionwill draw from [64].LagrangianA supersymmetry is a symmetry relating fermions F and bosonsB. Schemat-ically, this can be writtenQ |F 〉 ∼ |B〉 , Q |F 〉 ∼ |B〉 . (2.17)23SM fields SUSY partnersInteraction Mass︷ ︸︸ ︷ ︷ ︸︸ ︷Symbol Name Spin Symbol Name Symbol Name Spinq Quark 12 q˜ Squark q˜ Squark 0` Lepton 12˜` Slepton ˜` Slepton 0ν Neutrino 12 ν˜ Sneutrino ν˜ Sneutrino 0g Gluon 1 g˜ Gluino g˜ Gluino 12W± W boson 1 W˜± Wino H−d Higgs boson 0 H˜−d Higgsino χ˜±i Chargino12H+u Higgs boson 0 H˜+u HiggsinoB B boson 1 B˜ Bino W 0 W 0 boson 1 W˜ 0 Winoχ˜0j Neutralino12H0u Higgs boson 0 H˜0u HiggsinoH0d Higgs boson 0 H˜0d HiggsinoTable 2.2: The particle spectrum of SUSY. All SM fields and theircorresponding superpartners are tabulated. Note that i = 1, 2 andj = 1, ..., 4. Both interaction and mass eigenstates are shown for theSUSY fields.As with any symmetry, the goal is to be able to write combinations of op-erators (Lagrangian terms) which are invariant under the action of Q. Ingeneral this is achieved by understanding the precise group structure as-sociated with the symmetry, and then describing the fields as irreduciblerepresentations thereof. The first step towards a SUSY Lagrangian, then, isto write down the relevant Lie algebra.Before this is possible, it’s necessary to quickly review some details of theWeyl spinor notation. Recall [68] that the (restricted) Lorentz group is iso-morphic to two copies of SU(2): SO+(1, 3) ∼= SU(2)× SU(2). This meansthat all irreducible representations of this group can be catalogued by apair of usual SU(2) quantum numbers. The left- and right-handed spinors24are the (12 , 0) and (0,12) representations, respectively. There is then somefreedom of choice allowed when including spinors in a quantum field the-ory. So-called Dirac spinors ψD correspond to the reducible representation(12 , 0)⊕ (0,12). These arise naturally when considering plane wave solutionsto the Dirac equation and are therefore most familiar. Since the SM is achiral theory, it is often more convenient to treat the two irreducible spinorrepresentations on separate footing. This is the idea behind the Weyl formu-lation. The relationship between the two-component Weyl and more familiarfour-component Dirac spinors is as follows:ψD =(ξχ), (2.18)where the two components of each ξ (left-handed, L) and χ (right-handed,R) are complex Grassmann numbers. Note that the “bar” is part of thename of the R spinor; no mathematical operation is implied.Because ξ and χ transform differently under action of the Lorentz group, it isconventional to index them with different symbols. In particular, left(right)-handed spinors receive “undotted” (“dotted”) indices2. By abusing notationin an illustrative way, equation 2.18 can then be rewritten as follows:ψD =(ξαχα˙), (2.19)and the fact that L and R are complex conjugate representations may beexpressed asχ†α ≡ χα˙. (2.20)These conventions and definitions have been put in place to make it simpleto write down Lorentz invariant spinor products. With this notation, forexample, the general form of the free Lagrangian for a theory containing n2The indices can be raised and lowered by an antisymmetric quantity αβ = α˙β˙ .25fermions χi isLf = in∑iχα˙i (σµ)α˙α∂µχαi −12n,n∑i,j(mijχiαχαj +mijχα˙i χjα˙)≡ in∑iχiσµ∂µχi −12n,n∑i,j(mijχiχj +m∗ijχiχj)(2.21)where σµ ≡ (I,−~σ), and mij is the symmetric mass matrix.It is easiest to derive the SUSY algebra in the context of a simple toy super-symmetric model called the Wess-Zumino model [61]. This model featuresa Weyl fermion ψ and a complex scalar φ; these fields are massless and donot interact. The Lagrangian isLWZ = iψσµ∂µψ − ∂µφ∂µφ∗ (2.22)Now parametrize a supersymmetry between these fields with an infinitesimaltwo-component Weyl fermion α:δφ = αψα, δψα = −i(σµ)α∂µφ (2.23)It can be shown that the action is invariant δSWZ = 0 under this trans-formation. It’s also relatively straightforward to show that the commutator[δ1 , δ2 ] closes; i.e. gives another SUSY transformation. This latter proof re-quires that a non-interacting auxiliary field F be introduced to ensure closureoff-shell. Both of these facts together imply that equation 2.23, along withan associated transformation for F , is indeed a symmetry of LWZ + F ∗F .Noether’s theorem can therefore be used to compute the fermionic genera-tors of the algebra Qα and Qα˙, where the notation is deliberately reminiscentof equation 2.17. These supersymmetric Noether charges are known as su-percharges.The precise form of the supercharges is not important here. The importantfact is that their explicit forms can be used to verify the following super-26symmetry algebra:{Qα, Q¯α˙} = −2σµαα˙Pµ, {Qα, Qβ} = 0, {Q¯α˙, Q¯β˙} = 0, (2.24)where Pµ is the generator of spacetime translations, namely the usual to-tal energy-momentum operator. The full algebra for a supersymmetric fieldtheory, sometimes called the super-Poincare´ algebra [69], is then obtainedby writing down, in addition to equation 2.24, the usual Lie brackets for thePoincare´ group generators and their corresponding brackets with the SUSYgenerators.With this algebra3 in place, SUSY is characterized. It is now possible towrite down irreducible representations and use them to construct a super-symmetric extension of the SM. Intuitively, these representations are formedby grouping the bosonic and fermionic degrees of freedom related by SUSY(superpartners) into sets called supermultiplets [71]. In the Wess-Zuminomodel there is a single supermultiplet {ψ, φ} called a chiral supermultiplet.Similarly, supermultiplets containing a vector are called vector supermulti-plets. The chiral and vector supermultiplets of the MSSM were summarizedabove in table 2.2.The most natural language for writing SUSY Lagrangians involves so-calledsuperfields [71]. A superfield is a field defined on spacetime and four addi-tional Grassmannian coordinates Φ(xµ, θα, θα˙). These fields are constructedin such a way that their Taylor expansions contain the field content of agiven supermultiplet. Heuristically, for example, Φ ⊃ (φ, ψ, F ). Lagrangianswritten in terms of the familiar supermultiplet fields are then recovered byintegrating the fermionic coordinates out of particular functions of the su-perfields called superpotentials. This formalism makes it easy to write man-ifestly supersymmetric operator combinations.3Because it has both anti-commuting (fermionic) and commuting (bosonic) generators,the super-Poincare´ algebra is technically not a Lie algebra. It is in fact a more generalstructure called a Lie superalgebra [70].27It is now possible to understand the form of the MSSM Lagrangian LMSSMby cataloguing the terms produced by integrating its various superpotentials.A thorough discussion of the MSSM Lagrangian is beyond the scope ofthis thesis; a comprehensive term-by-term treatise has been prepared byKuroda [72], for example. The Lagrangian takes the following form [73]:LMSSM =∫d2θd2θ [K(Φi) +W (ΦC) +G(ΦV )] + LB. (2.25)A discussion of each term in equation 2.25 follows.• The first term involves a so-called Ka¨hler potential K, which here isa function of all chiral and vector superfields in the MSSM Φi. Whenfully expanded, this term contains kinetic terms for the (s)fermionsand Higgs(inos) as well as the interactions of these fields with thegauge bosons and gauginos.• The quantity W appearing in the second term is known as the MSSMsuperpotential and is a function of all chiral superfieldsΦC = {Hu, Hd, Q, L, u, d, e}:W = uyuQHu − dydQHd − eyeLHd + µHuHd, (2.26)where yu,d,e are 3 × 3 matrices of Yukawa couplings (i.e. they acton suppressed generational indices), and µ is called the Higgsino massparameter. W may therefore be understood as a supersymmetric gen-eralization of the analogous Yukawa interactions in equation 2.1. Itis important to point out that two SU(2) Higgs doublets Hu and Hdare needed in the MSSM as opposed to the single such doublet in theSM. This additional structure is necessary to avoid an anomaly in theEW sector. When the integral in equation 2.25 is performed, W con-tributes Yukawa terms for fermions and sfermions, as well as Higgsinomass terms.• The third term contains a function of the vector superfields called thegauge superpotential G(ΦV ). Upon integration it contributes kinetic28terms for the gauge bosons and gauginos as well as the relevant self-interactions.• The last term LB describes soft SUSY breaking. LMSSM as writtenabove is pre-SSB. Without LB, each field would receive the same massas its corresponding superpartner when Hu and Hd acquire VEVs. Inlight of, say, the various experimental sparticle mass limits mentionedin chapter 1, this situation is evidently not realized in nature. SUSYmust therefore be a broken symmetry. If SUSY is to be realistic,then, it can only be an exact symmetry of the underlying high energyLagrangian, and its low energy (hence “soft”) effective manifestationappears spontaneously broken. A multitude of breaking mechanismshave been proposed [74]. Experiments can currently only probe as highas the TeV scale, though, so it is more immediately useful to insertexplicit phenomenological SUSY breaking terms via LB. The conse-quence of this non-fundamental approach is a preponderance of freeparameters. Indeed, the highly economical form of equation 2.25 ob-scures 105 such parameters [75]. This fact presents a major challengeto the experimentalist. When designing an analysis it is important toavoid as much of this model-dependence as is possible. Further com-ments on this topic will be made in the next section. Explicitly, LBcontains additional sfermion-Higgsino couplings, and mass terms forthe gauginos, sfermions, and higgsinos which all violate SUSY.Charginos and NeutralinosFeynman rules can be perturbatively derived from LMSSM , and the experi-mentalist can then compare the predictions of SUSY to observations. Beforemoving on to the experimental details of the present analysis, though, it isnecessary to further understand the nature of charginos and neutralinos.As discussed above, the MSSM requires two Higgs doublets Hu ≡ (H+u , H0u)and Hd ≡ (H0d , H−d ). Each of these four fields forms a chiral supermul-tiplet with its fermionic Higgsino superpartner H˜±,0u,d . As was shown in ta-29ble 2.2, the electroweak (unbroken SU(2)L×U(1)Y ) gauge bosons, W±,0 andB0, each fall into vector supermultiplets with their respective superpartnersW˜±,0 and B˜0. Electroweak symmetry breaking in the MSSM, i.e. assign-ing VEVs to both Higgs doublets, causes mixing between the Higgsino andgaugino states. In particular, mixing between the charged Higgsinos andcharged winos yields four mass eigenstates called charginos χ˜±i . Similarly,mixing between the neutral Higgsinos, neutral wino, and bino yields fourmass eigenstates called neutralinos χ˜0j . Both sets of states are labeled interms of increasing mass.Define a neutralino mass term by collecting together post-EWSB Lagrangianterms which are quadratic in neutral gaugino and Higgsino states as follows:LMSSM ⊃ −12(ψ˜0)TMN˜ ψ˜0 + h.c., (2.27)where ψ˜0 = (B˜, W˜ 0, H˜0d , H˜0u) and the mass matrix is given byMN˜ =M1 0 −mZc(β)s(θW ) mZs(β)s(θW )0 M2 mZc(β)c(θW ) −mZs(β)c(θW )−mZc(β)s(θW ) mZc(β)c(θW ) 0 −µmZs(β)s(θW ) −mZs(β)c(θW ) −µ 0,(2.28)where M1 is the bino mass, M2 is the wino mass, the abbreviation s (c)has been used for sine (cosine), θW is the weak mixing angle, µ is the Hig-gsino mass parameter from equation 2.26, and tanβ is the ratio of HiggsVEVs. This is the representation of MN˜ in the neutral gauge eigenstatebasis specified by {B˜, W˜ 0, H˜0d , H˜0u}. If MN˜ is diagonalized by a matrix ΘN˜ ,the neutralino mass eigenstates are given by:χ˜0j ≡ (ΘN˜ )jkψ˜0k, (2.29)with their masses mχ˜0j as the corresponding eigenvalues.Charginos are characterized in a similar way. A chargino mass term has an30associated charged gauge basis {W˜+, H˜+u , W˜−, H˜−d } mass matrix:MC˜ =0 0 M2√2mW c(β)0 0√2mW s(β) µM2√2mW s(β) 0 0√2mW c(β) µ 0 0, (2.30)which can be diagonalized to give eigenstates χ˜±i corresponding to massesmχ˜±i.For future reference, note that the two-body chargino and neutralino decayswhich are generally considered to be most kinematically plausible [64] areχ˜±i −→ {χ˜0jW±, χ˜±1 Z, ν˜`±, ˜`±ν, χ˜±1 H},χ˜0j −→ {χ˜0kZ, χ˜±kW∓, ˜`±`∓, ν˜ν, χ˜0kH}. (2.31)Note also that the cross sections for processes involving these vertices willthen depend on the relative gauge eigenstate content of the various charginosand neutralinos; the terms “wino-like” and “bino-like” are often used to con-veniently characterize the dominant mixing content of these eigenstates.In hadron collider physics, the term “EW SUSY” refers to the direct pro-duction of charginos, neutralinos, or sleptons. This is to be contrasted with“strong SUSY” searches which are designed to observe direct productionof squarks or gluinos. The SUSY search to be presented in this disser-tation is optimized for events involving direct production of χ˜±1 χ˜02, and istherefore an EW SUSY search. A figure produced by the team behind thePROSPINO [76] NLO SUSY cross section calculation software is reproducedhere as figure 2.7. This gives a sense of how the cross sections for strongand EW SUSY at the 8 TeV LHC compare.3110 -310 -210 -1110200 400 600 800 1000 1200 1400 1600ν˜eν˜e* l˜el˜e*t˜1t˜1*q˜q˜q˜q˜*g˜g˜q˜g˜χ˜2og˜χ˜2oχ˜1+maverage [GeV]σtot[pb]: pp → SUSY√S = 8 TeVFigure 2.7: NLO cross sections for various SUSY processes at the8 TeV LHC as computed and plotted by the PROSPINO team. Theleft-most pink curve shows the direct production mode considered here.Phenomenology and MotivationBefore moving on to discuss the SUSY scenarios to be considered in thissearch, it is critical to explore some of the experimentally relevant conse-quences of supersymmetric Lagrangians such as the one in equation 2.25.This discussion will also prove to be a convenient context in which to illus-trate the importance of searching for SUSY at a collider.There are in fact other SUSY-respecting terms that could be added to thesuperpotential in equation 2.26. These terms have not been written be-cause they lead to predictions which do not agree with observations. Inparticular, these missing terms lead to violations of baryon and lepton num-ber conservation, e.g. prompt proton decay. The justification for the terms’omission is the postulate that the MSSM multiplicatively conserves so-calledR-parity [77]. This is a quantum number which can be defined for each field32as follows:PR ≡ (−1)3(B−L)+2s, (2.32)where s is the particle’s spin, B its baryon number, and L its lepton number.All SM particles (and both Higgs doublets) have PR = 1 and all superpart-ners have PR = −1, so R-parity conservation is a Z2 symmetry. This is usefulfor collider searches because it immediately implies that sparticles may onlybe produced in even numbers. Furthermore, if sparticles are produced, theircascade decays must terminate with the production of the lightest PR = −1SUSY particle (LSP) which is stable. Often the LSP is uncharged, andit therefore is an excellent WIMP DM candidate [78]. It is interesting tonote that, although the theoretical origins of R- and KK-parities are quitedisparate, their phenomenological consequences are strikingly similar. Thestudy of SUSY scenarios which violate R-parity conservation is associatedwith a vast literature [79], but no more will be said about this here.One of the most attractive features of SUSY is that certain supersymmetricscenarios predict unification of the strengths of the SM coupling constants.This is a necessary feature of a theory which can accommodate grand unifi-cation. When the MSSM renormalization group flow is studied, it predictsa unification of the inverse SM couplings at a scale Q ∼ 1016 GeV. This isillustrated in figure 2.8, which has been reproduced from Martin [64].Perhaps the strongest motivation for SUSY is its elegant solution of thehierarchy problem [64]. The squared SM Higgs mass parameter receivesdivergent loop corrections from all particles to which it couples directly orindirectly. Quadratically divergent corrections arise from fermions couplingto the Higgs with strength λf :∆m2H ≈ −|λf |28pi2ΛUV , (2.33)where ΛUV is the regularization cutoff. If the Planck scale is the scale of newphysics, then ΛUV is set roughly to this scale. To achieve a light physical33Figure 2.8: Running of SM couplings at two loop level. The dashedlines have been computed in the SM and the colored lines in the MSSM.The MSSM GUT scale is seen to be Q ∼ 1016 GeV. The red (blue) linehas been computed under the assumption that the sparticle masses areat a common scale of 0.5 (1.5) TeV.higgs mass O(100) GeV in agreement with experiment, these large correc-tions must cancel precisely with the bare Higgs mass. The disparity betweenthe EW and Planck scales therefore requires a precise, finely-tuned choicefor the bare Higgs mass [80]. In SUSY, each particle’s superpartner has theopposite spin. Therefore, for each quadratic divergence of the form shownin equation 2.33, there is a corresponding correction from the superpartnerwith the opposite sign. In this way the divergences are canceled and thehierarchy problem resolved.Although motivation has been presented for general SUSY searches, nothinghas yet been said to illustrate the importance of EW SUSY in particular.From equations 2.28 and 2.30, it’s clear that charginos and neutralinos coulda priori assume masses across a wide spectrum via judicious choices of M1,34M2, µ, and tanβ. However, appeals to the concept of naturalness can placerestrictions on these masses. To illustrate this in the context of the MSSM,note that the following formula holds at tree level [81]:−12m2Z = |µ|2 +m2Hu . (2.34)It is seen that if the sparticles which contribute to the RHS become veryheavy ( mZ), a precise cancellation (fine-tuning) is required to preserveequality. This gives insight into natural SUSY. Higgsinos receive massesdictated by µ and should therefore not be extremely heavy. Similarly, m2Huis corrected to two loops principally by t˜ and g˜, so these too should not beexceedingly massive. Masses of other sparticles do not play a strong role indetermining supersymmetric naturalness. This constitutes powerful moti-vation for EW SUSY searches at the TeV scale: The natural requirement oflight Higgsinos implies, due to mixing, that some charginos and neutralinosshould be light.Finally, some rationale must be given for choosing to search for EW SUSYin final states with three leptons. The key observation, as will be seenquantitatively in later chapters, is that SM backgrounds in the trileptonchannel tend to be quite small. For this reason it is possible to obtaincomparable sensitivity to strong SUSY searches despite the much smallersignal production cross sections (recall figure 2.7).2.3.2 Simplified ModelsIt was mentioned above that the large number of free parameters introducedby soft SUSY breaking is a challenge for collider searches. So-called simpli-fied models (SIMs) [82] have been designed to facilitate practical, process-wise sets of analyses which target particular final states. These are a classof phenomenological models which aim to encapsulate the general charac-teristics of models with SM partner fields (i.e. models possessing a paritylike PR or PKK) that make predictions in final states with jets, /ET , or lep-tons. Such models include SUSY and UED. This generality is achieved by35avoiding assumptions about couplings, interference terms, etc., and insteadbuilding a model from the ground up using only a small number of massesand branching fractions as parameters. This provides a simple frameworkin which to understand the general nature of a potential new signal. In thisanalysis two classes of SIM are utilized; a description of their properties willnow be given.In both classes of SIM to be considered, the basic SUSY production modeis associated direct production of wino-like, mass degenerate χ˜±1 and χ˜02. Asillustrated in figure 2.9, this mode is desirable because it has the largestproduction cross section of all direct weak gaugino modes. The LSP is abino-like χ˜01 and q˜ masses are set to O(100) TeV. This latter assumptionkinematically decouples q˜ from the cascades and ensures that no interfer-ence is present.Of course, the final state of interest is 3` + /ET . The two SIMs are differ-entiated by the nature of the cascades which yield these products. In onecase, left-handed sleptons are light, so that they mediate the cascades (“via˜`”). The other case features heavy sleptons, and therefore the cascades aremediated by SM W and Z bosons (“via WZ”). These choices are motivatedby recalling the list of plausible decays in equation 2.31. Feynman diagramsshowing the explicit decay chains of interest are found in figure 2.10, and adetailed catalog of the SIM parameters is shown in table 2.3.As described above, the gauginos’ branching ratios depend upon their mixingcontent. This implies that several other analyses are possible in the contextof χ˜±1 χ˜02 SIM. For example, an analysis targeting the case where χ˜02 → χ˜01His currently in preparation by ATLAS.2.4 The LHC Inverse ProblemAs is typically the case when searching for new scientific phenomena, thefunction which maps new physics hypotheses to their LHC signatures is not36 [GeV]02χ∼,±1χ∼m100 200 300 400 500 600 700 800NLO Cross Section [pb]310210110110210 @ 8 TeV02χ∼±1χ∼ @ 8 TeV+1χ∼±1χ∼Figure 2.9: The direct production cross section for χ˜±1 χ˜02 is largestamong all direct weak gaugino modes. The next largest mode χ˜±1 χ˜∓1 isshown here for comparison.χ˜±1χ˜02˜`/ν˜˜`/ν˜ppν/``/νχ˜01`/ν`/νχ˜01(a)χ˜±1χ˜02WZppχ˜01`νχ˜01``(b)Figure 2.10: Feynman diagrams showing cascades of interest in SIMvia sleptons (a) and via WZ (b). Note the similarity to figure 2.6.37Table 2.3: Parameters are tabulated for both varieties of SIM consid-ered in this analysis. All masses are listed in GeV. Parameters givenas a range are varied to generate grids of signal points. Note also thatmass degeneracy is assumed for all slepton flavors: me˜ = mµ˜ = mτ˜ .The term “heavy” here means that a particle is made sufficiently heavyso as to kinematically remove it from cascades.Parameter Via ˜` Via WZmχ˜±1= mχ˜02 100 — 700 100 — 400mχ˜01 0 — 600 ∧ < mχ˜02 0 — 300 ∧ < mχ˜02m˜`L12(mχ˜01 +mχ˜02)heavym˜`Rheavy heavymν˜ = m˜`Lheavymq˜ heavy heavyBR(χ˜±1 → ˜`±Lν) 0.5 0BR(χ˜±1 → `±ν˜) 0.5 0BR(χ˜02 → ˜`L`) 0.5 0BR(χ˜02 → ν˜ν) 0.5 0BR(χ˜±1 → χ˜01W±) 0 1BR(χ˜02 → χ˜01Z) 0 1injective. This fact, first systematically elucidated in the context of LHCsearches by Arkani-Hamed et al. [83], is known as the LHC inverse problem.It has already been shown, for example, that conservation of R– and KK–parity respectively implies that both SUSY and MUED can yield 3`+ /ET .Although no BSM signals have been observed at the LHC thus far, it is ofcourse critical to be prepared to “solve” the LHC inverse problem shouldthe need arise.38A potential discriminator arises from spin considerations. Note that KKexcitations have the same spin as their SM counterparts, but sparticles’spins differ by a half-unit. This fact leads to differences in the predictedform of angular distributions of the various decay products. Figure 2.11,reproduced from Moortgat-Pick et al. [84], illustrates this explicitly. Thisfigure shows an example of the differing shapes of the jet opening angledistributions in inclusive dijet production in UED and SUSY.Figure 2.11: Parton-level jet opening angle distributions for dijetproduction in simulated SUSY and UED events at√s = 14 TeV with asample mass spectrum taken from a minimal supergravity benchmarkpoint.39Chapter 3Overview of ATLASThe data used in this analysis were collected with the ATLAS detector atthe LHC in 2012. A brief description of this apparatus is presented in thischapter.3.1 The Large Hadron ColliderThe LHC [85] is a pp collider which is housed in a 27 km circumferencetunnel at CERN on the France–Switzerland border. The tunnel was previ-ously constructed for LEP and is located 50–175 m below ground. The 2012dataset used in this analysis has been collected with√s = 8 TeV; this is thehighest CM energy ever attained for collisions in a laboratory.A series of increasingly energetic accelerators, culminating with the SuperProton Synchrotron (SPS), prepare protons for injection into the LHC ring.Upon injection, the beams are focused and steered by more than 1,600 su-perconducting quadrupole and dipole magnets operating at 1.9 K. The beampipe features four interaction points (IPs) with design bunch crossing ratesof 40 MHz, and around each such point a detector experiment has beenconstructed. Two of these, ATLAS and CMS [86], have similar physics pro-grams entailing searches for general new physics and the Higgs boson. Theremaining two detectors, LHCb [87] and ALICE [88], have somewhat more40specialized programs. Figure 3.1 [89] shows a schematic of the LHC ringand the SPS. The positions of the four main detectors are also indicated inthis figure.To quantify the amount of data produced by a collider it is convenient toemploy the concept of integrated luminosity. The instantaneous luminosityL is the constant of proportionality between a cross section and an eventrate: N = Lσ, and it is therefore often expressed in units of b−1s−1, where1 b= 10−28 m2. When radio frequency (RF) cavities are used to groupprotons into bunches within each beam, as is done at the LHC, L can becomputed as follows [85]:L =N2b nbfrevγr4pinβ∗F, (3.1)where Nb is the number of particles per bunch, nb is the number of bunchesper beam, frev is the revolution frequency, γr is the protons’ relativisticfactor, n is the transverse beam emittance, β∗ is the optical beta function(distance from IP to double-width point), and F is a geometric reductionfactor related to the beam crossing angle. The 2012 dataset delivered by theLHC had a peak instantaneous luminosity of 5.4×1033 cm−2s−1 [90], and, ascan be seen in figure 3.2 [91], the total integrated luminosity recorded by AT-LAS was 21.3 fb−1. The distribution of the mean number of pp interactionsper bunch crossing in 2012 is also displayed in figure 3.2 [91].41 RH2 3RH 87UJ 4 6UA4 7UJ 4 7RA4 7UW 4 5US 4 5UL4 6TX4 6UJ 4 4UX4 5RA4 3UA4 3UL4 4UJ 4 3 RR 53UJ 5 3UXC5 5UL 54US C5 5P M5 4P X5 6RZ5 4UP 5 3UJ 5 6 1UJ 5 7 RR 57UJ 5 6P M5 6UL5 6TU5 6UD 62UJ 62UJ 63P M6 5UJ 6 4UA6 3RA6 3TD 62UP 62UL6 4P Z6 5P X6 4UJ 6 6UJ 6 7UJ 6 8UX6 5UA6 7RA6 7TD6 8UD6 8UP 68UL6 6TX6 4UW 6 5 US 6 5Point 7RR7 3RR7 7UJ 7 6P M7 6TZ7 6RA8 3UA 83UJ 83UJ 8 4UJ 8 2Point 8 PM 85P X8 4P Z8 5UX 85TX8 4UL 84UA8 7RA 87 UJ 86UJ 8 7UW 8 5US 85UL 86TI 8 UJ 88PGC 8TJ 8 RR1 3UJ 1 3RT1 2UJ 1 4US 1 5TI 1 2P M1 5P X1 4UX1 5UL1 4UJ 12RE 12 RE 88LS S 4P o in t 1 .8PMI 2UJ 1 7UJ 1 8UJ 1 6TI 1 8RR1 7PM 18 P X1 6 P X1 5US A1 5UL1 6UJ 2 2UJ 23UJ 2 4UA2 3RA2 3TI 2P GC2RA2 7UJ 2 6P X2 4UX2 5P M2 5UW 2 5US 2 5UL 26UL 24UJ 2 7 UA2 7 Point 2 ALICEPoint 4P Z 3 3P M3 2UJ 3 2 UJ 3 3RZ3 3TZ3 2Point 5 CMSPoint 6 LHC 'B'Point 1 ATLASS P S P X4 6P Z4 5P M4 5RT 18P o in t 3 .3P o in t 3 .2LHC PROJECT UNDERGROUND WORKS UP 2 5TT 40Existing StructuresLHC Project StructuresST-CE/JLB-hlm18/04/2003RE 32RE 28RE 38RE 42RE 48RE 52RE 58RE 62RE 68RE 72RE 78RE 82RE 22RE 18NFigure 3.1: A schematic of the LHC which shows the locations of allmajor detector experiments.42Day in 20121 fbTotal Integrated Luminosity 05101520251/4 1/6 1/8 1/10 1/12 = 8 TeVs PreliminaryATLASLHC DeliveredATLAS Recorded1Total Delivered: 22.8 fb1Total Recorded: 21.3 fb(a)Mean Number of Interactions per Crossing0 5 10 15 20 25 30 35 40 45 50/0.1]1Recorded Luminosity [pb020406080100120140 =8 TeVsOnline 2012, ATLAS 1Ldt=21.7 fb∫> = 20.7µ<(b)Figure 3.2: Integrated luminosity delivered by the LHC (green) andrecorded by ATLAS (yellow) throughout 2012 (a) and average numberof interactions per bunch crossing for the full 2012 dataset (b).433.2 ATLAS Coordinate SystemThe ATLAS detector [92] [62] weighs roughly 7,000 tonnes. It measures 44 min length and has a diameter of 25 m. It is therefore the largest collider de-tector ever constructed. The design philosophy of ATLAS is canonical for ageneral purpose detector. As shown in figure 3.3 [93], it features cylindrical,specialized subsystem layers of increasing radius centered around the IP andcollinear with the beam pipe at the IP. The remaining sections in this chap-ter will systematically elucidate these subsystems, but it is first necessaryto define the conventional coordinate system and describe some commonlyencountered notation.Figure 3.3: A schematic of the ATLAS detector.By convention, the IP is taken to be at the origin of a right-handed Cartesiancoordinate system (x, y, z). The axes are oriented so that the positive z-direction is aligned with the counter-clockwise beam and the x-axis pointstowards the center of the LHC. The xy-plane is called the transverse plane;points in this plane are often described with azimuthal polar coordinates44(r, φ). The angle measured from the z-axis is denoted by θ, but it is typicallymore convenient to work with the pseudorapidity1:η ≡ − ln tan(θ2). (3.2)3.3 Inner Detector and SolenoidThe LHC beam pipe has a radius of 30 mm. After traversing this, the firstATLAS subsystem which particles encounter is the inner detector (ID) [94].Covering a range 0.05 < r < 1.2 m, |η| < 2.5, and |z| < 3.1 m, the ID isa tracking system which makes transverse momentum ~pT ≡ (px, py) mea-surements with overall resolutionσpTpT= 0.05% × pT ⊕ 1%2[94]. Such mea-surements are possible because surrounding the ID is a r = 1.3 m solenoidalmagnet with field strength ∼2 T (see figure 3.4 [93]) which induces trans-verse plane Lorentz curvature in charged particle tracks. Note that this alsoallows charge determination. As is illustrated in figure 3.4 [93], three distinctsubsystems collectively comprise the ID. In order of increasing radius, theseare the pixel detector, the semiconductor tracker (SCT), and the transitionradiation tracker (TRT).3.3.1 Pixel DetectorThe pixel detector [94] is comprised of three barrel (r = 50.5, 88.5, 122.5 mm)and three endcap (|z| = 495, 580, 650 mm) layers, where each layer is itselfcomprised of 19 × 63 mm2 sensors. Each sensor then contains 47,232 Sipixels—most of which measure 50 × 400µm2. These facts imply that thepixel detector has approximately 80×106 total readout channels.The most important function of this subdetector is precision vertexing. Boththis and the desire for low noise occupancy necessitates the large channel1Pseudorapidity is a convenient quantity because for particles with speeds near c, η isapproximately equal to rapidity y, and ∆y is invariant under z-boosts.2Whenever transverse momenta or energies appear on the RHS of resolution expressionsin this chapter, the units are understood to be GeV.45multiplicity. The transverse and longitudinal resolutions of the various layersare between 10 and 115 µm [94], and together they average 3 hits per trackwith < 1 noise hit expected per bunch crossing.3.3.2 Semiconductor TrackerConsisting of four barrel layers (r = 0.30, 0.37, 0.44, 0.51 m) and nine endcaplayers (0.81 < |z| < 2.8 m), the SCT [94] is the most important subdetectorfor charged particle tracking. A layered sensor array design philosophy wascarried over from the pixel detector, but each SCT sensor is a more cost-effective collection of 1,500 12 cm×80 µm strips of Si. This gives a total of6.3×106 readout channels.Although the use of strips degrades the spatial resolution slightly with re-spect to the pixel detector (17 µm transverse and 580 µm longitudinal [94]),it enables the SCT to occupy a much larger volume. Tracks can thereforehave as many as 8 hits, thereby providing robust tracking information. TheSCT and pixel detector utilize a common cooling system and nominallyoperate at 266 K.3.3.3 Transition Radiation TrackerWhen a charged particle moves between media with differing dielectric con-stants, it emits so-called transition radiation and thereby loses an amountof energy proportional to its relativistic factor γ [95]. This is the prin-ciple which underlies transition radiation detectors such as ATLAS’ TRT(0.55 < r < 1.1 m, |z| < 2.7 m) [93].TRT detector elements are 2 mm radius drift chambers known as straws.The straws are oriented parallel to ATLAS in the barrel (lengths: 144 cm)and radially in the endcaps (lengths: 37 cm), and are each filled with a70% Xe, 27% CO2, 3% O2 gas mixture. Xenon is an ideal choice becauseof its high efficiency for transition radiation absorption. A gold-plated wireruns down the central longitudinal axis of each straw. A potential difference46−1530 V is set up across each wire so that the ionized electrons from the gasproduce an electrical pulse which is read out at the end of the straw. Thepattern of straws registering such ionization pulses gives tracking informa-tion with transverse resolution 130 µm [93]. Although this is slightly coarserthan the pixel detector and the SCT, the comparatively large volume of theTRT provides an average of 30 hits per track. Also noteworthy is the factthat regions between TRT straws are filled with polypropylene to encouragelarge amounts of electron transition radiation. This implies that the TRTis also able to identify electrons.47EnvelopesPixelSCT barrelSCT end-capTRT barrelTRT end-cap255<R<549mm|Z|<805mm251<R<610mm810<|Z|<2797mm554<R<1082mm|Z|<780mm617<R<1106mm827<|Z|<2744mm45.5<R<242mm|Z|<3092mmCryostatPPF1CryostatSolenoid coilz(mm)Beam-pipe Pixelsupport tubeSCT (end-cap)TRT(end-cap)1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8Pixel400.5495580650 749853.89341091.51299.91399.7 1771.4 2115.2 2505 2720.200R50.5R88.5R122.5R299R371R443R514R563R1066R1150R229R560R438.8R408R337.6R275R644R10042710848712 PPB1Radius(mm) TRT(barrel)SCT(barrel) Pixel PP13512ID end-platePixel400.5 495 580 65000R50.5R88.5R122.5 R88.8R149.6R34.3(a) ID schematicz (m)-3 -2 -1 0 1 2 3Field (Tesla)-0.500.511.52Bz at R=1.058 mBr at R=1.058 mBz at R=0.538 mBr at R=0.538 mBz at R=0.118 mBr at R=0.118 m(b) Solenoidal B fieldFigure 3.4: A schematic showing various dimensions of the three IDsubdetectors (a), and a plot of the z- and r-components of the solenoidalmagnetic field (b).483.4 CalorimetersAfter passing through the ID and its associated solenoid, particles enter theenergy measurement portion of ATLAS: the calorimeter system (1.4 < r <4.25 m, |η| < 4.9) [93]. Particle physics calorimeters function by destruc-tively interacting with incident particles, thereby initiating a series of iter-ative decays collectively called a shower. The properties of showers, whichcan broadly be classified as electromagnetic or hadronic, can then be mea-sured and used to reconstruct the energy and location of the original particle.As can be seen in figure 3.5 [93], the calorimetry strategy employed byATLAS involves liquid argon (LAr) sampling EM calorimeters in the barreland endcap (ECal), a tile hadronic calorimeter in the barrel (HCal), LArhadronic endcaps (HEC), and a LAr combined EM–hadronic calorimeterin the forward region (FCal). Each of these subsystems has been designedwith a balance between robust (η, r, z) coverage, high energy resolution, andcost-effectiveness in mind. The amount of calorimeter material (measuredin interaction lengths) presented to an incident particle is histogrammed infigure 3.5 [93].3.4.1 ElectromagneticEM showers occur when electrons and photons iteratively undergo bremsstrahlungand e+e− pair-production, respectively, in dense material. EM calorime-ters are specialized instruments which allow energy measurements to beextracted from measurements of the properties of showers of this type.The ATLAS ECal is constructed from alternating layers of lead and liquidargon; such an arrangement is called a Pb–LAr sampling calorimeter. Leadis an ideal choice for an absorber because its high density encourages devel-opment of EM showers. The particles in the shower then ionize the LAr,and the amount of ionization is measured with Cu electrodes and subse-quently mapped to an incident energy. The Pb absorbers are arranged inan accordion-like pattern to allow full azimuthal (φ) coverage. The ECal49achieves a resolution σEE =10%√E⊕ 0.7% [93] and covers a pseudorapidityrange |η| < 1.5 (1.4 < |η| < 3.2) in the barrel (endcap). Its radial extent is1.4 < r < 2 m.Both EM and hadronic (see below) calorimetry are performed by the FCal,which extends 3.1 < |η| < 4.9. The EM subsystem within the FCal is aCu–LAr sampling calorimeter with energy resolution σEE =100%√E⊕ 10% [93].Copper has been chosen to facilitate heat removal in the high particle fluxregions.3.4.2 HadronicWhen a hadron is incident on dense material a hadronic shower may beinitiated. These showers can contain both strongly and electromagneticallyinteracting particles (mostly pions [96]). Note that this is distinct from theprocess of hadronization, which creates jets of colorless hadrons from par-tons due to confinement, but hadronic calorimeters are necessary to measurejet energies.ATLAS’ hadronic calorimeters are located in the barrel (HCal coverage:|η| < 1.7, 2 < r < 4 m), endcaps (HEC coverage: 1.5 < |η| < 3.2), and for-ward region (FCal coverage: 3.1 < |η| < 4.9) which gives good hermeticity.Each subsystem attains resolution σEE =X%√E⊕ Y%, with X = 56.4, 50, 100and Y = 5.5, 3, 10 [93] for the HCal, HEC, and FCal, respectively.The HCal is a sampling calorimeter with steel absorbers and scintillatingplastic tile samplers.3 Both the HEC and the hadronic subsystem of theFCal are LAr sampling calorimeters. The former (latter) utilizes Cu (W)absorbers. As was seen in the material thickness plot in figure 3.5, all of thehadronic calorimeters are comprised of 3-4 layers of absorbers in order tomitigate any punch-through into the muon system.3For this reason it is also commonly referred to as the tile calorimeter50(a) Calorimeters0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 502468101214161820PseudorapidityInteraction lengthsEM caloTile1Tile2Tile3HEC0HEC1HEC2HEC3FCal1FCal2FCal3(b) Calorimetric interaction lengthsFigure 3.5: A schematic showing the EM and hadronic calorimeters(a), and a stacked histogram of the amount of calorimetric material inunits of the relevant materials’ interaction lengths (b). The unlabeledbrown (blue) histogram in (b) corresponds to the pre-sampler (materialbetween the calorimeters and MS).513.5 Muon Spectrometer and Toroidal MagnetsFilling the volume between 4.3 < r < 11 m and |η| < 2.7, the muon spec-trometer (MS) [93] provides dedicated tracking and trigger (see below) in-formation for muons.Muon pT measurements are inferred from r− z track curvature in the pres-ence of ATLAS’ eponymous air-core toroidal magnet system. This systemconsists of 8 toroid coils in the barrel (endcap) which collectively produce afield of roughly 0.5 T (1 T) while operating at 4.6 K. Each set of φ-symmetricendcap toroids is rotated by 22.5◦ with respect to the φ-symmetric barrelset to ensure optimal bending power and coverage. The toroid configurationis shown in both subfigures of figure 3.6 [93].Transverse momentum resolution of 10% for 1 TeV tracks within |η| < 2.7[93] is attained through use of two subdetectors: cathode strip chambers(CSC) in the endcaps, and monitored drift tubes (MDT) in both the barreland endcaps. Both of these systems are illustrated in figure 3.6.Like the TRT, the MDT is a collection of straws filled with ionizing gas (93%Ar, 7% CO2) and threaded with Au-plated wire for signal transmission. Inthe barrel, longitudinally oriented straws ≤6 m in length are grouped intothree layers (r = 5, 7.5, 10 m) of 16 chambers (“stations”) each. EndcapMDTs are similarly grouped into four layers (|z| = 7.4, 10.8, 14, 21.5 m)which together give ATLAS its characteristic shape (see figure 3.6).Particle counting rates are too large for proper MDT performance when|η| > 2.0 and |z| = 7.4 m. For this innermost endcap region, then, CSCs areused instead of MDTs. Similarly to MDTs, these are segmented azimuthallyinto chambers. However, their operation relies on measurement of inducedcharges on cathode strips rather than straw wire read-outs.Muon trigger capabilities are provided by resistive plate chambers (RPC)52and thin gap chambers (TGC) for |η| < 2.4. The next section providesfurther details on the trigger system.53(a) Barrel toroids(b) MS and toroid system schematicFigure 3.6: A photograph showing the orientation of the barrel toroids(a). The ID, solenoid, calorimeters, and MS are not present in thisphoto. Subfigure (b) shows a schematic of the major MS componentsand the toroid system.543.6 TriggerData are output from all subdetectors in the form of electrical signals; e.g.pulses from TRT anode wires. The trigger and data acquisition system(TDAQ) [93] collects these signals, scrutinizes them via a variety of algo-rithms, and finally stores events of interest for physics analysis.Storing a raw collision event observed by ATLAS requires roughly 25 MB,but this can be reduced to 1.3 MB with zero suppression [97]. Given thatthe LHC bunch crossing rate was 20 MHz (50 ns temporal spacing) in 2012,it is clearly not feasible to store every crossing event. In addition to itsimpracticality, it turns out that storing all events would not be useful forthe ATLAS physics program.At 7 TeV the inclusive inelastic pp scattering cross section was measured byATLAS to be 60.3 ± 2.1 mb [98]. As can be seen in figure 3.7 [99], typicalcross sections for SM processes of interest are on the order of 10–100 pbat this same CM energy. New physics cross sections may be considerablysmaller than this. The disparity between these cross sections implies thatthe vast majority of pp interactions lead to soft “minimum bias” events.These processes are irrelevant for most ATLAS analyses and can safely bediscarded (or, rather, heavily pre-scaled—see below). The automated mech-anism for deciding which events will be stored for later analysis is preciselythe trigger system. Because the present analysis is focused on extremelyrare processes involving final states with three leptons, the large event ratereduction afforded by the trigger is of critical importance.Given physical storage limitations, a practical data throughput rate wasfound to be ∼300 MB/s, although it can be as high as 600 MB/s in cer-tain runs [97]. The ATLAS trigger’s main goal, then, is to select approxi-mately 200 events from the 20×106 produced each second. This reductionis achieved by dividing the trigger functionality into three sequential levelswith access to increasingly detailed event properties: L1, L2, and the event55W Z WW Wt [pb]totalσ110210310410510120 fb113 fb15.8 fb15.8 fb14.6 fb12.1 fb14.6 fb14.6 fb11.0 fb11.0 fb135 pb135 pbtt t WZ ZZ = 7 TeVsLHC pp Theory )1Data (L = 0.035 4.6 fb = 8 TeVsLHC pp Theory )1Data (L = 5.8 20 fbATLAS PreliminaryFigure 3.7: ATLAS cross section measurements compared to theoryat 7 and 8 TeV for various SM production modes of interest. Note thatthese are much smaller than the inelastic cross section 60.3 mb.filter (EF).The largest event rate reduction 20 MHz→ 75 kHz occurs via the custom-built hardware which comprises L1. This receives input from the RPC,TGC, and calorimeters, and has a maximum of 3 µs to identify so-calledregions of interest (ROI) containing hard leptons, jets, large /ET , or largeET . If an event contains an ROI it becomes input for L2.Both L2 and the EF4 are software-based and are located in a dedicated fa-cility near the detector at CERN. L2 is a farm of 500 CPUs which receiveinput from L1 and the ID. It performs a limited reconstruction (see the nextchapter) within the ROI and must make event decisions in less than 40 ms.If an ROI satisfies certain properties, codified in so-called trigger sequences,the event is passed to the EF at a rate 3.5 kHz. The EF is then afforded4 s in which to employ sophisticated algorithms to fully rebuild and analyze4L2 and EF are collectively called the high-level trigger (HLT)56an event. This level is comprised of 1,800 CPUs and the rate reduction is3.5 kHz→ 200 Hz. EF is the final arbiter as to which events are storedto disk; its output is a summary of all trigger information called a triggerchain. The collection of all trigger chains is known as the trigger menu, andthis is completely customizable. Pre-scale factors can be set at each levelto further control throughput. These are factors which forcibly reduce theacceptance of a given chain by a factor 1n . This is achieved by keeping oneevent for every n which are successfully triggered upon.All events satisfying a chain from the menu are disseminated to collaborationmembers via the LHC Computing Grid [100]. Some explicit chain exampleswill be presented in chapter 6 when the event selection for this analysis isdescribed.57Chapter 4Reconstruction andIdentification of PhysicsObjectsHaving described the BSM scenarios of interest and the detector used tosearch for these, focus will now begin to shift to the particulars of the anal-ysis. This chapter briefly describes standard ATLAS reconstruction andidentification techniques leading to experimental definitions of the neces-sary physics objects: electrons, muons, jets, and /ET . Because of the rarityof multilepton events at the LHC, lepton identification plays a key role inthis analysis. The performance of these algorithms will be summarized.The selection criteria used for each object in the present analysis are thendescribed in detail. Note that the term “lepton” should, unless otherwiseindicated, be understood to mean e± or µ± for the remainder of this thesis.4.1 ElectronsThis section will present the performance of the standard electron recon-struction and identification algorithms. Electron cuts specific to this analy-sis will then be presented.584.1.1 Reconstruction and IdentificationThe process of establishing that an electron candidate has passed througha particle detector and the subsequent measurement of components of itsfour-momentum is called electron reconstruction. There is a standard AT-LAS algorithm used for this purpose [101].In the central region (|η| < 2.5), the first step towards reconstruction isrecognition of EM calorimeter energy clusters. This is achieved with a “slid-ing window” algorithm [102], wherein a window of size 3×5 units (wherea unit is 0.025×0.025 in (η, φ)) is swept across the ECal to find local ETmaxima. This algorithm identifies EM showers with ∼100% efficiency whenET > 15 GeV. ID information is then used to match these clusters to atrack. If a cluster and a track are found to match within ∆η < 0.05 and∆φ < 0.1 at the track point of impact, electron reconstruction proceeds tothe next step: energy determination. This is achieved by summing con-tributions from the ECal cluster cells identified by the sliding window, thepre-sampler estimate of the amount of energy lost by the candidate beforereaching the ECal, estimated leakage outside the cluster, and an estimate ofany punch-through energy loss. The transverse momentum components areobtained from the ID track curvature measurement in the solenoidal B field.Of course, there are no ID trackers in the far-forward region 2.5 < |η| < 4.9,so a slightly different algorithm is used here; three-dimensional clusters pro-vide the desired four-momentum reconstruction. The average efficiency ofelectron reconstruction was measured to be 98.7 ± 0.1 ± 0.2% in data; thisis illustrated in figure 4.1 [101].In the present analysis, the electrons of interest are hard, isolated, andprompt1. Many electrons incident upon ATLAS—e.g. those from photonconversions, Dalitz decays, and jets—do not fit these criteria. Electron iden-tification is the process by which these less desirable electrons are discarded,leaving a sample heavily enriched in electrons of interest. This is achieved by1“Hard” means high pT . Isolation will be described in detail below. “Prompt” meansthat the electron originates from the primary vertex.59Figure 4.1: Full η-dependence of the ATLAS electron reconstructionefficiency as measured in Z → ee decays in both data and simulation.The average value is 0.987.applying a series of cuts to the full set of reconstructed candidate electrons.ATLAS employs three standard identification working points reflecting thedesired level of purity to be attained: loose, medium, and tight [101]. Thisanalysis makes use of medium and tight electrons.Loose electrons are identified using variables defined only in terms of ECalmeasurements. These are mostly comprised of variables characterizing theshower shape. Medium electrons additionally include tracking information.Cuts on track quality are imposed, such as requiring the transverse impactparameter to satisfy |d0| < 5 mm (to reduce electrons from secondary ver-tices), and enforcing minimum pixel and SCT hit multiplicities (to improvethe track fits). Tight electrons impose further restrictions on track quality,e.g. minimum TRT hit multiplicities, and track–cluster matching. The effi-ciency of the identification working points has been measured in data usingsamples enriched in W → eν, Z → ee, and J/ψ → ee [101]. Although thereis some dependence on ET and η, the medium (tight) efficiency was found60to be roughly 0.85 (0.78).In addition to the efficiency measurements described above, correspondingMC simulated values were obtained [101]. Small differences, typically 1-2%,were observed. These differences are used to multiplicatively correct MCsimulations used in this analysis on an event-by-event basis. These samplesare described in chapter 5.4.1.2 Additional Selection CutsThe working points described in the previous section are the standard bench-mark for electron definitions across all ATLAS analyses. The present anal-ysis incorporates a series of additional identification cuts. As will be shownlater, the background (BG) estimate methodology requires the definition oftwo categories of electrons: baseline and signal.Baseline ElectronsThe starting point for defining baseline electrons is the set of medium iden-tification criteria. A transverse energy cut ET > 10 GeV is then applied.Calorimeter clusters are required to satisfy |η| < 2.5 to ensure that the cen-tral reconstruction algorithm has been used. There are known regions of theECal with dead optical transmitters; clusters in these areas are discarded.Finally, after passing through the overlap removal scheme (cf. section 4.4),electrons are deemed baseline.Signal ElectronsSignal electrons are the electrons of interest in this analysis. These are base-line electrons which satisfy a number of additional cuts.Two isolation requirements are imposed. The variable pcone30T is defined tobe the scalar sum of transverse momenta of all > 1 GeV tracks (except thoseof other baseline leptons) within ∆R ≡√∆η2 + ∆φ2 ≤ 0.3 of a baselineelectron track. An analogous variable Econe30T may then be defined in terms61of ECal clusters rather than tracks. Note also that Econe30T has a pile-upcorrection applied: Econe30T → Econe30T −ANv, where A = 20.15 (17.94) MeVin data (MC), and Nv is the multiplicity of ≥ 5 track vertices in the event.These corrections have been computed empirically by examining the aver-age isolation as a function of the number of primary vertices in both dataand simulations. The two isolation requirements are pcone30T < 0.16ET andEcone30T < 0.18ET .Two additional perigee parameter cuts are then placed to reduce non-promptelectrons. The d0 significance is required to satisfy |d0|/σd0 < 5, and thelongitudinal impact parameter must satisfy |z0 sin θ| < 0.4 mm. If, in addi-tion to all of these cuts, the electron passes the tight identification selection,it is deemed signal.4.2 MuonsSince muons are minimum ionizing particles which do not undergo signif-icant showering in the calorimeters, muon reconstruction algorithms differfrom their electron counterparts. Performance of these algorithms will besummarized and the muon selection cuts for this analysis will then be pre-sented.4.2.1 Reconstruction and IdentificationMuon reconstruction happens via two distinct and complementary sets ofalgorithms (“chains”): staco (statistical combination) and muid (muon iden-tification). Each chain is comprised of three algorithms, and each of thesereturns one of three2 muon types [103]:• Standalone muons are reconstructed entirely from MS tracking infor-mation. Track segments from the three muon stations are constructed,combined to form a single track, and then extrapolated to the IP.2There is a fourth, less commonly used type of muon which is reconstructed usingminimum ionization clusters from the ECal.62The staco (muid) algorithm which returns standalone muons is calledmuonboy (Moore).• Reconstruction of combined muons involves spatially matching inde-pendently reconstructed ID tracks and MS tracks. Since this type ofmuon has the highest purity, both chains derive their names from thealgorithms which return them. The overall vector of perigee parame-ters ~T is obtained by staco in the following form [103]:~T = (C−1ID + C−1MS)−1(C−1ID~TID + C−1MS~TMS), (4.1)where ~Ti and Ci are the vectors of track parameters and their asso-ciated covariance matrices, respectively, obtained from subsystem i.This shows that staco, as its name suggests, performs a statisticalcombination of the ID and MS measurements. The muid approach isto perform a global χ2-minimizing refit across all track hits from bothsubdetectors.• Segment tagged (or, more concisely, tagged) muons are seeded by IDtracks. These tracks are extrapolated to the MS, accounting for energyloss, and a spatially matching tracklet is then sought in the first MSstation. The staco (muid) chain makes use of an algorithm calledmutag (mugirl).The standard muons for ATLAS analyses are those returned by the stacochain. This analysis makes use of combined and tagged staco muons. Thereconstruction efficiency for both types has been measured in a > 99.9%pure sample of Z → µµ decays [104]. As can be seen in figure 4.2 [104],the efficiency is nowhere less than 0.98 in the central region |η| < 2.5. Notethat there are small efficiency differences between the measurement and theMC prediction. As in the electron case, these discrepancies are accountedfor by correcting MC event weights with a scale factor D/MC . The largestsuch discrepancy occurs at η ∼ 1.5 and was caused by a well understoodmis-modeling of the reconstruction efficiency in the ID [104].63η-2.5-2-1.5-1-0.500.511.522.5Efficiency 0.50.60.70.80.91Data, CB+ST muonsMC, CB+ST muonsData, CaloTag muonsMC, CaloTag muonsATLASPreliminaryData 2012, Chain 1 = 8 TeVs -1 L dt = 20.4 fb∫ > 20 GeVTpη-2.5-2-1.5-1-0.500.511.522.5Data/MC 0.9811.02Figure 4.2: η-dependence of the ATLAS muon reconstruction ef-ficiency as measured in Z → µµ decays in both data and simulation.The efficiency is shown for both combined (CB) and tagged (ST) muons.Similarly to electrons, muons of interest are identified with loose, medium,and tight sets of identification cuts for both staco and muid [105]. Thisanalysis adopts the loose working point along with a set of customized iden-tification cuts which will now be described.4.2.2 Additional Selection CutsBaseline MuonsBaseline muons are defined to be loose staco combined or tagged muonssatisfying several additional criteria. The transverse momentum must satisfypT > 10 GeV and the pseudorapidity must obey |η| < 2.40. A numberof pixel and SCT track hit restrictions are then imposed: nb > 0, np >1, nSCT > 5, and nh < 3, where nb is the number of b-layer (an innerlayer of the pixel tracker which improves impact parameter resolution) hits,np is the number of overall pixel hits, nSCT is the number of SCT hits,64and nh is the number of pixel and SCT track holes (i.e. missing expectedmeasurements). TRT outliers are defined to be either isolated straw pulsesor TRT tracks which do not spatially match a track from the pixel andSCT. In this analysis, the following restriction is placed on the TRT outliermultiplicity noTRT :if 0.1 < |η| < 1.9 : n > 5 and noTRT < 0.9nelse if (|η| < 0.1 or |η| > 1.9) and n > 5 : noTRT < 0.9n,where n is the total number of TRT hits including outliers: n = nTRT + noTRT .Note that pT is used for identification here instead of ET as was done forelectrons. The lack of calorimeter information necessitates this. Recallingthe resolutions of the ID and ECal given in chapter 3, it is clear that ETmeasurements are more precise for hard objects and are therefore preferablewhen a choice is available.Signal MuonsAfter overlap removal, signal muons are then required to satisfy additionaltrack quality requirements: |d0|σd0< 3, and |z0 sin θ| < 1 mm. An isolationcut is also imposed: pcone30T < 0.12pT , where pcone30T is vertex corrected:pcone30T → pcone30T −ANv, with A = 10.98 (6.27) MeV in data (MC).4.3 JetsJet reconstruction at ATLAS begins with recognition of topological clusters(topoclusters) in the HCal [102]. These are iteratively constructed clustersin which neighboring calorimeter cells are included if their read-out energiesare significantly larger than the known noise threshold. Topoclusters there-fore have variable size and shape, which differentiates them from the slidingwindow-based clusters of the ECal described in section 4.1.In general, a jet is expected to deposit several topoclusters. With this in65mind, the anti-kt jet clustering algorithm [106] takes all topoclusters froman event as input and returns a set of reconstructed jet objects. This isachieved by defining a metric which incorporates both energy and geomet-rical information:dij ≡ min(E−2T i , E−2Tj) ∆R2ijR2, (4.2)where i, j are cluster indices, and R = 0.4 in this analysis. This metricnaturally clusters soft particles around hard particles. The algorithm thenproceeds by iteratively grouping topoclusters into jets based upon their dijvalues [107].In order to map calorimeter signals to jet energies, it is necessary to performa calibration to determine the jet energy scale (JES). This can be achievedin a number of ways; e.g. by comparing the calorimeter read-out to thetracked momenta of isolated single particles [108]. The JES for the centralregion of the tile calorimeter is known within 4% for jet pT > 20 GeV.A number of identification cuts are applied to the jets in this analysis. Base-line jets are required to satisfy pT > 20 GeV and |η| < 4.5. Overlap removalis then performed. Signal jets are then selected by imposing |η| < 2.5 and arequirement on the jet vertex fraction (JVF). The JVF is a quantity defined,for each jet Ji and vertex Vj , as follows [109]:JVF(Ji, Vj) ≡∑kpT (Tijk )∑n,`pT (T in` ), (4.3)where T ijk is the kth track associated with Ji that has been matched to Vj .In this analysis each signal jet is required to satisfy JVF(Ji,PV)>0.5, wherePV is the primary vertex. This means that at least half of the jet’s trackedpT must be traceable to the PV, which is useful for pile-up suppression.Because they are one of the main products of t quark decays, b-jets areof particular importance to this analysis. To wit, it will be shown later66that vetoing events with > 0 b-jets provides good suppression of t and tt¯SM backgrounds. Identification of b-jets, also called b-tagging, typicallyrelies on the presence of a displaced vertex due to the long lifetimes of Bhadrons. The present analysis uses the MV1 algorithm [110] which identifiesb-jets with 0.85 efficiency; this algorithm passes inputs from other b-taggersinto a neural network. In particular, MV1 receives input from track–based,secondary vertex–based, and shower shape–based taggers. The signal jetkinematic cuts listed above have been chosen in accord with this algorithm’srequirements. MC event weights are corrected with multiplicative b-tagefficiency scale factors derived from data; this is analogous to the leptonreconstruction scale factors described above.4.4 Overlap Removal SchemeSeveral references have been made above to an overlap removal scheme towhich baseline electrons, muons, and jets are subject before the signal ob-jects are defined. The purpose of such a scheme is to mitigate any undesiredduplication between the reconstructed lepton objects or the between theleptons and jets. This procedure will now be described.• If two electrons i and j satisfy ∆Ri,j < 0.1, discard the softest of these.• If an electron and a jet satisfy ∆Re,j < 0.2, discard the jet.• If, after the above e–j overlap removal, a lepton and a jet satisfy∆R`,j < 0.4, discard the lepton.• If an electron and a muon satisfy ∆Re,µ < 0.1, discard them both.4.5 Missing Transverse MomentumConservation of momentum in the transverse plane and the hermetic de-sign of ATLAS imply that a significant imbalance in measured ~pT can beattributed to particles which have escaped the detector—say, neutrinos orperhaps χ˜01. This notion is made more precise by the definition of the missing67transverse momentum two-vector [111]:~/ET = −∑i~p iT , (4.4)where summation is over the set of observed particles. The missing trans-verse momentum3 is then defined to be the norm of this vector/ET =√/E2Tx + /E2Ty.The standard ATLAS definition of this quantity for use in analyses is [112]:~/ET =~/EcaloT +~/EcryoT +~/EµT , (4.5)where the calorimeter term ~/EcaloT describes calorimetric contributions, thecryostat term ~/EcryoT accounts for energy loss in the cryostat material betweenthe ECal and tile calorimeter, and the muon term ~/EµT includes muonic con-tributions. Some comments about these terms will now be made.The calorimeter term has components~/EcaloT = −Ncell∑iEi(sin θi cosφisin θi sinφi)(4.6)where Ei is the energy of the ith calorimeter cell whose angular position isspecified by θi and φi. The sum runs over all cells belonging to calorimeterclusters. Comparing this to equation 4.4 reveals that the ultra-relativisitcapproximation (E ∼ p) is being used to write energies instead of momenta.In the literature these two quantities are therefore often interchangeably la-beled and named with impunity in the context of /ET discussions.More refined calorimeter term measurements are obtained by using infor-mation from reconstructed physics objects. To this end, the term is broken3~/ET is also commonly referred to as the missing transverse energy vector. Its norm isthen also referred to as the missing transverse energy. See also the discussion followingequation 4.668up into object-specific contributions as follows:~/Ecalo,calibT =~/EeT +~/Eµ,caloT +~/EγT +~/EjT +~/ECOT , (4.7)where the superscript calib indicates that contributions of each of theseterms are drawn from the corresponding energy measurements obtained bythe calibrated reconstruction algorithms for each indicated object. Thecalorimeter muon term ~/Eµ,caloT parameterizes the minimum ionization en-ergy deposited by muons in the calorimeters. The so-called cell out term~/ECOT collects cells which were not associated with an object during recon-struction. ~/Ecalo,calibT replaces~/EcaloT in equation 4.5.The muon term in equation 4.5 is simply defined to be the negative sum ofreconstructed muon transverse momenta as measured by the MS:~/EµT = −∑i ~pµ,iT . Note that, as discussed above, pT measurements for iso-lated muons include a correction for calorimeter energy loss. Isolated muons,then, do not make a contribution to ~/Eµ,caloT in equation 4.7.Performance of the missing transverse momentum reconstruction has beenassessed by comparing MC predictions to data [113]. Results from thisstudy are reproduced in figure 4.3; excellent agreement was obtained. Inthe present analysis a baseline cut /ET > 50 GeV is used to avoid knownissues with soft /ET reconstruction [113]. It will be shown in the next chapterthat raising this baseline cut increases sensitivity to SUSY and MUED.69Figure 4.3: Comparison of data and MC simulated missing transversemomentum distributions in Z → µµ decays. The various MC contribu-tions have been weighted by their cross sections and the total numberof events was then normalized to data.70Chapter 5Monte Carlo SimulatedSamplesMonte Carlo simulated samples have been used extensively for SR optimiza-tion and sensitivity estimates. Signal and BG events have been simulatedwith a number of different MC generators; this will be elucidated in thefollowing sections. Realistic simulated datasets must include modeling ofMC-generated particles incident upon ATLAS. In all cases this has beenperformed with the GEANT4 detector simulation software [114]. Note thatthe same reconstruction algorithms which were described in chapter 4 areused for data and MC. The samples described in this section have also beenused to estimate the SM BG and statistically interpret the analysis; theseconsiderations will be explored in later chapters.5.1 BackgroundIt is of critical importance to understand and model all SM processes whichcan lead to the desired 3`+ /ET final state. Note that this includes processeswhich may include mis-identified leptons which are considered “fake” in thisanalysis (see chapter 7). Some basic properties of the relevant BG samplesare catalogued here.71Diboson modeling includes pp→ WZ/γ∗ → 3`ν, pp→ ZZ/γ∗ → 4`, 2`2ν1,and pp → WW → 2`2ν. All of these are modeled with SHERPA [115],and the resulting LO cross sections are scaled to NLO with MCFM [116]–based K-factors K = σNLOMCFM/σLOSHERPA. For WZ, e.g., the result isK ∼ 10.24 pb/9.75 pb ∼ 1.05.Top–anti-top pair production (tt) samples have been generated with POWHEG[117] and were normalized LO→NNLO with HATHOR [118]: 210.8→238.1 pb.Parton showering was modeled with PYTHIA [58].Triboson (WWZ, etc.) production was simulated with MadGraph 5 [119].Single top simulation was performed with MC@NLO [120] and AcerMC [121].All ttV j and V j samples have been generated with ALPGEN (except Mad-Graph ttWW ). Showering was performed in PYTHIA for all of these sam-ples.The CT10 [122] parton distribution function (PDF) set has been utilized forall SHERPA, POWHEG, and MC@NLO samples. The CTEQ6L1 set wasused for MadGraph and ALPGEN samples.5.2 SignalSUSYThe various SIM parameters were described in section 2.3.2. Herwig++ [123]has been used to generate all SIM via ˜`and SIM via WZ samples, and NLOcross sections were obtained from PROSPINO [76]. The CTEQ6L1 PDFset has been utilized.1The γ∗ will be dropped henceforth.72MUEDAll MUED samples were generated at LO with Herwig++ and CTEQ6L1;NLO cross sections are not available.5.3 Correction Factors for Simulated SamplesIn addition to the lepton reconstruction scale factors and b-tagging scalefactors described in chapter 4, two further corrections are applied to allMC samples. The first such correction accounts for the effects of pile-upinteractions. Recalling figure 3.2, it can be seen that the average num-ber of pp interactions per bunch crossing was 〈µ〉 = 20.7 in 2012 ATLASdata [91]. As previously discussed, the vast majority of these interactionsare minimum bias or QCD. This implies that when a hard scattering event istriggered and stored, ATLAS will also typically detect and record productsof several unrelated inelastic scattering events which happen to be takingplace at this time. This effect is known as pile-up, and it includes contribu-tions from within the hard bunch crossing (“in-time”) and from temporallynearby bunch crossings (“out-of-time”). Each MC event in a given sampleis reweighted with a scale factor such that the 〈µ〉 distribution agrees withthat observed in data.The ATLAS trigger system cannot, of course, be applied to MC events. Itis therefore necessary to pass MC samples through a software simulationof the trigger. Differences between the efficiencies of the trigger applied todata and its simulation applied to MC give rise to the final event-wise MCcorrection needed for this analysis2: TD/TMC , where the trigger efficienciesare defined asTD,MC =NpassNpass +Nfail∣∣∣∣D,MC. (5.1)2The values of this scale factor are obtained with a tag-and-probe technique appliedto Z → `` events; they typically reflect a 1-2% difference between data and MC.73Chapter 6Signal Region DefinitionsAfter selecting objects as described in chapter 4, the next project is to designa set of criteria for selecting full events. Since this is a blind analysis, theselection must be rigorously specified before comparing predictions to data.In order for a selection, called a signal region (SR), to be desirable, it shouldbe defined in such a way so as to preferentially select signal-like events.Selections with this property are said to have good “sensitivity” to newphysics scenarios. A means of quantitatively comparing and subsequentlyoptimizing the statistical significance of candidate SRs is therefore necessary.In this chapter, the optimization program and resulting signal regions willbe described in detail. The expected sensitivity will also be estimated.6.1 Baseline Event SelectionA number of standard cuts pertaining to data quality, trigger and detectorperformance, and other technical considerations are used in this analysis.These “baseline” cuts are described in this section. Most of the baselinecut thresholds were previously optimized for the 2 fb−1 ATLAS EW SUSYtrilepton analysis in 2010 [1].Table 6.1 shows the list of trigger chains used to select data events in thisanalysis. The chains are also used for the software trigger simulation dis-74cussed previously. A selected event must pass at least one of these chains.The pT thresholds given in table 6.1 ensure that the leptons are in the highefficiency (80-100%) “plateau” region of the turn-on curve for that particularchain. Signal leptons in a selected event must match the triggering lepton(s)to within ∆R < 0.15. The technical trigger chain names provide convenientencapsulations of the chain properties. For example, EF mu24i tight indi-cates the presence of a tight muon with pT > 24 GeV at the event filterlevel; the “i” denotes isolation.Table 6.1: Trigger chains used in this analysis. The explicit technicalnames and the offline pT thresholds are provided.Lepton flavor(s) Chain name Offline pT cut (GeV)Single isolated e EF el EF e24vhi medium1 25Single isolated µ EF mu24i tight 25Double eEF 2e12Tvh loose1 14,14EF e24vh medium1 e7 medium1 25,10Double µEF 2mu13 14,14EF mu18 tight mu8 EFFS 18,10Combined eµEF e12Tvh medium1 mu8 14,10EF mu18 tight e7 medium1 18,10Stable LHC beam conditions and good subsystem performance across AT-LAS cannot be taken for granted. If these conditions are satisfied duringa given data collection period, the events are recorded on a good runs list(GRL). Data events selected in this analysis must be part of the GRL cor-responding to the 2012 dataset.A set of quality control cuts are employed to further reduce events featur-ing instrumental or otherwise undesired effects. Cosmic muons are removed75by discarding events with muons satisfying |d0| > 0.2 mm or |z0| > 1 mm.Events containing a muon with a large track curvature uncertainty (σq/p|q/p| ≥0.2) are discarded. If the PV of an event has <5 associate tracks, the eventis cut away. Calorimeter quality cuts include avoiding cells which are knownto be malfunctioning, disregarding events with significant LAr noise, and ig-noring corrupted data. Spurious jets are known to arise from three sources:LHC beam anomalies, calorimeter noise spikes, and cosmic rays. These canbe identified by their LAr pulse shapes and the energy fraction deposited inthe various calorimeter systems.Because all signal scenarios considered in this analysis produce a SFOClepton pair in the final state, events without such a pair are ignored. Asignificant background due to Drell-Yan, J/ψ (m ∼ 3.1 GeV), and Υ (m ∼9.5 GeV) is present at low dilepton invariant mass. Therefore, events withany SFOC lepton pair satisfying mSFOC < 12 GeV are removed.The final baseline cut is the requirement of exactly 3 signal leptons. Thesecan be electrons, muons, or both. Leptonic tau decays are automaticallyincluded by the electron and muon reconstruction algorithms. Hadronic taudecays are not included; these will be considered in a planned update of thisanalysis which is in preparation at the time of this writing.6.2 Event Selection OptimizationThis section presents the full optimization of the key selection criteria whichare used to define the signal regions. The general strategy and figure of meritwill first be described. The explicit optimization will then be presented.6.2.1 StrategyThe goal is to design series of cuts which will mitigate SM backgrounds whileretaining good sensitivity to both SIM types and MUED. For simplicity, allSM processes are estimated purely from MC for this purpose. Appendix Adescribes the particulars of this estimate. The full BG estimate technique76is the subject of chapter 7.Note that the mass splitting between the LSP and the next-lightest neu-tralino (or, equivalently, the lightest chargino) ∆m21 = mχ˜0,±2,1−mχ˜01 charac-terizes the amount of phase space available to all final state particles in bothSIM scenarios. This observation, when coupled with the fact that χ˜02 candecay both via on-shell Z (mZ ∼ 91.2 GeV) and non-resonantly via off-shellZ or ˜`, will be seen to warrant definition of several signal regions which eachtarget complementary kinematic regimes of the SIM parameter spaces. Inparticular, it will be seen to be beneficial to consider signal regions both onand off the Z mass shell. Within each of these, kinematic cuts of varyingtightness can be used to obtain the desired sensitivity.MUED cascades are phenomenologically similar to SIM, with W±1 Z1 playinga role analogous to χ˜±1 χ˜02. The optimization logic is therefore similar, butthere is one noteworthy difference: the MUED cascades of interest in thisanalysis often produce hard jets (recall figure 2.6). A specialized SR will bedeveloped to exploit this feature.These considerations will be made more concrete when the optimizationvariables are presented explicitly in the next subsection. It is first necessary,however, to describe the figure of merit which is used to compare candidatecut thresholds.Recall that a p-value is the probability, under the null hypothesis (which inthis analysis is the SM), of obtaining experimental results at least as extremeas those observed. In high energy physics, it is canonical to instead reportthe number of standard deviations at which evaluation of the complementarystandard normal cumulative distribution function (CDF) would give p (orp/2 for a two-tailed hypothesis test). This is often called the statisticalsignificance:ZN =√2erf−1(1− 2p), (6.1)77where erf(x) is the error function. Note that this formula must be modifiedslightly for a two-tailed test, but in this analysis a one-tailed test is used.Exclusion at the 95% confidence level (CL), i.e. p = 0.05, therefore corre-sponds to ZN ∼ 1.64. The full statistical machinery which will later be usedto translate the results of this analysis into statistical significances is com-plex and computationally intensive. It is therefore desirable at this point toadopt a more pragmatic approach which can easily provide an approximatesignificance suitable for optimization.A simple Bayesian technique incorporating approximate systematic uncer-tainties can be used for this purpose [124]. In this formulation, an averagep-value is constructed by weighting conventional Poisson p-values with Bayesposteriors:pβ =∫ ∞0dB PP (D|B) pb(B|〈B〉), (6.2)where 〈B〉 is the background prediction, PP is a (complementary) PoissonCDF, D is the observed event count in data, and pb is the posterior. As-suming pb is a truncated normal distribution with standard deviation ∆Band a lower bound at B = 0, the approximate p-value becomespβ =∫ ∞0dB[1−Γ(bD + 1c, B)bDc!]exp[−(B − 〈B〉)22∆B2]√2pi∆B[1− Φ(−〈B〉∆B)] , (6.3)where Γ is the incomplete gamma function, and Φ is the standard normalCDF. In the following subsection, ZN will be approximated by using pβ inequation 6.1. 〈B〉 will be estimated from MC and ∆B = 0.3×〈B〉. It will beseen later that 30% is a reasonable uncertainty assumption for the purposesof benchmarking. To assess the sensitivity to new physics, the “data obser-vation” will be set to the expected total MC yield of signal and background:D = 〈S〉+ 〈B〉.Note that the baseline event selection attains approximate significances on78the order ZN . 0.03 for typical SIM benchmark points. This clearly illus-trates the necessity of further optimization.6.2.2 Threshold DeterminationEach analysis variable will be introduced in this section. Optimal cuts oneach variable were obtained by locally maximizing the approximate ZN . Anexample of this procedure is shown in figure 6.1. Background and signaldistributions will be shown for each variable.jMinimum N0 1 2 3 4 5 6 7 8 9 10 SM)∆ (30% NZ0123456789MUED (800,3) GeVMUED (700,3) GeVMUED (700,10) GeVMUED (700,40) GeVMUED (800,10) GeVMUED (800,40) GeVMUED (900,3) GeVMUED (900,10) GeVMUED (900,40) GeVMUED (1000,40) GeVMUED (1100,40) GeVATLAS Work in ProgressFigure 6.1: The approximate significance as a function of the lowerjet multiplicity Nj threshold is shown for several MUED model points.It is seen that requiring Nj ≥ 3 maximizes the significance.Multiplicity of b-JetsThe contribution from tt can be greatly reduced by vetoing events withat least one b-jet. The multiplicity of b-jets after the baseline selection is79displayed in figure 6.2Number of bjets0 1 2 3 4 5 6 7 8 9 10Events1101102103104101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMV + jetsWZZZtt VtttTribosonWWsm sleptons 500,0sm Z,W 250,0ATLAS Work in ProgressSIM sle s ( )SIM WZ (250,0)Figure 6.2: The b-jet multiplicity distribution is shown for the BGand representative signal points. All backgrounds are stacked and theuncertainties indicated are statistical only. The plots include all eventspassing the baseline selection.Z Mass WindowThe post-b-veto distribution of SFOC dilepton invariant mass is shown infigure 6.3. In events with multiple SFOC pairs, the SFOC mass nearestto mZ = 91.2 GeV is chosen. Note that the via WZ signal exhibits aresonant peak around the Z mass, whereas the via ˜` distribution does not.This suggests that the SRs should be broadly classified by whether theyreject (SRnoZ-type) or request (SRZ-type) a Z boson. Good performanceis obtained with a window mZ ± 10 GeV, but additional cuts will be placedon this variable below.80 [GeV]SFOSm0 50 100 150 200 250 300Events1101102103104101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMV + jetsWZZZttTribosontVttWWsm sleptons 500,0sm Z,W 250,0ATLAS Work in ProgressSIM sle s ( )SIM WZ (250,0)Figure 6.3: Values of mSFOC nearest to mZ are plotted after thebaseline selection and b-veto.Missing Transverse MomentumMissing transverse momentum, as defined in section 4.5, is expected to begenerated by the LSPs, LKPs, and neutrinos. /ET distributions for SRnoZ-type and SRZ-type regions are shown in figure 6.4. From this figure it can beseen that several /ET cuts are needed for sensitivity to various signal points inSRnoZ-type regions. Placing lower bounds at 50 GeV and 75 GeV gives thebest performance. SRZ-type SRs also require multiple /ET cuts. Figure 6.4indicates that using two bins 75< /ET <120 GeV and /ET >120 GeV is agood choice.SFOC Invariant MassTo further optimize the Z rejection window in SRnoZ-type regions, themSFOC distributions after the b-veto, 10 GeV Z-veto, and /ET > 50 GeV81or /ET > 75 GeV are respectively shown in figure 6.5. These distributionssuggest that the region above mZ is not sensitive for via WZ signal points,so requiring mSFOC < 81.2 GeV will be beneficial for these. To differentiatebetween low and intermediate mass regimes, it is helpful to place anotherbin edge at mSFOC = 60 GeV. High-mSFOC sensitivity for the via ˜` pointin figure 6.5 is preserved by defining one SRnoZ-type region which retainsthe high mSFOC tail.Transverse MassTransverse mass is useful for signal discrimination in cases where an invisiblefinal state particle is present. The definition used in this analysis is [111]:mT =√2p`T /ET [1− cos(φ` − φ/ET )], (6.4)where ` is defined to be the hardest lepton which does not enter into calcula-tion of the best Z mass. When defined in this way, the transverse mass givesa useful way to approximately reconstruct the W mass. Because it dependson both lepton kinematics and missing transverse momentum, this variablegives good discrimination for signal points with large mass splittings. Thisis shown explicitly in figure 6.6, and it is seen that mT > 110 GeV is anoptimal cut. Signal points with smaller mass splittings tend to be slightlymore sensitive at lower mT , so an orthogonality restriction mT < 110 GeVis used for these. As can be seen in figure 6.7, this same bin edge works wellin SRZ-type regions.Lepton Transverse MomentumCutting on the momentum of the sub-sub-leading lepton provides goodsensitivity to large mass-gap scenarios. This is shown in figure 6.8 forevents satisfying the baseline, b-veto, 10 GeV Z-veto, /ET > 75 GeV, andmT > 110 GeV. A cut p3T > 30 GeV is seen to give good sensitivity.82MUED: JetsIt was mentioned previously that the phenomenological similarity betweenSIM and MUED implies a similar optimization logic. The above approachtherefore applies to MUED as well. The presence of hard jets in MUED cas-cades of interest, though, gives an additional handle for optimization studieswhich will be discussed in this subsection.The mSFOC distribution after applying the baseline, a b-veto, 10 GeV Z-veto, and a preliminary missing transverse momentum cut /ET > 75 GeVis shown in figure 6.9. A window 20< mSFOC <81.2 GeV gives the bestperformance.The jet multiplicity distribution after applying the baseline, b-veto, 20<mSFOC <81.2 GeV, and a preliminary cut /ET > 75 GeV is shown in fig-ure 6.10. It is seen that requiring Nj ≥ 3 is optimal. This can be understoodby recalling table 2.1. The leading two-jet q∗q∗ production modes can beassociated with additional initial state radiation (ISR) jets, and the sub-leading q∗g∗ modes always have ≥3 jets.A /ET lower threshold significance scan at the baseline, b-veto, 20< mSFOC <81.2 GeV, and Nj ≥ 3 stage is shown in figure 6.11. Requiring /ET >120 GeV yields high significance for most points.83 [GeV]missTE0 50 100 150 200 250 300 350 400 450Events1101102103104101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMV + jetsZZWZttTribosontWWVttsm sleptons 500,0sm Z,W 250,0ATLAS Work in ProgressSIM sle s ( )SIM WZ (250,0)(a) [GeV]missTE0 50 100 150 200 250 300 350 400 450Events1101102103104101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZV + jetsZZttTribosonVtttWWsm Z,W 150,50sm Z,W 100,0sm Z,W 125,25ATLAS Work in ProgressSIM WZ (150,50)SIM WZ (1 0, 0)SIM WZ (125,25)(b)Figure 6.4: The /ET distributions for events passing baseline, b-veto,and 10 GeV Z-veto (a), and baseline, b-veto, and Z-request (b).84 [GeV]SFOSm0 50 100 150 200 250 300Events3102101101102101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZZZV + jetsttTribosontWWVttsm sleptons 500,0sm Z,W 250,0ATLAS Work in ProgressSIM sle s ( )SIM WZ (250,0)(a) SRnoZ-type: /ET > 50 GeV [GeV]SFOSm0 20 40 60 80 100 120 140 160 180 200Events3102101101102101 L dt = 20.7 fb∫ = 8 TeVs Total SMWZttZZTribosontWWVttV + jetssm Z,W 150,62.5ATLAS Work in ProgressSIM WZ (150,62.5)(b) SRnoZ-type: /ET > 75 GeVFigure 6.5: The mSFOC distribution for events passing the baseline,b-veto, 10 GeV Z-veto, and /ET > 50 GeV (a) or /ET > 75 GeV (b).85 [GeV]Tm0 50 100 150 200 250Events3102101101102101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZttZZTribosontWWVttV + jetssm sleptons 500,0sm Z,W 250,0ATLAS Work in ProgressSIM sle s ( )SIM WZ (250,0)Figure 6.6: The mT distribution for events satisfying the baseline,b-veto, 10 GeV Z-veto, and /ET > 75 GeV.86 [GeV]Tm0 20 40 60 80 100 120 140 160 180 200 220Events2101101102101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZV + jetsZZtttTribosonVttWWsm Z,W 150,50sm Z,W 100,0sm Z,W 125,25ATLAS Work in ProgressSIM WZ (150,50)SIM WZ (1 0, 0)SIM WZ (125,25)(a) [GeV]Tm0 20 40 60 80 100 120 140 160 180 200 220Events3102101101102101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZZZttTribosonVttWWsm Z,W 150,50sm Z,W 100,0sm Z,W 125,25ATLAS Work in ProgressSIM WZ (150,50)SIM WZ (1 0, 0)SIM WZ (125,25)(b)Figure 6.7: The mT distributions the baseline, b-veto, 10 GeV Zrequest, and 75 < /ET < 120 GeV (a), or /ET > 120 GeV (b).87 [GeV]TSubsubleading lepton p0 20 40 60 80 100 120 140Events3102101101101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZttTribosonZZWWVttsm sleptons 500,0sm Z,W 250,0ATLAS Work in ProgressSIM sle s ( )SIM WZ (250,0)Figure 6.8: The p3T distribution for events satisfying the baseline,b-veto, 10 GeV Z-veto, /ET > 75 GeV, and mT > 110 GeV.88 [GeV]SFOCm0 20 40 60 80 100 120 140 160 180 200Events2101101102101 L dt = 20.7 fb∫ = 8 TeVs Total SMWZttZZTribosontWWVttV + jetsMUED 700,40MUED 800,40MUED 900,40MUED 1000,40MUED 1100,40MUED 1200,40ATLAS Work in ProgressFigure 6.9: The mSFOC distribution for events passing the baseline,b-veto, 10 GeV Z-veto, and /ET > 75 GeV.89jN0 2 4 6 8 10 12 14Events2101101102101 L dt = 20.7 fb∫ = 8 TeVs Total SMWZttZZTribosonVttWWV + jetstMUED 700,40MUED 800,40MUED 900,40MUED 1000,40MUED 1100,40MUED 1200,40ATLAS Work in ProgressFigure 6.10: The Nj distribution for events passing the baseline, b-veto, 20 < mSFOC < 81.2 GeV, and /ET > 75 GeV. The significancescan corresponding to this distribution was shown in figure 6.1.90 threshold [GeV]missTE50 100 150 200 250 SM)∆ (30% NZ0123456789MUED (800,3) GeVMUED (700,3) GeVMUED (700,10) GeVMUED (700,40) GeVMUED (800,10) GeVMUED (800,40) GeVMUED (900,3) GeVMUED (900,10) GeVMUED (900,40) GeVMUED (1000,40) GeVMUED (1100,40) GeVATLAS Work in ProgressFigure 6.11: A significance scan at the baseline, b-veto, 20<mSFOC <81.2 GeV, and Nj ≥ 3 stage.916.3 Event Selection SummaryA set of SRnoZ-type and SRZ-type SRs have now been described. Thesehave been made orthogonal1 to facilitate a statistical combination of theresults (see chapter 8). Within each SR type, levels of tightness are conve-niently labeled with Roman letters a, b, c, and d. The SRs are summarizedin table 6.2.Table 6.2: Summary of the signal region definitions. All regions re-quire the baseline selection (notably `+SFOC) and a b-veto. Note thatSRnoZc events are removed from all other SRnoZ-type regions to ensureorthogonality.SR mSFOC (GeV) /ET (GeV) mT (GeV) p3T (GeV) Nj ⊥ vetoSRnoZa < 60 >50 – >10 – !SRnoZcSRnoZb (60, 81.2) >75 – >10 – !SRnoZcSRnoZc /∈ (81.2, 101.2) >75 >110 >30 – –SRnoZd (20, 81.2) >120 – >10 ≥ 3 !SRnoZcSRZa (81.2, 101.2) (75, 120) < 110 >10 – –SRZb (81.2, 101.2) (75, 120) > 110 >10 – –SRZc (81.2, 101.2) >120 >110 >10 – –The set of variables used for optimization in the previous section was{Nb,mSFOC , /ET ,mT , p3T , Nj}. This set was found to be complete in thesense that adding further variables did not improve the sensitivity.6.4 Approximate Expected SensitivityThis section presents the expected sensitivity estimate for all signal pointsin their most sensitive SRs. This will serve as a benchmark to assess theperformance of the full statistical interpretation described in chapter 8.Figure 6.12 shows that the best bulk sensitivity for SIM via ˜` is obtained1Two SRs are said to be “orthogonal” if their definitions prevent them from containingany of the same events.92with the tight cuts of SRnoZc. Complementary sensitivity to the compressedscenarios is added with the looser cuts of SRnoZa. Sensitivity is expectedto extend as high as mχ˜±,01,2∼ 700 GeV.On the other hand, figures 6.13 and 6.14 illustrate that sensitivity to SIMvia WZ is more complex, requiring both SRnoZ- and SRZ-type regions.The best bulk sensitivity, again obtained by exploiting the additional phasespace, comes from SRZb and c. Low mass, compressed, and sub-diagonal(∆m21 ∼ mZ) sensitivity are variously obtained with SRZa, SRnoZa, andSRnoZb. These SRs are seen to give expected sensitivity up to mχ˜±,01,2∼300 GeV.The most powerful region for MUED is the specialized SRnoZd. As can beseen in figure 6.15, sensitivity slightly past R−1 ∼ 1 TeV is expected at highΛR.93 [GeV]±1χ∼m0 100 200 300 400 500 600 700 [GeV] 0 1χ∼m050100150200250300350400450500 N020406080100120140 NATLAS Work in Progress l~SIM via (a) SRnoZa [GeV]±1χ∼m0 100 200 300 400 500 600 700 [GeV] 0 1χ∼m050100150200250300350400450500 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress l~SIM via (b) SRnoZa [GeV]±1χ∼m0 100 200 300 400 500 600 700 [GeV] 0 1χ∼m050100150200250300350400450500 N020406080100120140 NATLAS Work in Progress l~SIM via (c) SRnoZc [GeV]±1χ∼m0 100 200 300 400 500 600 700 [GeV] 0 1χ∼m050100150200250300350400450500 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress l~SIM via (d) SRnoZcFigure 6.12: Expected signal yields (left) and corresponding approxi-mate significances (right) are shown for SIM via ˜` in SRnoZa (top) andSRnoZc (bottom). All yields have been scaled to 20.7 fb−1.94 [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 N05101520253035404550 NATLAS Work in Progress SIM via WZ(a) SRnoZa [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress SIM via WZ(b) SRnoZa [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 N05101520253035404550 NATLAS Work in Progress SIM via WZ(c) SRnoZb [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress SIM via WZ(d) SRnoZbFigure 6.13: Expected signal yields (left) and corresponding approxi-mate significances (right) are shown for SIM via WZ in SRnoZa (top),and SRnoZb (bottom). All yields have been scaled to 20.7 fb−1.95 [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 N05101520253035404550 NATLAS Work in Progress SIM via WZ(a) SRZa [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress SIM via WZ(b) SRZa [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 N05101520253035404550 NATLAS Work in Progress SIM via WZ(c) SRZb [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress SIM via WZ(d) SRZb [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 N05101520253035404550 NATLAS Work in Progress SIM via WZ(e) SRZc [GeV]±1χ∼m0 100 200 300 400 500 [GeV] 0 1χ∼m0100200300400500 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress SIM via WZ(f) SRZcFigure 6.14: Expected signal yields (left) and corresponding approx-imate significances (right) are shown for SIM via WZ in SRZa (top),SRZb (middle), and SRZc (bottom). All yields have been scaled to20.7 fb−1.96 ) [GeV]1γ ≈ (1R700 800 900 1000 1100 1200 1300 RΛ510152025303540 N051015202530354045 NATLAS Work in Progress MUED(a) SRnoZd ) [GeV]1γ ≈ (1R700 800 900 1000 1100 1200 1300 RΛ510152025303540 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress MUED(b) SRnoZdFigure 6.15: Expected signal yields (a) and corresponding approxi-mate significances (b) are shown for MUED in SRnoZd. All yields havebeen scaled to 20.7 fb−1.97Chapter 7Standard Model BackgroundEstimateThis chapter gives a description of the methodology used to estimate theSM background in each SR. A wide variety of uncertainties associated withthis estimate are described and calculated. Comprehensive validation of theestimate is also presented.7.1 OverviewSM backgrounds can be classified as either irreducible or reducible. Irre-ducible BGs are those which contribute three real final state leptons, whereasreducible BGs rely on the presence of at least one “fake” lepton to produce3` + /ET . In this analysis, a real lepton is a prompt lepton from W , Z, orτ decays, whereas fake leptons are defined to be those due to jets—heavy(HF) and light flavor (LF)1—or from photon conversions. The irreducibleBGs are therefore WZ, ZZ, ttV , and triboson. Reducible BGs are tt, singlet, WW , and V j. Feynman diagrams for the two leading backgrounds, WZand tt, are shown in figure 7.1.1The “heavy” quark flavors in this analysis are b and c. Note in particular that leptonsoriginating from semileptonic heavy flavor decays are defined to be fake leptons in thisanalysis.98qqW WZLLL(a)ggttWWLbbL(b)Figure 7.1: Feynman diagram examples of the two leading BGs inthis analysis: s-channel WZ (a) and gluon fusion tt (b).The purely MC-based BG estimate which was used for optimization in chap-ter 6 does not distinguish between irreducible and reducible contributions;this technique is also used for the SRnoZd estimate and is described inappendix A. The estimate in all other SRs utilizes a more sophisticateddata-driven approach called the matrix method for the reducible BG, withirreducible contributions again estimated from MC. Both the matrix methodand MC-based estimates are associated with a number of uncertainties, andall of these are profiled as properly correlated nuisance parameters. The sig-nal regions are blinded to prevent bias. It is therefore necessary to validatethe BG estimate in a set of minimally orthogonal validation regions (VRs).All of these considerations are explored in detail in the proceeding sections.7.2 Reducible Background Estimate: The MatrixMethodThe reducible background component is estimated with a data-driven ma-trix technique [125] which is described in this section. The method is basedon the idea that, statistically speaking, real and fake leptons can be dif-ferentiated by their identification quality. A system of equations relating99kinematic lepton properties and the real–fake composition can be writtendown:NssNsbNbsNbb=12 1f2 f12 f1f21(1− 2) 1(1− f2) f1(1− 2) f1(1− f2)(1− 1)2 (1− 1)f2 (1− f1)2 (1− f1)f2(1− 1)(1− 2) (1− 1)(1− f2) (1− f1)(1− 2) (1− f1)(1− f2)NRRNRFNFRNFF,(7.1)where the various symbols are defined as follows:• NRR is the number of events wherein the sub-leading and sub-sub-leading leptons are real. NRF is the number of events wherein thesub-leading lepton is real and the sub-sub-leading lepton is fake, etc.Note that these yields are understood to be comprised of events withbaseline leptons. Note also that only a 4-dimensional column vector(and therefore 4×4 matrix rather than the expected 8×8) is requiredbecause the leading lepton was found to be R in & 99% of all selectedevents; two examples are shown in figure 7.2.• Nss is the number of events wherein the sub-leading and sub-sub-leading leptons are signal leptons2. Nsb is the number of events whereinthe sub-leading lepton is signal and the sub-sub-leading lepton is base-line and not signal, etc.• i is the identification probability (“efficiency”)—i.e. the probabilitythat a R baseline lepton passes the signal lepton requirements. Anindex is included because will generally be pT - and η-dependent, andtherefore 1,2 will assume different values according to the kinematicproperties of the sub- and sub-sub-leading leptons.• fj is the misidentification probability (“fake rate”)—i.e. the probabil-ity that a F baseline lepton passes the signal lepton requirements.2Note that Nss is the data observation of interest in the region to which the matrixmethod is being applied. If the region is a SR, Nss is the observed SR yield in data andtherefore must be blinded.100The vector components on the LHS of equation 7.1 are known by construc-tion. As will be described in the following subsections, all entries of thematrix can be measured. Therefore the real–fake composition can be ob-tained by performing a matrix inversion. When this is done, the reduciblebackground estimate is obtained in the following form:NRF +NFR +NFF =1(1 − f1)(2 − f2)[(12 − 1f2 − f12 + f1 + f2 − 1)Nss+ (12 − 1f2 − f12 + f2)Nsb + (12 − 1f2 − f12 + f1)Nbs+ (12 − 1f2 − f12)Nbb].(7.2)It was mentioned above that NRR,FR,RF,FF were assumed to reflect eventscontaining baseline leptons. This was necessary to be able to write down thesystem of equations in equation 7.1 in the first place. The event selectionused for the analysis, however, requires all leptons to pass the signal cuts.Equation 7.2 must therefore be scaled by the efficiencies and fake rates toobtain the final reducible BG estimate:Nred = 1f2NRF + f12NFR + f1f2NFF . (7.3)In addition to pT - and possibly η-dependence, fake rates generally exhibitdependence on the lepton flavor (` = e, µ), the fake type (LF, HF, con-version), and the type of SM process giving rise to the fake (top or gaugeboson). In a region X, then, the fake rate can be written as a weightedaverage:f `X =∑i,jsf i`RijX,`fij` , (7.4)where i (j) is an index encoding the fake type (BG process type), sf i` is ascale factor which accounts for data–MC discrepancies, RijX,` is the fractionof fakes of type i which are seeded by process j, and f ij` is the i-from-jfake rate. RijX,` and fij` are computed from MC simulations, while sfi` isderived from both data and MC. MC-derived weighted average efficienciesare similarly corrected with a data-driven scale factor. Measurements of the101various scale factors are presented in the following subsections.7.2.1 EfficienciesThe efficiency computation proceeds via a standard tag-and-probe tech-nique. An enriched sample of Z → `` is selected by enforcing the baselineevent selection and the presence of a SFOC baseline lepton pair satisfyinga 10 GeV Z-request. A “tag” lepton is identified by matching one of thesebaseline leptons to a single lepton trigger from table 6.1 and requiring that itpasses the signal lepton selection criteria. The efficiency is then obtained bycalculating the frequency with which the remaining “probe” lepton satisfiesthe signal criteria. If an event possesses two tags, both are counted as suc-cessful probes. The scale factor sf ` is defined to be the ratio of efficienciesobtained from data and MC; it is then applied to MC–derived cross sectionweighted average efficiencies in each SR.Efficiencies have been binned in pT , |η|, and the vertex multiplicity. Nosignificant dependence on any of these quantities has been observed. Asa representative example, figure 7.3 shows the pT -binned muon efficiencyand scale factor in data and MC. The final efficiency scale factors used inthe analysis are sf e = 0.996 ± 0.001 and sfµ = 0.995 ± 0.001, where theuncertainties are statistical.7.2.2 Fake Rate Scale FactorsThe fake rate measurements use the same general tag-and-probe strategythat was used for the efficiency scale factor measurements. Samples heavilyenriched in LF, HF, and conversions, respectively, are selected. High qualitytag leptons are then identified and used to test the baseline→signal proba-bility for fake probes.Figure 7.4 displays a representative selection of results. As was done forthe efficiencies, the results were binned in pT , |η|, and vertex multiplicity.As figure 7.4 suggests, no significant dependence on these quantities was102observed within uncertainties. Average scale factors have therefore beenused: sfLF` = 1.0 ± 0.1, sfHFe(µ) = 0.75 ± 0.05 (0.86 ± 0.03), and sfCe =1.22± 0.27. The uncertainties are discussed in the next section.103RealFakeEvents2101101102101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZV + jetsZZttTribosonWWtVttATLAS Work in Progress(a) SRnoZaRealFakeEvents3102101101102101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalTotal SMWZZZTribosonttVttWWATLAS Work in Progress(b) SRZcFigure 7.2: The leading lepton real–fake composition in SRnoZa (a)and SRZc (b).104 [GeV]TMuon p10 20 30 40 50 60 70 80 90 100Real Muon Efficiency0.860.880.90.920.940.960.981 DataMCATLAS Work in Progress(a) Efficiency / ndf 2χ 117.1 / 3p0 0.0001± 0.9979 [GeV]TMuon p10 20 30 40 50 60 70 80 90 100Scale Factor00.20.40.60.811.21.41.61.82 ATLAS Work in Progress(b) Scale factorFigure 7.3: Muon baseline→signal identification efficiency (a) andscale factor (b). Both are binned in pT .105 [GeV]TElectron p10 20 30 40 50 60 70 80 90 100HF Fake Rate00.10.20.30.40.50.60.70.80.91 DataMCATLAS Work in Progress(a) Fake rate: HF / ndf 2χ 0.7033 / 3p0 0.0484± 0.7462 [GeV]TElectron p10 20 30 40 50 60 70 80 90 100Scale Factor00.20.40.60.811.21.41.61.82 ATLAS Work in Progress(b) Scale factor: HF|η|0 0.5 1 1.5 2 2.5 3Fake rate00.050.10.150.20.250.30.350.40.450.5Data 2012Total MC SM = 8 TeVs 1L dt = 20.7 fb∫ATLAS Work in Progress(c) Fake rate: conversions|η|0 0.5 1 1.5 2 2.5 3Scale factor0.60.811.21.41.61.822.22.4 = 8 TeVs 1L dt = 20.7 fb∫ATLAS Work in Progress(d) Scale factor: conversionsFigure 7.4: Fake rates (left) and scale factors (right) for electronsfrom HF (top) and conversions (bottom). The HF plots are binned inelectron pT , and the conversion plots are binned in electron |η| withpeT > 15 GeV.1067.3 Sources of UncertaintyThis section contains a breakdown of all sources of uncertainty associatedwith the irreducible and reducible BG estimates. As will be explained inchapter 8, the statistical interpretation involves profiling all uncertainties asa set of potentially correlated Gaussian nuisance parameters. The percent-ages quoted in this section therefore describe the shift in the yield when agiven systematic is varied by ±1σ around its nominal central value.7.3.1 Uncertainties on Irreducible BackgroundsAll uncertainties considered for the MC-based irreducible BG estimate areshown in tables 7.1 through 7.3. Note that the typical total uncertaintyis roughly 30%. This tends to be dominated both by the statistical uncer-tainty from MC as well as several systematics—notably the generator choiceand cross section. Descriptions of all irreducible uncertainties will now beprovided.Stastical uncertainty arises from the finite size of the MC samples used forthe estimate. As explained in appendix A, this uncertainty is taken to bethe quadrature sum of the squares of the MC weights.WZ cross section systematics are calculated by quadrature-adding the un-certainty on the ATLAS cross section measurement [126] and the differencebetween this measurement and the NLO MCFM prediction; this proceduregives an uncertainty of 9%⊕ 8% = 12%. A 5% uncertainty is applied to theZZ cross section based upon an ATLAS measurement [126]. The theoreticalttV cross section uncertainty has been estimated to be 30% by Kardos etal. [127]. A conservative cross section systematic of 10% is applied to reflectthe absence of experimental cross section measurements for tribosons.To quantify the effect of the choice of MC generator on the leading irre-ducible WZ and ZZ backgrounds, a comparison has been made betweenSHERPA and POWHEG. The procedure involves scaling POWHEG to107SHERPA (the latter being treated as the central value) after the pre-selectionand lepton multiplicity cuts. The resulting difference in yields is thenquadrature-added to the (scaled) POWHEG statistical uncertainty in eachsignal region to give the final generator uncertainty.After the baseline cuts, the POWHEG WZ yield was scaled to that ofSHERPA with a scale factor of 1.07. The /ET distributions at the threelepton stage for each generator before and after this scaling are shown inFigure 7.5. As described above, the subsequent difference in shape betweenthese generators gives a systematic uncertainty for each signal region asshown in Table 7.4. A similar procedure was followed for ZZ. A conser-vative 100% generator systematic is included for tribosons; this is a smalleffect because triboson yields are small in all SRs.Systematics are associated with measurements of the energy scale and reso-lution for electrons and jets. The energy scale is a correction which must bemeasured as part of proper calibration of the calorimeter. Energy resolutionswere discussed in chapter 3; their uncertainties are computed by smearingthe transverse momentum of the relevant object. Similarly, the staco muonmomentum scale calibration is associated with uncertainties from the IDand MS. All of these systematics are provided as a set of standard binnedscale factors from the relevant ATLAS working groups. Note also that thepreviously described lepton reconstruction and b-tag scale factors are asso-ciated with errors. Uncertainty due to these is assessed by fluctuating thescale factors between their errors. Scale and resolution uncertainties for themissing transverse momentum cell out term (recall equation 4.7) are alsoincluded. All of these object-based systematics are typically small (. 5%).PDF sets are parameterized by a set of quantities Sj . These are commonlycalled eigenvectors because they can be fluctuated independently. The best-fit central values of each eigenvector are used in the analysis, and PDFuncertainties are obtained by shifting these up and down [128]. In thisanalysis these were found to be typically on the order of 1%.108 [GeV]missTE0 50 100 150 200 250 300 3503102101101102103101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalSherpa WZPowheg WZATLAS Work in Progress(a) [GeV]missTE0 50 100 150 200 250 300 3503102101101102103101 L dt = 20.7 fb∫ = 8 TeVsATLAS InternalPowheg WZSherpa WZATLAS Work in Progress(b)Figure 7.5: Unscaled (a) and Powheg-scaled (b) WZ /ET distributionsat the baseline stage.An uncertainty was computed for the previously discussed trigger efficiencyscale factor, but this was found to be negligible. A 3.6% systematic comesfrom the 2012 luminosity measurement [129].109Note that all sources of uncertainty described in this subsection are alsocomputed for each signal sample. Additionally, uncertainties on the QCDcoupling αs, the difference between CTEQ and MSTW PDF parametriza-tions, and the process scales are included for the signal samples. Theseuncertainties range from 20-40% in total.7.3.2 Uncertainties on Reducible BackgroundsUncertainties on the reducible background estimate are due to the real effi-ciencies, each term in equation 7.4, and the statistics of the sample selectedwith baseline leptons. As shown in table 7.5, the total uncertainties are oforder 40− 80%. Each source of uncertainty will now be described.Dependence of the efficiencies on η introduces a small systematic in each SR.These were found to be negligible and are therefore not shown in table 7.5.A conservative systematic is applied to account for potential uncertaintyin the calculation of the fractions RijX,`. This effects a fluctuation of theweighted average fake rates of size ∼ ±10%.Statistical uncertainties are considered for the Nss, etc. data yields and fakerates f ij in each SR; these are added in quadrature and the resulting valuesrange between ∼ 7− 70%.The fake rates f ij used in the analysis are computed in each SR withoutapplying the various /ET cuts. This was found to give a large reduction inthe statistical uncertainty while introducing a comparatively moderate sys-tematic shift of ∼ 5− 65% depending on the SR.The data and MC control region fake rates used to define the scale factorssf i are associated with statistical uncertainties. They are also associatedwith uncertainties obtained by varying the cuts used to define the controlregions. When both of these sources of error are added in quadrature, scale110factor uncertainties . 13% are obtained.Note that when applying the matrix method, the values on the LHS of equa-tion 7.1 are obtained from data. A closure test, wherein these values areinstead obtained from the fully MC-based estimate, can therefore be usedto validate the method. Validation is achieved by comparing the resultingreducible BG estimate with fully MC-derived yields as input to the knownfake composition from MC. When this was done, agreement within errorswas observed in all regions, and therefore no systematic is needed to accountfor this potential bias.For the fully MC-based estimate in SRnoZd, all sources of uncertainty dis-cussed in section 7.3.1 were computed for the reducible BG components.The total reducible uncertainty in this SR is 96.5% and is dominated byMC statistics.111Table 7.1: Uncertainties on irreducible SM yields in SRnoZa, b, andc.Triboson ZZ tt¯V WZ TotalSRnoZaExpected Events 1.69 13.76 0.23 49.56 65.23Electron energy scale 0.17,-0.53% 4.92,-4.27% 0.0,0.0% 1.16,-1.31% 1.92,-1.91%Electron energy ratio -0.16,-0.36% -0.2,0.32% 0.0,0.0% 0.44,-0.26% 0.29,-0.14%Muon spectrometer track p resolution 0.28,0.04% 0.02,-0.35% 0.0,0.0% -0.22,0.03% -0.16,-0.05%Muon inner detector track p resolution 0.0,-0.31% 0.0,0.02% 0.0,0.0% -0.27,0.03% -0.2,0.02%Jet energy scale -0.06,1.76% 7.65,-4.39% 0.0,0.0% 2.3,1.42% 3.36,0.19%Jet energy resolution 0.67,0.67% 7.3,7.3% 36.0,36.0% 6.73,6.73% 6.8,6.8%/ET soft term scale -0.42,-0.46% 21.93,-15.72% 0.0,0.0% 4.27,-2.97% 7.86,-5.58%/ET soft term resolution -0.37,-0.37% 3.39,3.39% 0.0,0.0% 0.15,0.15% 0.82,0.82%b-tagging 2.23,-2.31% 2.94,-3.02% 61.48,-76.77% 3.11,-3.2% 3.26,-3.4%Electron ID/reconstruction efficiency 0.39,-6.0% 1.85,-7.53% -0.62,-7.02% 0.81,-6.83% 1.01,-6.96%Muon ID/reconstruction efficiency -0.1,-1.0% -0.09,-0.99% -0.05,-0.67% -0.1,-1.04% -0.1,-1.03%MC statistics 3.94,-3.94% 6.37,-6.37% 54.76,-54.76% 4.59,-4.59% 3.74,-3.74%Luminosity 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6%Generator 100.0 % 49.4 % 0.0 % 6.9 % 18.25%PDF 0.0,0.0% 2.6,-2.71% 0.0,0.0% 1.98,2.18% 2.06,1.08%Cross section 10.0 % 5.0 % 30.0 % 12.0 % 10.54%Total 100.67,-100.87% 56.27,-54.25% 94.81,-105.6% 17.62,-18.61% 24.71,-24.8%SRnoZbExpected Events 0.63 1.76 0.21 19.52 22.11Electron energy scale 1.35,-1.11% 0.0,-3.68% 0.0,0.0% 2.99,-2.28% 2.68,-2.33%Electron energy ratio 1.08,-0.07% 0.0,-0.48% 0.0,0.0% 0.96,-1.28% 0.88,-1.17%Muon spectrometer track p resolution -1.11,-0.11% 0.0,0.0% 0.0,0.0% -0.73,0.63% -0.67,0.55%Muon inner detector track p resolution 0.0,-0.62% 0.0,-0.48% 0.0,0.0% 0.82,-0.06% 0.72,-0.11%Jet energy scale 2.78,0.09% 10.61,-7.47% 0.0,46.9% 4.31,6.1% 4.73,5.23%Jet energy resolution 1.35,1.35% 16.77,16.77% 43.16,43.16% 6.73,6.73% 7.71,7.71%/ET soft term scale 1.57,-1.05% 34.57,-23.63% 0.0,0.0% 7.22,-1.82% 9.16,-3.52%/ET soft term resolution -0.48,-0.48% -5.36,-5.36% 0.0,0.0% 0.82,0.82% 0.28,0.28%b-tagging 2.25,-2.29% 2.18,-2.19% 28.75,-29.03% 3.28,-3.38% 3.4,-3.49%Electron ID/reconstruction efficiency 0.45,-5.22% 1.01,-5.46% -0.23,-1.84% 0.41,-4.78% 0.45,-4.82%Muon ID/reconstruction efficiency -0.07,-1.02% -0.14,-0.95% -0.4,-1.74% -0.11,-1.08% -0.12,-1.07%MC statistics 6.41,-6.41% 18.29,-18.29% 54.86,-54.86% 7.54,-7.54% 6.84,-6.84%Luminosity 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6%Generator 100.0 % 38.4 % 0.0 % 7.0 % 12.09%PDF 0.0,0.0% 2.75,-2.67% 0.0,0.0% 2.28,2.39% 2.23,1.9%Cross section 10.0 % 5.0 % 30.0 % 12.0 % 11.55%Total 100.87,-100.96% 58.97,-53.18% 81.31,-93.99% 20.17,-19.94% 23.04,-22.04%SRnoZcExpected Events 0.81 0.25 0.21 2.12 3.4Electron energy scale 1.04,-2.07% 0.0,0.0% 0.0,-29.58% 7.85,-7.57% 5.15,-7.05%Electron energy ratio 0.58,0.21% 0.0,0.0% 0.0,29.58% 0.0,6.51% 0.14,5.94%Muon spectrometer track p resolution 0.16,-0.02% 3.11,0.0% 0.0,0.0% 0.0,0.0% 0.27,-0.0%Muon inner detector track p resolution 0.0,0.17% 0.0,0.0% 0.0,0.0% 5.27,0.0% 3.29,0.04%Jet energy scale 1.05,-0.02% 0.0,35.9% 0.0,69.5% 5.5,-0.42% 3.68,6.68%Jet energy resolution 3.09,3.09% 0.0,0.0% 103.23,103.23% 11.33,11.33% 14.2,14.2%/ET soft term scale -0.04,-2.1% 3.11,0.0% 0.0,0.0% 11.51,-2.32% 7.41,-1.95%/ET soft term resolution 0.78,0.78% 0.0,0.0% 0.0,0.0% 6.68,6.68% 4.36,4.36%b-tagging 2.35,-2.43% 6.32,-6.32% 10.39,-10.67% 3.98,-4.12% 4.16,-4.28%Electron ID/reconstruction efficiency -0.0,-3.29% 1.94,0.21% -0.18,-5.46% 0.72,-2.59% 0.58,-2.73%Muon ID/reconstruction efficiency -0.05,-1.04% -0.48,-1.91% 0.2,-0.37% -0.04,-1.07% -0.06,-1.08%MC statistics 5.64,-5.64% 54.82,-54.82% 51.78,-51.78% 20.6,-20.6% 13.93,-13.93%Luminosity 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6%Generator 100.0 % 14.4 % 0.0 % 65.9 % 66.2%PDF 0.0,0.0% 9.12,-8.29% 0.0,0.0% 1.86,2.27% 1.83,0.81%Cross section 10.0 % 5.0 % 30.0 % 12.0 % 12.12%Total 100.81,-100.9% 58.28,-68.2% 119.83,-144.83% 73.27,-72.34% 71.3,-71.54%112Table 7.2: Uncertainties on irreducible SM yields in SRnoZd.Triboson ZZ tt¯V WZ TotalSRnoZdExpected Events 0.01 0.07 0.06 0.35 0.48Electron energy scale 0.0,0.0% 83.31,0.0% 0.0,0.0% 0.0,0.0% 11.42,0.0%Electron energy ratio 0.0,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0%Muon spectrometer track p resolution 29.59,0.0% 0.0,0.0% 0.0,0.0% 35.9,0.0% 26.39,0.0%Muon inner detector track p resolution 0.0,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0%Jet energy scale 0.0,36.78% 0.0,-83.31% 0.0,17.83% 0.0,15.8% 0.0,2.86%Jet energy resolution 21.53,21.53% 0.0,0.0% 0.0,0.0% 47.17,47.17% 34.35,34.35%/ET soft term scale 29.59,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0% 0.56,0.0%/ET soft term resolution 0.0,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0%b-tagging 16.63,-19.04% 14.38,-15.67% 58.26,-59.5% 18.25,-20.41% 22.67,-24.6%Electron ID/reconstruction efficiency 0.27,-3.99% 14.57,-15.69% 0.0,0.0% -0.0,-3.8% 2.0,-4.96%Muon ID/reconstruction efficiency -0.31,-1.27% -0.04,-0.23% -0.75,-2.45% -0.13,-1.21% -0.2,-1.23%MC statistics 43.64,-43.64% 84.96,-84.96% 100.0,-100.0% 44.89,-44.89% 36.52,-36.52%Luminosity 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6%Generator 100.0 % 65.1 % 0.0 % 115.0 % 93.57%PDF 0.0,0.0% 2.41,-2.61% 0.0,0.0% 1.82,2.11% 1.63,1.14%Cross section 10.0 % 5.0 % 30.0 % 12.0 % 13.24%Total 120.45,-119.22% 137.33,-137.6% 119.61,-121.56% 138.73,-135.31% 113.16,-109.99%113Table 7.3: Uncertainties on irreducible SM yields in all SRZ-typeregions.Triboson ZZ tt¯V WZ TotalSRZaExpected Events 0.54 8.88 0.43 235.05 244.9Electron energy scale 2.68,-2.12% 0.52,-2.99% 0.0,0.0% 0.39,-0.19% 0.4,-0.3%Electron energy ratio -0.39,0.49% 1.63,0.91% 0.0,26.64% 0.06,0.04% 0.11,0.12%Muon spectrometer track p resolution 1.17,-0.28% 0.48,0.15% 26.64,0.0% -0.13,0.11% -0.06,0.11%Muon inner detector track p resolution 0.71,1.18% 0.0,0.15% 0.0,0.0% -0.03,0.15% -0.02,0.15%Jet energy scale 3.3,2.64% 1.34,7.25% 26.64,21.24% 1.71,1.04% 1.74,1.3%Jet energy resolution 2.95,2.95% 7.76,7.76% 19.64,19.64% 2.88,2.88% 3.08,3.08%/ET soft term scale -1.35,0.32% 10.88,-6.69% 0.0,0.0% 2.61,-2.35% 2.9,-2.5%/ET soft term resolution -0.5,-0.5% 1.95,1.95% -0.94,-0.94% -0.24,-0.24% -0.16,-0.16%b-tagging 2.56,-2.63% 3.33,-3.43% 46.28,-56.32% 3.07,-3.17% 3.15,-3.28%Electron ID/reconstruction efficiency 0.36,-4.72% 0.37,-3.61% 0.07,-6.06% 0.41,-4.98% 0.41,-4.93%Muon ID/reconstruction efficiency -0.1,-1.05% -0.08,-1.14% 0.05,-0.82% -0.1,-1.05% -0.1,-1.05%MC statistics 5.92,-5.92% 8.51,-8.51% 40.41,-40.41% 2.13,-2.13% 2.07,-2.07%Luminosity 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6%Generator 100.0 % 10.7 % 0.0 % 1.6 % 2.14%PDF 0.0,0.0% 1.85,-2.01% 0.0,0.0% 1.74,2.0% 1.74,1.85%Cross section 10.0 % 5.0 % 30.0 % 12.0 % 11.77%Total 100.92,-101.0% 20.66,-20.64% 80.59,-85.46% 13.96,-14.8% 13.96,-14.75%SRZbExpected Events 0.43 0.95 0.22 18.68 20.29Electron energy scale 2.06,-2.58% 21.65,-20.82% 0.0,0.0% 2.08,-7.7% 2.97,-8.12%Electron energy ratio -0.65,0.29% 0.0,-6.89% 0.0,0.0% 0.3,-0.31% 0.26,-0.6%Muon spectrometer track p resolution -0.36,-0.21% 5.51,0.0% 0.0,0.0% 0.1,-0.12% 0.34,-0.12%Muon inner detector track p resolution 0.2,-0.36% 0.0,0.0% 0.0,0.0% -1.81,-0.15% -1.66,-0.14%Jet energy scale -0.06,3.66% 17.68,-10.14% 0.0,18.39% 1.7,7.57% 2.39,6.77%Jet energy resolution 0.34,0.34% 15.47,15.47% 4.64,4.64% 4.84,4.84% 5.24,5.24%/ET soft term scale 1.55,-2.07% 6.16,4.82% 0.0,0.0% 13.73,-16.89% 12.97,-15.37%/ET soft term resolution 0.72,0.72% 2.67,2.67% 0.0,0.0% 3.02,3.02% 2.93,2.93%b-tagging 2.95,-3.0% 1.86,-1.9% 38.4,-64.33% 3.3,-3.45% 3.61,-4.03%Electron ID/reconstruction efficiency 0.03,-4.37% 2.73,-3.99% 0.17,-1.53% 0.65,-3.14% 0.73,-3.19%Muon ID/reconstruction efficiency -0.08,-1.01% -0.05,-0.91% -0.04,-1.38% -0.08,-1.13% -0.08,-1.12%MC statistics 6.62,-6.62% 25.45,-25.45% 57.33,-57.33% 7.46,-7.46% 7.0,-7.0%Luminosity 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6%Generator 100.0 % 16.8 % 0.0 % 5.9 % 8.36%PDF 0.0,0.0% 2.33,-2.82% 0.0,0.0% 2.0,2.15% 1.95,1.84%Cross section 10.0 % 5.0 % 30.0 % 12.0 % 11.83%Total 100.86,-101.05% 45.61,-43.01% 75.47,-93.29% 22.24,-26.64% 22.6,-26.21%SRZcExpected Events 0.29 0.39 0.1 5.01 5.79Electron energy scale 0.58,-1.0% 0.0,0.0% 0.0,0.0% 8.44,-10.02% 7.33,-8.73%Electron energy ratio -0.02,0.49% 0.0,0.0% 0.0,0.0% 0.0,0.61% -0.0,0.55%Muon spectrometer track p resolution 0.44,0.28% 0.0,0.0% 0.0,0.0% -0.29,0.0% -0.22,0.01%Muon inner detector track p resolution -0.05,0.0% 0.0,0.0% 0.0,0.0% 0.0,0.0% -0.0,0.0%Jet energy scale 0.05,2.43% -7.58,1.46% 0.0,0.0% 8.23,0.99% 6.62,1.08%Jet energy resolution 2.85,2.85% 4.52,4.52% 38.25,38.25% 2.77,2.77% 3.51,3.51%/ET soft term scale -0.84,1.11% 0.0,-32.99% 0.0,0.0% 3.94,-4.74% 3.37,-6.26%/ET soft term resolution -1.22,-1.22% -33.02,-33.02% 0.0,0.0% -3.3,-3.3% -5.13,-5.13%b-tagging 3.34,-3.4% 2.35,-2.35% 7.74,-8.19% 6.02,-6.47% 5.67,-6.07%Electron ID/reconstruction efficiency 0.14,-4.19% 1.04,-1.32% 0.29,-2.03% 0.96,-3.24% 0.91,-3.14%Muon ID/reconstruction efficiency -0.04,-1.07% -0.29,-1.39% 0.03,-1.08% 0.02,-0.95% -0.01,-0.99%MC statistics 6.37,-6.37% 41.46,-41.46% 95.95,-95.95% 14.22,-14.22% 12.73,-12.73%Luminosity 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6% 3.6,-3.6%Generator 100.0 % 35.4 % 0.0 % 12.9 % 18.55%PDF 0.0,0.0% 3.43,-4.47% 0.0,0.0% 1.37,1.67% 1.41,1.15%Cross section 10.0 % 5.0 % 30.0 % 12.0 % 11.74%Total 100.87,-101.0% 64.78,-72.39% 107.9,-107.95% 27.16,-26.92% 28.98,-29.35%114Table 7.4: WZ generator systematics have been computed in eachsignal region as shown here. All yields are scaled to 20.7 fb−1 and alluncertainties are statistical. The POWHEG yields have been scaled toSHERPA at the three lepton stage with a scale factor of 1.07.Region SHERPA WZ POWHEG WZ (scaled) Generator systematicSRnoZa 49.6±2.3 46.5±1.4 6.86%SRnoZb 19.5±1.5 20.4±1.0 6.96%SRnoZc 2.12±0.44 3.46±0.41 65.9%SRnoZd 0.35±0.16 0.72±0.15 115%SRZa 235.0±5.1 236.1±3.6 1.60%SRZb 18.7±1.4 19.2±1.0 5.86%SRZc 5.01±0.7 5.37±0.53 12.9%Table 7.5: Uncertainties on the reducible BG estimate in all relevantSRs.SRnoZa SRnoZb SRnoZc SRZa SRZb SRZcExpected Events 31.0 7.08 1.03 4.28 1.70 0.46Statistics +7.3,-7.3% +12,-12% +38,-38% +34,-34% +35,-35% +71,-71%Fractions +12,-12% +19,-19% +5,-14% +29,-29% +8,-9% +20,-26%/ET dependence +42,-36% +64,-64% +10,-9% +33,-26% +6,-5% +16,-13%Scale factors +7,-6% +13,-13% +1,-1% +4,-4% +0,-0% +1,-1%Total +45,-39% +66,-50% +40,-42% +84,-111% +37,-38% +76,-78%1157.4 Background Estimate ValidationBefore unblinding the analysis, it is necessary to validate the backgroundestimate technique. This is achieved by defining a number of VRs which aresimilar but orthogonal to the SRs. The definitions of these regions are givenin table 7.6 below; it is seen that orthogonalization is achieved by loweringthe /ET cut or requiring the presence of at least one b-jet. Because the VRsare not blinded, they permit realistic performance benchmarking of the BGestimate.Each region targets particular BG components. VRnoZa(b) targets WZ∗,Z∗Z∗, Z∗ + j (tt) by cutting 35 < /ET < 50 GeV (requiring ≥ 1 b-jet).Similarly, VRZa(b) targets WZ, Z + j (WZ).Table 7.6: Validation region definitions.N` SFOC pair Z boson /ET (GeV) Nb Target processVRnoZa 3 request veto 35–50 0 WZ∗, Z∗Z∗, Z∗ + jVRnoZb 3 request veto > 50 ≥ 1 ttVRZa 3 request request 30–50 0 WZ, Z + jVRZb 3 request request > 50 ≥ 1 WZThe comparison between SM predictions and observations in data for allVRs is displayed in table 7.7. The full background estimate (including thematrix method) is used for this estimate; the corresponding table for theMC-based estimate can be found in appendix A. Note that agreement isachieved within errors in all VRs. This fact, coupled with the agreementseen in the selection of VR distributions shown in figure 7.6, validates themethodology.116Table 7.7: Predictions and observations in all validation regions. Un-certainties are systematic and statistical.Selection VRnoZa VRnoZb VRZa VRZbTriboson 1.4±1.4 0.5±0.5 0.6±0.6 0.26±0.27ZZ 128±87 4.5±2.8 108±23 6.9±2.2ttV 2.9±1.2 21±7 7.4±2.6 26±8WZ 110±21 34±15 545±89 138±38Σ SM irreducible 242±90 60±16 662±92 171±39SM reducible 146±55 72±45 376±138 27±13Σ SM 388±106 132±48 1038±166 198±41Data 463 141 1131 171117Events/1 GeV110110210310410510 = 8 TeVs 1L dt = 20.7 fb∫ATLAS Internal DataTotal SMReducibleDibosonsTribosons Vtt [GeV]TLepton 2 p0 50 100 150 200 250Data/SM00.511.52Work in Progress(a) VRnoZaEvents/1 GeV110110210310410510 = 8 TeVs 1L dt = 20.7 fb∫ATLAS Internal DataTotal SMReducibleDibosonsTribosons Vtt [GeV]missTE100 200 300 400 500Data/SM00.511.52Work in Progress(b) VRnoZbEvents/1 GeV110110210310410510 = 8 TeVs 1L dt = 20.7 fb∫ATLAS Internal DataTotal SMReducibleDibosonsTribosons Vtt [GeV]lllM0 100 200 300 400 500Data/SM00.511.52Work in Progress(c) VRZaEvents/1 GeV110110210310410510 = 8 TeVs 1L dt = 20.7 fb∫ATLAS Internal DataTotal SMReducibleDibosonsTribosons Vttbjet multiplicity0 1 2 3 4 5 6Data/SM00.511.52Work in Progress(d) VRZbFigure 7.6: Distributions of p2T (a), /ET (b), M``` (c), and Nb (d) fordata and the full BG estimate are overlaid in the indicated validationregions. Uncertainties on the BG are statistical and systematic.√Nstatistical error bars are included on the data.118Chapter 8Results and InterpretationThis chapter presents the full suite of results. A comparison between dataobservations and BG predictions in each SR will be shown and discussed.The interpretation of this comparison requires elucidation of a statisticalmethod called the CLs technique [130]. This technique is then used to set95% CL limits on the parameter spaces of MUED and SUSY.8.1 Signal Region ObservationsTable 8.1 shows the final BG estimates and the unblinded observations indata in all SRs. The reducible SM contributions in SRnoZa, b, and c, and allSRZ-type regions (SRnoZd) have been estimated using the matrix method(MC), and the irreducible contributions have been estimated purely withMC.Remarkable agreement between SM prediction and observation is obtainedin all signal regions. To further illustrate this fact, various SR distributionsare provided in figures 8.1 and 8.2. From the p-values p0, it is clear thatno significant excess1 can be claimed from these null results; the derivationof this “discovery” p-value will be explained in due course. The next stepis therefore to translate the results into constraints (in the form of 95% CL1By convention, a 3σ (5σ) excess is considered evidence (discovery) of new phenomenain experimental high energy physics.119Table 8.1: Full BG estimate compared to data in all SRs. Errors arestatistical and systematic.Selection SRnoZa SRnoZb SRnoZc SRnoZd SRZa SRZb SRZcTriboson 1.7±1.7 0.6±0.6 0.8±0.8 0.01±0.01 0.5±0.5 0.4±0.4 0.29±0.29ZZ 14±8 1.8±1.0 0.25±0.17 0.07±0.09 8.9±1.8 1.0±0.4 0.39±0.28tt¯V 0.23±0.23 0.21±0.19 0.21±0.30 0.06±0.07 0.4±0.4 0.22±0.21 0.10±0.10WZ 50±9 20±4 2.1±1.6 0.35±0.48 235±35 19±5 5.0±1.4Σ SM irreducible 65±12 22±4 3.4±1.8 0.48±0.50 245±35 20±5 5.8±1.4SM reducible 31±14 7±5 1.0±0.4 0.57±0.55 4±5 1.7±0.7 0.5±0.4Σ SM 96±19 29±6 4.4±1.8 1.06±0.74 249±35 22±5 6.3±1.5Data 101 32 5 2 273 23 6p0 0.41 0.37 0.40 0.22 0.23 0.44 0.50limits) on the SIM and MUED parameter spaces.120Events / 25 GeV110210310410 = 8 TeVs 1L dt = 20.7 fb∫SRnoZaATLAS Preliminary DataTotal SMReducibleDibosonsTribosons Vtt via slep 192.5, 157.520χ 1±χ [GeV]missTE50 100 150Data/SM00.511.52(a) SRnoZaEvents / 10 GeV110210310 = 8 TeVs 1L dt = 20.7 fb∫SRnoZbATLAS Internal DataTotal SMReducibleDibosonsTribosons Vtt via WZ 150, 7520χ 1±χ [GeV]TLepton 3 p0 20 40 60 80 100 120 140 160 180Data/SM00.511.52Work in Progress(b) SRnoZbEvents / 10 GeV110110210310 = 8 TeVs 1L dt = 20.7 fb∫SRnoZcATLAS Internal DataTotal SMReducibleDibosonsTribosons Vtt via slep 500, 020χ 1±χ [GeV]TLepton 2 p0 50 100 150Data/SM00.511.52Work in Progress(c) SRnoZcFigure 8.1: Distributions of /ET (a), p3T (b), and p2T (c) for data andthe full BG estimate are overlaid in the indicated SRnoZ-type regions.Uncertainties on the BG are statistical and systematic.√N statisticalerror bars are included on the data.121Events / 10 GeV110110210310410510 = 8 TeVs 1L dt = 20.7 fb∫SRZaATLAS Internal DataTotal SMReducibleDibosonsTribosons Vtt via WZ 100, 020χ 1±χ [GeV]TLepton 1 p0 100 200 300 400 500 600Data/SM00.511.52Work in Progress(a) SRZaEvents / 40 GeV110210310410 = 8 TeVs 1L dt = 20.7 fb∫SRZbATLAS Preliminary DataTotal SMReducibleDibosonsTribosons Vtt via WZ 150, 020χ 1±χ [GeV]Tm100 200 300Data/SM00.511.52(b) SRZbEvents / 30 GeV110210 = 8 TeVs 1L dt = 20.7 fb∫SRZcATLAS Preliminary DataTotal SMReducibleDibosonsTribosons Vtt via WZ 250, 020χ 1±χ [GeV]missTE100 150 200 250Data/SM00.511.52(c) SRZcFigure 8.2: Distributions of p1T (a), mT (b), and /ET (c) for data andthe full BG estimate are overlaid in the indicated SRZ-type regions.Uncertainties on the BG are statistical and systematic.√N statisticalerror bars are included on the data.1228.2 Methodology for Statistical Interpretation ofResultsFor SUSY analyses at the LHC, statistical interpretations are convention-ally carried out using the modified frequentist CLs prescription [130]. Thisis a frequentist upper limit setting method, but the traditional p-value ismodified in a conservative way. An outline of the method will now be given.A likelihood function is constructed which has the general form [131]L(nSR|µ, b, ~θ ) = P (nSR|λSR(µ, b, ~θ ))× Ps(~θ0, ~θ ), (8.1)where nSR is the number of events observed in data in a given SR, µ is thesignal strength (see below), b is the BG estimate, ~θ is a vector of nuisanceparameters (systematics) with nominal values ~θ 0, P is a Poisson distribu-tion for nSR with mean λSR, and Ps is a probability density function (PDF)for the nuisance parameters. The signal strength µ is an arbitrary factorwhich modifies the nominal signal cross section: σs → µσs. The BG-onlycase corresponds to µ = 0, and µ = 1 corresponds to the nominal S+BGcase.Notice that the likelihood in equation 8.1 has been written as a product oftwo independent probabilities: the probability to observe nSR events in dataand the probability that the nuisance parameters take on particular values ~θ.Systematic uncertainties contribute to both of these factors. On one hand,Ps serves to constrain the systematics in fits. In this analysis, this is assumedto take the form of a product of standard normal distributions [131]:Ps(~θ0, ~θ ) =Ns∏iφ(θi − θ0i ), (8.2)where Ns is the number of nuisance parameters to be considered. On theother hand, the degree of impact of each systematic is accounted for explic-itly in λSR. Without systematics, this would have the form λSR = µs + b,123where s is the expected signal yield. If, for example, nuisance parameterθ1 is associated with an 11% BG yield shift (recall table 7.1), this must bemodified2: λSR = µs+ b+ 0.11bθ1.All correlations are introduced by describing multiple systematics with thesame nuisance parameter. This allows modeling of region–wise (e.g. crosssection uncertainties), process–wise (e.g. jet energy scale), and region–process–wise (e.g. luminosity) correlations. When all region-wise corre-lations are accounted for, statistical combinations of multiple signal regionscan be performed by defining a new likelihood function as a product of like-lihoods of the single-SR form in equation 8.1.With the likelihood in place, a profile log-likelihood ratio test statistic canbe defined:q˜µ ≡−2 lnL(µ, ˆˆθ(µ))L(0, ˆˆθ(0)), µˆ < 0−2 lnL(µ, ˆˆθ(µ))L(µˆ, θˆ), 0 ≤ µˆ ≤ µ0, µˆ > µ,(8.3)where µˆ and θˆ are maximum likelihood estimators (MLEs), and ˆˆθ(µ) is aconditional MLE for a given µ. Note that the vector arrow ~ on θ has beensuppressed for notational simplicity. Usage of this test statistic is canonicalfor ATLAS SUSY searches [132]. The value of q˜µ observed in data is thenfound by setting µ = 1, although other values of µ may also be tested. Acomment will be made on this below.Monte Carlo pseudo-experiments (“toys”) are then used to build the PDFf(q˜µ) in the S+BG case f(q˜1|ˆˆθ(µ = 1, obs)) and in the BG-only case f(q˜0|ˆˆθ(µ =0, obs)). The conditional MLEs used here are the values obtained from thedata observation—although the nuisance parameters float in the extremiza-2Note in particular that this form of λSR, when considered in conjunction with equa-tion 8.2, appropriately incorporates the desired influence of the systematics when theyassume their nominal values and their ±1σ shifts.124tions used to compute q˜µ. This means that the nuisance parameters are setto their observed conditional MLE values in order to create (and then sam-ple) P (nSR). This gives a new pseudo-data value of nSR, which is then usedto compute a value of q˜µ in the same way as was initially done to obtain theobserved value in data. This procedure is iterated and a PDF is obtained.An example is shown in figure 8.3.Profile Likelihood Ratio0 1 2 3 4 5 6 7 8110210310410510 =1)µ| µq~f(=0)µ| µq~f(obsµq~Figure 8.3: The non-normalized distribution of the profile log-likelihood ratio test statistic is shown for S+BG (µ = 1) and BG-only(µ = 0) hypotheses. The signal here is a SIM grid point with CLs ∼ 5%.1.5× 104 toy experiments have been used, and a value q˜ obs1 = 1.79 wasseen in data.Two p-values are then defined. One of these describes the S+BG hypothesis:p1 ≡∫ ∞q˜obs1dq˜1 f(q˜1|ˆˆθ(µ = 1, obs)), (8.4)and the other describes the BG-only (null) hypothesis:p0 ≡ 1−∫ ∞q˜obs1dq˜0 f(q˜0|ˆˆθ(µ = 0, obs)). (8.5)125Finally, the modified CLs p-value is defined to beCLs ≡p11− p0, (8.6)and new physics models with CLs ≤ 0.05 are excluded at ≥95% CL. Acontour can be drawn through such models to obtain the observed limit.Expected limits can be generated in a number of ways. The most obvioustechnique is to simply replace the data observation by the expected BG andrepeat the above procedure. The ±1σ expected error bands are obtained byconverting the expected limit at CLs = 0.05 to an equivalent significanceusing equation 6.1 (which gives ∼ 1.64) and then drawing contours through0.64 and 2.64.The CLs prescription is therefore essentially a standard frequentist hypoth-esis test, but the normalization in equation 8.6 renders it conservative. Thenormalization provides robustness against cases where the S+BG and BG-only q˜µ distributions are not well separated—i.e. cases where exclusion canoccur despite poor sensitivity in a traditional hypothesis test using p1 only.In these cases p0 is large, so CLs becomes large.Although the above method fixes µ = 1 from the outset, it is also possibleto set limits by performing a scan across µ values. A 95% CL upper limiton µ is then obtained for each signal point by finding the value of µ whichgives CLs = 0.05. This approach is often used for one-dimensional limitssuch as those on Higgs boson masses [133]. These limit setting paradigmsare equivalent in the sense that they will exclude the same model points,but the ±1σ bands of course have different meanings.8.3 Visible Cross Section LimitsAlthough the SRs have been optimized for sensitivity to particular classesof BSM scenarios, it is possible to interpret the analysis results in a model126independent way. As will be explained in the present section, this is achievedby setting limits on the so-called visible cross section.By scanning input signal yields, a hypothetical signal yield N excS which wouldgive CLs = 0.05 can be obtained in each SR. This is interpreted as a modelindependent 95% CL upper limit on all hypothetical new physics scenariosproducing SR events. It is often, however, more convenient to think in termsof cross sections. To this end, the NS limit can readily be translated to alimit on the so-called BSM visible cross section: σexcV = NexcS /L. Results ofthese calculations are displayed in table 8.2.Table 8.2: Expected and observed 95% CL upper limits on the visiblecross section and equivalent limits on signal yields are shown in eachSR.SRnoZa SRnoZb SRnoZc SRnoZd SRZa SRZb SRZcExpected Events 96 ± 19 29 ± 6 4.4 ± 1.8 1.06±0.74 249 ± 35 22 ± 5 6.3 ± 1.5Observed Events 101 32 5 2 273 23 6p0-value 0.41 0.37 0.40 0.22 0.23 0.44 0.5NexcS (exp) 39.3 16.3 6.2 2.9 67.9 13.2 6.7NexcS (obs) 41.8 18.0 6.8 4.4 83.7 13.9 6.5σexcV (exp) [fb] 1.90 0.79 0.30 0.14 3.28 0.64 0.32σexcV (obs) [fb] 2.02 0.87 0.33 0.21 4.04 0.67 0.31Note that the visible cross section is related to the cross section of a givensignal model by folding in the acceptance and efficiency for that model:σV = A× σS . The acceptance is defined to be the efficiency of all fiducialcuts (i.e. cuts applied to truth- and parton-level physics objects), whereas is the efficiency of all reconstruction-level cuts applied to events and objectspassing the fiducial cuts. In this language, A× is then the overall efficiencyof an event selection. As an example, A × ∼ 5% in the SIM via ˜` bulk.This provides two additional interpretations of the observed limit contours:They can be thought of as contours drawn through NS = N excS or throughσS = σexcV /(A× ).1278.4 MUED InterpretationFigure 8.4 displays the expected and observed 95% CL limits on the MUEDparameter space in SRnoZd. Also shown are the±1σ contours resulting fromup- and downward fluctuation of the theory uncertainties on the MUED sig-nal. As a conservative convention, the observed limit is taken to be the +1σtheory uncertainty curve. All contours are obtained by linear interpolationfrom the underlying discrete grid. The full map of CLs values can be foundin appendix B.Compactification scales . 950 GeV are excluded at moderate to high ΛR,and the expected limit reaches past 1 TeV. At the time of this writing, thisis the most stringent experimental MUED limit in existence.8.5 SUSY InterpretationsThe 95% CL limits on the SIM via WZ and via ˜` parameter spaces areshown in figure 8.5. Full CLs maps are available in appendix B. Both limitshave been set using a statistical combination of SRnoZa, b, c, and all SRZ-type regions.The via WZ (˜`) limit extends as high as mχ˜±,01,2∼600 (310) GeV. By com-paring these results to the blue curves in figure 8.5, both limits are seen tobe considerably more stringent than those obtained from the 13 fb−1 versionof this analysis [3].As discussed in chapter 6, the region ∆m21 ∼ mZ is particularly challengingfor SIM via WZ sensitivity due to the preponderance of on-shell Z decays.Sensitivity in this region may be improved in future analyses by reducingthe granularity of the SR bins.128 ) [GeV]1γ ≈ (1R700 800 900 1000 1100 1200 1300 RΛ510152025303540 ATLAS Work in Progress1 L dt = 20.7 fb∫ = 8 TeVsMUED)µ3L (e, )theoryMUEDσ1 ±Observed limit ()expσ1 ±Expected limit (Figure 8.4: 95% CL exclusion limit placed on the MUED parameterspace.129 [GeV]1±χ∼, 20χ∼m100 200 300 400 500 600 700 [GeV]0 1χ∼m01002003004005006000 1χ∼ < m0 2χ∼m10χ∼ = 2m20χ∼m02χ∼ = m±1χ∼m)/202χ∼ + m01χ∼m = ( Ll~ m)ν ν∼l (Ll~ ν∼), l ν ν∼l(Ll~ ν Ll~ → 02χ∼ ±1χ∼ 01χ∼) ν ν l l (01χ∼ ν l →ATLAS Preliminary=8 TeVs, 1 L dt = 20.7 fb∫ )theorySUSYσ1 ±Observed limit ( )expσ1 ±Expected limit ( = 8 TeVs, 1ATLAS 13.0 fbAll limits at 95% CL(a) Via ˜` [GeV]1±χ∼, 20χ∼m100 150 200 250 300 350 400 [GeV]0 1χ∼m0501001502002503000 1χ∼ < m0 2χ∼mZ = m10χ∼ m20χ∼m10χ∼ = 2m20χ∼m02χ∼ = m±1χ∼m10χ∼ (*) Z10χ∼ (*) W→ 02χ∼ ±1χ∼ATLAS Preliminary=8 TeVs, 1 L dt = 20.7 fb∫ )theorySUSYσ1 ±Observed limit ( )expσ1 ±Expected limit ( = 8 TeVs, 1ATLAS 13.0 fbAll limits at 95% CL(b) Via WZFigure 8.5: 95% CL exclusion limits placed on the SIM via ˜` (a) andvia WZ (b) parameter spaces.130Chapter 9Looking AheadAt the time of this writing the LHC is being upgraded in preparation for a∼14 TeV run which is set to begin in 2015. This run is projected to collectapproximately 100 fb−1 by 2017. Another shutdown in 2018 will be usedto upgrade the luminosity to roughly 2 × 1034 cm−2s−1, and a subsequentrun until 2022 is expected to collect up to 300 fb−1. A final proposed lumi-nosity upgrade to 5× 1034 cm−2s−1 (the so-called High Luminosity LHC) isplanned to accrue 3000 fb−1 by 2030.As was explained in chapter 2, MUED’s R−1 parameter is bounded fromabove by cosmology: R−1 . 1.4 TeV. The limit shown in chapter 8 con-strains this parameter from below: R−1 & 1 TeV. This chapter presents astudy which assesses the potential of the 14 TeV LHC to either discoverMUED or close this 400 GeV gap, thereby simplifying the LHC inverseproblem. Detailed 14 TeV studies for SUSY have already been performedby ATLAS [134].A 14 TeV MUED grid was simulated with Herwig++, and the resultingcross sections are compared to their 8 TeV values in figure 9.1. It is seenthat the 14 TeV cross section increases by at least an order of magnitudewith respect to 8 TeV. The 14 TeV grid extends up to R−1 =1.8 TeV.131Using the approximate pβ-value of equation 6.3, an expected SRnoZd limitfor MUED with 20.7 fb−1 of 14 TeV collisions is shown in figure 9.2. Severaladditional approximations have been used to obtain this limit. For sim-plicity, the background is assumed to be comprised entirely of the leadingWZ and tt contributions. All quantities entering the WZ object and eventselections are purely MC truth-level, but they have been smeared to matchthe various subdetector resolutions. The tt yield has been obtained by scal-ing the 8 TeV yield by the ratio of HATHOR–derived NNLO cross sections:σ14TeV/σ8TeV ∼ 4.1. The total expected BG is 14 events, and a total un-certainty of 30% is assumed for the purpose of computing the significance.Despite these approximations, it is clear that 14 TeV analyses will be ableto exclude MUED at the 95% CL with .21 fb−1 of data.1/R [GeV]700 800 900 1000 1100 1200 1300 (nb)LOσ5104103102101101 R = 3Λ14 TeV, R = 10Λ14 TeV, R = 40Λ14 TeV, R = 3Λ8 TeV, R = 10Λ8 TeV, R = 40Λ8 TeV, ATLAS Work in ProgressFigure 9.1: LO Herwig++ cross section comparison for MUED at 8and 14 TeV. Note that a trilepton generator filter efficiency ∼5% hasnot been applied here.132 ) [GeV]1γ ≈ (1R800 1000 1200 1400 1600 1800 RΛ510152025303540 SM)∆ (30% NZ012345678 SM)∆ (30% NZATLAS Work in Progress = 14 TeVs , 1 L dt = 20.7 fb∫Figure 9.2: Approximate expected sensitivity to MUED with20.7 fb−1 of 14 TeV collisions. The black contour indicates the 95%CL limit.133Chapter 10ConclusionThe 20.7 fb−1 2012 ATLAS dataset has been used to perform a search forEW SUSY and MUED in final states with three leptons and missing trans-verse momentum. No significant excess was observed in seven optimizedsignal regions. These null results were translated into 95% CL limits on theparameter spaces of SIM and MUED.The MUED limit excludes orbifold compactification scales below ∼950 GeV;this is the most stringent existing lower bound on the high ΛR regime ofthis model. WMAP data place an upper bound R−1 .1.4 TeV. Prelimi-nary studies were presented which suggest that sensitivity to scales up to∼1.7 TeV will be possible early in the 14 TeV LHC run.SIM interpretations have been presented which constrain scenarios featuringdirect production of weak gauginos in both light and heavy slepton regimes.The SIM via ˜` (WZ) limit excludes lightest chargino and next-to-lightestneutralino masses as large as ∼600 (310) GeV. 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ATL-PHYS-PUB-2011-011,2011. → pages 126[134] The ATLAS Collaboration. Prospects for benchmark supersymmetrysearches at the high luminosity LHC with the ATLAS detector.ATLAS-PHYS-PUB-2013-011, 2013. → pages 131, 134146Appendix AMonte Carlo-BasedBackground EstimateA fully Monte Carlo-based BG estimate technique has been used for SRnoZdand for optimization of all SRs. All samples used for this estimate are de-scribed in chapter 5. This appendix contains detailed tabulated informationabout the yields at each stage of the cutflow (tables A.1 through A.3) aswell as validation of the method (table A.4).Note that tables A.1 and A.3 express statistical uncertainties only. Theseare computed using a Poisson assumption. Each sample contributes a yieldNs =Nps∑iwi ±√√√√√Nps∑jw2j , (A.1)where wi are the MC event weights, and Nps events from sample s passedthe relevant cuts. The yields and uncertainties are then scaled to theircorresponding values at 20.7 fb−1 with a factor 20.7 fb−1/LMC , where LMCis the sample luminosity. The “total” entries in the tables are then obtainedby adding yields linearly and adding uncertainties in quadrature. A subtletyarises when a cut removes all events from a given sample: Quoting an exactlyvanishing error for such a sample is obviously inaccurate. The prescription147used here is to report the yield as 0.0+1.1−0.0×20.7LMC, where 1.1 is the parameterof a Poisson distribution for which observing zero events is a 1σ fluctuation.In case of a composite yield, the minimum LMC is conservatively chosen.148Table A.1: MC yield estimates and statistical uncertainties for reducible and irreducible SM backgroundsat all stages of the SRnoZa,b,c cutflows. Note that the small overlap of SRnoZa,b with SRnoZc has not beenremoved here.SRnoZa SRnoZb SRnoZcSelection 3` b-veto Z-veto /ET > 50 GeV m`` < 60 GeV /ET > 75 GeV 60< m`` <81 GeV mT > 110 GeV p3T > 30 GeVtt¯ + Z 52.88±1.83 3.71±0.50 0.77±0.20 0.34±0.12 0.18±0.11 0.19±0.09 0.10±0.07 0.16±0.09 0.08±0.06tt¯ +W 25.44±1.35 1.43±0.32 1.15±0.29 0.61±0.2 0.1±0.1 0.47±0.18 0.13±0.09 0.13±0.09 0.13±0.09ZZ 1565.04±10.21 1435.69±9.72 1018.88±8.20 37.8±1.47 13.91±0.88 4.98±0.55 1.86±0.33 0.59±0.19 0.25±0.14Tri− boson 16.27±0.20 11.64±0.17 8.32±0.15 5.49±0.12 1.80±0.07 3.46±0.11 0.76±0.04 1.78±0.07 0.81±0.05WZ 2399.69±16.31 2044.15±14.91 404.39±6.60 152.82±4.05 50.11±2.28 60.11±2.54 20.03±1.49 8.67±0.94 2.12±0.44Σ SM irreducible 4059.32±19.37 3496.63±17.81 1433.52±10.54 197.04±4.31 66.10±2.45 69.21±2.61 22.9±1.53 11.33±0.98 3.40±0.47tt¯ 249.53±5.73 51.45±2.64 42.72±2.41 25.67±1.85 10.46±1.18 14.79±1.41 4.26±0.75 4.43±0.77 0.6±0.3t 14.29±2.55 10.13±2.18 7.27±1.86 4.11±1.42 0.32±0.78 1.23±0.92 0.2±0.2 0.00±0.29 0.00±0.29WW 6.8±0.64 4.06±0.48 3.61±0.46 1.71±0.32 0.55±0.18 0.83±0.22 0.15±0.1 0.35±0.14 0.07±0.04Z + LF 2223.53±95.81 2051.53±91.63 1184.67±69.08 29.52±10.08 13.09±6.96 0.00±9.87 0.00±9.87 0.00±9.87 0.00±9.87Z +HF 600.5±28.86 448.27±24.95 91.02±10.4 6.28±2.5 0.85±0.85 0.00±1.44 0.00±1.44 0.00±1.44 0.00±1.44W + j 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023Σ SM reducible 3094.65±100.26 2565.45±95.03 1329.30±69.92 67.28±10.65 25.27±7.15 16.85±10.07 4.61±9.97 4.78±10.01 0.67±9.98Total Bkg. 7153.97±102.12 6062.07±96.69 2762.81±70.71 264.32±11.49 91.38±7.56 86.07±10.40 27.51±10.08 16.12±10.08 4.07±9.99sm sleptons 500,0 28.5±0.5 24.9±0.4 24.1±0.4 23.2±0.4 0.7±0.1 22.1±0.4 0.7±0.1 19.2±0.4 18.4±0.4ZN (15% ∆SM) 0.03 0.03 0.06 0.5 0.0 1.4 0.0 3.4 5.7sm Z,W 250,0 40.0±0.7 36.4±0.7 2.0±0.2 1.7±0.2 0.3±0.1 1.4±0.1 0.8±0.1 0.8±0.1 0.4±0.1ZN (15% ∆SM) 0.04 0.04 0.01 0.03 0.0 0.1 0.0 0.0 0.0149Table A.2: MC yield estimates and statistical uncertainties for reducible and irreducible SM backgroundsat all stages of the SRnoZd cutflow.SRnoZdSelection 3` SFOC b-veto Z-veto /ET >120GeV 20< m`` <81 GeV Nj ≥3tt+ Z 52.88±1.83 51.54±1.81 3.71±0.50 0.77±0.20 0.08±0.06 0.08±0.06 0.00±0.05tt+W 25.44±1.35 19.53±1.19 1.43±0.32 1.15±0.29 0.30±0.15 0.06±0.06 0.06±0.06ZZ 1565.04±10.21 1559.05±10.19 1435.69±9.72 1018.88±8.20 0.60±0.19 0.34±0.14 0.07±0.06Triboson 16.27±0.20 12.72±0.17 11.64±0.17 8.32±0.15 1.06±0.05 0.46±0.030 0.009±0.004WZ 2399.69±16.31 2385.01±16.25 2044.15±14.91 404.39±6.60 15.06±1.28 6.55±0.82 0.35±0.02Σ SM irreducible 4059.32±19.37 4027.85±19.31 3496.63±17.81 1433.52±10.54 17.1±1.3 7.49±0.84 0.49±0.10tt 249.53±5.73 189.87±5.01 51.45±2.64 42.72±2.41 3.42±0.68 2.41±0.57 0.57±0.30t 14.29±2.55 13.22±2.49 10.13±2.18 7.27±1.86 0.0±0.3 0.0±0.3 0.0±0.3WW 6.80±0.64 5.38±0.57 4.06±0.48 3.61±0.46 0.31±0.14 0.0±0.1 0.0±0.1Z + LF 2223.53±95.81 2214.40±95.59 2051.53±91.63 1184.67±69.08 0.00±0.01 0.00±0.01 0.00±0.01Z +HF 600.50±28.86 599.02±28.84 448.27±24.95 91.02±10.40 0.0±0.1 0.0±0.1 0.0±0.1W + j 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023 0.0±0.00023Σ SM reducible 3094.65±100.26 3021.89±100.01 2565.45±95.03 1329.30±69.92 3.73±0.76 2.41±0.66 0.57±0.44Tot BG 7153.97±102.12 7049.74±101.85 6062.07±96.69 2762.81±70.71 20.83±1.51 9.90±1.07 1.06±0.45150Table A.3: MC yield estimates and statistical uncertainties for reducible and irreducible SM backgroundsat all stages of the SRZ-type cutflows.SRZa SRZb SRZcSelection Z req. 75< /ET <120 GeV mT <110 GeV mT >110 GeV /ET > 120GeV mT >110GeVtt¯+ Z 2.9±0.5 0.53±0.19 0.43±0.17 0.10±0.09 0.51±0.20 0.10±0.10tt¯+W 0.27±0.14 0.12±0.09 0.00±0.05 0.12±0.09 0.004±0.004 0.004±0.004ZZ 417±5 9.8±0.8 8.9±0.8 0.95±0.25 2.0±0.4 0.39±0.16Tri− boson 3.33±0.08 0.97±0.04 0.536±0.032 0.433±0.029 0.549±0.026 0.290±0.018WZ 1640±13 254±5 235±5 18.7±1.4 77.8±2.9 5.0±0.7Σ SM irreducible 2063±14 265±5 245±5 20.3±1.4 80.9±2.9 5.8±0.7tt¯ 8.7±1.1 2.7±0.6 2.2±0.5 0.46±0.27 0.58±0.25 0.24±0.17t 2.9±1.1 1.0±0.7 1.0±0.7 0.00±0.29 0.00±0.29 0.00±0.29WW 0.45±0.14 0.06±0.05 0.06±0.05 0.00±0.05 0.07±0.05 0.05±0.05Z + LF 867±60 16±8 8±5 8±6 0±4 0±4Z +HF 357±23 0.0±1.4 0.0±1.4 0.0±1.4 0.00±1.4 0.00±1.4W + j 0.00±0.00023 0.00±0.00023 0.00±0.00023 0.00±0.00023 0.00±0.00023 0.00±0.00023Σ SM reducible 1236±64 20±8 11±6 9±6 0.7±4.2 0.30±4.18Total Bkg. 3299±66 285±10 256±8 29±6 82±5 6±4sm sleptons 500,0 0.8±0.1 0.06±0.02 0.008±0.007 0.05±0.02 0.7±0.1 0.7±0.1ZN (15% ∆SM) 0.0 0.0 0.01 0.0 0.0 0.0sm Z,W 250,0 34.4±0.7 9.2±0.4 4.7±0.3 4.6±0.3 17.7±0.5 12.0±0.4ZN (15% ∆SM) 0.1 0.2 0.1 0.5 1.1 3.6151Table A.4: Validation region predictions compared to data observa-tions. Errors are statistical and systematic.Selection VRnoZa VRnoZb VRZa VRZbTriboson 1.4±1.4 0.5±0.5 0.6±0.6 0.26±0.27ZZ 128±87 4.5±2.8 108±23 6.9±2.2tt¯V 2.9±1.2 21±7 7.4±2.6 26±8WZ 110±21 34±15 545±89 138±38Σ SM irreducible 242±90 60±16 662±92 171±39tt¯ 25±4 78±8 7.7±1.4 13.3±2.22t 1.6±1.1 2.0±0.9 0.7±0.8 0.6±0.9WW 0.63±0.26 0.96±0.32 0.06±0.15 0.18±0.17V + j 168±58 4±4 294±69 15±6Σ SM reducible 195±58 84±10 302±69 29±7Σ SM 437±107 145±19 964±115 200±40Data 463 141 1131 171152Appendix BComplete CLs MapsThe limit contours shown in chapter 8 are isolines drawn through CLs =0.05(±1σ). Complete sets of observed CLs values are shown for SIM infigure B.1 and for MUED in figure B.2. Values between grid points areobtained with linear interpolation.15300.10.20.30.40.50.60.70.80.9 [GeV]1±χ∼, 20χ∼m200 300 400 500 600 700 800 [GeV]0 1χ∼m0100200300400500600 CL observed 0.00 0.00 0.00 0.00 0.07 0.51 0.83 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.27 0.69 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.52 0.83 0.00 0.00 0.23 0.00 0.27 0.70 0.00 0.00 0.00 0.01 0.76 0.00 0.52 0.08 0.00 0.02 0.11 0.27 0.29 0.69 0.05 0.17 0.83 0.37 0.60 0.85 0.22 0.62 0.72 0.79 0.93 0.64 0.68 0.86 0.97ATLAS Work in Progress(a) SIM via ˜`00.10.20.30.40.50.60.70.80.9 [GeV]1±χ∼, 20χ∼m100 150 200 250 300 350 400 450 500 [GeV]0 1χ∼m050100150200250300350400450 CL observed 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.12 0.32 0.53 0.69 0.00 0.03 0.00 0.00 0.00 0.00 0.00 .00 .00 .00 .05 0.00 .00 0.00 .00 0.00 0.03 0.13 0.30 0.51 0.00 0.13 0.00 0.00 0.10 0.01 0.54 0.01 0.04 0.21 0.03 0.06 0.17 0.34 0.53 0.70 0.29 0.45 0.18 0.23 0.40 0.56 0.64 0.67 0.41 0.45 0.59 0.71 0.83 0.80 0.60 0.64 0.91 0.91 0.77 0.78 0.95 0.93 0.97 0.96 0.98ATLAS Work in Progress(b) SIM via WZFigure B.1: Observed CLs values across both SIM grids.1541/R [GeV]700 800 900 1000 1100 1200 1300 RΛ05101520253035400.10.20.30.40.50.60.70.80.90.79 0.79 0.85 0.91 0.90 0.90 0.930.00 0.01 0.03 0.16 0.33 0.61 0.750.00 0.00 0.01 0.06 0.29 0.64 0.76CL observedATLAS Work in ProgressFigure B.2: Observed CLs values across the MUED grid.155
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A search for supersymmetry and universal extra dimensions in final states with three leptons and missing… King, Samuel 2014
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Title | A search for supersymmetry and universal extra dimensions in final states with three leptons and missing transverse momentum in 20.7 inverse femtobarns of 8 TeV pp collisions with the ATLAS detector |
Creator |
King, Samuel |
Publisher | University of British Columbia |
Date Issued | 2014 |
Description | This dissertation presents a search for direct production of charginos and neutralinos in final states with three leptons and missing transverse momentum in 20.7 inverse femtobarns of 8 TeV (center of mass) proton-proton collisions delivered by the Large Hadron Collider and collected with the ATLAS detector. The Standard Model augmented with the minimal formulation of universal extra dimensions (MUED) is phenomenologically similar to supersymmetry. This search is also sensitive to MUED cascades characterized by the presence of n=1 Kaluza-Klein excitations of Standard Model W and Z bosons. No significant excess over Standard Model predictions is observed. The results are interpreted in the context of simplified supersymmetric models and MUED. New limits are set at the 95% confidence level on the parameter spaces of these models. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2014-04-22 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivs 2.5 Canada |
DOI | 10.14288/1.0167428 |
URI | http://hdl.handle.net/2429/46557 |
Degree |
Doctor of Philosophy - PhD |
Program |
Physics |
Affiliation |
Science, Faculty of Physics and Astronomy, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 2014-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ |
AggregatedSourceRepository | DSpace |
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