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Search for Heavy Narrow Resonances Decaying to Dimuons with the CMS Detector

Permanent Link: http://ufdc.ufl.edu/UFE0045198/00001

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Title: Search for Heavy Narrow Resonances Decaying to Dimuons with the CMS Detector
Physical Description: 1 online resource (176 p.)
Language: english
Creator: Kypreos, Theodore N
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: physics
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract: The search for high-mass resonances decaying to dimuons is one of the flagship exotic searches for the CMS physics program. This search was performed using sqrt s = 8 TeV pp collision data collected by the CMS experiment taken from April to June 2012. The samples used correspond to an integrated luminosity of 4.1 fb sup -1. No evidence for new physics beyond the standard model is observed, so 95 % CL upper limits on the cross section times branching fraction of a new dimuon resonance relative Z boson are obtained using this dataset. Upper limits are interpreted in the context of two \zprime models: the Sequential Standard Model with standard model-like couplings and the superstring-inspired Z sub psi. The 95 % CL lower mass limits obtained are 2270 GeV for the Z sub SSM and 1940 GeV for the Z sub psi. These limits are more stringent than the previous results from CMS.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Theodore N Kypreos.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Furic, Ivan Kresimir.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-05-31

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045198:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045198/00001

Material Information

Title: Search for Heavy Narrow Resonances Decaying to Dimuons with the CMS Detector
Physical Description: 1 online resource (176 p.)
Language: english
Creator: Kypreos, Theodore N
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: physics
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The search for high-mass resonances decaying to dimuons is one of the flagship exotic searches for the CMS physics program. This search was performed using sqrt s = 8 TeV pp collision data collected by the CMS experiment taken from April to June 2012. The samples used correspond to an integrated luminosity of 4.1 fb sup -1. No evidence for new physics beyond the standard model is observed, so 95 % CL upper limits on the cross section times branching fraction of a new dimuon resonance relative Z boson are obtained using this dataset. Upper limits are interpreted in the context of two \zprime models: the Sequential Standard Model with standard model-like couplings and the superstring-inspired Z sub psi. The 95 % CL lower mass limits obtained are 2270 GeV for the Z sub SSM and 1940 GeV for the Z sub psi. These limits are more stringent than the previous results from CMS.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Theodore N Kypreos.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Furic, Ivan Kresimir.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045198:00001


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SEARCHFORHEAVYNARROWRESONANCESDECAYINGTODIMUONSWITH THECMSDETECTOR By THEODORENICHOLASKYPREOS ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2013

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c 2013TheodoreNicholasKypreos 2

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ACKNOWLEDGMENTS Iwouldrstliketoacknowledgemywife,Mary,forobviousreasons.Thesesame reaonsextendtomyfamily,manyofwhomdidnotlivetoseemenishthisendeavor. Iwouldliketoacknowledgemyadvisor,IvanFuri`'c,forhisguidanceandsupport overtheselastyearsofgraduateresearch.Hetaughtmediligenceandthatnumbers mustalwaysmakesense. IwouldliketothanksomeofmyclosefriendsandcolleaguesatCERNfortheir support.IthankSamHarperforalwaysbeingavailableforafrankdiscussion,Greg RaknessforhisdirectionwiththeCSCs.IalsowishtothankGianPierodiGiovanniand MicheledeGruttolaforteachingmemandatoryItalianandhowtoenjoyacoffeebreak, aswellastheirintellectualguidance. IalsomustsaythatIcouldnothavegottenbyatCERNwithoutthefriendshipof GabrielYbeles-Smit,RyanCarroll,AnnaPhan,KeithRose,GraysonWilliams,John BabbandAndyKubick. 3

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TABLEOFCONTENTS page ACKNOWLEDGMENTS..................................3 LISTOFTABLES......................................6 LISTOFFIGURES.....................................8 ABSTRACT.........................................16 CHAPTER 1INTRODUCTION...................................17 2THEORETICALBACKGROUND..........................19 2.1Drell-YanProcess...............................20 2.2SearchMotivation...............................21 3EXPERIMENTALAPPARATUS...........................26 3.1TheLargeHadronCollider..........................26 3.2TheCompactMuonSolenoidExperiment..................27 3.2.1CoordinateSystem...........................29 3.2.2InnerTracker..............................29 3.2.3ElectronCalorimeter..........................31 3.2.4HadronCalorimeter..........................33 3.2.5SuperconductingSolenoid.......................34 3.2.6MuonSystem..............................35 3.2.7Trigger..................................36 4MUONRECONSTRUCTION............................50 4.1MuonReconstructionConsiderations.....................50 4.2OfineMuonIdentication...........................54 4.3MomentumResolution.............................56 4.4AbsoluteMomentumScaleUsingtheEndpointMethod.........58 4.4.1MockDataTemplateMDTTechnique................59 4.4.2Bootstrap................................60 4.5MuonIsolation.................................61 5DATASELECTION..................................74 5.1GoodRuns...................................74 5.2TriggerSelection................................75 5.3EventSelection.................................76 5.4Simulation....................................79 4

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6ANALYSIS......................................87 6.1Normalizationtothe Z 0 resonance......................88 6.2Backgrounds..................................90 6.2.1Drell-Yanbackground.........................90 6.2.2Non-DYPromptLeptonBackroundsandthe e ControlSpectrum ......................................91 6.2.3JetBackgroundsandtheSame-SignControlRegion........92 6.2.4Cosmic-RayMuonBackgroundContamination...........97 6.3Resolution....................................98 6.4Limits......................................99 6.5SystematicUncertainties...........................101 7RESULTS.......................................123 8CONCLUSION....................................129 APPENDIX ACOSMICMUONSUNDERGROUND........................131 BMUONCHARGEMISIDENTIFICATION......................138 CPULLDISTRIBUTIONS...............................141 DTRACKERALIGNMENTANDWEAKModes...................145 EQCDBACKGROUNDESTIMATION........................149 E.1Closuretests..................................149 E.2FakeRatewithBackgroundSubtraction...................151 E.3IsolationCorrelations..............................152 FENDPOINT......................................161 F.1DependenceontheMomentumScaleProbe................161 F.2ComparingDataandSimulationMethods..................162 F.3Uncertainties..................................163 REFERENCES.......................................170 BIOGRAPHICALSKETCH................................176 5

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LISTOFTABLES Table page 2-1Left-handedofquarksandleptonsandtheirassociatedcharges.........24 3-1Proton-protoncollisionparametersrelevanttoCMS................40 3-2ParametersdescribingCMSECALenergyresolution...............42 3-3MainoperatingparametersoftheCMSsuperconductingsolenoidmagnetfor anominalmagneticuxdensityof 4 T .......................45 5-1 PYTHIA parametersforageneral E 6 Z 0 model...................81 5-2Datasetsandtheassociatedrunrangesusedforthisanalysis..........82 5-3Summaryofsimulatedsignalandbackgroundprocesssamplesusedtogenerated with p s =7TeV .Theprogramslistedinthatcolumnhighlightdepartures fromusingplain PYTHIA foreverything,e.g. MADGRAPH or POWHEG .........82 5-4Summaryofsimulatedsignalandbackgroundprocesssamplesusedtogenerated with p s =8TeV .Theprogramslistedinthatcolumnhighlightdepartures fromusingplain PYTHIA foreverything,e.g. MADGRAPH or POWHEG .........85 6-1Background-subtracted Z 0 candidatecountsobservedunder 7 TeV and 8 TeV runningconditions..................................103 6-2FittedparametervaluesfortheDrellYancontinuum...............103 6-3Data-drivenpredictionofthedimuonbackgroundfromdijetsfakingmuons, forbothopposite-signandsame-signevents.Errorsarestatisticalonly.....113 6-4Data-drivenpredictionofthedimuonbackgroundfromW + jetsanddijetsfaking muons,forbothopposite-signandsame-signevents...............115 6-5Summaryofsystematicsevaluatedforthe Z 0 search...............116 7-1Thenumberofdileptoneventswithinvariantmassinthecontrolregion 120 < m `` < 200 GeV andinthesearchregion m `` > 200 GeV foranintegrated luminosityof 4.1fb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 inthedimuonchanneland 3.6fb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 inthedielectronchannel. Thetotalbackgroundisthesumoftheeventsforthestandardmodelprocesses listed.Theyieldsfromsimulationarerelativelynormalizedusingtheexpected crosssections,andoverallthesimulationisnormalizedtothedatausingthe numberofeventsinthemasswindow 60 )]TJ/F22 11.9552 Tf 13 0 Td [(120 GeV .Uncertaintiesinclude bothstatisticalandsystematiccomponentsaddedinquadrature.........124 8-1Masslowerlimitsatthe 95% CLonspecicmodelsobtainedusingdilepton dataat p s =7 and 8 TeV separatelyandcombined...............130 6

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E-1SummaryofadditionalmuonenrichedQCDsimulationsamplesgenerated using PYTHIA .Samplesarebinnedintermsofthepartontransversemomentum, ^ p T ,whichisageneratorquantity..........................153 7

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LISTOFFIGURES Figure page 2-1LeadingorderFeynmandiagramcreatingtwoopposite-signleptonsinthe nalstate,includingatheoretical Z 0 vectorboson.................24 2-2Feynmandiagramshowingthequark-antiquarkannihilationintoaneutral Z = propagatorthatdecaysintoaleptonpair......................24 2-3InvariantmassdistributionsforRS1processwithDrell-Yanbackgroundatthe LHC.Fromtoptobottom,thecurvesareforcouplingvalues k = M Planck =1,0.5,0.1,0.05,0.01 ..........................25 3-1TheLHCinjectorcomplex..............................38 3-2ExpandedviewoftheCMSdetector........................39 3-3SliceoftheCMSdetectorinthe r )]TJ/F25 11.9552 Tf 13.285 0 Td [( planeshowingthepathsofdifferent particles........................................39 3-4Generallayoutofthepixeldetector.........................40 3-5Generallayoutofthesiliconstripdetector......................40 3-6Leadtungstatecrystal.................................41 3-7LayoutoftheCMSECAL...............................41 3-8Room-temperaturelongitudinalopticaltransmissionandradio-luminesence atsteady-state 57 Co excitation 122 keV forproduction PbWO 4 crystals...42 3-9LongitudinalviewoftheCMSdetectorshowingthelocationsofthehadron barrelHB,endcapHE,outerHO,andforwardHFcalorimeters......43 3-10SchematicviewsoftheCMSsolenoidwiththenumberingconventionforthe azimuthalsectorsS,wheelsW,barrelyokelayersLandendcapdisks D.TCisthetailcatcher,anadditionalsteellayerpresentinthecentral barrelwheel W 0 only................................43 3-11Valueof j B j leftandeldlinesrightpredictedonthelongitudinalsection oftheCMSdetector,fortheundergroundmodelatacentralmagneticux densityof 3.8 T .Eacheldlinerepresentsa 6 Wb incrementinthemagnetic ux...........................................44 3-12RepresentativeguresshowingtheoperationoftheCMSmuonsystem....46 3-13ThelayoutofaDTchamberinsideamuonbarrelstation.............47 3-14SchematicviewoftheRPC..............................47 8

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3-15SchematicviewofaCSCchamber.........................48 3-16ArchitectureoftheCMSLevel )]TJ/F22 11.9552 Tf 9.298 0 Td [(1 trigger.......................49 3-17OverviewoftheCMStriggercontrolsystem....................49 4-1Stoppingpower= h d E = d x i forpositivemuonsincopperasafunctionof = p = Mc overnineordersofmagnitudeinmomentum.Solidcurvesindicatethe totalstoppingpower.................................63 4-2Muonradiationlossesasafunctionofmuonenergyin GeV brokendowninto directpair-production,bremsstrahlung,andphotonuclearinteractions......63 4-3Productionofelectronsbymuonstraversingmatterasafunctionofthemuon momentumviaionization,whichislabeledasDeltarays,Bremsstrahlung, andpairproduction..................................64 4-4Distributionofthedistanceofhitsfromthenominalmuontrackduetoshowering inducedbyamuoniniron.Theinsertshowstheprobabilityofthenumberof additionalhits.....................................65 4-5Simple 3 )]TJ/F20 11.9552 Tf 12.622 0 Td [(pointdiagramofthemeasurementofamuontrack. r istheradius ofthehelicalpathfromacentralpointforaparticletraversingthroughalength L s isthesagitta...................................66 4-6CosmicmuoncrossingtheCMSdetectorfromtoptobottomleavinghitsin themuonsystem,tracker,andcalorimeter.....................67 4-7ThesampleRMStruncatedat 1 andGaussiantstothe q = p T relativeresiduals comparingtheoutputsforresultswiththetrackertandglobalmuontswith theTunePalgorithm.................................67 4-8WidthsandmeansoftheGaussiantsofthemuon q = p T pullscomparingthe outputsforresultswiththetrackertandglobalmuontswiththeTuneP algorithm........................................68 4-9Simulatedeffectofabiasinq/ p T ona 1 TeV Z 0 withthetrueresonancein black,thetrackerresolutioninblueandthetrackerresolutionwithabiasin shadedredfora 0.1 c/TeV biasanda 0.5 c/TeV bias..............68 4-10Simulatedeffectofabiasinq/ p T ona 3 TeV Z 0 withthetrueresonancein black,thetrackerresolutioninblueandthetrackerresolutionwithabiasin shadedredfora 0.1 c/TeV biasanda 0.5 c/TeV bias..............69 4-11Demonstrationofthesimulation-basedgeneralendpointmethod........70 4-12Demonstrationofthepurelydatadrivenendpointmethod............71 4-13Demonstrationofthepurelydata-drivenendpointmethod.Theresulting 2 versus distributionwhenthereisa =1 c/TeV biasinjected.........72 9

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4-14Fordimuonsonthe Z 0 peak 60 < m < 120 GeV for 2011 collisonconditions ontopand 2012 collisionconditionsonthebottom.Thefractionofmuonsotherwise selectedusingtheseanalysiscutsthatfailacutonthetracker-onlyrelative isolationat 0.1 blacktrianglesoracutonthetracker-plus-calorimetersrelative isolationat 0.15 redsquares,asafunctionofthenumberofreconstructed primaryvertices....................................73 5-1L 1 efcienciesforthe L1SingleMu16 pathfor 2011 and 2012 data........81 5-2Asafunctionofinvariantmass,thecombinedreconstructionandselection efciencyfordimuonspassingselectioninsimulationwithrespecttotriggered eventsinacceptanceredcircles,withrespecttoalleventsinacceptance greensquares,andthetotalacceptancetimesefciencybluetriangles. Thebluecurveisattothetotalacceptancetimesefciencyinthedimuon massrangefrom 200 to 2000 GeV ..........................83 5-3Theratioofthenumberofeventsintheregion 60 < m < 120 GeV thatpass allselectioncutstothenumberofeventspassingallcutsbuttheoneindicated, formaincutsintheeventselection.Efciencymeasuredfromdataisshown inblackcircles,andpredictionbythesimulationlabeledasMCisshownin magentahistogram..................................84 5-4Therapiditydistributionfor Z = productionattheLHCforaninvariantmass M =250 GeV .TheLO,NLO,andNNLOresultshavebeenincluded.The bandsindicatetheresidualenergyscaledependences..............84 5-5Data-simulationcomparisonsfor 4.5fb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 of p s =8TeV data...........86 6-1Upperlimitsasafunctionoftheresonancemass M ontheproductionratio R ofcrosssectiontimesbranchingfractionintoleptonpairsfor Z 0 SSM Z 0 Z 0 St and G KK productiontothesamequantityforZbosons.Shadedgreenandyellow bandscorrespondtothe 68% and 95% quantilesfortheexpectedlimits.The predictedcrosssectionratiosareshownasbands,withwidthsindicatingthe theoreticaluncertainties.Thedifferencesinthewidthsreecttheuncertainties intheKfactorsused..................................104 6-2ATLAScollaborationresultshowingtheexpectedandobserved 95% C.L.upper limitoncrosssectiontimesbranchingfractionofthetheoretical Z 0 models...105 6-3ComparisonoftheshapesfortheDYmassspectraobtainedwith PYTHIA black histogramand POWHEG redhistogram;thebottomplotshowstherelativedifference betweenthetwo...................................106 6-4FittothesimulatedDrellYandimuonmassspectrumtopandtheresiduals asafunctionofthemassbottom.........................107 10

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6-5Therelativedifferencebetweenmuondataandthettedparameterizationof thesimulatedbackground,wherethelatterisnormalizedtodata,isshown invariousmassbins.Thebinningwaschosentohaveaminimumwidthof 20 GeV andtohaveatleast 10 eventsineachbin.Thebinwidthisrepresented bythehorizontalerrorbarsthatisnotanuncertainty...............108 6-6ExampleFeynmandiagramsthatgivetwoleptonsofanyavorinthenal state..........................................109 6-7Theobservedopposite-sign e dileptoninvariantmassspectrumdatapoints. Thelledredhistogramshowsthecontributiontothespectrumfrom t t and othersourcesofpromptleptonstW,dibosonproduction, Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(,asderived fromsimulations.Thebackgroundwhereatleastoneofthereconstructed objectsisnotarealleptonisshowninyellowandestimatedfromthedata usingthesame-sign e spectrum........................110 6-8Thelledhistogramsinredcolorsshowthecontributiontothespectrumfrom t t andothersourcesofpromptleptonstW,diboson, Z 0 ,asderived fromsimulations.Backgroundsfromsourceswhereatleastoneofthereconstructed objectsisnotarealleptonareshowninbluecolorsW + jets, Z 0 Z 0 ee andinyellowmultijets...............................111 6-9SimulatedQCDmuonsthataregeneratedwith PYTHIA andsimulatedforthe CMSdetectorresponsewith GEANT .Eventswhereexactlyonemuonarefound inthesimulatedeventareaccepted.........................112 6-10The distributionofsimulationwhereonemuonisobservedinthenalstate thatpassesfailsisolationshowninlogarithmicandlinearscales........113 6-11Data-simulationcomparisondistributionsin p T and forsinglemuonevents givena,anyisolation;b,passingisolation;c,failingisolation.Blacklinesrepresent data,theredshadeissimulation..........................114 6-12Re-weighteddistributionofexpecteddimuoneventsfromdijeteventswhere thetwoobservedhaveopposingchargeandthesamecharge.[1].......115 6-13Re-weighteddistributionofexpecteddimuoneventsfromW + jeteventswhere thetwoobservedhaveopposingchargeandthesamecharge..........115 6-14Controlplotthatisasanadditionaldi-muoncross-checkonstandardmodel backgroundrates.Theobservedsame-sign dileptoninvariantmassspectrum datapoints.Thelledhistogramsinredcolorsshowthecontributiontothe spectrumfrom t t andothersourcesofpromptleptonstW,dibosonproduction, Z 0 ,asderivedfromsimulations.Thebackgroundsfromsourceswhere atleastoneofthereconstructedobjectsisnotarealleptonW + jets,dijetis inyellow........................................116 11

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6-15Thecumulativedistributionoftheinvariantmassspectrumof events. Thepointswitherrorbarsrepresentthedata;thehistogramsrepresentthe expectationsfromSMprocesses..........................117 6-16Thedimuoninvariantmassspectrumandthemuonazimuthalangle distribution forcosmic-raydimuonevents,asidentiedbyfailingtheanti-cosmicselection criteria.........................................117 6-17Comparisonbetweendataandsimulationforthedistributionofthe3Dangle whichisdenedasthedifferenceof andtheanglebetweenmuontracks inthe3-space.Distributionsareshownstartingfromthedefaultselectiondetailed inChapter5exceptingthecuton .........................118 6-18Simulated Z 0 invariantmassresolutionasafunctionofthetheoretical Z 0 mass. SecondorderpolynomialttotheTunePalgorithmisshown.........119 6-19Muonresolutionestimatorfrom 2012 cosmic-raymuons.Trackertinblackis comparedwiththeTunePhighp T algorithminbluetriangles.........120 6-20Generalendpointresultsinbinsof .Data-drivenbiasmeasurementwitha p T > 45 GeV p T > 100 GeV requirementontheleftrightplotsrespectively...121 6-21Generalendpointresultsinbinsof restrictedto j j < 1 .Left-handplot showsthebiasmeasuredasafunctionof forthetracker.Right-handplot showsthebiasmeasuredasafunctionof forthefullmuont.........121 6-22Ratioon R between p s =7,8 TeV asafunctionofthetheoreticalmass Z 0 usingthe Z 0 modelasthereference........................122 7-1The + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(invariantmassspectrum.Thepointswitherrorbarsrepresentdata; thehistogramsrepresentexpectationsfromstandardmodelprocesses: Z = t t andothersourcesofpromptleptonstW,dibosonproduction, Z 0 ,and jetbackgroundsthathaveatleastonemuonembedded.............125 7-2Thecumulativedistributionoftheinvariantmassspectrumof + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(events. Thepointswitherrorsrepresentdata;histogramsrepresenttheexpectations fromstandardmodelprocesses...........................126 7-3Upperlimitsasafunctionofresonancemass M ontheproductionratio R of crosssectiontimesbranchingfractionintomuonpairsfor Z 0 SSM and Z 0 boson productiontothesamequantityfor Z 0 bosons...................127 7-4Upperlimitsasafunctionofresonancemass, M ,onthecrosssectiontimes branchingfractionproductionratio, R ,of Z 0 SSM and Z 0 modelsdecayingto ee and + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(pairstothesamechannelsfor Z 0 bosonsforthecombined 7+ 8 TeV data.Shadedgreenandyellowbandscorrespondtothe 68% and 95% quantilesfortheexpectedlimits...........................127 12

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7-5Upperlimitsasafunctionofresonancemass, M ,onthecrosssectiontimes branchingfractionproductionratio, R ,of Z 0 SSM and Z 0 modelsdecayingto ee and + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(pairstothesamechannelsfor Z 0 bosonsforthecombined 7+ 8 TeV data.Shadedgreenandyellowbandscorrespondtothe 68% and 95% quantilesfortheexpectedlimits...........................128 A-1Verticaluxesofcosmicraysintheatmospherewith E > 1 GeV .Thepoints showmeasurementsof )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(with E > 1 GeV ....................133 A-2Verticaluxesofcosmicraysintheatmospherewith E > 1 GeV .Thepoints showmeasurementsof )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(with E > 1 GeV ....................134 A-3SimulatedcosmicmuonsfromthesurfaceoftheEarthpropagatedtotheCMS detector.TheCMSdetectorisshownasthedashedtriangle.Themainshaft andtwoaccessshaftsaremodeledandshownasblackcircles.[2]......134 A-4Energyspectrumofmuonsindatablackpointsmeasuredwithglobalmuons. Comparisonwith GEANT simulationblue/greenhistogramisshown,withsimulation normalizedtodata..................................135 A-5ThethreeCMSresults,andtheircombination,asafunctionofmuonmomentum. Datapointsareplacedatthebinaverage,withthepointsfromthestandalone andglobal-muonanalysesoffsethorizontallyby 10% forclarity........136 A-6TheCMSresult,asafunctionoftheverticalcomponentofthemuonmomentum, togetherwithsomepreviousmeasurementsandatofthepion-kaonmodel totheCMSdata...................................137 B-1RateofchargemisassignmentasafunctionofpTofthetrackertrackreconstructed inthetophemisphere,forstandalonemuonssquares,trackertrackstriangles, globalmuonscircles,andtheTPFMSretupside-downtriangles......140 C-1Exampledistributionofpseudo-experimentsgeneratedfromEquationC with =4.1 ......................................142 C-2Pulldistributiononthemeasuredparameter ^ .ThepullisttedtoaGaussian distribution.......................................143 C-3Pulldistributiononthemeasuredparameter ^ withover-estimateduncertainties. ThepullisttedtoaGaussiandistribution.....................143 C-4Pulldistributiononthemeasuredparameter ^ whenthereisabiason ^ .....144 D-1Reconstructedmasspeakpositionsfor Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(decaysasafunctionof forthe + .Blackshowsthesimulateddesignconditions.Redshowsdata withtheMillipedealignmentalgorithm.Blueshowsdataafterthevertexconstraint isadded........................................147 13

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D-2Resultofthebootstrapgeneralendpointmethodtfortheoveralbiasin q = p T RedpointslabeledasPromptalignmentshowdatabeforethevertexconstraint isappliedasafunctionof .BlackpointslabeledasNovalignmentshow themeasuredbiasafterthevertexconstraintisappliedasafunctionof ...147 D-3Reconstructedmasspeakpositionsfor Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(decaysasafunctionof forthe + and )]TJ/F20 11.9552 Tf 7.085 -4.338 Td [(.Blackshowsthemean Z 0 massin 2012 datausedinthis dissertation.Redshowsthemean Z 0 massin 2012 simulationusedinthis dissertation......................................148 E-1InvariantmassdistributionofQCDdijetevents.Opposite-signeventsareshown inblue;same-signeventsareshowninred....................154 E-2Weightmapinbinsof p T and producedaccordingto w p T = N pass = N fail for 1 p T p T < 0.3 ...................................155 E-3Comparisonbetweenthetrueblackandpredictedredsingle-muonspectrum ofjetsfakingmuonsinQCDsimulation.......................156 E-4ComparisonbetweentheobservedandpredictedQCDdimuonspectrumfor theclassofeventswhereexactlyonemuonpassesisolation.Blacklineswith errorbarsrepresentthesimulatedtruedistribution.Theredhistogramrepresents thepredictionofthere-rewightedspectrumfromeventswherebothmuons failisolation......................................157 E-5ComparisonbetweentheobservedandpredictedQCDdimuonspectrumfor theclassofeventswherebothmuonsisolation.Blacklineswitherrorbars representthesimulatedtruedistribution.Theredhistogramrepresentsthe predictionofthere-rewightedspectrumfromeventswherebothmuonsfail isolation........................................158 E-6ComparisonbetweentheobservedandpredictedQCDdimuonspectrumfor theclassofeventswhereexactlyonemuonpassesisolationwithlooserselection. Blacklineswitherrorbarsrepresentthesimulatedtruedistribution.Thered histogramrepresentsthepredictionofthere-rewightedspectrumfromevents whereexactlyonemuonfailsisolation.......................158 E-7QCDjetfakerateinsimulationasafunctionof p T .Blackismeasuredfrom eventswhereonlyonemuonisobserved.Blueisthedimuonfakeratefor dimuoneventswhere M > 60 GeV .Redisthedimuonfakeratefordimuon eventswhere M < 60 GeV .............................159 E-8BreakdownoftheisolationclassesofdimuoneventsinQCDsimulation.Black dotsrepresentanyisolation.Bluehistogramiswhenbothmuonsfailisolation. Redhistogramiswhenexactlyonemuonfailsisolation.Greenhistogramis whenbothmuonspassisolation..........................160 14

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F-1Modelofinjectingtwobiaseswithasmoothtransitioningcurvethatdepends onthetransversemomentum.Theinjectedmodelbiasstartswitha 2 =0.1 c/TeV bias.Aninectionpointisplacedatthemomentumscaleof =150 GeV withatransitionwidth, =0.1 c/GeV ,thatendswithanalbiasof 1 = 0.5 c/TeV .......................................165 F-2Blackpointsrepresentthemeasuredbiaslabeledasaveragebiasasafunction oftheminimum p T labeledasmuon p T cutrequiredforeventstoenterinto thet.Redlineshowstheappliedbias.......................166 F-3Pullmeanvs. p T cutofffor200pseudo-experiments...............166 F-4ComparisonindatawithbootstrapandMDTendpointmethods.Blackisthe bootstrapmethodlabeleddatabalancingandredistheMDTmethodlabeled MCttodata....................................167 F-5Measurementofthebiasintransversecurvature, ,in 2012 simulationwith thebootstrapmethod.................................168 F-6Pulldistributionsfor 200 toysimulationsusingMINOSerrorsandparabolic errors.........................................168 F-7Pullmeansandwidthsfor400toyexperimentsasafunctionoftheinjected bias..........................................169 15

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy SEARCHFORHEAVYNARROWRESONANCESDECAYINGTODIMUONSWITH THECMSDETECTOR By TheodoreNicholasKypreos May2013 Chair:IvanK.Furi c Major:Physics Thesearchforhigh-massresonancesdecayingtodimuonsisoneoftheagship searchesfortheCMSphysicsprogram.Thissearchwasperformedusing p s =8 TeV pp collisiondatacollectedbytheCMSexperimenttakenfromApriltoJune 2012 .The samplesusedcorrespondtoanintegratedluminosityof 4.1fb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .Noevidencefornew physicsbeyondthestandardmodelisobserved.Limitsonthecrosssectiontimes branchingfractionofanewdimuonresonancerelativeZbosonareobtained.Thelimits areinterpretedinthecontextofthecouplingsoftwo Z 0 models:theSequentialStandard Modelwithstandard-model-likecouplingsandthesuperstring-inspired Z 0 .A Z 0 SSM lighter than 2260 GeV ,anda Z 0 lighterthan 1960 GeV areexcludedat 95% condencelevel. TheselimitsaremorestringentthanthepreviousresultsfromCMS. 16

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CHAPTER1 INTRODUCTION Manytheoreticalmodelspredictnewheavyresonances,withmassesinexcess of 1 TeV,andwithpropertiessimilartothoseof Z 0 bosons.Thesehypotheticalheavy relativesofthe Z 0 bosonareoftenreferredtoas Z 0 bosons.Similartohowphotons,W andZbosonsaremediatorsofweakinteraction,the Z 0 bosonwouldbeacarrierofa newforce.Observinga Z 0 bosonwouldimplyadiscoveryofanew,fthforce,addingto theknowngravitational,strong,weak,andelectromagneticforces,andfundamentally changingourunderstandingofhownatureworks.Thus,searchesforheavyresonances areagshipanalysesforhighenergyparticleexperiments. Experimentswhichstudytheproductsofproton-protonorproton-antiprotonbeam collisionsarecalledhadroncolliderexperiments.Thecollidinghadronsprotonsand anti-protonsarenotpoint-likeobjects,theyarecomposedofpartons-quarksand gluons.Theseconstituentpartonsarethepoint-likeobjectswhichcollide,buttheyonly carryfractionsofthetotalhadronmomentum.Whilethehadronbeamenergiesarevery preciselycontrolled,theactualpartoncollisionsspanawiderangeofenergies.This iswhyhadroncolliderexperimentsareoftenreferredtoasdiscoverymachines.The inherentenergyspreadofthepartoncollisionsallowshadroncolliderstosweeplarge rangesofenergiesinsearchofnewparticles,whereasleptoncollidersmustbetuned tothedesiredcollisionenergy.Thisisalsowhythehadroncolliderwiththehighest collisionenergyimmediatelybecomesthefrontierparticlephysicsresearchfacility. Currently,thehadroncolliderwiththehighestcollisionenergyistheLarge HadronColliderLHC.ThisdissertationanalyzesLHCproton-protoncollisionswith center-of-massenergiesof 7 and 8 TeV.Eventhoughonlyafractionofthetotalbeam energyiscarriedbythecollidingpartons,heavyresonanceswithmassessignicantly above1TeVcanbeproducediftheyexist.PriortotheLHC,thehighestenergyhadron collisionswereproducedattheFermilabTevatron,wherethecenter-of-massenergyof 17

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p p collisionswas 1.96 TeV.Tevatroncollisionswerenotabletoproducenewparticles withmassessignicantlyabove 1 TeV.LHCcollisions,duetotheirhighenergies,clearly openanewenergydomainforheavyresonancesearches. Whenprobingfornewphenomena,itisveryusefultohaverobustexperimental tools.Muonparticlesproducesomeofthecleanestsignaturesinparticleexperiments. TheexperimentusedtocollectthedataforthisdissertationistheCompactMuon SolenoiddetectorCMS,whosenameimpliesthatitsdesignisoptimizedformuon detection.Overtheyears,theUniversityofFloridagrouphasstronglycontributedto thedesign,production,testing,andcommissioningoftheCMSmuondetectionand triggeringsystems.Asearchforheavy Z 0 resonancesdecayingtomuonpairscombines theuniqueopportunitiesofLHCcollisionswiththestrongesttechnicalexpertiseofthe UFgroup,andwaschosenasthetopicforthisdissertation. ThesearchforTeV-scaledimuonresonancespresentssometechnicalchallenges. Atenergiesapproaching 1 TeV,muonparticlesoftencauseshowersofsecondary particleswheninteractingwithmatter.Thisleadstodifcultiesinpreciselyreconstructing muontrajectoriesandmeasuringthemuonmomenta.Severalmethodsdocumentedin thisdissertationweredevelopedinordertodealwithreconstructionissuesandbiases specictoTeV-rangemuons. Thisdissertationisorganizedasfollows:Chapter2providesabasicdescription ofthestandardmodelofparticleinteractionsandthetheoreticalmotivationsthatare relevanttothissearch,Chapter3describestheexperimentalapparatus,Chapter4 providesanoverviewofmuonreconstructionandidenticationwiththeCMSdetector, Chapter5,describestheselectionofdimuonevents,Chapter6presentsthesearch fornewphysicsinthedimuonspectrum,Chapter7summarizesthesearchresults andplaceslimitsonmodelsofnewphysicsprocessesthatinvolvehighmassdimuon resonances,andconclusionsarepresentedinChapter8. 18

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CHAPTER2 THEORETICALBACKGROUND TheStandardModelSMofelementaryparticlephysicsisbuiltuponobserved symmetrieswiththeintentofunifyingtheknownlawsofphysics.Therststepin buildingtheSMwastheformulationofthequantumtheoryofelectromagnetism, quantumelectrodynamics QED[3].QEDwaslaterextendedtoincludetheweak interactionsforthecombinedtheoryfor electroweak EWKinteractions[4,5]. TheSMstartsbydescribingthefundamentalfermionparticlesquarksandleptons asDiracelds.Requiringlocalgaugeinvariancetothe SU I xU Y symmetrygives risetoasetofintermediatevectorbosonelds.The U Y hasquantumnumbersof weakhyperchargeand SU I hasquantumnumbersofweakisospin.Thegaugeboson eldscanbeorganizedtocorrespondtocomponentsoftheEWKmediatorbosonsW Z 0 ,and ,whichautomaticallycoupletothequarkandleptonelds.However,gauge vectoreldsintroducedtoassurelocalgaugeinvariancearemassless,whiletheWand Zbosonsaremassive.Theadditionalcomponentsofthevectoreldswhichmakethem massiveareproducedthroughtheprocessofspontaneoussymmetrybreaking.TheSM proposesthatthissymmetryisbrokenspontaneouslythroughtheHiggsmechanismthat predictsamassive spin )]TJ/F22 11.9552 Tf 12.289 0 Td [(0 boson,knownastheHiggsboson[610].Asofthewriting ofthisdissertation,aHiggscandidatehasbeenobservedbytheCMSandATLAS experimentsontheLHC[11,12].TheexactnatureofthisHiggsbosoncandidateisnot yetknown.ItisthusfarconsistentwiththeSMHiggs,andstudiesofitspropertiesare anactivetopicinparticlephysics. EWKinteractionsonlydescribepartoftheSM,theothercomponentisthetheory ofstrongforceinteractions.Strongforceinteractionsgoverntheinteractionsbetween anotherclassoffermionsknownasquarks.Initially,threeavorsofparticleswere proposed[13].Subsequentexperimentsledtofurtherquarkdiscoveriesandthe formulationofatheoryofstrongforceinteractions quantumchromodynamics QCD 19

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thatismediatedbyeightmasslessgluons.QCDhassixmassivequarkswithanew quantumnumbercalledcolorred,blueandgreenwherequarkscarryonecolor chargeandgluonseachcarrytwocolorcharges.Thetheoryofstronginteractionsis representedbythesymmetrygroup: SU color Quarksandgluonsarenotfoundasfreeparticlesinnature,butrathertheyarealways boundinsideofhadronsthatcarrynonetcolorcharge.thatarebuiltofquarks, anti-quarks,andgluons.Forhistoricalreasons,quarksandgluonsarereferredto as partons inthecontextofmodelingthestructureofhadrons.Thestructureofhadrons arecalled partondensity/distributionfunctions [14]PDFs.Theknownquarksand leptonsthatmakeupthefundamentalparticlesoftheSMaresummarizedinTable2-1. TheSMisgivenbythelocalsymmetrygroup: SU color SU I U Y Thisisaugmentedbytheconceptofspontaneoussymmetrybreaking,whichexplains howEWKtheoryisbrokenintotheelectromagneticandweakforcesatlowermass. ThisworksearchesforphysicsbeyondthecurrentSMthatisgivenbysymmetries thatarepotentiallyrestoredathigherenergyscales,producinghighermassforce carriersthatcouldunifythelawsofphysics.Thisworkfocusesonageneralsearchfora neutralgaugebosonthathascouplingssimilartothe Z 0 boson.TheFeynmandiagram associatedwiththissearchisgiveninFigure2-1,andincludesanyresonantparticle thatcandecaytotwomuons. 2.1Drell-YanProcess ThedominantSMbackgroundthatisrelevanttothisanalysiscomesfromwhen aquark-antiquarkpairannihilatetoproduceapairofleptonsinthenalstate.This processismediatedbya Z oroffshellphoton, ,asrepresentedbytheFeynman 20

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diagraminFigure2-2.Thisprocesswasrststudiedtheoreticallyasanelectromagnetic processinconnectiontodeepinelasticscatteringoveradecadebeforethediscoveryof theneutralgaugebosonandisgenerallyreferredtoastheDrell-YanDYprocess[15, 16]. AttheLHC,thequarkcanbeoneofthevalencequarks,buttheantiquark necessarilycomesfromtheseaofquark-antiquarkpairsandgluonsthatareinthe bodyoftheproton.TheprobabilityofanantiquarkcarryingfractionXoftheproton's momentumismodeledthrough partondensityfunctions PDFs,whichareinferredfrom othermeasurementsandtheoreticalpredictions. 2.2SearchMotivation Theelectromagneticandweakforcesappearasseparateforcesatlowenergies ofparticleinteractions.EWKtheorypredictsaunicationatahigherenergyscale O 100 GeV wherethesymmetryofthetwoforcesisrestored.Withcurrent experimentalknowledge,thestrongandEWKforcesareindifferentsymmetrygroups. AnaturalextensionoftheSMistotreatthestrong,weakandelectromagneticforcesas manifestationsofthesamefundamentalinteraction.Thesymmetryofthefundamental interactionisrestoredatveryhighenergies.Suchoverarchingcomplexsymmetries areoftenreferredtoas granduniedtheories GUTs.Manyofthesetheoriespredict anarrowmassresonancefromanewvectorboson,whichisgenericallyreferredtoas a Z 0 ,thatdecaystodimuons.Anewhigh-massdimuonresonancehasnotyetbeen observed,butLHChasthepotentialtoeitherdiscoverorstringentlylimitthephase spaceoftheoreticalpredictions.Thissectionprovidessomeoftheoreticalbackground forthehigh-massdimuonresonancesearchbutisnotexhaustive. Asmentionedabove,theunderlyingpremisebehindGUTmodelsistodescribethe SMasalow-energymanifestationofahighersymmetry.TherstGUTmodelwasmade usingthe SU symmetrygroup,whichisthesmallestsymmetrygrouptocontainthe SMasrepresentedinEquation2[17].Oneoftheassociatedpredictionsfrom SU 21

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GUTsisthenitelifetimeoftheproton,whichhasthusfarbeenexperimentallyexcluded uptoroughlythelifetimeoftheuniverse[17,18]. The Z 0 arisesinavarietyofGUTmodels,butitcanbegenericallyexpressedusing amodel-independentapproach[19],whereadditional U symmetrymayormaynotbe embeddedinahighersymmetry, SU color SU I U Y U 0 AGUTcontaininga Z 0 mayalsopredictothernewparticlesaswelllikechargedbosons, additionalHiggsbosons,andfermions.The SO extensiontotheSMisoftencited asameansofcreatinganadditional U ,becauseitaddsa Z 0 andaright-handed neutrinototheSM[19].Thecouplingsfora Z 0 modelcanbewrittensothatthereare vectorandaxialcouplingstothefermionelds: L Z 0 = g 0 4cos W f )]TJ/F39 11.9552 Tf 5.479 -9.684 Td [(g V )]TJ/F39 11.9552 Tf 11.955 0 Td [(g A 5 f Z 0 where W istheWeinbergangledenedsuchthat cos W = m W = m Z =80.38 = 91.2= 0.88 [18,20].Thetwocouplings, g f V and g f A arevectorandaxialcouplingsrespectively. Thesecouplingsdependonthechoiceofthe U 0 modelandneednotbegeneration independentingeneral.Acommonbenchmarkmodelforthe Z 0 searchisa Z 0 that hasthesamefermioncouplingsastheSM Z 0 boson[1921].Thisisreferredtoas thesequentialstandardmodel Z 0 ,or Z 0 SSM .Acommonclassof Z 0 modelsareinspired by E 6 symmetrybreaking.Thesemodelsproducea U 0 -likebrokensymmetryasin Equation2wherethe U 0 -likesymmetryisgivenby: U 0 =cos U +sin U Theothercommonbenchmarkmodelusedforthisanalysisassumes sin =1 ,andis referredtoas Z 0 [22].Intermsofsymmetries,the Z 0 modelcouplingsaregivenwhen E 6 breaksdownto SO U [23]. 22

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Modelsoflargeextradimensionshavebeenproposedtoexplainwhythegravitational forceisveryweakwhencomparedtothestrongandEWKforces.Thisisalsoknownas thehierarchyproblem[24,25].TheKaluza-KleinKKmodeltheorizesthattherecould beafthdimensionthatisniteinsizeandprojectedontoasmallcircleinaprocess calledcompactication.Thecompactdimensionplacesperiodicboundaryconditions ontheparticleactingonit,creatingdiscretestatesthatareknownasKKexcitations.If thesizeoftheextradimensionsareofthePlancklength 1 = M Planck 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(20 GeV )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ,the theoryiswellbeyondexperimentalreachanduntestable[18,26].TheRandall-Sundrum RS[27]modelbuildsonpreviousideasofextradimensions,andpredictsobservable massresonancesfromKKexcitationsthatdecaytodimuons[28].Theseresonances wouldbeidentiedastensorspin2 particles,whichwouldbedeterminedifoneor moreresonantexcessesareobservedtodistinguishaG froma Z 0 .RSgravitons, denotedasG ,aregovernedbythemassoftherstgraviton, m 1 ,andtheparameter, k = M Planck [28,29].Thecouplingvaluestakenasareferenceinthisanalysisare k = M Planck =0.1,0.01 ,where k M Planck and M Planck isthereducedPlanckmass[30]. ThegraphinFigure2-3showsthemassspectrumoftheRSgravitonexcitationsgiven by m n = kx n e )]TJ/F40 7.9701 Tf 6.587 0 Td [(kr c where r c isthecompacticationradiusoftheextradimensionand x n arerootsof the J 1 Besselfunctionthatdescribethemassexcitationspacings[31].Gluon-gluon initiatedprocesseswillalsocontributetotheDYspectrumiftheRSgravitonmodelis accurate[28]. Insummary,collisionsproducedattheLHCwillbeabletoeitherdiscoveranew dimuonresonanceorsetnewmorestringentlimitsontheavailablephasespace forthesemodels.Ifaresonanceisdiscovered,itsattributeswillbestudiedinorder todistinguishbetween G and Z 0 models.Methodsformodel-discriminationarenot 23

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consideredinthiswork,buttheyareconsidered[32]bytheCMScollaborationinthe eventofadiscovery. Table2-1.Left-handedofquarksandleptonsandtheirassociatedcharges. generation 123Q/e Leptons e e )]TJ/F30 11.9552 Tf 12.066 19.641 Td [( L )]TJ/F30 11.9552 Tf 12.066 19.641 Td [( L )]TJ/F30 11.9552 Tf 12.066 19.641 Td [( L 0 )]TJ/F22 11.9552 Tf 9.298 0 Td [(1 Quarks u d L s c L t b L 2 = 3 )]TJ/F22 11.9552 Tf 9.299 0 Td [(1 = 3 Figure2-1.LeadingorderFeynmandiagramcreatingtwoopposite-signleptonsinthe nalstate,includingatheoretical Z 0 vectorboson. Figure2-2.Feynmandiagramshowingthequark-antiquarkannihilationintoaneutral Z = propagatorthatdecaysintoaleptonpair. 24

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Figure2-3.InvariantmassdistributionsforRS1processwithDrell-Yanbackgroundat theLHC.Fromtoptobottom,thecurvesareforcouplingvalues k = M Planck =1,0.5,0.1,0.05,0.01 25

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CHAPTER3 EXPERIMENTALAPPARATUS 3.1TheLargeHadronCollider TheLHCisaproton-protoncolliderconstructedattheConseilEurop eenpour laRechercheNucl eaireCERN,whichislocatedinMeyrin,Switzerland.TheLHC isplacedinsidethe 27 km tunnelthatpreviouslyhostedtheLEPelectron-positron collider[33].TheLHCisdesignedtoaccelerateeachbeamofprotonstoanenergyof 7 TeV ,foratotalcenter-of-massenergyof p s =14 TeV .CMSisageneralpurpose detectorthatisplacedatoneofthefourinteractionpointsoftheLHCcollider. TheCMSdetectorisbuilttohandleinstantanteousLHCluminositiesofupto L =10 34 cm )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 ,whichcorrespondstoabout 1 billionproton-protoninteractionsper second[34].In2011,theLHCoperatedwitha p s =7 TeV center-of-massenergy.In 2012,thecenter-of-massenergyofLHCcollisionswas 8 TeV Protonsareacceleratedtotheirnalenergythroughamulti-stageprocess.The processbeginswithacontainerofhydrogengasH 2 .Hydrogenisionizedandthe electronsarestrippedusinganelectriceldtocreateH + ionsprotons[35].Protons rstenterthelinearacceleratorLINAC2.TheLINACacceleratingthemto 50 MeV Protonsthenenterintoaseriesofboosterrings.First,theygointothePSBooster wheretheyareacceleratedto 1.4 GeV .ThenextboosteristheProtonSynchrotron PSwhereprotonsareacceleratedto 25 GeV .ProtonsthenproceedintotheSuper ProtonSynchrotronSPS,wheretheyareacceleratedtoamomentumof 450 GeV Finally,protonsareinjectedintotheLHCwheretheyareacceleratedtothenal collisionenergy.ThisprocessisgraphicallysummarizedinFigure3-1[36].TheLHCis comprisedof1232dipolemagnetswithradiofrequencycavitiesthatincreasetheproton energyby 0.5 MeV /turncalledkicks.Thenumberofcollisionsischaracterizedas luminosity,whichisgivenby: L = fk B N 2 p 4 n F 26

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where istheLorentzfactor, f isthefrequencyofrevolution, k B isthenumberof buncheswith N p protonsperbunch.Thebeamsizeisexpressedintermsofthe normalizedtransverseemittance, n ,andthebetatronfunctionattheinteraction pointIP, .Finally, F isthereductionfactorofthecrossingangle.Inordertocreate ahigherluminosity,itisnecessarytohavehigh-populationnarrowbuncheswithlow emittancecollidewithhighfrequency.TheLHCmachineparameterspertainingtoCMS operationsarelistedinTable3-1[37]. 3.2TheCompactMuonSolenoidExperiment DatausedforthisdissertationwascollectedwiththeCMSdetector.Anexpanded semi-openviewofCMSisshowninFigure3-2.CMSisoneoftwomulti-purpose detectorsdesignedtocollectLHCdataforgeneralstandardmodelmeasurementsand fornewphysicssearches.Itisinstalledinanundergroundcavernbelowthevillageof Cessy,France,atIPnumber 5 oftheLHCring.Thelocationis 46 18.59 0 northlatitude and 6 4.62 0 eastlongitude.Thecenterofthedetectoris 89 m belowtheEarth'ssurface and 420 m abovesealevel.ThematerialaboveCMSis 50 m ofmorainesfollowedby 20 m ofmolasserock.Anaccessshaftwitha 20.5 m diameterisdisplaced 14 m from thecenterofCMSalongthebeamaxis;itrisesverticallytothesurface.Theaccess shaftiscoveredbyamovableconcreteplatethatis 2.25 m thick[38]. Atnominaldesignconditions,theLHCwilldeliveraninstantaneousluminosityof 10 34 cm )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .Whenthisismultipliedbytheproton-proton pp crosssectionof 100 mb 10 9 pp interactionsarepredictedtooccureverysecond.Theinstantaneousluminosity ismeasuredinrealtimebyCMSonlinesoftwarewhereitpeakedat 4 10 33 cm )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 in 2011 and 7 10 33 cm )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 in 2012 [39,40].ThedesignoftheCMSexperiment isdrivenbythenominaloperationalenvironmentoftheLHC.CMSmusthavethe spatialgranularityandresponsetimetodisentanglethelargenumberofparticlesper bunchcrossingwhilealsobeingradiationhardtosurvivethehigh-uxofprotons.Each subdetectorfeedsintotheCMStriggeringsystemthatreducesthe O 400 MHz rate 27

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tothe O 100 Hz ratethatcanbeprocessedandstoredbytheDataAcquisitionDAQ System. Thedetectoritselfhasalayeredcongurationofcomplementarysubsystems. Beforeparticlescreatedinthecollisionencounterthedetector,theypassthrougha berylliumbeampipe.Berylliumwaschosenforitslowatomicnumberandabilityto maintainavacuum.Alowatomicnumbermeansthatparticlesarelikelytopassthrough thebeampipewithminimalinteractionbeforehittingtheinnermostdetector.The innermostdetectorsurroundingthebeampipeisthesiliconpixeldetectorsystemthatis positionedforoptimaltrackingandvertexresolution.Locatedoutsidethepixeldetector arehigh-granularitysiliconstriplayersforprecisiontrackingandvertexreconstruction whencombinedwiththepixels.TheelectromagneticcalorimeterECAL,madewith scintillatingleadtungstatePbWO 4 crystalsislocatedoutsidethestripdetectorin ordertomeasureelectromagneticenergydeposits.OutsidetheECAListhehadronic calorimeterHCALsystemformeasuringenergyfromhadronicshowers.Outside theHCAListightlywrappedsuperconductingwirethatformsasuperconducting solenoidthatprovidesamagneticeldforthesilicontrackingdetectors.Themagnet issurroundedbyseveralironyokesthatreturnthemagneticeldofthesolenoid.The yokesprovideamagneticeldforthegaseousoutermuonspectrometersystems.In thecentralbarrelyokearefourinterspersedstationsofdrifttubeDTchambersand supplementalresistiveplatechambersRPCs.Theendcapscomprisefourlayersof cathodestripchambersCSCsthatarealsointerspersedwithRPCsintheendcaps. ThepathofdifferentparticlesisvisualizedinFigure3-3.Thisamalgamofdetectors disambiguatesthekindsofparticleinteractionseventsseenintheLHCcollision environment.Thetrajectoriesofionizingparticleselectrons,muons,chargedhadrons arebentinthemagneticeld.Thepositionsoftheseionizingparticlesareprecisely measuredbythesilicontrackerforaconsequentlyhigh-precisionmeasurement ofthetransversemomentum.ElectronsdeposittheirenergyintheECALthrough 28

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electromagneticshowersandchargedhadronsleaveenergyintheHCALviahadronic showers.AsminimumionizingparticlesMIPs,muonsexperienceverylittleenergyloss astheytraversethecalorimeters,somuonsareidentiedbytheadditionaltracksthat theyleaveinthemuonspectrometer.Therelevantinteractionsofmuonswithmatter aredescribedlaterinChapter4.1.Missingtransverseenergy = E T ismeasuredviathe imbalanceoftransversemomentumasmeasuredbyallsubsystemsandisasignature ofneutrinosorother,newparticlesthatdonotinteractwithmatter. 3.2.1CoordinateSystem TheCMScollaborationhasadoptedacylindricalcoordinatesystemwherethe originiscenteredatthenominalcollisionpointinsidetheexperiment.The x -axispoints radiallyinwardwithrespecttotheLHCringwhilethe y -axispointsverticallyupward. The z -axisiscolinearwiththebeampipeinthedirectionofthecounter-clockwisebeam. Thepolarangle, ,ismeasuredwithrespecttothepositivedirectionofthe z -axis. Pseudorapidity, ,isdenedintermsof suchthat = )]TJ/F22 11.9552 Tf 11.291 0 Td [(ln tan )]TJ/F26 7.9701 Tf 6.799 -4.977 Td [( 2 .Thedifference inpseudorapiditybetweentwoparticles, ,isaninvariantquantity.Theazimuthal angle, ,ismeasuredfromthe x -axisinthe x )]TJ/F39 11.9552 Tf 12.64 0 Td [(y transverseplaneofthedetector. Themomentumandenergymeasuredinthetransverseplanewithrespecttothe beamdirectionaredenotedby p T and E T respectively.Fortracking,thetransverseand longitudinalimpactparameterswithrespecttothecollisionpointaredenotedas d 0 and d z ,respectively. 3.2.2InnerTracker TheCMSinnertrackerisdesignedtopreciselyandefcientlymeasurethe trajectoriesofchargedparticlestraversingthevolumeofCMS.Toachievethis,the innertrackerisbuiltusingsiliconsemiconductordetectortechnology.Fundamentally, asilicondetectorisareverse-biasedp-njunction.Whenachargedparticlepasses throughthematerialofthesilicondetector,itcausesionization.Forsemiconductors,this 29

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meansthatelectron-holepairsareproduced.Electronsdrifttowardstheanodewhilethe holesrelocatetowardsthecathodewherechargeisgathered. Theinnermostsystemofthetrackeristhesiliconpixeldetectorthatoperates between 4.4 cm and 10.2 cm fromthecenterofthebeampipe.Thepixelsystemis dividedintothe barrel PXBand endcap regionsPXEwitha 15 )]TJ/F22 11.9552 Tf 12.819 0 Td [(20 m position resolution,wherethepositionresolutionisthesmallestGaussianuncertaintybetween thetrueandmeasuredpositionofapixelmeasurement.Thepixelsystemsprovide pseudorapiditycoverageupto j j < 2.5 ;thelayoutofthepixeldetectorisgivenin Figure3-4[37]. Outsidethepixelsystemisthesiliconstriptracker,whichisdividedintofour subsystems.Inthebarrelregion,thestriptrackerisseparatedintothe trackerinner barrel TIBand trackerouterbarrel TOBregions.TheTIBisdividedintofourlayers thatareorientedtogive r )]TJ/F25 11.9552 Tf 13.022 0 Td [( positionmeasurements.Thersttwolayershavea pitchof 80 m andthesecondtwolayershaveapitchof 120 m .Thepitchisthe center-to-centerdisplacementbetweensensors.ThersttwolayersoftheTIBhave secondarymicrostripdetectorsattachedtothebackofthe r )]TJ/F25 11.9552 Tf 11.258 0 Td [( measurementstripsthat arealignedtoprovidean r )]TJ/F39 11.9552 Tf 12.511 0 Td [(z measurement,aswell.Layersthatprovideboth r )]TJ/F25 11.9552 Tf 12.511 0 Td [( and r )]TJ/F39 11.9552 Tf 12.573 0 Td [(z measurementsarecalledstereolayers.TheTIBhasasingle-point r )]TJ/F25 11.9552 Tf 12.572 0 Td [( resolutionof 24 )]TJ/F22 11.9552 Tf 12.196 0 Td [(34 m andan r )]TJ/F39 11.9552 Tf 12.196 0 Td [(z resolutionof 230 m .TheTOBismadeupofsix striplayersorientedin r )]TJ/F25 11.9552 Tf 11.766 0 Td [( thathaveapitchvaryingfrom 120 m to 180 m .Thelayout ofthestripdetectorisgiveninFigure3-5[37]. LiketheTIB,thersttwolayersoftheTOBalsoprovidestereohitinformation.The TOBhasan r )]TJ/F25 11.9552 Tf 12.719 0 Td [( resolutionthatvariesfrom 35 )]TJ/F22 11.9552 Tf 12.719 0 Td [(52 m andan r )]TJ/F39 11.9552 Tf 12.719 0 Td [(z resolutionof 530 m .Theendcapsystemsofthestriptrackeraredividedintothe trackerendcap TECand trackerinnerdisk TIDsystemsthataremirroredaroundthebarrel.Each TECismadeupofninediskswithapitchthataveragesbetween 94 m and 184 m EachTIDismadeupofthreelayersandisplacedtollinthegapsbetweentheTIB 30

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andTEC.ThepitchfortheTIDaveragesbetween 100 m and 141 m .Microstripsare arrangedintheTECandTIDtopointradiallyinwardstowardthebeamlineforprecision r )]TJ/F25 11.9552 Tf 12.419 0 Td [( measurements.ThersttworingsoftheTIDhavestereolayers.Theinnermost twolayersoftheTEC,aswellasthefthlayerfromtheinnermostlayerhavestereo layers.ThethicknessofmicrostripsintheTECrangefrom 320 m to 500 m .Inthe TID,themicrostripshaveathicknessof 320 m Thecombinationofthesiliconpixelandstriptrackingsystemspermittheidentication ofchargedparticlesastheytraversetheCMSvolume.Chargedparticles,such aselectrons,pions,kaonsandmuons,createhitsinthesilicontrackerthrough minimumionizationofthesilicon.Neutralhadronsleavenoinformationinthetracker. Hitsfromtheinnerpixelandstriptrackersubsystemsarebuiltandusedforfulltrack reconstructiontoidentifythetrackparameters: p T d 0 and d z 3.2.3ElectronCalorimeter TheCMSECALsystemisdesignedtomeasuretheenergyofelectromagnetic showers.TheECALissituatedrightoutsidetheinnertrackingsysteminsidethe hadroniccalorimeterandsolenoidinordertoachievethebestpossibleenergy resolutionforphotonsandelectrons.Thecalorimeterismadeupof 75,848 scintillating leadtungstate PbWO 4 crystalsFigure3-6,with 61,200 crystalsinthebarrel and 7,324 ineachendcap[41].Leadtungstatewaschosenbecauseofitshigh density 8.3 g = cm 3 ,shortradiationlength X 0 =0.89 cm ,andasmallMoli ereradius R M =2.2 cm .Theradiationlengthisamaterialpropertythatisdenedastheaverage distancerequiredtoreducetheenergyofanelectronbythefactor 1 = e [42].TheMoli ere radiusisacharacteristicpropertyofscintillatingmaterialthatdenestheradiusofa cylinderthatcontains 90% oftheshowerenergy.Thescintillatingdecaytimeisabout 25 ns andiscomparabletothetimeseparationbetweenLHCbunches.Apreshower detectorislocatedinfrontofthescintillatingcrystalstohelpidentifyneutralpionsinthe 31

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endcaps 1.653 < j j < 2.6 anddiscriminateMIPs.ThelayoutoftheECALisshownin Figure3-7[37]. Inthebarrel,theECALcrystalsarearrangedtohavea 360 -foldgranularityin anda 2 85 -foldgranularityin .Tomaximizescintillatorcoverage,thecrystalsin thebarrelaretaperedsuchthattheinnerdimensionsofeachcrystalhaveafrontface of 22 22 mm 2 andarearfaceof 26 26 mm 2 withacrystallengthof 230 mm = 25.8 radiationlengths X 0 [18].Thephotodetectorsusedinthebarrelregionare commerciallyproducedHamamatsutypeS8148avalanchephotodiodesAPDs[43]. TheAPDshavea 5 5 mm 2 sensitivearea.TwoAPDsaregluedtothebackofeach crystalandarereadoutinparallel.EachAPDhasaquantumefciencyof 75 2% in theregionwheretheleadtungstatecrystalshavepeaklightemission 430 nm as showninFigure3-8[44,45].Thequantumefciencyindicatesthefractionofincident photonsthatproduceprimarychargecarriers. TheendcaplayoutoftheECALissuchthatidenticalcrystalsaregroupedinto 5 5 clustersofsuper-crystalsSCsandpartialSCs.TheSCsandpartialSCsare arrangedinarectangular x )]TJ/F39 11.9552 Tf 12.415 0 Td [(y gridwithcrystalspointingtoafocus 1300 mm beyond thenominalinteractionpoint.Eachendcapisbuiltintotwohalf-cylinderdeesthatare eachmadeof 138 standardSCsand 18 partialSCs.Theendcapcrystalshavefrontface dimensionsof 28.62 28.62 mm 2 andrearfacedimensionsof 30 30 mm 2 withacrystal lengthof 220 mm =24.7 X 0 .Theneutronradiationuxisexpectedtobetoohighfor APDs[46].Thephotodetectorschosenfortheendcapregionarevacuumphototriodes VPTs.VPTsarephotomultiplierswithonegainstage.TheVPTsmadefortheCMS ECALarespeciallydesignedtohandlethehighlevelofradiatonintheendcap[47].The VPTshaveadiameterof 25 mm andoneVPTisgluedtothebackofeachcrystalinthe endcap.EachVPThasaquantumefciencyof 22% inthe 430 nm wavelengthrange. ThepreshowerESisatwo-layersamplingcalorimeter.TherstlayeroftheESis comprisedofleadinordertoinitiateelectromagneticshowersinphotonsandelectrons. 32

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ThesecondESlayerisasiliconstripsensortomeasureenergydepositsandtransverse showerproles.BeforereachingtherstlayeroftheES,particlespassthrough 2 X 0 of material;therstESlayeraddsanadditionalradiationlengthsothat 95% ofphotons startandelectromagneticshowerbeforereachingthesecondESplane. TheenergyresolutionoftheCMSECALsystemisparameterizedby E E 2 = a E 2 + b p E 2 + c 2 EistheelectronenergydepositedintotheECALasmeasuredin GeV E istheuncertaintyon E a isatermfornoiseoriginatinginthephysicalelectronics, digitizationprocess,andpileupenergy. b isastochastictermrelatedtostatistical uctuations,suchasshowercontainment,photoelectronstatisticsanddeadmaterial. c isthemaincontributiontouncertaintyandcomesfromnon-uniformitiesinlight collection,energyleakagefromthecrystal,andintercalibrationerrors.Theresolution parametersforEquation3aresummarizedinTable3-2[37]. 3.2.4HadronCalorimeter TheCMShadroncalorimeterHCALissituatedbetweentheECALandthe solenoid.TheHCALfacilitatesthereconstructionofhadronjets,neutrinos,andpotential signalscharacterizedbysubstantial = E T .TheHCALisseparatedintofourdifferent regions.The hadronbarrel HBcoversthecentralbarrelregionofthedetectorwhere j j < 1.3 .TheHBissupplementedbythe hadronouter HOsystemthatislocated outsidethesolenoidinthesame j j < 1.3 region;theHOisatailcatcherthat suppressesleakagefromthebackofthecalorimeterintothemuonsystem.The hadron endcap HEprovidescoverageoftheendcapregiondenedwhere 1.3 < j j < 3.0 .The farforwardregionofthedetectordenedby 3.0 < j j < 5.0 iscoveredbythe hadron forward HFsystem.ThelongitudinallayoutoftheHCALisshowninFigure3-9[45]. TheactiveregionoftheHCALcomprisesplasticscintillatortiles;thetilesare embeddedwithawavelengthshiftingWLSberreadout.Theactivescintillating 33

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elementsareinterspersedwithlayersofbrassscintillatingmaterialthatinitiateshadronic showers.ThecombinationoftheHCALandECALsystemsmakeforacomplete calorimetrysystem,fordistinguishingbetweenhadronicandelectromagneticshowering. ThecompactqualierintheCMSexperimentreferstotheplacementofthecalorimetry excludingtheHOinsidethefreeboreofthesolenoid. TheHBregionisdividedinto )]TJ/F25 11.9552 Tf 12.838 0 Td [( sectorssoastohaveauniformgranularity of =0.087 0.087 withboltedwedgestominimizecracks.Theeffective absorberthicknessoftheHBismeasuredininteractionlengths I ,whichis 5.82 I at eta =0 =90 andincreaseswiththepolarangle as 1 = sin withrespectto =90 suchthat I =10.6 at j j =1.3 [18].TheHEismadeof 19 activeplastic scintillatorlayersthatareinterspersedwithbrassplateabsorbers.Thebrassplateshave athicknessof 78 mm andtheplasticscintillatorsare 3.7 mm thick.IncludingtheECAL material,thisgivesatotalofabout 10 I intheendcapcalorimeters.TheHFsystemacts astheonlineluminositymonitor.Inordertowithstandtheextremeparticleuxofthe LHC,itisbuiltwithquartzberastheactivematerial.Inordertodifferentiatebetween electromagneticandhadronicshowers.theHFisdividedintotwolongitudinalsegments ofactivematerial.Halfofthebersrunthroughthefull 165 cm I 10 depthofthe absorber;theotherhalfoftheactivebersstart 22 cm intotheabsorber. 3.2.5SuperconductingSolenoid ThesuperconductingsolenoidmagnetforCMSislocatedoutsideoftheECAL andisdesignedtogeneratea 4 T magneticuxdensityinafreeboreof 6 m in diameterand 12.5 m inlength.Thisisenclosedinsidea 12000 t yokemadeofcommon structuralsteel[48].Theyokecomprisesvethree-layereddodecagonalbarrelwheels, cappedonbothendswiththreedisks,foratotalofelevenlargeelements.Theyoke returnstheuxofthesuperconductingsolenoidandactsasanabsorberforthemuon spectrometer.Themappingofthemagneticeld,includingtheuxinthereturn,is showninFigure3-11[49]. 34

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ThemainoperatingparametersoftheCMSsuperconductingsolenoidare summarizedinTable3-3.TheCMScollaborationmadethedecisiontoreducethe nominalcurrentfrom 19.14 kA to 18.16 kA togivea 3.8 T centralmagneticux density[50]. 3.2.6MuonSystem Outsidethesolenoidandinterleavedwiththereturnyoke,theCMSdetectorhas threetypesofgaseousdetectorsystemsthatexisttotriggeronmuonsandperform outertrackingwiththereturneld.Thebarrelmuonsystem j j < 1.3 has drifttube DTchambersand resistiveplatechambers RPCs.Theendcapmuonsystemhas cathodestripchambers CSCsprovidingcoveragefor 0.9 < j j < 2.4 andadditional partialcoverageupto j j < 1.6 ofRPCs.Aquarter-view r )]TJ/F39 11.9552 Tf 12.757 0 Td [(z layoutofthemuon systemisshowninFigure3-12[37,51].Aneventdisplayshowsamuoncandidate crossingtheDTandCSCchambersintheregionwheretheyoverlap. TheDTsystemisdividedintofourstationsthatareorientedintoconcentricrings aroundthebeampipe.DTchambersaregas-lledtubesthatmeasurethetimeittakes forelectronscreatedbytheionizationofatravelingparticleinthegastotraveldriven byanappliedelectriceldtoanodewiresplacedinthesystem.IntherstthreeDT stations,therearetwelvelayersofdrifttubes.Thetwelvelayersaredividedintothree groupsof superlayers SLs.TheSLsareorientedsothattherstandthirdprovide r )]TJ/F25 11.9552 Tf 12.14 0 Td [( measurementsandthemiddlelayerprovidesan r )]TJ/F39 11.9552 Tf 12.14 0 Td [(z measurement,asshownin Figure3-13[37].ThefourthDTstationisdifferentinthatithasonlytwoSLsthatboth measurein r )]TJ/F25 11.9552 Tf 11.749 0 Td [( .TheDTsystemhasaspatialresolutionof 100 m in r )]TJ/F25 11.9552 Tf 11.748 0 Td [( and 150 m in r )]TJ/F39 11.9552 Tf 12.696 0 Td [(z .WhenamuonleavesatrackintheDT,localreconstructionisperformedat themuonstationleveltocreateatracksegmentthatcontainspositionandtrajectory information.Thesegmentisbuiltfromalignedhitsfromtwodifferentlayersinthesame station.Segmentreconstructionisbuiltinparallelon r )]TJ/F25 11.9552 Tf 12.189 0 Td [( and r )]TJ/F39 11.9552 Tf 12.189 0 Td [(z projections,which arecombinedattheendtocreateathreedimensional-segment. 35

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RPCsareacomplementarymuontriggersystem.EachRPCisaparallelplate gas-lledchambermadeoftwolayers.Anelectriceldisappliedtocollectcharged particlesinananode.TherearesixlayersofRPCssandwichedin-betweentheDTs inthebarrelregion.Intheendcapregion,eachCSClayerwilleventuallyhavean associatedRPClayerupto j j < 2.1 ,whiletheCSCscontinuecoverageupto j j < 2.4 CSCsarewirechambersthatcompriseofradialcathodestripswithintersecting anodewireplanes.Theanodewiresthatpointalong arepositionedradially outwardin r .Thereareseventrapezoidalpanelsineachstation,creatingsixlayers formeasurements.ThelayoutofaCSCchamberisgiveninFigure3-15[37].Charged particlesthationizeinthegasproduceachargeontheanodewireandanimage chargeonthecathodestrips.ThisorientationallowstheCSCstomeasurespatial coordinatesin r and z withan r )]TJ/F25 11.9552 Tf 12.322 0 Td [( resolutionbetween 75 m and 200 m [37,52]. LocalreconstructionintheCSCsisdonewiththesignalsfromthecathodestripsand anodewires.Muonhitsarecreatedbyclusteringthechargeofneighboringstripsand estimatingthepositionfromtheinducedcharge.Segmentsarereconstructedineach CSCstation.Hitsareinitiallyclusteredbasedonallpairsofhitsthatareconsistentwith straightlines.Ifalargenumberofhitsarefoundtypicallylargerthan 20 ,theclustering algorithmattemptstoprunehitstoincreaseperformance[53].Succesiveattemptsare performedtoaddhitsfromadditionallayerstothestraightlineapproximation.Thebest ttothehitsisusedtocreatethesegment[37]. 3.2.7Trigger AttheLHCinstantaneousdesignluminosityof 10 34 cm )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ,buncheswillcollide every 25 ns afrequencyof 40 MHz withanaverageofabout 20 proton-protoncollisions percrossing.Sincetheaverageeventsizeisabout 1 MB ,CMScannotstoreevery LHCeventsothisratehastobereduced.Eventsconsistofalloutputteddatanecessary forfullreconstructionoftheproton-protoncollision.Thisisdoneintwostages:rstby the Level-1 L1Triggerandthenbythe High-LevelTrigger HLT[54,55].TheCMS 36

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L1triggersystemisbuiltofcustom,congurableelectronicsdesignedtoanalyzeevery crossingwithcoarsegranularitytodetermineifthecollisioneventcontainsinteresting physicsobjects.Individualmuonandcalorimetersubsystemsreporttheirndingsto higherlevelcontrolstructures.Themuonandcalorimetertriggersystemsareultimately combinedinthe globaltrigger ,followingthehierarchyshowninFigure3-16[37].Once theGThasdeterminedthataneventisinterestingtoinitiatethereadoutofthedetector data,a L 1 Accept L1Asignalissentout.Asthebuffersizesonthedetectorfront-ends arenite,theL1Asignalmustarriveatthedetectorswithinabout 3 )]TJ/F22 11.9552 Tf 12.799 0 Td [(4 s [54].The outputrateofL1AsfromtheglobalL 1 triggerisdesignedtobelessthan 100 kHz High-resolutiondetectordataismaintainedinpipelinedmemorylocatedinthefront-end electronics.Thehighresolutiondataisreadoutandpassedonfornalreconstruction inselectedevents.Thesystemwhichgathersthehighresolutiondetectordataiscalled theDataAcquisitionSystemDAQ. TheowofL1AscomingfromtheGTcanbeinhibitedbythe triggercontrolsystem TCSforoneofanynumberofreasons:detectorhardwaremaybebusysendinghigh resolutiondatathroughtheDAQsystem,subsystemdatabuffersarellingupandneed timetobereadout,ortheapplicationofrulesonthespacingofL1As.Thedeadtime inducedbytheTCSismonitoredbytheGTandacorrectionisappliedonthemeasured livetimeofthedetector.Thestatusofsubsystemhardwareismonitoredlocallybythe subsystemandtransmittedtotheTCSviaaFastMonitoringsystem.Afterpassing throughtheTCS,theL1Aisdistributedtoalldetectorfront-endsthroughthe timing, trigger,andcontrol TTCsystem,whichalsodistributestheclockandsynchronous signalstoperformfastoperationssuchasresettingtheeventcounter.Uponreceiptof theL1A,eachfrontendmodulereadsoutthehighresolutiondetectordatawhichhas beenstoredinpipelinedmemory,andispassedonfornalreconstructioninselected events.ThelogicalowbetweentheGT,TCSandDAQisshowninFigure3-17[37]. 37

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WhentheDAQaccessestherawdata,thatdataissenttotheHLT.TheHLTisan on-sitecomputerfarmthatperformsfastreconstructionalgorithmsthatturnlow-level rawdataintoalistofusablehigh-levelphysicsobjects,suchasmuons,electrons, = E T andjets.ThisfastreconstructionenablestheHLTtoapplyamorestringentselectionon theavailablefast-reconstructedhigh-levelphysicsobjects.TheHLTcategorizeseach eventbyitsconstituentphysicsobjectstheparticlesthatareseenanddecidesifthat eventispotentiallyinterestingforofinephysicsanalysis.Ofinephysicsanalyses collaboratetodenetriggerpathsfortheHLTthatgovernwhattheHLTdeterminesto beinteresting.RatesofdifferentHLTtriggerpathsareestimatedandalgorithmpaths aredesignedtomaximizeandbalanceratesfordifferentofinephysicsanalyses.The nalrateatwhichtheHLTselectseventsfortheDAQtosendforofineanalysisisabout 100 Hz EventsbuiltbytheDAQaremarkedbytheruninwhichtheyweretaken,the luminositysectionofthebeamll,andtheeventnumbernumberofthatll.Physics eventsthatarewrittenoutbytheDAQarecategorizedbytheCMScomputingnetwork into primarydatasets tooptimizeuseraccess. Figure3-1.TheLHCinjectorcomplex. 38

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Figure3-2.ExpandedviewoftheCMSdetector. Figure3-3.SliceoftheCMSdetectorinthe r )]TJ/F25 11.9552 Tf 11.955 0 Td [( planeshowingthepathsofdifferent particles. 39

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Table3-1.Proton-protoncollisionparametersrelevanttoCMS. Energypernucleon E 7 TeV Dipoleeldat B 8.33 T DesignLuminosity L 10 34 cm )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 Bunchseparation 25 ns Numberofbunches k B 2808 Numberofparticlesperbunch N p 1.15 10 11 -valueatIP 0.55 m RMSbeamradiusatIP 16.7 m Luminositylifetime L 15 hr Numberofcollisions/crossing n c 20 Figure3-4.Generallayoutofthepixeldetector. Figure3-5.Generallayoutofthesiliconstripdetector. 40

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Figure3-6.Leadtungstatecrystal. Figure3-7.LayoutoftheCMSECAL. 41

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Table3-2.ParametersdescribingCMSECALenergyresolution. ECALparametervalue a 0 12 b 2 8% c 0 30% Figure3-8.Room-temperaturelongitudinalopticaltransmissionand radio-luminesenceatsteady-state 57 Co excitation 122 keV for production PbWO 4 crystals. 42

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Figure3-9.LongitudinalviewoftheCMSdetectorshowingthelocationsofthehadron barrelHB,endcapHE,outerHO,andforwardHFcalorimeters. Figure3-10.SchematicviewsoftheCMSsolenoidwiththenumberingconventionfor theazimuthalsectorsS,wheelsW,barrelyokelayersLandendcap disksD.TCisthetailcatcher,anadditionalsteellayerpresentinthe centralbarrelwheel W 0 only. 43

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Figure3-11.Valueof j B j leftandeldlinesrightpredictedonthelongitudinalsection oftheCMSdetector,fortheundergroundmodelatacentralmagneticux densityof 3.8 T .Eacheldlinerepresentsa 6 Wb incrementinthe magneticux. 44

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Table3-3.MainoperatingparametersoftheCMSsuperconductingsolenoidmagnetfor anominalmagneticuxdensityof 4 T GeneralParameters Magneticlength 12.5 m Coldborediameter 6.3 m Centralmagneticinduction 4 T totalAmpere-turns 41.7 MA-turns Nominalcurrent 19.14 kA Inductance 14.2 H Storedenergy 2.6 GJ ColdMass Radialthicknessofcoldmass 312 mm Radiationthicknessofcoldmass 3.9 X 0 Weightofcoldmass 220 t Maximuminductiononconductor 4.6 T Temperaturemarginw.r.t.operatingtemperature 1.8 T Storedenergy/unitcoldmass 11.6 kJ/kg IronYoke Outerdiameteroftheironats 14 m Lengthofbarrel 13 m Ironlayerthicknessinthebarrel 300,630 and 630 mm Massofironinthebarrel 6000 t Thicknessofirondisksintheendcaps 250,600 and 600 mm Massofironperendcap 2000 t Totalmassofironinthereturnyoke 10000 t 45

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ALayoutofone-quarteroftheCMSmuonsystem. BAneventdisplayofamuoncrossingtheDTandCSCchambersinthe overlapregion. Figure3-12.RepresentativeguresshowingtheoperationoftheCMSmuonsystem. 46

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Figure3-13.ThelayoutofaDTchamberinsideamuonbarrelstation. Figure3-14.SchematicviewoftheRPC. 47

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Figure3-15.SchematicviewofaCSCchamber. 48

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Figure3-16.ArchitectureoftheCMSLevel )]TJ/F22 11.9552 Tf 9.298 0 Td [(1 trigger. Figure3-17.OverviewoftheCMStriggercontrolsystem. 49

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CHAPTER4 MUONRECONSTRUCTION Theanalysisonwhichthisdissertationisbuiltreliesheavilyonthesimultaneous reconstructionoftwomuonobjects.Itisimportantthatmuonshaveahighlyefcient reconstructionwithexcellentmomentumresolution.Theabilitytodistinguishbetween muonsthatcomefrompromptdecaysofrareprocessesandmuonsthatcomefrom QCDjetsisalsoanimportantfeature. Muonreconstructionandperformancehavebeenstudiedusingmuonsfrom secondarycosmicraysandfromcollisionmuons.Thisanalysisisdrivenmoreby highp T muonreconstruction,sothereisafocusonhighermomentumeffects. Thischapterrstdiscussestheinteractionsofmuonswithmatterandgeneral reconstructionconsiderationsinSection4.1.Section4.2describesofinemuon identication.Section4.3describeshowmuonresolutionisestimatedindata. Section4.4describeshowthehighp T momentumscaleismeasuredandhowthe uncertaintyonthehighp T momentumscaleisconstrained.Section4.5describesthe muonisolationvariablethatindicatesifmuonsarefromajet. 4.1MuonReconstructionConsiderations Relativisticchargedparticlesinteractwithmatter,whichcausesthetravelling particletoloseenergy.Muonsloseenergythroughionizationandradiativeprocesses, whicharedescribedbelow.Thetotalmuonenergylossisapproximatelyexpressedasa functionofthetraversedmaterial: )]TJ/F39 11.9552 Tf 13.151 8.088 Td [(dE dx = a + b E where a islossthroughionizationand b istheenergylostthroughradiation[18]. Both a and b dependontheparticle'senergyandtheintrinsicpropertiesofthematerial. Theaveragemuonenergylossviewedasthestoppingpowerformuonsinteracting 50

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withcopperusedasacommonreferencematerialisshowninFigure4-1acrossnine ordersofmagnitudeofmomentum p = M c [18,56]. Ionizationoccurswhenmuonstransferkineticenergyontoelectronsboundin atomsormolecules.Theelectronsareexcitedbytheenergytransfer.MIPslose,on average,closetotheminimumamountofenergythatcanbelostintheseinteractions. Muonsaresubjecttothreekindsofenergyloss:bremsstrahlung 1 ,directproduction of e + e )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(pairs,andphotonuclearinteractions.Bremsstrahlung[57]radiationhappens whenchargedparticlesaredecelerated.Pairproductioniscausedbyphotonsinthe atomicnucleareld.Photonuclearinteractionsarefrominelasticscatteringbetween themuonandthenucleus[56].ThesecondterminEquation4iswrittenasasumof thesethreeeffects: b tot = b pair + b brem + b nuclear Thecontributionofindependentradiativeeffectstomuonenergylossisshownin Figure4-2[56].Nuclearinteractionsaregenerallyneglectedgiventheeffectisfarbelow pairproductionandbremsstrahlung. Radiativeprocessesarecharacteristicofelectromagneticshowers,andcausea highhitmultiplicityintrackingdetectorsifamuonshowerisoccurs.Muonshowers occurwhenamuonradiatesahardelectronthatinturnradiatestocreatemultiplehits. Figure4-3[58]summarizestherateofelectroncreationbymuonsthroughionization, bremsstrahlung,andpairproductionasafunctionofmuonmomentum[56].This couldbeinitiated,forexample,bythecalorimetersoranironplateintheyoke.The characteristicsofmuonshoweringaresummarizedinFigure4-4.Themaingureshows thedistanceofhitsfromthetrack;theinsertshowsthenumberofassociatedhits[58]. 1 DerivedfromtheGermanwords: bremsen tobrake+ Strahlung radiation 51

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Whenionizationlossesareequaltoradiationlosses,themuonisatits critical energy forthematerial, E c .Below E c ,mostmuonenergylossisfromionization; above E c ,energylossisdominatedbyradiativeeffects.Forcopper, E c =315 GeV asseeninFigure4-1;for PbWO 4 E c =160 +5 )]TJ/F23 7.9701 Tf 6.587 0 Td [(6 8 GeV asmeasuredbytheCMS collaboration[56,59].Formostofthemomentumregimewheremuonsarecommonly seenintheCMSapparatusittakes p T 2.5 GeV foramuontobevisibleinthemuon system,muonsleaveenergymostlythroughminimumionization[51].TheLHCalso produceshigh-energymuonsthataresusceptibletoexperiencingelectromagnetic showers. Muonstraversingamediumaredeectedbymanysmallanglescattersdueto interactionswithnucleiviaCoulombscattering[18,60].Insmallanglescattering,a muonentersamediumandexitswithasmallanglefromtheentrancepoint.Theangle ofdeection, 0 ,isapproximatedby 0 = 13.6 MeV cp z p x = X 0 [ 1+0.038ln x = X 0 ] where p c ,and z arethemomentum,velocityandchargenumber. x = X 0 isthe thicknessofthemediumintermsofradiationlengths[18,61].Asthemomentum increases,theeffecton 0 becomeslesssignicant.Thedeectionangleofcharged particleshasbeenusedtomeasurethemomentumofchargedparticles[62,63]. Forlaterdiscussionsaboutthemomentumscale,itisbenecialtosummarizethe basicsofchargedparticletrackinginauniformmagneticeldignoringenergyloss.The measurementofthemomentumisdonebycalculatingthetrajectoryofarelativistic chargedparticleinapurelymagneticeld.ThisisgivenbytherelativisticLarmorradius, r = p T qB ristheradiusofcurvatureofthehelixmadebythetravelingparticle.qisthe electriccharge. p T istherelativisticmomentuminthedirectionperpendiculartothe 52

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magneticeld, p T = m v t ,where istheLorentzFactor[18,57,64].Thephysical measurementofatrajectoryissimpliedassumingthreepointsinFigure4-5,quantity thatismeasuredisthe sagitta 2 ,s.Thesagittaisadeectionofthetrajectoryofa muonthattraversesapathlength, L ,inamagneticeld[18,64].Elementarygeometry relatesthesagittatotheradiusofcurvatureforsmall s = r )]TJ/F22 11.9552 Tf 11.955 0 Td [(cos = r 2 sin 2 2 r 2 8 r L 2 8 s Whenthisiscombinedwiththeknownphysics, s = 1 8 qL 2 B p T Forthreetrackmeasurementsat x 1,2,3 inFigure4-5,thesagittaisgivenby: s = x 2 )]TJ/F22 11.9552 Tf 13.15 8.088 Td [(1 2 x 3 )]TJ/F39 11.9552 Tf 11.955 0 Td [(x 1 s = x 2 )]TJ/F22 11.9552 Tf 13.15 8.087 Td [(1 2 x 1 )]TJ/F22 11.9552 Tf 13.151 8.087 Td [(1 2 x 3 Iftheerrorsareequalanduncorrelated,theuncertaintyisgivenby s = r 3 2 x Intermsoftherelativeuncertaintyonthe p T measurement, p T p T = s s = p 96 x p T BL 2 2 Alsoreferredtointrigonometryastheversine, s = r 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [(cos 53

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Therelativeuncertaintyonthe p T measurementdegradeslinearlywith x and p T Itimproveslinearlywith B andquadraticallywiththe L .Themeasureoftracker performanceisthengivenby p T p 2 T whichisequivalenttomeasuringtheuncertaintyon q = p T [64].Itisconvenienttodene the transversecurvature ofamuonas q = p T 4.2OfineMuonIdentication CMSsoftwareisdesignedtoperformmuonreconstructionusingboththemuon spectrometerandtheinnertracker.Therearetwogeneralapproachesformuon reconstructionandnalidentication: GlobalMuonreconstruction ,whichisan outside-inapproach,and TrackerMuonreconstruction ,whichisaninside-out approach.EachmuonasidentiedbyCMShasbeenttedbyseveralalgorithmsthat willbedescribedinthissectionregardingofinemuonidentication.Onlinemuon identicationisdiscussedwiththemuontriggerinChapter5.2. Themuonsystemcanbeusedwithoutthetrackertoreconstructmuons.Inthis case,tracktsthatareproducedarecalled standalone muons.Standalonemuon reconstructionusestracksegmentsproducedfromlocalmuonreconstructionas describedinSection3.2.6.Thetracksegmentscontaincoarseestimatesonthe trackposition,momentumanddirection.StandalonetracksaretusingtheKalman lter[65,66]techniquestartingwithsegmentsfoundintheinnermostchamberasa startingseed[37].Thestateinformationispropagatedusing GEANT GEANT isdiscussed inChapter5.4,fromthestartingseedtothenextstation,wherecompatiblehitsare soughttobuildcompletetracks.Multiplescattering,energylossinthematerial,and themagneticeldareallconsideredduringpropagation.Propagationisupdatedat eachstationwhereamatchisfoundandrepeateduntiltheoutermostmuonstation isreached.AbackwardKalmanlterisappliedstartingfromtheoutermoststation andthetrackparametersaredenedattheinnermostmuonstation.Thetrackis 54

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nallyextrapolatedtothenominalIP,whichisdenedbythebeam-spot,whichisthe envelopeofthecollidingbeams.Thenalstandalonemuontisperformedwithavertex constraintonthetrackparameters. TracksinthetrackerareproducedusingasimilarKalman-lteringmethod.Hits inthetrackerarereconstructedbyclusteringenergydepositsinthestripsorpixels foraspatialpositionandanestimateonitsuncertainty.Seedsaregeneratedusingat leastthreehits,ortwohitsandaconstrainttothebeam-spot.Seedsarepropagatedto successivedetectionlayersandthetrackparametersareupdatedtothemostrecent layerbyatusingthemethodofleast-squares.Morethanonehitmaybecompatible withthepreviouslayer,somultipletracksmaybecreatedaseachsuccessivedetection layeriscrossed.Apairoftrackcandidatesareregardedasambiguousiftheyshare atleasthalfofthehitsusedintherespectivets.Inthiscase,thetrackwiththeleast numberofhitsisdiscarded.Ifthetrackcandidateshavethesamenumberofhits,the trackwiththehighest 2 isdiscarded.Thenaltracktcombinesallthehitsforthetrack candidatebetweentherstandlast 3 hitsinthetrack. Globalmuonreconstructionstartswithstandalonemuontracksandmatchesthem withtheindependentlyreconstructedtrackertracks.Themuonandtrackerhitsare combinedandtheKalmanlteringprocedureisrepeatedtocreatea global muont. Trackermuonreconstructionstartswithtracksreconstructedinthesilicontracker andextrapolatesthetrajectoriesintothemuonsystem.Iftheextrapolatedtrackcanbe matchedtoatleastonemuonsegmentashorttrackstubmadefromDTandCSChits fromasinglestation,theextrapolatedtrackqualiesasa trackermuon .Trackermuon reconstructionisdesignedtobemoreefcientforlow-momentumevents p / 5 GeV whereonlyinformationfromonemuonstationisneededtocreateatrackermuon. 3 Thersthitistheradiallyinnermosthitforahighp T track.Lowmomentumtracks maybendradiallyinward. 55

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CMSmuonreconstructionprovidesthetrajectoryparametersforthestandalone, trackerandglobaltracksforeverymuoncandidate.Forhighp T muons p T & 100 GeV theglobalmuontcanimprovethetransversemomentumresolutioncomparedtothe tracker-onlyt.Additionalalgorithmsbasedonglobalmuonreconstructionusedto improvemomentumresolutionarediscussedwiththeresolutioninChapter4.3. 4.3MomentumResolution Asmuonspassthroughtheironreturnyokeofthemagnet,theirtrajectoriesare alteredbymultiplescatteringandradiativelosses.Highp T muons p T & 100 GeV are onlyslightlydeectedbythemagneticeld,sothesetracksappearstraight.Showers cansignicantlyaltermuonreconstructionperformancebydegradinglocalchamber reconstructiondescribedinChapter3.2.6orbyconfusingpatternrecognitionandtrack tting[51]. Inordertocombatsignicantresolutionlossfromshowers,twomuonre-tsare usedtooptimizethemuont.Bothre-tsusethehitsfromtheglobalmuontasa reference.The Tracker-Plus-First-Muon-Station TPFMSroutineusesalloftheavailable trackerhitsandtruncateshitsfromthemuonspectrometerattherstobservedstation. Theassumptionwiththisalgorithmisthatmuonsfartheralonginthetrajectorythat crossmoreironaremorelikelytobecontaminatedbyshowers[51].The Picky t prunesmuonhitsinchambersthatappeartocontainashowerchamberswithahigh hitoccupancy.Hitsusedinthetmusthavea 2 withrespecttothetrajectorybelowa pre-determinedthreshold.Toimprovemuonidentication,analgorithmwasdeveloped tochoosethebesttrackt,onamuon-by-muonbasis,betweenthetracker,TPFMSand pickymuonts;itwasdubbedtheTunePalgorithm.TheTunePalgorithmselects thebesttrackbasedonthetailprobability,whichistheprobabilitythattheobserved 2 islargerthanthenominal 2 .TheTunePalgorithmbeginswiththepickytand comparesthepickyttailprobabilitywiththetailprobabilityofthetrackert.Ifthe trackerthasasignicantlybettertailprobability,thetrackertischosen.Thetail 56

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probabilityofthechosentracktpickyortrackeriscomparedtothetailprobabilityof theTPFMSt,andthetwiththebettertailprobabilityisselectedasthetracktthatis chosenbytheTunePhighp T muonoptimizationalgorithm. TheperformanceoftheTunePhighp T muonreconstructionalgorithmwas studiedextensivelyusingmuonsfromsecondarycosmicrays.Cosmicraymuonsare amajorsourceofmuonswithhightransversemomentum.Areviewofthecosmicray muonbackgroundandtheunderstandingofcosmicraymuonsinCMSisprovided inAppendixA.CosmicraymuonsenterCMSfromthetopofthedetectorandexit throughthebottomaftertheytraversethevolumeofCMS.Whilecosmicraymuons areintheupperhemisphereofCMS,theyaredepositinghitsininareversedtime orderingtocollisionmuonsemanatingfromthecenterofthedetector.Specializedmuon reconstructionisusedforcosmicraymuonsameansofmeasuringreconstruction performance.Thespecializedalgorithmsmodifythenavigationofmuonsthroughthe detectortoreectthereversetime-orderingintheupperhemisphere.Thespecialized muonreconstructionallowsmuonstobereconstructedasonelongtrackthatuses thewholeCMSvolume,orastwoindependentmuons.Figure4-6[38]depictsa cosmicmuoncrossingtheCMSvolumethatshowstheorientationofhowmuons arereconstructedinthetopandbottomhemispheresoftheCMSdetector.When acosmicraymuonisreconstructedasindependenttopandbottommuons,itis actuallytwoindependentasfarasthetrackerisconcernedmeasurementsofthe samemuon'strajectoryparametersatthepointofclosestapproachtothecenterofthe detector.The q = p T resolutionoftheCMSdetectorisestimatedinadata-drivenmanner usingcosmicmuons.Thisisdonewiththerelativeresidualofthetwoindependent tracks: R q = p T = q = p T top )]TJ/F22 11.9552 Tf 11.955 -0.166 Td [( q = p T bottom p 2 q = p T bottom wheretopandbottomrefertothetwoducialhalf-cylindersofCMSbisectedbythe y =0 plane.Thenormalizedrelativeresidualalsocalledapulldistribution,whichis 57

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describedinAppendixCisdenedas P q = p T = q = p T top )]TJ/F22 11.9552 Tf 11.956 -0.166 Td [( q = p T bottom q 2 q = p T top + 2 q = p T bottom inordertostudythebehavioroferrorsfromthetrackt.Figure4-7showstheRMSand fromGaussiantstotherelativeresidualdenedinEquation4[51].Theresolution isdependentonthetrackerfromlowtointermediate p T regimesupto 100 GeV .After 100 GeV ,thereisanimprovementintheresidualwhenhitsfromthemuonsystem areaddedintothet.ThepullsfromEquation4aregiveninFigure4-8,andare closetobeingunitGaussiansinamajorityofthe p T range.Athigher p T ,theuncertainty assignedtothe p T ofthetrackt,tendtobeoverestimatedbythetracker-onlytand underestimatedbythegobalmuont[51]. 4.4AbsoluteMomentumScaleUsingtheEndpointMethod Theabsolutemuonmomentumscaleofsagitta-basedmeasurementsisacritical componentinthemeasurementofhigh-momentummuons.Thisisbecuasehigh momentummuonshaveasmallradiusofcurvatureandappearasnearlystraighttracks. Theabsolutemomentumscalebiasisdenedasanoverallshiftinthetransverse curvaturesuchthat q = p T q = p T + where istheabsolutemomentumscalebiasmeasuredintermsof q = p T .Inthis convention, ismeasuredin c/TeV .Amomentumscalebiasof 1 c/TeV means thatadetectoreffectisinducingadditionaldeectioninthereconstructedtrajectory whichequivalenttothatofa 1 TeV muon.A 5 c/TeV biaswouldimplyadditional detector-induceddeectionthatisequivalenttothatofa 200 GeV muon,whichis considerablylarger.Theconventionisintuitivealargermomentumbiasimpliesa largerfalsedeectionisinduced,andthemeasurementofthemuonmomentumismore distorted. 58

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Fora 1 TeV Z 0 ,arelativelysmallbiasof 1 c/TeV amountstoaworseningofthe resolutioncomparedtothenominaltrackerresolutionbuta 5 c/TeV biascompletely shiftsthepeakasshowninFigure4-9.Themodelingofthisbiasfromtheassociated weakmodedistortionofthetracker.Weakmodesaresystematicdistortionsofthe detectoralignmentthatbiastrackparametermeasurements.Theweakbiasmodeledin thissectioncomesfroma -dependentdistortionof q = p T ,suchas = A cos )]TJ/F25 11.9552 Tf 11.955 0 Td [(! where A istheamplitudeofthebiasand omega isaphase.Weakmodesindetector alignmentarediscussedfurtherinAppendixF.Thesamebiasesareimposedona 3 TeV resonanceinFigure4-10,wherethe 1 c/TeV biasagainaffectsthetracker resolutionforadditional,butnowdrastic,smearing;whereasthe 5 c/TeV biastranslates themeanoftheresonancedownby 40% andcreatesalongtail,illustratinghowweak modestructurescanbedisastrousforanydimuonresonancesearchandbecome increasinglytroublesomeathighermasses. Forcosmicraymuonsandcollisionprocessesthatgeneratemuonsinthenalstate Z = ,themomentumspectrumendsas p T !1 theendpointwhichiswherethe transversecurvaturespectrumapproacheszerofor + and )]TJ/F20 11.9552 Tf 7.084 -4.339 Td [(.Ifacurvaturebiasis present,therewillbeadistortioninthe q = p T spectrum,leavinganon-zerominimum. Twocomplementarymethodsareusedtotestforanendpointbiasthatarepresented inSection4.4.1,where MockDataTemplate MDTtechniqueispresentedand Section4.4.2inwhichthefullydata-driven bootstrap techniqueispresented.Additional studiesandcomparisonsregardingtheendpointaredocumentedinAppendixF. 4.4.1MockDataTemplateMDTTechnique TheMDTtechniqueformeasuringthemomentumbiaswasoriginallyreferredtoas thecosmicendpointmethodbecauseitwasrstusedoncosmicraymuonsaspart 59

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ofthemeasurementofthechargeratioofcosmicraymuons[38,67].Itisexpandedto alsoincludetheDrellYanprocess. Trackingbiasesaremeasuredbycomparingthe q = p T distributionsbetweendata andsimulationbyperforminga 2 testbetweenthetwodistributions[6871].Thisis illustratedbyrstplottingthecurvaturedistributionformockdataandsimulationwith =0 inFigure4-11Awheresimulationisnormalizedtodata.Amockbias, ,isinjected intosimulationasillustratedinFigure4-11B.Arbitrarybiaseswhere > 0 and < 0 are showninredandblue,respectively.Anon-zerobias, ,producesanoverallshiftinthe q = p T spectrum.Arangeofbiasesissteppedthroughinordertocoverarangeof q = p T spectra,whichisshownintheheatmapinFigure4-11C.The 2 betweenthesimulated q = p T distributionforeachstepin andtheresulting 2 distributionisproducedin Figure4-11D.Theminimumofthe 2 distributioninFigure4-11Disfoundbyttingthe 2 shapewithahighorderpolynomialsmoothingfunction. 4.4.2Bootstrap For DY decays,twomuonsareproducedinthenalstatewithnotendencyto createmore + than )]TJ/F20 11.9552 Tf 7.085 -4.339 Td [(.Themuontransversecurvaturedistributionforthisprocessis presentedinFigure4-12A.Thebootstrapmethodexploitsthesymmetryinthenumber ofpositiveandnegativemuonsbyperforminga 2 comparisontestbetweenthe j q = p T j distributionsofthepositiveandnegativemuons. Whennon-zero isintroduced,the j q = p T j spectraareshiftedtotheleftand right.TheresultofthisbiasisshowninFigure4-12B,wheremockdataisshownwitha simulatedbiasof =1 c/TeV .Acorrectionvalue 0 = )]TJ/F25 11.9552 Tf 9.298 0 Td [( isaddedtothebiasedmock datainsteps,anda 2 testisperformedbetweenthetwospectraforeachvalueofthe correction.Thismethodwillalwaysreturnacorrectionvalueforthedata, )]TJ/F25 11.9552 Tf 9.299 0 Td [( ,tomake the j q = p T j symmetric,whereastheMDTmethodwillalwaysreturnabiasrequired forsimulationtomatchdata, .Figure4-13illustratesthismethodwherea 1 c/TeV curvaturebiasisinjectedintomockdataandthescanin 2 isperformedinthesame 60

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mannerastheMDTmethod.This 2 scanproducestheexpectedsignchangeand returns =0.99 0.02[ c/TeV ] asexpected. Inpractice,thebootstrapmethodisthepreferredchoiceforgeneralusage becauseitdoesnotrelyonsimulation.Centrallyproducedsimulationhasamisaligned geometryapplied,soabiasisalreadypresentthatmustbesubtracted.Thebootstrap issensitivetosimulatedmisalignments,soitcanbeusedtomakeone-to-one comparisonsontheabsolutemomentumscalebetweendataandsimulation. 4.5MuonIsolation Itisimportanttobeabletodifferentiatepromptmuonsfrommuonsthatare embeddedinQCDjets.Muonisolationisadiscriminatingvariablethatreferstothe energyowintheneighborhoodofareconstructedmuon.InQCDprocesses,gluons arefrequentlyradiatedfromatravelingparton,resultinginaconeofparticlesinthe samegeneraldirectionofthegluon-radiatingparton.Thecollectionofthesepartons intooneobjectcompriseajet.Twoisolationalgorithmsareconsideredregarding the Z 0 analysis. Relativetrackerisolation p T = p T ,considersanyreconstructed trackertrackwhosetrajectoryiswithinaconearoundthemuontrackdirection, R q 2 + 2 < 0.3 andnormalizesthistothereconstructedmuon p T Combinedrelativeisolation p T + E T = p T considersthesamesummationofthetracker isolation,butincludestheenergydepositedinthecalorimeterscomputedwithrespect tothenominalcenterofthedetectorwithinthesame R < 0.3 cone[51].Prompt muonslikethosefromW and Z 0 muonstendtohavelittleenergyowaroundthemuon comparedtoQCDprocesses.Anymuonwith p T = p T belowadesiredthresholdis consideredtobeisolated.IsolatedmuonsthatoriginatefromQCDjetsarereferredtoas fakes becausetheyareQCDjets. AstheinstantaneousluminosityoftheLHCincreases,morecollisionsper bunchcrossingareproduced,andthatcausesmoreenergydepositstobeleftin thecalorimeters.Thisleadstomoreinteractionspereventandanincreaseddifculty 61

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indeterminingwhichvertexisassociatedwithwhatenergy;thiseffectiscalled pileup .Totesttheeffectofpile-uponisolation,muonsfrom Z 0 decysareused. Thequantityofinterestregarding Z 0 decaysisthefractionofeventsfailing anisolationrequirementasafunctionofnumberofprimaryverticesreconstructedin theevent.TheisolationvariablehasbeenstudiedbyCMSanddenitionsofaloose isolationcuthavebeenidentied[51].Fortestingthecombinedrelativeisolation,a loose 15% cutisconsidered;therelativetrackerisolationisconsideredwithasimilarly loose 10% cut.Figure4-14showsthefractionof Z 0 eventsthatarerejectedwhen usingrelativetracker-onlyisolationandtracker-plus-calorimeterisolationfor 2011 top and 2012 bottomLHCluminosityconditions[30,72].Thefractionofmuonsfailing relativeisolationsteadilyincreasesasafunctionofthenumberofprimaryverticeswhen calorimeterinformationisincludedintheisolation.Theeffectoftracker-onlyisolationis keptunder O 1% withverylittleincreasefor 2011 and 2012 instantaneousluminosity conditions[30,72].Inordertokeepthe Z 0 analysisrelativelypile-upindependent,and thereforemorerobust,a p T = p T < 0.1 cutonrelativetrackerisolationisappliedforall muonsselectedforanalysis.Itisunnecessarytore-weightthepile-updistributionin simulationtomatchdatagiventhesmallobservedeffect. 62

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Figure4-1.Stoppingpower= h d E = d x i forpositivemuonsincopperasafunctionof = p = Mc overnineordersofmagnitudeinmomentum.Solidcurves indicatethetotalstoppingpower. Figure4-2.Muonradiationlossesasafunctionofmuonenergyin GeV brokendown intodirectpair-production,bremsstrahlung,andphotonuclearinteractions. 63

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Figure4-3.Productionofelectronsbymuonstraversingmatterasafunctionofthe muonmomentumviaionization,whichislabeledasDeltarays, Bremsstrahlung,andpairproduction. 64

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Figure4-4.Distributionofthedistanceofhitsfromthenominalmuontrackdueto showeringinducedbyamuoniniron.Theinsertshowstheprobabilityofthe numberofadditionalhits. 65

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Figure4-5.Simple 3 )]TJ/F20 11.9552 Tf 12.622 0 Td [(pointdiagramofthemeasurementofamuontrack. r isthe radiusofthehelicalpathfromacentralpointforaparticletraversingthrough alength L s isthesagitta. 66

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Figure4-6.CosmicmuoncrossingtheCMSdetectorfromtoptobottomleavinghitsin themuonsystem,tracker,andcalorimeter. Figure4-7.ThesampleRMStruncatedat 1 andGaussiantstothe q = p T relative residualscomparingtheoutputsforresultswiththetrackertandglobal muontswiththeTunePalgorithm. 67

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Figure4-8.WidthsandmeansoftheGaussiantsofthemuon q = p T pullscomparing theoutputsforresultswiththetrackertandglobalmuontswiththeTune Palgorithm. Figure4-9.Simulatedeffectofabiasinq/ p T ona 1 TeV Z 0 withthetrueresonancein black,thetrackerresolutioninblueandthetrackerresolutionwithabiasin shadedredfora 0.1 c/TeV biasanda 0.5 c/TeV bias. 68

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Figure4-10.Simulatedeffectofabiasinq/ p T ona 3 TeV Z 0 withthetrueresonancein black,thetrackerresolutioninblueandthetrackerresolutionwithabiasin shadedredfora 0.1 c/TeV biasanda 0.5 c/TeV bias. 69

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AMockdataoverlayedwithsimulationwiththe absenceofanybias. BTheshiftfrommockdatawithnobias =0 to mockdatawithalargeinjectedbias. CArangeofthe q = p T spectrumwithstepsinthe applied DThe 2 betweenthemockdataandthesimulationdistributions,whichisttedforaminimum. Figure4-11.Demonstrationofthesimulation-basedgeneralendpointmethod. 70

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ATheoverlayof j q = p T j forpositive-andnegativecurvaturedistributionswith =0 inmockdata. BTheoverlayof j q = p T j forpositive-and negative-curvaturedistributionswith =1 c/TeV inmockdata Figure4-12.Demonstrationofthepurelydatadrivenendpointmethod. 71

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Figure4-13.Demonstrationofthepurelydata-drivenendpointmethod.Theresulting 2 versus distributionwhenthereisa =1 c/TeV biasinjected. 72

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Figure4-14.Fordimuonsonthe Z 0 peak 60 < m < 120 GeV for 2011 collison conditionsontopand 2012 collisionconditionsonthebottom.Thefraction ofmuonsotherwiseselectedusingtheseanalysiscutsthatfailacutonthe tracker-onlyrelativeisolationat 0.1 blacktrianglesoracutonthe tracker-plus-calorimetersrelativeisolationat 0.15 redsquares,asa functionofthenumberofreconstructedprimaryvertices. 73

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CHAPTER5 DATASELECTION Thissectiondetailshowdataareselectedforuseinthisanalysisanddescribes how pp collisionsandtheCMSdetectoraresimulated.ThedescriptionofCMSrun certicationisinSection5.1.TriggerrequirementsaredescribedinSection5.2. Eventselectionfromtheprimarydatasettothenaldimuoncleaningisdescribedin Section5.3.ThesimulationusedinthisanalysisisdescribedinSection5.4. 5.1GoodRuns Toensurethatthedatacollectedforthisanalysisishomogeneousamong thedifferentdetectorcomponentsandacceptableforphysicsanalysis,theCMS collaborationusestheconceptofgoodruns.Thisanalysisusesastabletrigger pathdiscussedinSection5.2anddoesnotrelyonsubsystemsthatdonotcontribute tomuonreconstruction. DatatakingisorganizedbytheDAQintoincreasingrunnumbers.Whenarun isstarted,itisdividedinto 23 s luminositysections[73],whichdenotethesmallest indivisibleamountofdatatobeusedinananalysis.Individualsubsystemssometimes temporarilymalfunctionduringarunordonotparticipateinarunaltogether,which meansthatnotalldetectorsareproducingusabledata.Inorderfordetectordatato beusableforphysics,itthedetectorresponsemustbehomogeneoussuchthatitcan bepredictedbysimulation.Eachsubsystemhasismarkedas GOOD or BAD bysettinga booleanbitintheCMSrunrecordthatcanbesetforeachindividualluminositysection. Subsystemsaremonitoredbyshiftpersonnelandonlinesoftware,whoareresponsible forinitiallysettingthebitandnotingextranecessaryinformationabouttheruninthe shiftlog.Bitsarereviewedandapprovedbytheappropriatevalidationsubgroupinside theCMScollaboration.. 74

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Acentrallyproduced JavaScriptObjectNotation JSON 1 ledenotestheaccepted subsystems.Whenallsubsystemsbitsaremarkedas GOOD ,theJSONleisreferredto asgolden.Strictlymuon-basedanalysesdonotrequireallsubsystembitstobe GOOD sothereisanadditionalcentrallyproducedJSONlethatismarkedasMuonPhys thatdoesnotrequire GOOD bitsonsubsystemsthatarenotexplicitlyrequiredformuon analysis. 5.2TriggerSelection EachtriggerpathinCMSisawell-denedsequenceofL 1 andHLTtriggers.The acceptanceofaL 1 pathprecedespartialeventreconstructionbytheHLTcomputing farm.TheL 1 pathalsoservestoinitiateHLTdecisionsequencesforatriggerdecision, suchthateachHLTpathhasanL 1 pathwhichcanbethelogical OR ofmultipleL 1 pathsthatmustrstbeaccepted.TheHLTmakesthenaldecision. InordertocontroltriggerpathswithhighacceptanceratesatL 1 orHLT,CMS employsthetechniqueoftriggerpre-scaling.Atriggerthathasaprescalefactor, n ,will onlypassevery n th eventthatsatisesthetriggercondition.Forsomeprescaledtrigger paths,theprescaleischangeddynamicallyduringtherun.Theprescalesarechanged basedontheinstantaneousluminosityoftheLHC.Theinstantaneousluminosity decreaseswithtimeduringeachprotonllbecausetheprotonsinthellareusedby collidingbunchesforphysics.Theoveralltriggerratethusdecreasessoprescalescan belessenedasrunsprogresstotakefulladvantageofcollisiondata. TheL 1 paththatinitiatesHLTreconstructionforthisanalysisis L1 SingleMu16 TheL 1 muontriggersystemreconstructsamuoncandidateandestimatesits p T tobe above 16 GeV .TheefciencyoftriggeringatL 1 throughthispathchangedbetween 2011 collisionsat p s =7TeV and 2012 collisionsat p s =8TeV .TheL 1 trigger reconstructionefcienciesforthe p s =7TeV and p s =8TeV erasofCMSoperations 1 http://www.json.org/ 75

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areshowninFigure5-1forthe L1SingleMu16 triggerpathasafunctionof p T [74,75]. ChangesintheL 1 efciencyaremostlyduetochangesintheCSCtriggeralgorithms thatappliedanew p T assignmentalgorithmtoreducetherateby O 30% atthecostof an O 1% dropinefciency. TheHLTpathusedforthisanalysisisthe HLT SingleMu40 eta2p1 .Asingle-muon pathwaschosenforthisanalysisbecausemuonshoweringpotentiallyreducestrigger efciency,andrequiringonlyonemuontriggerreducesthechanceofrejectingadimuon candidatebecausethe p T ofonemuonwascatastrophicallymisreconstrucedbecause ofthehighhitmultiplicityinthemuonsystem.Requiringonlyonemuonpermitsthis classofeventstopassthroughtheTunePalgorithmdescribedinChapter4.3thatare intendedtorecoverthisclassofevents. Thetechnicalimplementationofthistriggerrequiresthatthetriggeredmuonmust haveatransversemomentumgreaterthan 40 GeV andbewithin j j < 2.1 .TheHLT efcienciesaresummarizedwiththeselectionefcienciesinFigure5-2[74,75]. Thisanalysisalsousestwoprescaledhighleveltriggerpaths.In 2011 ,the prescaledsinglemuonpathwas HLT Mu 15 whichhadatotalprescaleof 2000 and requiredthatthetriggeredmuonhave p T > 15 GeV .In 2012 datataking,the HLT Mu24 eta2p1 triggerpathwasusedwithatotalprescaleof 250 .The 2012 path requiredthatthetriggeredmuonhave p T > 24 GeV and j j < 2.1 5.3EventSelection The Z 0 analysisusesthe /SingleMu primarydataset;thespecicdatasetsarelisted inTable5-2.The 2011 )]TJ/F20 11.9552 Tf 9.299 0 Td [(eradataweretakenat p s =7TeV andthe 2012 )]TJ/F20 11.9552 Tf 9.299 0 Td [(eradata weretakenat p s =8TeV .Fortheanalysisofthe 2011 datasets,theCMSanalysis softwareversionusedwas CMSSW 4 4 2 .Data-takingforthe 2012 analysisexperienced anupgradeintheCMSanalysissoftwareto CMSSW 5 2 3 Inordertolteroutbeambackgrounds,tracksusedtocreatemuonsmust bemarkedas highpurity [76].AprimaryvertexPVmarkedasgoodmustbe 76

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resconstructedofineineveryconsideredevent.Tobemarkedasgood,aPVmustbe composedofatleastfourtracksthatarelocatedwithin j r j < 2 cm and j z j < 24 cm ofthenominalIP.RequiringaPVispowerfulforrejectingcosmicraymuonsthattrigger inemptybunchcrossingsthatcanproducefakedimuonswhentheytraversetheCMS volumeneartheIP. Onlymuonsthatarereconstructedinthemuonidenticationasglobaland trackermuonsareconsideredinthisanalysis.The p T oftheofinereconstruction muonmustbeatleast 45 GeV inordertoensurethatthemuonisintheplateauofthe single-muontriggerefciency.Usingthetrackertcompositetothereconstructedmuon, thetransverseimpactparameterwithrespecttothenominalbeamspotmustbewithin 2 mm .Inordertoensurethatmuonsaretwellanduseadequateinformationfrom thetrackerandmuonspectrometertoguardagainstover-determinedts,theglobal muontrackcompositetotheidentiedmuonmustuseaminimumof 1 pixelhit, 1 muon hitand 9 trackerlayers.Thetrackermuonidenticationprocessmustbematchedto segmentsinatleasttwomuonstations.Theefciencyofthemuonreconstructionand muonselectionrequirementsdescribedabovewasstudiedbytheCMScollaboration throughthemuonphysicsobjectgroup.Muonsfrom Z 0 decayswereusedtoperform tag-and-probeefciencymeasurement[51]withtheselectedmuonasatagand tracksobservedintheinnertrackerasprobes.Theefciencyofallaboveselectionis measuredtobe 90.9 0.1stat. %in j j < 1.2 and 92.6 0.1stat. %in 1.2 < j j < 2.4 Themeasureofagreementbetweendataandsimulationisascalefactor,whichis denedastheratioofdatatosimulationthatarefoundtobe 0.987 0.001stat. and 0.995 0.001stat. for j j < 1.2 and 1.2 < j j < 2.4 respectively[51,72,77,78]. InordertoreducecontaminationfromeventswheremuonscomefromQCDjets, muonsmustpassarelativetracker-onlyisolationcut.The p T ofothertrackswithina coneradius r ,where r = q 2 + 2 ,butexcludingthemuontrackitselfmust belessthan 10% ofthe p T asestimatedfromthetrackertofthereconstructedmuon. 77

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Theefciencyofthetracker-onlyisolationcutis 98.8 0.1stat. %,withascalefactorof 1.001 0.001stat. [78]. Dimuonsareformedwhenevertwomuonsareselectedwiththeabovecriteria.One ofthereconstructedmuonsinthedimuoncandidatemustbeaconrmedmatchwiththe HLTobjectthatredthetriggerinthesingle-muonpath.Themuonmustbematched within R < 0.2 ofthetriggerobjecttobeconrmed.Sincethisanalysisissearching foranewneutralboson,thetwomuonsmustbeofoppositecharge.Therateatwhich muonchargeisassignedincorrectlywasstudiedinsimulationandindatausingcosmic rayeventsandwasfoundtobe 0.5% formuonswith p T upto 300 GeV [79].Areviewof thechargemisidenticationstudyisdoneinAppendixB.Dimuoneventswheremuon chargesareidenticalarestudiedseparatelyasacontrolsample. Inordertoreducethebackgroundfromcosmicraymuonsthatpasstheimpact parameterrequirementandarein-timewithacollisionevent,thethree-dimensional anglebetweentwomuons'momentamustbelessthan )]TJ/F22 11.9552 Tf 11.956 0 Td [(0.02 rad Asanadditionaldimuonqualityconstraint,acommon-vertextisperformedusing thebesttracktfromeachofthetwomuons,usingtheKalmanlter[65]formulation, tocomputethekinematicsofthedimuonsystem.Thisensuresthatthetwomuons originatefromthesamevertex,andonlydimuoneventswherethe 2 < 10 ofthe vertex-constrainedtareaccepted.Thereisalwaysexactlyonedegreeoffreedomfrom vertexing.Thekinematictrajectoriesofthebesttracktsfromeachofthetwomuons areupdatedusingthevertexconstraintandtheresultingmassisusedforthenal analysisinput. Thereisanegligiblefractionofcandidatedimuonswheremorethanoneopposite-sign dimuonisproduced;whenthishappens,onlythedimuonwiththehighestinvariantmass iskept.Thedimuoncandidatethatpassesallselectioncriteriadenotesaphysicsevent forthe Z 0 analysis. 78

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Theacceptance,triggerandfullselectionefcienciesforthe 2011 )]TJ/F20 11.9552 Tf 9.298 0 Td [(eraand 2012 )]TJ/F20 11.9552 Tf 9.298 0 Td [(eradataarepresentedintopandbottomplotsinFigure5-2respectively[74,75]. Thereisanoverall 10% reductioninefciencyfor 2012 datathatiscausedbythemuon qualitycriterionontheminimumnumberoftrackerlayersinthetrackt.Software changesintrackerreconstructionareresponsibleforthisreductioninefciency. Figure5-3showstheN-1efciencies,wheretheefciencyofeachcutispresented withrespecttotheapplicationofallotherqualitycriteria,for 2011 and 2012 dataaswell asthe 2012 simulationtodemonstratethelossinefciencycausedbythecutontracker layersisexpectedindetectorsimulationwiththeappliedsoftwarechangesinthetrack reconstructionsoftware[1]. 5.4Simulation Knownphysicsprocessesandthebehaviorofthedetectorareaccountedforwith simulation.Inthisdissertation,wewillusetheconventionofreferringtosimulationsof thecollisionanditsproductsasgeneratedevents,andthesimulationsofthedetector responseassimplysimulation.Thissectiondescribestheeventgeneratorsand detectorsimulationthatareused,andcompareslowlevelmuonqualitymonitoring distributionsbetweendataandsimulation. Theprimaryeventgeneratoris PYTHIA v 6.4 [80]. PYTHIA isageneralsimulator oflepton-lepton,lepton-hadron,andhadron-hadroninteractions.Itencapsulates abroadrangeoftheoreticalmodelsincluding Z 0 and G gravitonmodels. PYTHIA generallyprovidesanleading-orderLOtheoreticalapproximationforitssimulationof physicsprocessessinceitonlyconsiderstheleadingparton-partoninteraction.The MAGRAPH 5.1 [81]eventgeneratorwasusedimprovemodelpartoninteractionsatLO andnext-to-leading-orderNLOforjets.The POWHEG .[82]eventgeneratorisoptimized forheavyquarkgenerationinhadron-hadroncollisionsandisaccuratetoNLO[8385]. The MADGRAPH and POWHEG generatorsareinterfaceddirectlywith PYTHIA tocreatethe chainofgeneratedparticles.Thenext-to-next-to-leading-orderNNLOcontributions 79

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arecheckedwith FEWZ [86]forelectroweakinteractions.Asummaryofthescaleof theLO NLOandNLO NNLOcorrectionsisshowninFigure5-4.Thesimulation samplesusedfortheprimary p s =7TeV analysisarelistedinTable5-3[72].Samples forthe p s =8TeV analysisarelistedinTable5-4[30].Thedetectorresponseto simulatedphysicsprocessesaresimulatedusing GEANT [87]. GEANT describesthe generatedparticleinteractionwiththedetector, ThePDFsetusedforsimulationwasCTEQ6.1[88],Theanalysisresultswere checkedagainsttheMSTW2008PDFset,andfoundtoagreewell[89].Theuncertainties onthePDFsarediscussedwiththeanalysisinChapter6.5. The Z 0 modeldescribedinChapter2.2isusedasthetemplatemodelforanarrow dimuonresonance.Thisisimplementedin PYTHIA withtheLagrangianconventionfrom Equation2.TheinputsaredenedinTable5-1[20]. Inordertovalidatethatthedetectorbehaviorisunderstoodandpredictable, low-levelmuonqualitymonitoringdistributionsarecomparedbetweendataand simulation.Thecomparisonshownbelowarefor 2012 datatakenat p s =8TeV ,withan estimatedintegratedluminosityof 4.5fb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .Inadditiontoprovidinglistsofparticlesand theirkinematicpropertiesforeachgeneratedcollision,theeventgeneratorsalsoreport thetotalnumberofeventsgeneratedandthecorrespondingintegratedcrosssection. Fromthisinformationwecancomputereweightingfactorsforthesimulatedsamplesto correspondtotheintegratedluminosity, L ,ofobserveddata: w = L N gen where istheproductioncrosssectionofthegeneratedprocessand N gen isthenumber ofeventsgeneratedinthespecicsample.Thelow-levelreconstructedmuonquality monitoringdistributionsarecomparedingure5-5forthenumberoftrackerpixelhits, thetotalnumberoftrackerhits,thenumberoftrackerlayers,thenumberofmuonhits, andthenumberofmuonsegmentmatches.Adashedlinemarkstheanalysisselection 80

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Table5-1. PYTHIA parametersforageneral E 6 Z 0 model. PYTHIA parametervalue PARU121 4sin p 6 sin W PARU122 p 10cos )]TJ 6.587 6.645 Td [(p 6sin 3 sin W PARU123 0 PARU124 p 10cos + p 6sin 3 sin W PARU125 )]TJ/F23 7.9701 Tf 6.587 0 Td [(4sin p 6 sin W PARU126 p 10cos )]TJ 6.587 6.645 Td [(p 6sin 3 sin W PARU127 p 10cos )]TJ 6.587 6.645 Td [(p 6sin 6 sin W PARU128 p 10cos )]TJ 6.587 6.645 Td [(p 6sin 6 sin W requirements.Thenormalized 2 distributionoftheglobalmuontisalsocheckedto ensurethatqualityofnalmuonttingissimilarbetweendataandsimulation.Inall monitoringdistributions,thereisgoodagreementbetweendataandsimulation,which indicatesthattheCMSresponseisconsistentandunderstood. Figure5-1.L 1 efcienciesforthe L1SingleMu16 pathfor 2011 and 2012 data. 81

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Table5-2.Datasetsandtheassociatedrunrangesusedforthisanalysis. 2011 datasetsat p s =7TeV Runrangeheight /SingleMu/Run2011A-08Nov2011-v1/AOD160431 /SingleMu/Run2011B-19Nov2011-v1/AOD175832 2012 datasetsat p s =8TeV Runrange /SingleMu/Run2012A-PromptReco-v1/AOD190645 /SingleMu/Run2012B-PromptReco-v1/AOD193834 Table5-3.Summaryofsimulatedsignalandbackgroundprocesssamplesusedto generatedwith p s =7TeV .Theprogramslistedinthatcolumnhighlight departuresfromusingplain PYTHIA foreverything,e.g. MADGRAPH or POWHEG ProcessProgramGenerationparameters pb.Events Z 0 ,SSM PYTHIA M =750 GeV 20400 M =1000 GeV 20328 M =1250 GeV 20088 M =1500 GeV 20412 M =1750 GeV 20758 DY + )]TJ/F84 9.9626 Tf 36.797 -3.616 Td [(PYTHIA M > 20 GeV 1631 2148325 M > 120 GeV 7 954550 M > 200 GeV 0 9755000 M > 500 GeV 0 02755000 M > 800 GeV 0 003155000 M > 1000 GeV 9 7 10 )]TJ/F23 6.9738 Tf 6.227 0 Td [(4 55000 DY + )]TJ/F84 9.9626 Tf 36.797 -3.616 Td [(POWHEG M > 20 GeV 1631 29743564 M > 120 GeV 7 946394 M > 200 GeV 0 9748800 M > 500 GeV 0 02755000 M > 800 GeV 0 003155000 M > 1000 GeV 9 7 10 )]TJ/F23 6.9738 Tf 6.227 0 Td [(4 46589 DY + )]TJ/F84 9.9626 Tf 37.837 -3.615 Td [(PYTHIA M + )]TJ/F11 9.9626 Tf 9.492 -3.615 Td [(> 20 GeV 1631 02032536 t t PYTHIA 157 01089625 t t MADGRAPH 157 03701947 tW MADGRAPH 10 6489417 WW PYTHIA 43 04225916 WZ PYTHIA 18 04265243 ZZ PYTHIA 5 92108608 W PYTHIA j j < 2.55861 02087693 W + jets MADGRAPH 2 8 10 4 15110974 InclusiveQCD PYTHIA ^ p T > 20 GeV, 8 5 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(4 20416038 j j < 2.5 p T > 15 GeV 82

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A 2011 simulation B 2012 simulation Figure5-2.Asafunctionofinvariantmass,thecombinedreconstructionandselection efciencyfordimuonspassingselectioninsimulationwithrespectto triggeredeventsinacceptanceredcircles,withrespecttoalleventsin acceptancegreensquares,andthetotalacceptancetimesefciencyblue triangles.Thebluecurveisattothetotalacceptancetimesefciencyin thedimuonmassrangefrom 200 to 2000 GeV 83

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Figure5-3.Theratioofthenumberofeventsintheregion 60 < m < 120 GeV thatpass allselectioncutstothenumberofeventspassingallcutsbuttheone indicated,formaincutsintheeventselection.Efciencymeasuredfrom dataisshowninblackcircles,andpredictionbythesimulationlabeledas MCisshowninmagentahistogram. Figure5-4.Therapiditydistributionfor Z = productionattheLHCforaninvariantmass M =250 GeV .TheLO,NLO,andNNLOresultshavebeenincluded.The bandsindicatetheresidualenergyscaledependences. 84

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Table5-4.Summaryofsimulatedsignalandbackgroundprocesssamplesusedto generatedwith p s =8TeV .Theprogramslistedinthatcolumnhighlight departuresfromusingplain PYTHIA foreverything,e.g. MADGRAPH or POWHEG ProcessProgramGenerationparameters pb.Events Z 0 SSM + )]TJ/F84 9.9626 Tf 30.907 -3.615 Td [(PYTHIA M =750 GeV 0 14 LO25040 M =1000 GeV 0 0369 LO25040 M =1250 GeV 0 0129 LO25344 M =1500 GeV 0 00433 LO25344 M =1750 GeV 0 00172 LO25272 M =2000 GeV 6 88 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(4 LO25092 M =2250 GeV 2 93 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(4 LO25104 M =2500 GeV 1 27 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(4 LO25344 M =2750 GeV 5 55 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(5 LO25376 M =3000 GeV 2 5 10 )]TJ/F23 6.9738 Tf 6.227 0 Td [(5 LO25040 DY + )]TJ/F84 9.9626 Tf 36.797 -3.616 Td [(PYTHIA M > 20 GeV 1915 .NNLO2000016 M > 120 GeV 11 94 LO 1.26849454 M > 200 GeV 1 49 LO 1.26850400 M > 500 GeV 4 51 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(2 LO 1.26850560 M > 800 GeV 5 71 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(3 LO 1.26850400 M > 1000 GeV 1 89 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(2 LO 1.26850005 M > 1300 GeV 4 50 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(4 LO 1.26850560 M > 1600 GeV 1 18 10 )]TJ/F23 6.9738 Tf 6.226 0 Td [(4 LO 1.26850112 DY + )]TJ/F84 9.9626 Tf 37.837 -3.615 Td [(PYTHIA M + )]TJ/F11 9.9626 Tf 9.16 -0.111 Td [(> 20 GeV 1915 .NNLO1987776 t t MADGRAPH 225 2 NLO6736135 tW POWHEG 11 2 NLO497658 tW POWHEG 11 2 NLO493460 WW PYTHIA 57 1 NLO10000431 WZ PYTHIA 32 3 NLO9996622 ZZ PYTHIA 8 3 NLO9799908 W PYTHIA j j < 2.59130 0 LO4769224 W + jets MADGRAPH 36257 .NNLO18393090 InclusiveQCD PYTHIA ^ p T > 20 GeV, 3 64 10 8 3.7 10 )]TJ/F23 6.9738 Tf 6.227 0 Td [(4 LO7529312 j j < 2.5 p T > 15 GeV 85

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AThenumberofhitsinthepixeldetector. BThenumberoftracker-muonsegmentmatches permuon. CThenumberofhitsinthewholesilicontracker. DThenumberoftrackerlayerswherehitswere foundforeachmuon. EThenumberofDTandCSCsegmentsandRPC hitsinthemuonchambers. FThe 2 /d.o.f.fortheglobalmuonts. Figure5-5.Data-simulationcomparisonsfor 4.5fb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 of p s =8TeV data. 86

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CHAPTER6 ANALYSIS Thischapteroutlinestheanalysisstrategyforthehigh-massdimuonresonance search.Theresultsfromthisdissertationbuildsontheknowledgefromthepublished resultsfromthesearchdonewiththeCMSdetectoronLHCcollisionsat p s = 7TeV [72,90].Figure6-1presentsthe 2011 resultswith p s =7TeV dataonthe searchforheavynarrowdileptonresonances[72].The channelisnotincluded norisitconsideredinthisdissertation.Thedimuonanddielectronchannelsboth showapotentialexcessofdileptonatthe 1 TeV scale[72].TheATLAScollaboration analysisshowninFigure6-2demonstratessimilarbehaviorinthesameneighborhood asCMS[91].Thisstructurefurthermotivatesthecontinuedsearchforthe Z 0 with p s =8TeV data.Theanalysisdescribedinthisdissertationdirectlybuildsonthe previousiterations,andtheresultsarecombinedwiththe p s =7TeV analysisinorder tomakethestrongestpossiblescienticstatement. Astraightforwardanalysissearchstrategyisappliedinthissearch.Twomuonsof oppositechargeareselectedandtheinvariantmassofthesystemiscalculated.Inthe absenceofanynewresonantsignal,theinvariantmassdistributionwillbeasmooth distributionthatfollowstheDrell-YanDYprocess[15].Anewresonancewillfollow aBreit-Wignerresonancedistributionthatisconvolvedwiththedetectorresolution function.Thestatisticalanalysisusedtointerpretthedataisashapeanalysisthatscans thedataforaresonantpeakbyperforminganunbinnedmaximumlikelihoodt.Thet makesnoassumptionsontheabsolutebackgroundlevel.Theoutputofthelikelihoodt isusedtosetcondencelimitsontheabsolutenumberofexpectedeventsasafunction ofthemassofthehypothesized Z 0 resonance. 87

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Thisanalysischoosestoparamaterizethesearchintermsoftheratioof Z 0 to Z 0 eventsanddenetheparameterofinterest, R : R = pp Z 0 + X `` + X pp Z 0 + X `` + X = Z 0 Z 0 Z 0 N Z 0 Z 0 isthelimitontheexpectednumberofsignalevents. Z 0 istheacceptance timesefciencyforreconstructing Z 0 events. Z 0 istheacceptancetimesefciency forreconstructing Z 0 events,and N Z 0 isthenumberof Z 0 eventsthatarecounted. Reportingthesearchintermsof R eliminatestheuncertaintyintheintegrated luminosityandcausesformanysystematicuncertaintiesfromdetectoreffectsto cancelintheratio. Themethodfornormalizationtothe Z 0 resonanceispresentedinSection6.1. Backgroundsconsideredinthisanalysisandthecontrolregionsarediscussedin Section6.2.Systematicuncertaintiesconsideredforthisanalysisaredescribedin Section6.5andthestatisticalanalysisisdiscussedinSection6.4. 6.1Normalizationtothe Z 0 resonance The Z 0 crosssectionmeasurementwasperformedbytheCMScollaboration viacountingeventsinawidemasswindow 60 < M < 120 GeV aroundthe Z 0 resonance[9294].Thisanalysisfollowsthatsameapproachforcounting Z 0 events.Thesamedimuonqualitycriteriausedforthe Z 0 analysisisappliedtothe selectionof Z 0 events.Followingtheinitial Z 0 analysis,onlydimuoneventsthatfall within 60 < M < 120 GeV arecountedtowards N Z 0 .Theacceptancetimesefciencyis measuredinsimulationandvalidatedwithdata. The Z 0 analysisrequiresthatallselectedmuonshave p T > 45 GeV inorderto beintheplateauofthetriggerefciencycurveforthelowestunprescaledsinglemuon triggerpath.Thisminimumrequirementonthemuon p T sculptstheshapeofthe Z 0 peakbycuttingdeeplyintotheefciencyofaccepting Z 0 events.Toreducesculpting, 88

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aprescaledtriggerwithalowerthresholdontheminimummuon p T isapplied.The cutonthe p T thresholdwasfoundtobesuboptimalinthein 2011 analysisleadingto anincreaseinefciencyforthemeasurementdiscussedindissertation.Theofine p T thresholdissummarizedinTable6-1[30,72]. Thenumberofexpectedbackgroundeventsfromsimulationisestimatedforthe luminosityoftheprescaledtrigger.TheexpectednonZ 0 backgroundsaresubtracted fromtheobservedspectrum.Thebackgroundlevelissmallandonlycomprises O 0.2% ofthe Z 0 acceptancewindow.Inthe 2010 incarnationofthisanalysis,the Z 0 productioncrosssection, )]TJ/F22 11.9552 Tf 5.479 -9.684 Td [(Z 0 ,analysiswasreproducedexactlybythe Z 0 analysis[90].TheCMScollaborationnolongermeasuresthe Z 0 inthismannerand hastransitionedtomeasuringthedifferentialcrosssectionasafunctionoftheinvariant mass d = dm [95].Asacross-checkforthisanalysis,thepredictedNNLO Z 0 cross sectionof 1117 pb iscomparedwiththemeasured Z 0 crosssectionof 1115 pb usingthe valuesfromTable6-1. Thelargestuncertaintyfromnormalizingthe Z 0 tothe Z 0 comesfromthedifference ingeometricalacceptancesofthe Z 0 and Z 0 bosonsaredifferent.Aconservative systematicuncertaintyof O 2% isappliedtotheacceptance-times-efciencyratio of Z 0 to Z 0 bosonsthatisbasedonthevariationsofvectorbosonacceptancefrom generatorstudies[93,96,97]. Individualmuonsthatcompriseadimuonpairaremoreenergeticasthemass ofthedimuonpairincreases.Higherenergymuonsaremorelikelytoexperience bremsstrahlungradiationinthecalorimetersorintheironyoke,creatingsecondary particles,alsoknownasmuonsshowersasdiscussedinChapter4.1[18,57]. Showersleakingintomuonchamberscreatelargeoccupanciesandcancorruptmuon identicationand p T assignmentofthereconstructedmuon.Ahighoccupancyalso leadstoasmalldeclineinthedimuondetectionefciencyasafunctionofthedimuon mass.Theneteffectofincreasingchamberoccupancyfrommuonshowersisfoundto 89

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beof O 2% ,whichisappliedasasystematicuncertaintyonthenormalization.The systematicuncertaintiesduetogeometricacceptanceandtheincreasedhitmultiplicity areaddedinquadraturetoobtain 3% astheoverallsystematicuncertaintydueto normalization. 6.2Backgrounds ThissectionconsidersSMbackgroundscompositetothe Z 0 analysis.Thedominant irreducibleSMbackgroundforthissearchisfromthe DY + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(processwhich isdiscussedinSection6.2.1.AftertheDYbackground,otherbackgroundsthatcan producetwopromptisolatedmuonsinthenalstateareconsidered.Theseinclude t t ,tW,Z + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(anddibosonWW,WZ,ZZprocessesandareestimatedusing simulation.Toverifythatthesimulationfrompromptnon-DYbackgroundsarenot under-representedindata,the M e spectrumismonitored.The e nalstateconsists oftwoleptonswithdifferentavor,sotheDYprocessdoesnotdirectlycontributeto the e spectrum.The e spectrumisdiscussedinSection6.2.2QCD-originateddijet andW + jetprocessesproducemuonsthatarenotisolated.Simulationisstatistically insufcienttoestimatethisclassofbackground,soQCDcontaminationisestimated usingdata-drivenmethods,whichisdiscussedinSection6.2.3.Muonsfromcosmic raysarealsoconsideredasapotentialdimuonbackground.Sincecosmicraymuons enterthedetectorfromthesky,oneeventcanappearastwoopposite-signmuons. Thisbackgroundishighlysuppressedbyanti-cosmicselectionrequirements,whichare discussedinSection6.2.4 6.2.1Drell-Yanbackground TheDYbackgroundisthedominantirriduciblebackgroundforthisanalysis.TheDY continuumisasteeplyfallingsmoothspectrum.Thisanalysissearchesforanexcess onasmoothbackground,soonlytheshapeoftheDYisimportant.TheshapeoftheDY backgroundisparameterizedbytheanalyticfunction: P m j a b DY = e am m b 90

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Theparametersofthebackgroundshapearedeterminedbyattothesimulated LOdimuonmassspectrumwith PYTHIA .Theshapefrom PYTHIA wascomparedtothe POWHEG NLObackgroundshape.Anegligibledifferencebetweenthettedshapeofthe twoisshowninFigure6-3[77].Thettothebackgroundshapeultimatelyuses PYTHIA .TheanalyticaltispresentedinFigure6-4[1].Thesummaryofthetparameters usedforthe 2011 and 2012 anlysesisgiveninTable6-2[1,77].Theperformanceofthe simulation-derivedtischeckedindata.Therelativedifferencebetweenobservedmuon dataandthesimulatedbackgroundisshowninFigure6-5[30]. 6.2.2Non-DYPromptLeptonBackroundsandthe e ControlSpectrum Thebackgroundcontributionof t t andotherpromptdibosonprocessesispredicted insimulationtobesmallcomparedtothemainDYbackground.Ifthe t t contributionis notsubstantiallylargerindatathaninsimulation,itistoosmalltoaffectthelimitandcan beignoredatthatstage. Inordertotestthatthe t t anddibosoncomponenttothebackgroundiscomparable betweendataandsimulation,theelectron-muon e spectrumisusedasacontrol region.Aresonancehastodecaytoleptonsofthesameavorwhenitdirectlydecacys. In t t anddibosondecays,itispossibletohaveleptonsofdifferentavorsinthenal statebecauseneutrinosoranti-neutrinosareemittedasappropriatetoconservelepton number.Figure6-6showsexampledecayswheretwoleptonsanyavorarefoundinthe nalstatefora t t andWWdibosondecay. The e backgroundisna velyexpectedtobeapproximatelytwicethesizeofthe dimuonbackgroundfor t t anddibosonprocessesbeforeaccountingforthedifference geometricacceptancebetweenelectronsandmuons.Ifthereispooragreement,the e spectrumcanproduceanewestimateofnon-DYpromptmuonbackgroundsby re-scaling e toaccountfordifferencesinmuonandelectronacceptance. Forthe e distribution, 3.6fb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 ofdatafromthe golden JSONleisused.Ineach e pair,themuonisrequiredtopassallmuonqualityselectioncriteria;dimuonselection 91

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criteriaarenotappliedfor e events.Forelectronidentication,thesameselection usedbythe highenergyelectronpairs HEEPanalysisgroup 1 isapplied[98].The HEEPgroupalsousesthe e methodtoestimatethe t t /dibosoncontributiontothe dielectronchannelofthe Z 0 search.The e spectrumcomparisonpresentedin Figure6-7showsnosubstantialexcesswithrespecttopredictionsfromsimulationin the t t /dibosonbackgroundcontributionintheopposite-signdistribution[30].Figure6-8 showsthetotal e spectrumdistributionforallchargedleptonpairsinFigure6-8Aand inthesame-signchargedleptonpairspectruminFigure6-8B.Thetotal e spectrumis mostlycomprisedof t t eventsasshownFigure6-8[30].Thesame-sign e spectrum isdominatedby t t ,butotherpromptleptonsandQCDjetsarelargercomparedtothe opposite-signedspectrum.TheQCDjetcomponentisconsideredindependentlyinthe Section6.2.3. 6.2.3JetBackgroundsandtheSame-SignControlRegion Efcientmuonreconstructionyieldsalargenumberofmuonsthatoriginatefrom jets.Jetshaveacommonsignatureandareobservedasamultipletracksmoving insimilartrajectories.Quarksinthesejetswilldecaytomuons,butmuonswillbe embeddedinaclusteroftracks.Selectingmuonsthatareisolatedasdescribedin Section4.5efcientlyrejectsmuonsthatareembeddedinjets.Whiletheefciencyof rejectingtheseeventsishigh,aniterateofQCD-derivedmuonsbeingmis-tagged aspromptmuonspersists.Simulationdoesapoorjobatpredictingthisbackground becausethenumberofeventsrequiredtostudythisprocessistoolargeforexisting computingresources.Fromtheavailablesimulation,thepredictionistoosparsetomake anyprecisestatementsaboutthejetbackground.Data-drivenestimationsoftheQCD dimuonandW + jetsbackgroundsarethusperformed.Additionalclosuretestsofthis methodwithsystematicstudiesaredetailedinAppendixE. 1 https://twiki.cern.ch/twiki/bin/viewauth/CMS/HEEPElectronID 92

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Thedata-drivenpredictionisperformedbyestimatingeventweightsbasedonthe probabilityofanon-promptmuonbeingmis-identiedasprompt.Whatfollowshereis adescriptionofhowweightsarecalculatedusingeventswhereexactlyonemuonhas passedselectioncriteriaexceptnocutisappliedonisolation.Allmuonsthatoriginate fromQCDjeteventsmayeitherpassorfailmuonisolationrequirements: N QCD = N pass + N fail ThetotalnumberofQCDevents, N QCD ,isthesumofjet-embeddedmuonsthat passisolationselection, N pass mis-identiedmuons,andtheabsolutenumberof jet-embeddedmuonsthatfailisolation, N fail .Thisisre-writtenintermsof fake and rejection rates: N QCD = f N QCD + r N QCD The fakerate f ,istheprobabilitythatajetwithamuonembeddedwillbemis-identied asapromptmuon: f = N pass N QCD Thecorresponding rejectionrate isdenedas r = N fail N QCD =1 )]TJ/F39 11.9552 Tf 11.955 0 Td [(f Theaimisestimateofthenumberofacceptedfakemuonsfromthenumberofrejected fakemuons.Thenumberofacceptedfakemuons, N pass ,isdirectlyconnectedto N fail 93

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by: N pass = f N QCD = f N fail r =N fail f r Thisisbrokendowntoaper-muonlevel,thenumberofeventsthatpassisolationis estimatedwiththesumofweights: ^ N pass = N fail X i =1 f i r i ^ N pass = N fail X i =1 w i where isthesetofmuonkinematicvariablesthatparameterizetheper-muon fake/rejectionrates.Expandingthefakeandrejectionrates,theweightisexpressed astheratioofthenumberofeventsthatpassisolationtothenumberofeventsthatfail isolation: w i = N QCD pass N QCD fail Equation6showsthatitisnotnecessarytoknowtheabsolutefake/rejectionrates. Thefake/rejectionratescomefromanabsoluteQCDnormalization,buttheper-event weightdoesnotrequireanabsolutenormalization. Thekinematicparametersusedtodescribethemuonweightare p T and .These twoparametersareenoughtoaccuratelyrepresentmuontrajectories,sincethedetector is -symmetric.Figure6-9showsthedata-simulationcomparionsfor p T and inthe sampleofeventswhereonlyonemuonisobservedforwhenthemuonhasnoisolation restiction,passesisolationorfailsisolation.TheQCDbackgroundissimulatedusing PYTHIA andthedetectorissimulatedusing GEANT [1].Avastmajority O 90% of muonsembeddedinjetsarepredictedtofailisolation.The Z 0 analysisusesaBayesian 94

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methodtoestimateindatathenumberofQCDjetswithanembeddedmuonthat passisolation, ^ N pass andthenumberofQCDjetswithanembeddedmuonthatfail isolation, ^ N fail .Thedimuonjetsimulationisnon-existent,butsimulationisabletomake apredictionforonejetsthathaveonemuoninthenalstate.Amorerecentmethod thatsubtractsknownbackgroundshasbeenstudiedtocalculate ^ N pass = ^ N fail thiswas notusedfortheanalysisonwhichthisdissertationisbased,soitisdescribedwiththe closuretestsinAppendixE. Inacollisionenvironmentofthemuonspectrumwhereexactlyonemuonis observed,thenumberofQCDmuonsinthesamplecanbeestimatediftherelativeQCD compositionisknownusingBayes'theorem: ^ N QCD pass =N obs pass p QCD j pass ^ N QCD fail =N obs fail p QCD j fail w b = N obs pass p QCD j pass N obs fail p QCD j fail where N obs pass N obs fail aretheobservedspectraindataand p QCD j pass p QCD j pass arederivedfromsimulation. p QCD j pass p QCD j pass isthefractionofeventsin simulationthatarefromQCDgiventhemuonpassedfailedisolation. Equation6isafundamentallyBayesianargumentforestimatingtheper-event weight, w b ,andthusreliesonsomepriorknowledgeabouttheQCDspectrumfor instanceswhenonemuonisfoundinthenalstate.ItassumesthatQCDcomposition ofeventsthatpassisolationcomparedtootherprocessesarenotvastlyunder/over-estimated. Figure6-10showsthebreakdownofsimulationwhenonemuonisfoundinthenal statethatpassandfailisolation.ThesamplethatpassesisolationisdominatedbyW bosonevents.Thesamplethatfailsisolationisdominatedbyjets.Ifthereisreasonably goodagreementbetweentheobservedspectrumandsimulation, w b willbeclosetoan unbiasedestimatoroftherealper-muonweight, w 95

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Thereisreasonablygoodagreementbetweendataandsimulation,asshownin Figure6-9,fortheisolatedsingle-muonspectrum,soitisassumedthattheQCDcross sectionisreasonablywellmodeledforsingle-muonwithrespecttotheEWK+ t t cross sections.Theagreementnotasgoodfortheanti-isolatedmuonspectra,withfewer eventsareobservedinthebarrelthanpredictedandmoreeventsareobservedinthe endcapthanpredicted.Mostoftheeventsinthe Z 0 analysisarefoundinthecentral barrelregion,whichcanbeseeninthepseudorapidityspectrumofsimulatedDYevents inFigure6-10,sothecontributionofthisuncertaintyissmallcomparedtotheoverall centraleventsandhasarelativelysmalleffectonthebackgroundestimate. Inordertoestimatethedimuoninvariantdistributionfakemuonsfromjets,the spectrumwherebothmuonsfailisolationisused.Whenbothmuonsfailisolation,a highlypuresampleoffakesfromQCDdijetsisobtained.Thetwomuonsintheevent areassignedweightsfromtablebuiltusingEquation6,whichiscreatedusingthe uncorrelatedsamplewhereexactlyonemuonisfoundintheeventrecord.Theweights fromthetwomuonsaremultipliedtogetherandappliedtotheevent,assumingthat theeventsareuncorrelated.Correlationsbetweenmuonsreducetheeventweightby anegligibleamountandisdiscussedinAppendixE.3.Thedijetestimatesseparated intoopposite-signandsame-signshapeestimatesarepresentedinFigure6-12.The predictedratesinvariousmassregionsaregiveninTable6-3[1].Inthesignalregionfor the Z 0 analysis,thebackgroundisfoundtobenegligible. InordertoestimatetheW + jetbackground,theclassofeventswhereexactlyone muonisfoundtofailisolationisused.Whentherequirementisaugmentedsothat exactlyonemuonintheeventfailsisolation,thereisasubstantialbackgroundfrom t t /diboson/dijetevents.The t t /dibosoncomponentisestimatedfromsimulationandthe dijetcomponentisestimatedfromdatabyusinganaverageeventweightinsteadof amultiplicativeweight,whichisdescribedinmoredetailinAppendixE.Thefraction oftheone-pass-one-failsamplethatisfromW + jetismassdependentsothatthe 96

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W + jetshareoftheone-pass-one-failsampleincreaseswithinvariantmass.TheW + jet contributiontoone-pass-one-failspectrumisestimatedtobe 15 )]TJ/F22 11.9552 Tf 12.367 0 Td [(20% upto 400 GeV ofthisclassofeventswhereonemuonfailsisolation,soaconservative 20% scale factorisappliedonthere-weightedspectrumupto 400 GeV .Above 400 GeV ,theW + jet contributiontothespectrumofeventswhereonemuonfailsisolationistakentobe 100% tobeconservativesincethehighmasscomponentisonerealWandarandom jet.Thepredictedsame-andopposite-signspectraareshowninFigure6-13[1].The tabularpredictionoftheW + jetbackgroundisgiveninTable6-4[1].ThepredictedQCD contaminationisnegligibleforthissearch. Asanadditionalcrosscheckthatcomprisesthepromptandjetbackgrounds,the same-signdimuonspectrumcomparisonismadebetweendataandsimulation.The predictedandsimulatedbackgroundsfrompromptandfakeleptonsarecomparedwith theobservedsame-signdimuonspectrumindatainFigure6-14[1].Thecomplementary cumulativesame-signdimuoninvariantmassdistributionispresentedinFigure6-15[30]. Thespectraagreesuchthatthenon-DYbackgroundsarenegligiblecomparedtothe dominantDYbackground. 6.2.4Cosmic-RayMuonBackgroundContamination Dimuonswithhighinvariantmassaresusceptibletocontaminationfromsingle secondarycosmic-raymuonsenteringthedetectorfromtheoutside.Thesemuons canbereconstructedasapairofoppositelychargedmuonswithhightransverse momentum.Thecosmic-raymuonbackgroundisstronglysuppressedforseveral independentreasons.First,theymusttraversethedetectorin-timewithacollision eventthatcontainsaprimaryvertex.TheymustalsobeneartheIPbeforethey canbereconstructedasahigh-ptopposite-signdimuonevent.Theseeventsare suppressedfurtherbylteringonthethree-dimensionalangle, ,betweenthetwo muonsmomenta[51,99]. 97

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Tostudycosmicrayeventsthatenterintothedimuonsample,eventsthatfail anyoftheanti-cosmicselectioncriteriaareisolatedandstudied.Theefciency ofcosmicmuonselectionhasbeenstudiedwithdedicatedcosmic-raymuondata collection,andestimatesontheefcienciesofcosmicselectionareappliedonthe samplethathasbeenrejectedbyanti-cosmicselectioncriteria.Thedimuonmassand per-muonazimuthalangledistributionsforeventsfailinganti-cosmicselectioncriteria areshowninFigure6-16[1].Theresultingmassdistributionisbroadandextends intothehigh-massregion.The distributionpeaksintheverticaldirection, = 2 andvanishesatnear-horizontalangles 0, ,whichisexpectedforcosmic-ray muons.Figure6-17showthedistributionoftheopeningangle, ,fordimuonswithmass m > 50 GeV withthedefaultandloosenedmuonselectioncriteria[1].Themuontiming andimpactparametercutsforeventsindatawith < 0.01 showthattheeventswith > 0.002 areconsistentwithoriginatingfrom pp collisions,Eventswith < 0.002 arenot consistentwithbeingfrom pp collisions,indicatingthattheyaremorelikelyoriginating fromsecondarycosmicrays. Startingwithalooseselectiononinvariantmasswhere M > 50 GeV ,alldimuon selectioncriteriaexceptthecuton areapplied.With < 0.002 5 eventsarefound. RemovingthePVrequirementgives 21 suchevents,andremovingthecutonthe muons'impactparametergives 5 events.RemovingboththePVandimpactparameter requirementsyields 21 events. Whenthisisextendedtohighermassregions, N cosmics =4 arefoundfor m > 120 GeV and N cosmics =2 arefoundfor m > 200 GeV intheabsenceofacuton Cosmic-raymuoncontaminationisthenreducedtoanegligiblelevelbyapplyingthecut on ,whichisknowntobe > 99% efcientatrejectingcosmic-raymuons[97]. 6.3Resolution Thesensitivityofthemuonanalysisisdrivenbytheestimateofthemuon resolution.Theperformanceofthehighp T muonalgorithmscomparedtooneofthe 98

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muontsaloneisshowninFigure6-18[1].Cosmicraymuonsareusedtotestthatthe muoncocktailsperformbetterthanthetrackertaloneindatainFigure6-19[1],this followsthemethoddescribedinChapter4.3. Thedata-drivengeneralendpointmethodthatwasdescribedinChapter4.4.2 isusedtocheckforanybiasintheabsolutemomentumscaleinbinsof for p T > 45 GeV and p T > 100 GeV probes.The projectionoftheendpointisshownin Figure6-20withthatmeasuresabiasof 0.1 c/TeV thatisstillconsistentinmostareas withnoobservablebias[1].Themaximumbiasseenof 0.1 c/TeV correspondstothe transversemomentumfora 10 TeV track.Theendpointbiasofthemuontrackts usingthetrackerandtracker + muonsystemasafunctionof inthebarrel < 1 isshowninFigure6-21[1].Thereisanobservable -dependentbiasobservedwith anamplitudeof 0.1 c/TeV thatcorrespondstothetransversecurvatureofa 5 TeV track.Themeasuredbiasisthesameforthetrackerandmuonts.This )]TJ/F20 11.9552 Tf 9.298 0 Td [(dependence onthetransversecurvatureismodeledinsimulationwiththesameamplitudeof 0.1 c/TeV .The )]TJ/F20 11.9552 Tf 9.299 0 Td [(dependenceinsimulationisshowninFigure6-21anddiscussed inAppendixF.2.Thiseffectisalreadyaccountedforintheresolutionestimatefrom simulation. 6.4Limits Thissectiondescribesthestatisticalprocedureforproducingupperlimitsonthe ratioofarareprocessofunknownmassthatisnormalizedtothenumberofobserved Z 0 eventsmasscountedinalowermasswindow, R Anextendedunbinnedlikelihoodfunctionisusedtomodelthesignaland background probabilitydensityfunctions pdfs 2 .Thebackgroundpdf, f B m j a b ,isthe analyticalshapeoftheDYcontinuumpresentedinEquation6.Thetemplatepdfused tomodelatheoreticalsignalistheconvolutionofarelativisticBreit-Wignerresonance 2 NottobeconfusedwithPDFforthePartonDensityFunction. 99

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havingawidthof )]TJ/F20 11.9552 Tf 10.098 0 Td [(andmass M withaGaussianresolutionfunctionofwidth g .The ROOT[100]implementationoftheVoigt[101,102]functionisusedtoapproximate thesignalshape.Thereferencewidthofthe Z 0 istakenfromofthe Z 0 modelwhere )]TJ/F26 7.9701 Tf 6.775 -1.793 Td [( =0.6% M .The Z 0 widthischosenasareferencebecauseitprovidesasufciently narrowresonancesuchthatdetectorresolutiondominates.Thebackgroundshapefor eachaddedchannelisnormalizedtothenumberofobservedeventsindataabove 200 GeV .Theextendedlikelihoodfunction, L ,is L m j R M ,, g a b B = N e )]TJ/F26 7.9701 Tf 6.586 0 Td [( N N Y i =1 S R f S + B f B where m representstheobservableinthemeasurement,whichisthetheinvariant massofleptonpairs. N isthetotalnumberofobservedeventswhere M `` > 200 GeV B isthePoissonmeanofthetotalnumberofexpectedbackgroundevents. 'isthe Poissonmeanofthedistributionfromwhich N isanobservationsuchthat = B + S Inordertocombinethe p s =7TeV with p s =8TeV data,ascalefactorisapplied ontheratioof R .Thisscalefactorisgivenby R b m = R a m Z 0 b Z b Z 0 a Z a where isthecrosssection, a and b arethetwoCOMenergiesinthemodel.The NNLO Z 0 crosssectionsusedfor 7 TeV and 8 TeV datawere 970 pb and 1117 pb respectively. PYTHIA wasusedtogeneratecrosssectionswith Z 0 modelparameters. Theratioof R isshowninFigure6-22,wherethereisalinearrelationshiponthe predicted Z 0 crosssectionasafunctionofthetheoretical Z 0 massbetween 7 TeV and 8 TeV collisions. Upperlimitsarecreatedfor R withBayesiancredibleintervals[18].Bayesian credibleintervalsaredenedfromBayes'theorem: f j x p x = L x j p 100

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where x representsmodeldata, representsthemodelparametersand representsthenuisanceparametersofthemodel. L isthelikelihoodfunction,and p isthepriorpdfdescribingthemodelparameters.Anintegralisperformedover nuisanceparameterstoobtain: p j x 0 x = L x j p Theposteriorpdfisthenwrittendownas p j x = L x j p p x = L x j p R L x j p d Giventheposteriorpdfof R ,the 95 condencelevel CLupperlimitisdenedon R 95 suchthat Z R 95 0 p R j x d R =0.95. Theintegralisperformedusingthe MarkovChainMonteCarlo MCMC[103]technique ofintegrationandwasimplementedinRooStatsframework[104106].Thenuisance parametersofthemodelaredescribedwiththesystematicuncertaintiesinSection6.5. 6.5SystematicUncertainties Systematicuncertaintiesinthehighmassdimuonspectrumarisefromdifferent aspectsofdetectorperformanceandandfromtheoreticaluncertaintiesonsignaland backgroundmodels.Thissectionsummarizesthetypesofsystematiceffectsthat ultimatelyaffectthisanalysis.First,therearetheuncertaintiesonthenormalization. Thisincludestheuncertaintyontheratioofefcienciesfor Z 0 and Z 0 productionand theabsolutenormalizationonthenumberofobserved Z 0 bosons.Thesecondclassof uncertaintiesaffectthepredictedbackgroundamplitude, b inEquation6,thatisthe expectednumberofbackgroundevents. AsdiscussedinChapter6.1,normalizingtothe Z 0 countenhancestherobustness ofthisanalysis.Thisguardsagainstknownandpotentiallyunknownsystematic 101

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uncertaintiesthatoccurwhenanabsolutecrosssectionisprovided.Theprocedurefor settinglimitsproducesanupperlimitonthenumberofobserved Z 0 bosons, N Z 0 Othersystematiceffectsareontheabsolutebackgroundamplitude.Thelargest sourceuncertaintyonthebackgroundamplitudeisfromtheuncertaintyonknown PDFs.PDFuncertaintiesrangefrom 5% atlowmassandincreasesto 20% atthe 2 TeV massscale[97].Largeuncertaintiesonthebackgroundamplitudehaveadiminishing effectonthecalculatedlimitastheinvariantmassincreasesbecausetheabsolute backgrounddecreasestolessthan 1 event.ThePDFuncertaintyisaveragedto 10% Theuncertaintyonthe t t backgroundcrosssectionis 15% ,thisisaddeddirectlyinto theuncertaintyonthebackgroundamplitudeasaconservativesafetyfactor.The t t contributiontothelimitwasstudiedbyvaryingtheamplitudeofthebackgroundshape andwasfoundtohavenoeffectonthelimitathighmass.Collectingalltheuncertainties contributingtothebackgroundamplitude,asystematicestimateof 20% isassignedto coverknownsystematicsandotherunconsideredsources.Thesummaryoftheapplied systematicuncertaintiesappliedtothisanalysisisgiveninTable6-5. Inordertoincorporatesystematicuncertaintiesintothelimit,theyareincorporated intotheBayesiansoftwareframework.Thebackgroundamplitudeismodiedto incorporatethesystematicunceratainty: b =^ mu b 1+ b b b istheexpectedbackgroundamplitudecalculatedwiththecountsobservedin data. b istheuncertaintyonthebackgroundyield. b isanormallydistributed nuisanceparameterthatisintegratedoveraspartofthelikelihoodmodel,whichusesa log-normalprior. Theuncertaintyontheefciencyratiodoesnotaffectthelimitonthenumberof Z 0 events,butitdoesaffect R : R = s 102

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Table6-1.Background-subtracted Z 0 candidatecountsobservedunder 7 TeV and 8 TeV runningconditions. p sN obs Z 0 )]TJ/F39 11.9552 Tf 11.956 0 Td [(N bkg SIM efciencytriggerpath p T thresholdprescale 7 TeV 68027% HLT Mu 15 40 GeV 2000 8 TeV 523029% HLT Mu24 eta2p1 27 GeV 250 Table6-2.FittedparametervaluesfortheDrellYancontinuum. p sab 7 TeV )]TJ/F22 11.9552 Tf 9.298 0 Td [(2.423 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(3 )]TJ/F22 11.9552 Tf 9.298 0 Td [(3.62 8 TeV )]TJ/F22 11.9552 Tf 9.299 0 Td [(2.002 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(3 )]TJ/F22 11.9552 Tf 9.298 0 Td [(3.66 where 1 = Z 0 N Z 0 Z 0 Theuncertaintyontheefciencyratioismodeledasagaussiandistributednuisance parameteron R thatisfoldedintothelikelihoodmodel: s = R 1+ wherealog-normalpriordistributionisassumedforthenuisanceparameter. Themuonresolutionincreaseswithmass,andthemomentumscaleisconstrained tobe 1% uptothe 5 TeV scale.Thishasanegligibleeffectonthelimitcomparedtothe 6% andisnotaddedintothemuonmodel. 103

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A + )]TJ/F20 9.9626 Tf 9.495 -3.615 Td [(nalstate B ee nalstate Cdileptonnalstate Figure6-1.Upperlimitsasafunctionoftheresonancemass M ontheproductionratio R ofcrosssectiontimesbranchingfractionintoleptonpairsfor Z 0 SSM Z 0 Z 0 St ,and G KK productiontothesamequantityforZbosons.Shadedgreen andyellowbandscorrespondtothe 68% and 95% quantilesfortheexpected limits.Thepredictedcrosssectionratiosareshownasbands,withwidths indicatingthetheoreticaluncertainties.Thedifferencesinthewidthsreect theuncertaintiesintheKfactorsused. 104

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Figure6-2.ATLAScollaborationresultshowingtheexpectedandobserved 95% C.L. upperlimitoncrosssectiontimesbranchingfractionofthetheoretical Z 0 models. 105

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Figure6-3.ComparisonoftheshapesfortheDYmassspectraobtainedwith PYTHIA blackhistogramand POWHEG redhistogram;thebottomplotshowsthe relativedifferencebetweenthetwo. 106

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Figure6-4.FittothesimulatedDrellYandimuonmassspectrumtopandtheresiduals asafunctionofthemassbottom. 107

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Figure6-5.Therelativedifferencebetweenmuondataandthettedparameterizationof thesimulatedbackground,wherethelatterisnormalizedtodata,isshownin variousmassbins.Thebinningwaschosentohaveaminimumwidthof 20 GeV andtohaveatleast 10 eventsineachbin.Thebinwidthis representedbythehorizontalerrorbarsthatisnotanuncertainty. 108

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A t t diagramwithtwonalstateleptons BWWdecaytotwoleptons Figure6-6.ExampleFeynmandiagramsthatgivetwoleptonsofanyavorinthenal state. 109

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Figure6-7.Theobservedopposite-sign e dileptoninvariantmassspectrumdata points.Thelledredhistogramshowsthecontributiontothespectrumfrom t t andothersourcesofpromptleptonstW,dibosonproduction, Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(, asderivedfromsimulations.Thebackgroundwhereatleastoneofthe reconstructedobjectsisnotarealleptonisshowninyellowandestimated fromthedatausingthesame-sign e spectrum. 110

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ATheobserved e dileptoninvariantmassspectrum BTheobservedsame-sign e dileptoninvariantmassspectrum. Figure6-8.Thelledhistogramsinredcolorsshowthecontributiontothespectrum from t t andothersourcesofpromptleptonstW,diboson, Z 0 ,as derivedfromsimulations.Backgroundsfromsourceswhereatleastoneof thereconstructedobjectsisnotarealleptonareshowninbluecolors W + jets, Z 0 Z 0 eeandinyellowmultijets. 111

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A p T distributionQCDsimulation B distributionQCDsimulation Figure6-9.SimulatedQCDmuonsthataregeneratedwith PYTHIA andsimulatedforthe CMSdetectorresponsewith GEANT .Eventswhereexactlyonemuonare foundinthesimulatedeventareaccepted. 112

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Figure6-10.The distributionofsimulationwhereonemuonisobservedinthenal statethatpassesfailsisolationshowninlogarithmicandlinearscales. Table6-3.Data-drivenpredictionofthedimuonbackgroundfromdijetsfakingmuons,for bothopposite-signandsame-signevents.Errorsarestatisticalonly. MassregionGeVQCDopp.-signQCDsame-sign 120 )]TJ/F22 11.9552 Tf 11.955 0 Td [(20011.0 0.406.20 0.33 200 )]TJ/F22 11.9552 Tf 11.955 0 Td [(4002.5 0.201.20 0.13 > 400 < 0.010.04 0.04 113

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A p T leftand rightdisributionswithnoisolationrequirement. B p T leftand rightdisributionswheremuonsarerequiredtopassisolation. C p T leftand rightdisributionsmuonsarerequiredtofailisolation. Figure6-11.Data-simulationcomparisondistributionsin p T and forsinglemuon eventsgivena,anyisolation;b,passingisolation;c,failingisolation.Black linesrepresentdata,theredshadeissimulation. 114

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Figure6-12.Re-weighteddistributionofexpecteddimuoneventsfromdijetevents wherethetwoobservedhaveopposingchargeandthesamecharge.[1] Figure6-13.Re-weighteddistributionofexpecteddimuoneventsfromW + jetevents wherethetwoobservedhaveopposingchargeandthesamecharge. Table6-4.Data-drivenpredictionofthedimuonbackgroundfromW + jetsanddijets fakingmuons,forbothopposite-signandsame-signevents. MassregionGeVW + jetsopp.-signW + jetssame-sign 120 )]TJ/F22 11.9552 Tf 11.955 0 Td [(20015.0 3.08.4 2.5 200 )]TJ/F22 11.9552 Tf 11.955 0 Td [(4005.0 1.83.3 1.2 400 )]TJ/F22 11.9552 Tf 11.955 0 Td [(6001.4 0.50.8 0.3 > 6000.2 0.10.4 0.2 115

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Figure6-14.Controlplotthatisasanadditionaldi-muoncross-checkonstandard modelbackgroundrates.Theobservedsame-sign dileptoninvariant massspectrumdatapoints.Thelledhistogramsinredcolorsshowthe contributiontothespectrumfrom t t andothersourcesofpromptleptons tW,dibosonproduction, Z 0 ,asderivedfromsimulations.The backgroundsfromsourceswhereatleastoneofthereconstructedobjects isnotarealleptonW + jets,dijetisinyellow. Table6-5.Summaryofsystematicsevaluatedforthe Z 0 search. Observablesouceuncertainty Z 0 acc. eff./ Z 0 acc. eff. Z 0 normlaization 3% backgroundamplitude t t contamination 15% backgroundamplitudePDFuncertainties 5 )]TJ/F22 11.9552 Tf 11.955 0 Td [(20% 10% average backgroundamplitudetotaluncertainty 20% 116

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Figure6-15.Thecumulativedistributionoftheinvariantmassspectrumof events. Thepointswitherrorbarsrepresentthedata;thehistogramsrepresentthe expectationsfromSMprocesses. Figure6-16.Thedimuoninvariantmassspectrumandthemuonazimuthalangle distributionforcosmic-raydimuonevents,asidentiedbyfailingthe anti-cosmicselectioncriteria. 117

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ADefaultselection. BThePVrequirementremoved. CTheimpactparametercutremoved. DBoththePVandimpactparametercutsremoved. Figure6-17.Comparisonbetweendataandsimulationforthedistributionofthe3D angle whichisdenedasthedifferenceof andtheanglebetween muontracksinthe3-space.Distributionsareshownstartingfromthe defaultselectiondetailedinChapter5exceptingthecuton 118

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Figure6-18.Simulated Z 0 invariantmassresolutionasafunctionofthetheoretical Z 0 mass.SecondorderpolynomialttotheTunePalgorithmisshown. 119

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Figure6-19.Muonresolutionestimatorfrom 2012 cosmic-raymuons.Trackertinblack iscomparedwiththeTunePhighp T algorithminbluetriangles. 120

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Figure6-20.Generalendpointresultsinbinsof .Data-drivenbiasmeasurementwith a p T > 45 GeV p T > 100 GeV requirementontheleftrightplots respectively. Figure6-21.Generalendpointresultsinbinsof restrictedto j j < 1 .Left-handplot showsthebiasmeasuredasafunctionof forthetracker.Right-handplot showsthebiasmeasuredasafunctionof forthefullmuont. 121

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Figure6-22.Ratioon R between p s =7,8 TeV asafunctionofthetheoreticalmass Z 0 usingthe Z 0 modelasthereference. 122

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CHAPTER7 RESULTS TheprecedingchaptershavedealtwithunderstandingSMdimuonproduction, muonreconstructionbytheCMSdetector,andthesearchforanewdimuonresonance intheDYspectrum.Thischaptersummarizestheresultsandsubsequentcombination withthedielectronchannel.MostSMprocessesaremodeledwellwithsimulation,and jetbackgroundsthatareunder-representedinsimulationaremeasuredviadata-driven methods.Thesame-signdimuonspectrumandtheelectron-muonspectrumboth demonstratethatthebackgroundsforahigh-massdimuonsearchareunderstood. Muonmomentumresolutionismeasuredinsimulationandveriedbycosmicraydata. A -dependentbiasinthemuon q = p T spectrumismodeledinsimulationtomimicwhat isobservedindata,soitisaccountedforintheresolutionmodel.Theabsolutemuon momentumscaleuncertaintyisconstrainedtobenegligibleatthisscale. Forvisualcomparisonbetweendataandsimulation,simulationisnormalizedtothe integratedluminositymeasuredbytheCMScollaborationof 4.1fb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .Thecomparison betweendataandsimulationofthedimuonspectrumforoppositelychargedmuonsis giveninFigure7-1.Thecumulativedistribution,theintegratednumberofeventswhere M + M isgiveninFigure7-2.Thereisnoobservableresonantexcessinthedimuon spectrum.Thebackgroundyieldsforthedimuonanddielectronchannelsarepresented inTable7-1[30]. Forthebenchmark Z 0 and Z 0 SSM crosssections,theleadingorderpredictions usetheCTEQ6.1PDFsetwithamass-dependentNNLOcorrectionfactor[107 109].Thepredictedcrosssectionsarecalculatedfordileptonsgeneratedwithin 40% ofthenominalresonancemass.TheNNLO Z 0 crosssectioninthe 60 )]TJ/F22 11.9552 Tf 13.016 0 Td [(120 GeV normalizationmasswindowiscalculatedusing FEWZ tobe 1.117 nb witha 4% theoretical uncertainty[110112]. 123

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Figure7-3showstheobservedlimiton R asafunctionoftheprobedresonance massinblack.Thebluedashedlinerepresentsthemedianexpectedlimit.Thegreen andyellowbandsrepresentthe 68% and 95% quantilesaboutthemedianexpectedlimit respectively.Thetwosolidlinesshowthepredictedcrosssectiondependenceofthe resonancemassforthe Z 0 and Z 0 SSM models.Thedimuonchannel,describedindetailin thisdissertation,sets 95% CLlowermasslimitsof 2270 GeV and 1940 GeV forthe Z 0 SSM and Z 0 modelsrespectively.Theselimitsimproveontheresult 2011 analysis,whichset lowerlimitsat 2150 GeV Z 0 SSM and 1810 GeV Z 0 [72]. Theelectronandmuonchannelsarecombinedandthelimitfor p s =8TeV is presentedinFigure7-4[30].The p s =8TeV dataaremergedwiththe p s =7TeV analysisforthecombinedlikelihood[72].Thelimitsforthecombined p s =7,8 TeV datasetsarepresentedinFigure7-5[30,72].Thecombinedelectronandmuon channelsset 95% CLlowermasslimitsof 2590 GeV and 2260 GeV forthe Z 0 SSM and Z 0 modelsrespectively.RSgravitonsareconsideredinthecombinedlimitswith k = M Pl = 0.01,0.05 andareexcludedbelow 2390 GeV and 2030 GeV respectively. Table7-1.Thenumberofdileptoneventswithinvariantmassinthecontrolregion 120 < m `` < 200 GeV andinthesearchregion m `` > 200 GeV foran integratedluminosityof 4.1fb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 inthedimuonchanneland 3.6fb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 inthe dielectronchannel.Thetotalbackgroundisthesumoftheeventsforthe standardmodelprocesseslisted.Theyieldsfromsimulationarerelatively normalizedusingtheexpectedcrosssections,andoverallthesimulationis normalizedtothedatausingthenumberofeventsinthemasswindow 60 )]TJ/F22 11.9552 Tf 11.955 0 Td [(120 GeV .Uncertaintiesincludebothstatisticalandsystematic componentsaddedinquadrature. SourceNumberofevents DimuonsampleDielectronsample 120 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200 GeV > 200 GeV 120 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200 GeV > 200 GeV Data138313503120302904 Totalbackground13007 5893627 160 12241 5922968 258 Z 0 = 11703 5712919 139 10657 5332198 220 t t +others1278 146698 78 1222 183557 84 jets26 310 1 362 181213 106 124

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Figure7-1.The + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(invariantmassspectrum.Thepointswitherrorbarsrepresent data;thehistogramsrepresentexpectationsfromstandardmodelprocesses: Z = t t andothersourcesofpromptleptonstW,dibosonproduction, Z 0 ,andjetbackgroundsthathaveatleastonemuonembedded. 125

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Figure7-2.Thecumulativedistributionoftheinvariantmassspectrumof + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(events. Thepointswitherrorsrepresentdata;histogramsrepresenttheexpectations fromstandardmodelprocesses. 126

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Figure7-3.Upperlimitsasafunctionofresonancemass M ontheproductionratio R ofcrosssectiontimesbranchingfractionintomuonpairsfor Z 0 SSM and Z 0 bosonproductiontothesamequantityfor Z 0 bosons. Figure7-4.Upperlimitsasafunctionofresonancemass, M ,onthecrosssectiontimes branchingfractionproductionratio, R ,of Z 0 SSM and Z 0 modelsdecayingto ee and + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(pairstothesamechannelsfor Z 0 bosonsforthecombined 7+8 TeV data.Shadedgreenandyellowbandscorrespondtothe 68% and 95% quantilesfortheexpectedlimits. 127

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Figure7-5.Upperlimitsasafunctionofresonancemass, M ,onthecrosssectiontimes branchingfractionproductionratio, R ,of Z 0 SSM and Z 0 modelsdecayingto ee and + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(pairstothesamechannelsfor Z 0 bosonsforthecombined 7+8 TeV data.Shadedgreenandyellowbandscorrespondtothe 68% and 95% quantilesfortheexpectedlimits. 128

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CHAPTER8 CONCLUSION Thisdissertationhaspresentedasearchforanarrowresonancedecayingto dimuons,combiningdatafromthe p s =7 and 8 TeV runningperiodsoftheCERN LHCandgatheredbytheCMSdetector.Thetheoreticalmotivationforthissearchwas reviewedinChapter2TheCMSdetector,whichisdescribedinChapter3iswellsuited forasearchforhigh-massdimuonresonances.Thisisdemonstratedbytheexcellent performanceofmuonreconstruction,describedinChapter4.Theperformanceof muonreconstructionisimportantinmanysearchesfornewphysics.Muonswithlarge transversemomentumareespeciallysensitivetosmallsystematicbiases,sothisbias mustbeconstrained.Thisanalysisdemonstratesthatthisbiasisconstrainedforthe dimuonresonancesearchusingtheendpointtthatwasdevelopedinthecontextof muonreconstructionandthealignmentofthetracker.Theendpointttoconstrainthe absolutemuonmomentumscalehassincebecomeastandardtoolforhighp T muon validation[51,72,90].Thetriggeranddataselectionareoptimizedasdescribedin Chapter5. ThedominantbackgroundinthedimuonchannelisthatfromDrell-Yanproduction, asshowninChapter6.ThisbackgroundisdeterminedbyNLOtheoreticalpredictions andsimulateddetectorperformance.The t t anddibosonbackgroundispredictedin simulationtobenegligibletothehigh-massdimuonsearch,andthisisvalidatedin datausingtheuncorrelated e background.Thebackgroundduetojetconstituents misidentiedaspromptmuonsisuniquelydifculttodeterminebecauseofrelative infrequencyoftheprocess,andtheefciencylteringouttheseeventswithisolation requirementinthemuonselectioncriteria.Data-drivenmethodsweredeveloped aspartofthisanalysistoestimatethedijetandW + jetQCDbackgroundsthatare under-representedinsimulation.Themethoddevelopedforthisanalysishasbeenused 129

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sincethersthigh-massdimuonresonancesearchdonebyCMS[90]andextendedinto otherdimuonsearches[72,113]. Anunbinnedmaximumlikelihoodtisusedtomodeldatawithbackground-only andsignal-plus-backgroundhypotheses.ABayesiananalysisisusedtosetlimits ontheproductioncrosssectionratio, R ,ofahigh-massdimuonresonance.The dimuonchannelaloneexcludesthebenchmark Z 0 SSM and Z 0 modelswithmassesbelow 2270 GeV and 1940 GeV respectivelyat 95% CL.Whencombinedwith 7 TeV data andinformationfromthedielectronanalysis,the Z 0 SSM and Z 0 modelsareexcluded formassesbelow 2590 GeV and 2260 GeV respectivelyat 95% CL.RSgravitonsfor thecombineddielectronanddimuonanalysiswith 7+8 TeV ,andRSgravitonswith k = M Pl =0.01,0.05 areexcludedbelow 2390 GeV and 2030 GeV respectively.The p s =7 [72]and 8 TeV andcombined 7+8 TeV [30]limitsaresummarizedinTable8-1. Theselimitsarecurrentlythemoststringentlimitsforthe Z 0 andGravitonmodels considered. The 1 TeV structurethatseemedtobeappearinginthe 2011 datasetinthe dielectronanddimuonchannelsdoesnotrecurin 2012 data.Nonarrowdilepton resonancesareobservedintheanalyzeddata.Thisresultplaceslimitsontheratio, R thatconstrainstheavailablephasespaceofpossibilitiesofsimilartheoreticalmodels. Thedimuonanalysispioneersotheranalysesthatusethehighestmomentummuons observableinCMSasprovidedbytheLHC. Table8-1.Masslowerlimitsatthe 95% CLonspecicmodelsobtainedusingdilepton dataat p s =7 and 8 TeV separatelyandcombined. Model MassLimits GeV 7 TeV 8 TeV 7+8 TeV Z 0 SSM 233024402590 Z 0 200021102260 G KK k = M Pl =0.1 214022602390 G KK k = M Pl =0.05 181019002030 130

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APPENDIXA COSMICMUONSUNDERGROUND High-energycosmicrayparticlescollidewithairnucleiintheupperlayersofthe Earth'satmosphere;theseincidentextraterrestrialparticlesarecalled primary cosmic rays.Mostoftheprimarycosmicrayspectrumiscomprisedofprotonsandneutrons, withmoreprotonsthanneutronsinthisspectrum. Secondary cosmicraysarethe collisionproductsfromprimarieshittingtheEarth'satmosphere.Theverticaluxesof themajorsecondarycosmicraycomponentsisshowninFigureA-1[18].Thelargest componentstotheuxofsecondarycosmicraysarefrommuonsandmuonneutrinos. Thismakesmuonsthemostprevalentchargeparticleobservedatsealevel.Muons andneutrinosarethenaldecaychainproductsofchargedmesonscreatedbyhadron fractionizationintheatmosphere.Theproductionofpositivelychargedmesonsmostly pionsandkaonsisfavoredbecausemostoftheprimarycosmicraysareprotons. Thisleadstoanexcessof + over )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(inthesecondarycosmicrayspectrum,andthe subsequentdenitionofthemuonchargeratio: R = N + N )]TJ/F20 11.9552 Tf 188.898 7.902 Td [(A MuonsloseenergyviaionizationandradiativelossesasdiscussedinChapter4.1. FromthematerialbudgetdescriptionbetweentheCMScavernandthesurface describedinChapter3.2,thetotalmaterialtraversedbynear-verticalmuonschanges between 6 m and 175 m oftheequivalentwater.Energylossinthematerialisexpected tobeabout 0.15% higherfor + thanfor )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(becauseofslightlylargerionization losses[114].Theaveragedistanceamuoncantravel,its range R ,issummarized inFigureA-2.FigureA-2showsthemuonrangeforstandardrock = gcm )]TJ/F23 7.9701 Tf 6.586 0 Td [(2 with therangegivenintermsoftheequivalentdistanceinwater[18].Theenergyloss parameters a and b arealsogivenforstandardrock.High-energycosmicraymuons areeasilycapableofpenetratingtheamalgamofmaterialaboveCMS,butlow-energy 131

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cosmicraymuonsarelikelystopped.Theplacementoftheshaftallowsforalarger uxoflow-momentumcosmicraymuons.FigureA-3showsthemodelofsimulated cosmicraymuonspassingthroughtheaccessshaftswithacleareffectontheintensity. FigureA-4showsthecomparisonbetweendataandsimulationofthemuonenergy spectrumobservedbytheCMSdetector,wheresimulationhasbeennormalizedto data[2].TheCMScollaborationadditionallyperformedthemeasurementofthecosmic muonchargeratio[38]asdescribedinEquationA.Thechargeratioanalysiswas performedinparallelwiththeCMSdetectorinplaceundergroundatfullmagneticeld withusingglobalmuonsfortheirprecisionresolutionandstandalonemuonsfortheir efciencyatdetectingcosmicraymuonsbecauseofthewidertarget.Theglobaland standalonemuonresultsareextrapolatedthroughthematerialbudgetbetweenthe cavernandtheEarth'ssurface.Theextrapolatedresultwascombinedwithtestdata takenwhentheCMSdetectorwasaboveground.Theglobalaveragetofthecharge ratiotothethreeresultswasperformedasafunctionofmuonmomentum,asshown inFigureA-5.TheCMSresultwascombinedwithsomeprecedingmeasurementsof thechargeratioandttedtothepion-kaonmodel[18,38]thatdescribethemomentum dependenceofthechargeratio.ThenalresultispresentedinFigureA-6,whichshows goodagreementbetweentheCMStandothermeasurements.Thiswastherst physicsanalysistousemuonswiththecompleteCMSdetector,anditproducedthe mostprecisemeasurementofthechargeratioatthetimebelow 0.5 TeV 132

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FigureA-1.Verticaluxesofcosmicraysintheatmospherewith E > 1 GeV .Thepoints showmeasurementsof )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(with E > 1 GeV 133

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FigureA-2.Verticaluxesofcosmicraysintheatmospherewith E > 1 GeV .Thepoints showmeasurementsof )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(with E > 1 GeV FigureA-3.SimulatedcosmicmuonsfromthesurfaceoftheEarthpropagatedtothe CMSdetector.TheCMSdetectorisshownasthedashedtriangle.The mainshaftandtwoaccessshaftsaremodeledandshownasblack circles.[2] 134

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FigureA-4.Energyspectrumofmuonsindatablackpointsmeasuredwithglobal muons.Comparisonwith GEANT simulationblue/greenhistogramisshown, withsimulationnormalizedtodata. 135

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FigureA-5.ThethreeCMSresults,andtheircombination,asafunctionofmuon momentum.Datapointsareplacedatthebinaverage,withthepointsfrom thestandaloneandglobal-muonanalysesoffsethorizontallyby 10% for clarity. 136

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FigureA-6.TheCMSresult,asafunctionoftheverticalcomponentofthemuon momentum,togetherwithsomepreviousmeasurementsandatofthe pion-kaonmodeltotheCMSdata. 137

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APPENDIXB MUONCHARGEMISIDENTIFICATION Thisappendixsummarizeshowthemuonchargemisidenticationratewas measuredindatausingcosmicraymuondataasitwasdescribedinReference[79]. DedicatedcosmicrayrunsweretakenduringOctober-November2008asanexercise totesttheperformanceofthesolenoid.Thisexerciseledtothecollectionofmore than 270 millioncosmicrayeventswitha 3.8 T axialeldpresentinthesolenoid. Theperformanceofmuonreconstructionwasalsotestedduringthisperiod.Cosmic muonsarestudiedbyreconstructingsinglecosmicraymuoneventsastwoseparate measurementsofthesamemuonusingthetopbottomhemispheresoftheCMS detector. Oneofthemuonperformancestudiesconductedwasontheperformanceof chargeassignment.Thetrackerandmuonsystemsaredesignedtoprovideaprecise meaurementof q = p T uptoaveryhighmomentum,butsomelowrateofwherethe chargeisidentiedincorrectlychargemisidenticationisexpected.Thisisdueinpart tocomplicationsinmuonreconstructionthatarisewhenhigh-multiplicyshowersappear inthemuonsystem. Chargemisassignmentoccursatalowrate,soitiscrucialtohaveapuretest sample.Thedominantbackgroundcausingchargemisidenticationisfromcosmic muonshowerswheremultiplemuonssimultaneouslytraversethemuonsystem.In high-multiplicityevents,thetopandbottommuonlegsmaynotcomefromthesame muonthatwouldaddarandombackgroundcomponenttothemisidentication measurement.Tocombatarandombackground,exactlytwostandalonemuons optimizedforcosmicreconstructionarerequiredtobepresentintheevent.Standalone muonreconstructionishighlyefcienctformuondetection,sotherequirementofthe existenceofexactlytwomuonsproducesanextremelypuresampleofsingle-muon events. 138

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Forcosmicraymuons,eventswherechargemismeasurementoccurcanbe identiedbyjustrequiringthatthetwomuonshavedifferentcharges.Themismeasurement rateisthenthefractionofeventswherethemeasuredchargesdisagreewithrespectto alltriggeredmuons.Chargemisassignmentisrelatedtomismeasurementofthe q = p T of tracks,soitisnecessarytoknowwhichmuonisidentiedcorrectly.Themuoninthetop hemisphereistakenasthereferencemuon,andastrictselectionisappliedtoensure thatthetopmuonhasthecorrectcharge.Thetopmuonisonlyacceptedasareference tageventonlyifthetrackerandspecializedhighp T muontsconcuronthemuon chargemeasurement.Becausechargemisidenticationisanartifactofcomplicationsin muonreconstruction,itishighlyunlikelythatalltsofthemuontwillconvergetothe misidentiedcharge. Theprobabilitythatthetopandbottomtracksdisagreeonthechargemeasurement isshowninFigureB-1asafunctionof p top T .Thestandalonemuonchargeassignment givespoorperformanceas p T increases.Thetracker-only,globalandhighp T algorithm tsofthemuontrackparametersallhaveverylowratesofchargemisidentifationat lowmomentum.Athighp T ,thespecializedmuontsprovidethebestperformance athighmomentumwithaslightimprovementonthetracker-onlytandasubstantial improvementontheglobalmuont.Regardlessofrelativeperformance,charge misassignmentprobabilityremainsbelow 0.1% for p T < 100 GeV .Thecharge misassignmentbecomesabout 1% when p T 500 GeV 139

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FigureB-1.RateofchargemisassignmentasafunctionofpTofthetrackertrack reconstructedinthetophemisphere,forstandalonemuonssquares, trackertrackstriangles,globalmuonscircles,andtheTPFMSret upside-downtriangles. 140

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APPENDIXC PULLDISTRIBUTIONS Apulldistributionisacommonstatisticaltoolforevaluatingthebehaviorofa minimizationroutineoranyprocessthatinvolvesparameterestimation.Ifarandom variable, x isgeneratedwithamean, ,andwidth, ,it'snaturaltodeneapullas p = x )]TJ/F25 11.9552 Tf 11.955 0 Td [( C Thisiscompletelyanalogoustoa z )]TJ/F20 11.9552 Tf 9.299 0 Td [(substitutioninmathematics[115].Thepull distribution, p ,willbeaunitnormaldistributionbyconstruction.Unitnormaldistributions haveunitwidthandanullmean. Intermsofparameterestimation,apullisdenedinthecontextofhowwella parameterismeasured.Supposeforexamplethatthereisaprocessthatfollowsa exponentialdistribution: f = 1 e )]TJ/F40 7.9701 Tf 6.587 0 Td [(t = C Pseudo-experimentsaregeneratedthatfollow f inFigureC-1totestthebehaviorof atwithanexpecteddistribution.Ifadistributionismodeledwellbythisfunctionthe measurementof ^ shouldbeaGaussiandistributionaroundthegeneratedvalue, gen .Thepulldistributionfor p p = gen )]TJ/F22 11.9552 Tf 12.352 0 Td [(^ C willbeaGaussianeventhoughthedistribution, f willbenon-Gaussian.Totestthe pullofthettedparameter ^ inEquationC, 4000 ensemblesofpseudo-experiments whereanaverageof 1000 eventsaregeneratedineachpseudoexperiment.Thepull forthe 4000 ensemblesisshowninFigureC-2,whichisconsistentwithaunitnormal Gaussiandistribution.Iftheuncertaintyon ^ isover-estimated,thepulldistributionwill bemorenarrowasshowninFigureC-3A.Likewise,under-estimatederrorswillcause forthepulltobemuchmorebroadlikeinFigureC-3B. 141

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Ifthereisameasurementbiason ^ ,thepulldistributionwillhaveanoverallshift, butstillbeclosetohavingunitwidth.FigureC-4Ashowstheaffectofabiason ^ .The biasissmallerwhen isover-estimatedasinFigureC-4B.Thebiashasasubstantially largereffectonthepullswhenthe isunder-estimatedlikeinFigureC-4C. FigureC-1.Exampledistributionofpseudo-experimentsgeneratedfromEquationC with =4.1 142

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FigureC-2.Pulldistributiononthemeasuredparameter ^ .Thepullisttedtoa Gaussiandistribution. A 1.4 B 0.6 FigureC-3.Pulldistributiononthemeasuredparameter ^ withover-estimated uncertainties.ThepullisttedtoaGaussiandistribution. 143

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A ^ ^ )]TJ/F22 9.9626 Tf 9.963 0 Td [(0.2 B ^ ^ )]TJ/F22 9.9626 Tf 9.963 0 Td [(0.2 1.4 C ^ ^ )]TJ/F22 9.9626 Tf 9.962 0 Td [(0.2 0.6 FigureC-4.Pulldistributiononthemeasuredparameter ^ whenthereisabiason ^ 144

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APPENDIXD TRACKERALIGNMENTANDWEAKMODES TheperformanceoftheCMStrackerthatwasdiscussedinChapter3.2.2isonly benecialifthepositionsofthepixelsandstripsareknowntowithinafewmicrometers. Thepositioningofindividualdetectormoduleswithrespecttotheglobalcoordinatesof CMSisthealignmentofthedetector.Inordertoknowthealignmenttothemicrometer level,theMillipedeIItrack-basedalignmentalgorithmdescribedbelowisusedto measuremodulepositions[116]. Track-basedalignmentistreatedasaleast-squaresminimizationproblem.The 2 costfunctionisthesquareoftheresidualsbetweenthetrackandhit,andnormalizedby theuncertainty: 2 = tracks X i hitmeasurements X j m ij )]TJ/F39 11.9552 Tf 11.956 0 Td [(f ij p q j ij 2 D where m ij arethehitpositionswithindependentuncertainties, ij .Thetrackmodel, f ij ,predictsthepositionofthemeasuredtrajectorywithrespecttothehitandrelieson alignment p andtrack q j parameters.Allcorrelationsbetweenhitpositionsaretaken intoaccountwhenminimizingthe 2 function. Evenwiththe 2 minimization,therecanexistsystematicdistortionsofthe detectorgeometrythatarebalancedoutwithoutchangingthe 2 .Suchdistortions cansignicantlybiasthemeasuredtrackparametersandarereferredtoasweak modes.Onewaytondweakmodesistoaddadditionalconstraintstotheminimization toremovegeometricsymmetriesthatallowweakmodestoremainundetected.CMS appliesavertexconstraintondimuonsystem,wheretwotracksarereplacedwith acommonttedobject.Forinstance,thedependenceoftheresonancemassona coherentlytwisteddeformationin follows: @ M 2 @ = M 2 p + @ p + @ + M 2 p )]TJ/F25 11.9552 Tf 10.864 12.834 Td [(@ p )]TJETq1 0 0 1 306.014 124.603 cm[]0 d 0 J 0.478 w 0 0 m 20.48 0 l SQBT/F25 11.9552 Tf 309.63 113.414 Td [(@ = 2 M 2 B z p + z )]TJ/F39 11.9552 Tf 11.955 0 Td [(p )]TJ/F40 7.9701 Tf -0.389 -7.892 Td [(z D 145

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where B z isthestrengthofthemagneticuxdensityalongthe z )]TJ/F20 11.9552 Tf 9.299 0 Td [(axis, p + p )]TJ/F20 11.9552 Tf 7.084 -4.338 Td [(and p + z p )]TJ/F40 7.9701 Tf -0.389 -7.294 Td [(z arethemomentumandlongitudinalmomentumofthepositivelynegatively chargedparticle,respectively[117].FigureD-1showsthepeak Z 0 masspositionasa functionof + [118].Theresultbeforethemassconstraintshowssignicantshifting intheobservedZmass.Totestforweakmodesathighp T ,thebootstrapendpointt methoddescribedinChapter4.4isused.FigureD-2showstheendpointtwith 45 GeV and 100 GeV probesontheminimummuon p T [77].Theendpointshowsaclearbias in q = p T asafunctionof whentheunconstrainedalignmentalgorithmisusedin 2011 data.Afterthevertexconstraintisapplied,theendpointtshowsa thatisconsistent withhavingnobias. Thereisalsoapotentialweakmodein thatarisesasasystematicrotationofthe tracker.Trackerrotationsmanifestasasinusoidalofthecentral Z 0 massasafunction of .Theexactnatureoftherotationisnotyetfullyunderstoodindata,butasimilar rotationhasbeeninducedintosimulation.FigureD-3showsthecomparisonbetween dataandsimulationfor 2012 dataforthemean Z 0 massasafunctionof forthe [1]. Theamplitudesindataandsimulationmatchwell,andthephasebetweenthe + and )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(areexactlyoutofphase.Theamplitude, A ,ofthesinusoidalwaveisconvertedtoa biasintransversecurvatureby: amp = 2 A cos )]TJ/F25 11.9552 Tf 11.956 0 Td [(! M 2 Z D Tosimulatetheweakmoderotationona Z 0 ,the Z 0 isassumedtodecayatrest.The p T ofeachmuonissmearedby p bias T = q p T + D where isthebias.ThisapplicationcreatestheeffectsseeninChapter4.4. 146

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FigureD-1.Reconstructedmasspeakpositionsfor Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(decaysasafunctionof forthe + .Blackshowsthesimulateddesignconditions.Redshowsdata withtheMillipedealignmentalgorithm.Blueshowsdataafterthevertex constraintisadded. A 45 GeV probe B 100 GeV probe FigureD-2.Resultofthebootstrapgeneralendpointmethodtfortheoveralbiasin q = p T .RedpointslabeledasPromptalignmentshowdatabeforethevertex constraintisappliedasafunctionof .BlackpointslabeledasNov alignmentshowthemeasuredbiasafterthevertexconstraintisappliedas afunctionof 147

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A for + B for )]TJ/F20 11.9552 Tf -367.64 -31.605 Td [(FigureD-3.Reconstructedmasspeakpositionsfor Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(decaysasafunctionof forthe + and )]TJ/F20 11.9552 Tf 7.085 -4.339 Td [(.Blackshowsthemean Z 0 massin 2012 datausedin thisdissertation.Redshowsthemean Z 0 massin 2012 simulationusedin thisdissertation. 148

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APPENDIXE QCDBACKGROUNDESTIMATION ThisappendixsupplementstheQCDbackgroundestimationwithadditionalstudies surroundingthemethod.SectionE.1demonstratestheproof-of-principlewithrelaxed selection.SectionE.2documentsanadditonalmethodforfutureestimationofthe jetfakeratethatwasnotappliedinthisthesisanalysis.SectionE.3considersthe assumptioninsimulationthatthetwojetsareuncorrelatedwhenfakingmuons. E.1Closuretests SimulationpredictsnodimuonQCDbackground,makingitdifculttoensurethat themethodologyaroundtheQCDclosureissound.Thissectiondescribestheclosure teststhathavebeenperformedonthismethod. Thismethodusesthesamequalitycutsasthe Z 0 analysis,whichisinherently efcientatremovingQCDcontamination.Thersttaskistolooseneventselection tocreateasamplethatcanbestudied.Supplementalsimulationisusedtoperform theseclosureteststhatarebinnedintermsofthepartontransversemomentum;the supplementalsamplesusedtoperformtheseclosuretestsarelistedinTableE-1. FigureE-8showstheunstackeddistributionsofdi-muoneventsforfourdifferent classesofdimuoneventsinQCDsimulationwithdifferentisolationcriteriadescribed below.. Any-iso doesnotimposeanykindofisolationrequirementonthedimuonevent. Fail-Fail requiresthatbothmuonsintheeventarerejectedbecauseoftheisolation requirement. Pass-Fail requiresthatexactlyoneofthetwomuonsintheeventis rejectedbecauseoftheisolationrequirement. Pass-Pass requiresthatbothmuons beacceptedbytheisolationrequirementandareacceptedintotheanalysis.The transversemomentumcutisreducedto 40 GeV andtherelativetrackerisolationcutis rstreducedfrom 1 p T p T < 0.1 to 1 p T p T < 0.3 ,makingacomparisonfordi-muon samplespossible.With 1 p T p T < 0.3 ,thefail-failclassofeventsisstilllargerthanthe pass-failclassofevents.Thecutonisolationisreducedfurtherto 1 p T p T < 0.4 for 149

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additionalstatisticstostudygoingfromthepass-failclassofeventstothepass-pass classofevents.FigureE-8AshowsthesparsenessoftheQCDdistributioninsimulation anddemonstratesthenecessityofthedata-drivenmethodforthismethod.Thefail-fail classofeventsstronglydominatesthisspectrum. Thersttestofthismethodistoshowthatthere-weightingworksforasample comprisedentirelyofQCDmuons.TheweightmapinFigureE-2ismadeusingQCD simulationwhereonlyonemuonisobservedinthenalstate. There-weightedpredictedspectrumisrstcomparedwiththetrueisolated spectrumforsingle-muoneventsforthe p T ,andpdistributionsasshowninFigureE-3. Theblackpointsisthetrueisolateddistributionfromsimulationandtheredhistogram distributionistheresultofthere-weighteddistributionofmuonthatfailisolationusing theweightfromEquation6.Weexpecttheretobegoodagreementbetweenthe estimatedandtrue p T and distributionsbecausethefakeandrejectionratesare binnedintermsofthosevariablesandthisisobserved.Themomentumdistribution ofthemuonsembeddedinjetsiswhatultimatelyproducesthemassofthedimuon system.Ifthe p T and distributionscandescribethetrackparametersofthejetfaking amuon,themomentumdistribution,p,mustbepredictedwellcomparedtotruth. Themomentumdistributionisfoundtocomparewelltothetruesimulatedmomentum distributionofmuonsembeddedinjets. TheQCDjetbackgroundisforeventswheretherearetwomuonsinthenalstate. Foreachobservedmuon,aweightisassignedagainusingEquation6.Thismethod usesthefactthatobserveddimuoneventswherebothmuoneventsfailisolationis stronglydominatedbydijetevents.Therstclosuretestistousethe Fail-Fail classof eventstoestimatethe Pass-Fail classofjetevents.Forthe Pass-Fail class,oneofthe twomuonswillfakearealmuonbutitisnotknownwhichmuondoesthissotheaverage weightofthetwomuonsisappliedtotheevent.Thecomparisonofthetrue Pass-Fail 150

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andthe estimatedPass-Fail distributionsisshowninFigureE-4wheretheestimated distributionrepresentswelltheshapeofthetrueobserveddistribution. Forthecasewherebothjetsfakemuons,bothweightstotheeventasamultiplicative productwiththeconservativeassumptionthatthejetsareuncorrelated.Thecomparison beweentheobservedandestimatedpass-passdistributionsisshowninFigureE-5Afor 1 p T p T < 0.3,0.4 .Theestimateddistributionisslightlysystematicallyovertheobserved distributionwhenthe 1 p T p T < 0.3 isused.thisismainlybecausethe Pass-Pass classofeventsistoosparsetobeaccurateTotestthis,thecomparisonismadeagain inFigureE-5Bfortheobserved Pass-Pass andestimated Pass-Pass distributionsfor 1 p T p T < 0.4 .The 1 p T p T < 0.4 isnotappropriatetotesttheabilityforthefail-fail distributiontopredictthepass-faildistributionbecausethetwodistributionshaveroughly thesamestatistics,whichwouldnotbeanappropriatecomparison. Thethefail-failclassofeventsbestclassieseventsindatathathavetwojets.To covertheW + jetbackgroundwhereonemuonisembeddedinajetandtheotheris fromarealpromptmuon,thepass-failspectrumisused.Inadditiontousingthefail-fail classofjeteventstoestimatethepass-passclassofjetevents,wecanusethepass-fail classofeventstoestimatethepass-passeventclass.FigureE-6showsthecomparison betweenthepredictedandobservedpass-passeventsandshowsgoodagreement betweenthetruepass-passbackgroundandthepass-passbackgroundestimatedfrom pass-failevents. E.2FakeRatewithBackgroundSubtraction AnadditionalmethodforestimatingthefakeratefortheQCDisbeingreviewed. Thereasoningisthatthecurrentmethodrequiressomeinputfromsimulationbased ontheQCDcrosssectioninrelationtotheWcrosssection.Forbackgroundswhere exactlyonemuonisobservedinthenalstate,thespectrumismostlycomprisedof W eventswithadditionaleffectsfrom Z eventswithonemuonfallingout ofacceptance, t t andothersmallNLObackgroundsthatproduceasinglemuon.Ithas 151

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beenproposedtosubtractthesebackgroundsfromthesampletobeleftwithonlyQCD events.Theestimationisasfollows: ^ n pass = n data pass )]TJ/F22 11.9552 Tf 14.6 2.524 Td [(^ L EWK+NLO pass ^ n fail = n data fail )]TJ/F22 11.9552 Tf 14.6 2.524 Td [(^ L EWK+NLO fail w = n data pass )]TJ/F22 11.9552 Tf 14.601 2.524 Td [(^ L n EWK+NLO pass n data fail )]TJ/F22 11.9552 Tf 14.6 2.524 Td [(^ L n EWK+NLO fail E where ^ n istheestimatednumberofeventsthatpass/failisolation. ^ L istheestimated integratedluminosity.Thebenetisthatthisdoesnotrequireanyaprioriinformation aboutQCD.Thedetractionisthatrequiressubtractingverylargenumbersandan estimateoftheintegratedluminosity.Theintegratedluminosityisestimatedby normalizingsimulationtothenumber Z 0 eventsobservedindata,takingawaysome ofthatuncertainty.Thismethodisstillcapableofproducingnegativeweightswhenever simulatedexpectationsareabovewhatisobserved.Becausethenumbersarelarge, thiscanbecausedbysub-percentsystematicerrorsinsimulatedefciencesorcross sections. E.3IsolationCorrelations Thismethodforre-weightingthespectrumwheremuonsfailisolationisuseful becauseitrequiresonlymuonreconstruction.Onemajorassumptionisthatthejetsare uncorrelated,meaningthattheprobabilityofamuonbeingmis-taggedasarealmuon insteadofasamuonembeddedinajetisnotrelatedtotheothermuonfoundinthe event.Forhigh )]TJ/F15 11.9552 Tf 9.298 0 Td [(p T searches,thisisamorereasonableassumptionforQCDprocesses giventhattopquarkcontributionsareconsideredseparately. ThefullQCDinvariantmassdistributionssurvivingthisselectionareshownin FigureE-1wheretheyareseparatedbysame-signandopposite-signcategories. Atlow-mass,thereisanincreasedproductionofopposite-signeventsrelativeto opposite-signevents,thisisfrompseudo-scalarresonancesquarkresonanceslike the J = thatdecaystotwomuons.Thepeakinmasscloserto 100 GeV issculpted 152

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bythe Z 0 selectionontransversemomentum.Asinvariantmassincreases,relative opposite-sign/same-signproductiondecreases,butstillwitha 50% largerexpectation ofopposite-signeventsfrompairproduction.Usingsimulation,thefakerate,whichis theprobabilitythatamuoncompositetoajetwillpassisolation,ischeckedforevents withoneandtwojetswithmuons.FigureE-7showsthatfakeratemeasuredfrom single-muonQCDeventsissteadyinall p T binsatabout 10.5 0.5% .Thesingle muoneventfakerateislargerthanthedimuoneventfakerateforhighermassevents M > 60 GeV whichisabout 8.5 2% notingthatthetwodistributionsarestatistically independent.Thefakerateforlow-mass M < 60 GeV eventsaresignicantlylower becauseofrealpromptdimuonsfromquarkresonancedecays.Forhigh-massevents, it'sasafeassumptionthatmuonsareindependent,knowingthatthefakerateislikely over-estimatedby O 2%. TableE-1.SummaryofadditionalmuonenrichedQCDsimulationsamplesgenerated using PYTHIA .Samplesarebinnedintermsofthepartontransverse momentum, ^ p T ,whichisageneratorquantity. ^ p T [ GeV ] range [pb]lterefciencyevents 20 < ^ p T < 302 87 10 8 0.00653974069 30 < ^ p T < 506 61 10 7 0.01228362963 50 < ^ p T < 808 08 10 6 0.021810321623 80 < ^ p T < 1201 02 10 6 0.03959238642 120 < ^ p T < 1701 58 10 5 0.04738029501 170 < ^ p T < 3003 40 10 4 0.06766634850 300 < ^ p T < 4701 76 10 3 0.08646357717 470 < ^ p T < 600115 20.10243048510 600 < ^ p T < 80027 010.09963484905 800 < ^ p T < 10003 570.10332193079 ^ p T > 10000 7740.10973795519 153

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FigureE-1.InvariantmassdistributionofQCDdijetevents.Opposite-signeventsare showninblue;same-signeventsareshowninred. 154

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FigureE-2.Weightmapinbinsof p T and producedaccordingto w p T = N pass = N fail for 1 p T p T < 0.3 155

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A p T B Cp FigureE-3.Comparisonbetweenthetrueblackandpredictedredsingle-muon spectrumofjetsfakingmuonsinQCDsimulation. 156

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FigureE-4.ComparisonbetweentheobservedandpredictedQCDdimuonspectrum fortheclassofeventswhereexactlyonemuonpassesisolation.Blacklines witherrorbarsrepresentthesimulatedtruedistribution.Theredhistogram representsthepredictionofthere-rewightedspectrumfromeventswhere bothmuonsfailisolation. 157

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A 1 p T p T < 0.3 B 1 p T p T < 0.4 FigureE-5.ComparisonbetweentheobservedandpredictedQCDdimuonspectrum fortheclassofeventswherebothmuonsisolation.Blacklineswitherror barsrepresentthesimulatedtruedistribution.Theredhistogramrepresents thepredictionofthere-rewightedspectrumfromeventswherebothmuons failisolation. FigureE-6.ComparisonbetweentheobservedandpredictedQCDdimuonspectrum fortheclassofeventswhereexactlyonemuonpassesisolationwithlooser selection.Blacklineswitherrorbarsrepresentthesimulatedtrue distribution.Theredhistogramrepresentsthepredictionofthere-rewighted spectrumfromeventswhereexactlyonemuonfailsisolation. 158

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FigureE-7.QCDjetfakerateinsimulationasafunctionof p T .Blackismeasuredfrom eventswhereonlyonemuonisobserved.Blueisthedimuonfakeratefor dimuoneventswhere M > 60 GeV .Redisthedimuonfakeratefor dimuoneventswhere M < 60 GeV 159

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A 1 p T p T < 0.1 B 1 p T p T < 0.3 C 1 p T p T < 0.4 FigureE-8.BreakdownoftheisolationclassesofdimuoneventsinQCDsimulation. Blackdotsrepresentanyisolation.Bluehistogramiswhenbothmuonsfail isolation.Redhistogramiswhenexactlyonemuonfailsisolation.Green histogramiswhenbothmuonspassisolation. 160

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APPENDIXF ENDPOINT Thisappendixsupplementstheendpointdiscussioninthetext.SectionF.1 discussestheincreaasingthereachofthemomentumscaleandthesensitivityof theendpointmethodtoascale-dependentbias.SectionF.2discussesthefunctional applicationoftheMDTandbootstrapmethodsandtheuseofthebootstrapmethod tovalidatesimulationincomparisonwithdataaswellastheself-consistencyof thesimulatedmisalignmentscenario.Uncertaintiesonthemeasuredbiasand considerationstothemomentumscalearediscussedinChapterF.3. F.1DependenceontheMomentumScaleProbe Oneofthebenetsoftheendpointmethodisthatthereachofthebiasmeasurement followswhatisobservable.Withmomentumscalemeasurementsthatdependonknown resonanceslikethe Z 0 ,likethosethatweredescribedinAppendixD,themomentum scaleisconstrainedtothevaluesaccessableatthatresonance.If issmallorhasa momentumdependence,themomentumscalemeasuredfromaresonancecanbeblind tothechangingeffect. Theendpointdoesnotmeausurethemeanofattedresonance,butratherrelies onthesymmetryof q = p T .Thispropertyofthemethodallowsittoaccessanymass, therebyopeninguptheavailablemomentumdistribution.Thedesiredmomentumscale canbechosenbyselectingeventswithhighermomentumfortting. Thispropertyofthemethodistestedwithaspecialsimulation.Twobiasesare injectedintomockdatawherethebiasshowninFigureF-1isgivenby: p T = 1 1 2 1+ Erf p T )]TJ/F25 11.9552 Tf 11.955 0 Td [( + 2 1 2 1 )]TJ/F50 11.9552 Tf 11.955 0 Td [(Erf p T )]TJ/F25 11.9552 Tf 11.955 0 Td [( F where 1 and 2 aretheappliedbiases, isthecentralmomentumwherethe changesfrom 2 1 withasmoothingparameter .FigureF-2shows labeled asaveragebiasmeasuredbythebiastasafunctionoftheprobe p T labeledas p T 161

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cut.Astheprobe p T isincreased,thecompositionofthe q = p T spectrumissuchthatit isdominatedbyeventsthatareaffectedby 1 .Theendpointmethodquicklybecomes sensitivetothe appliedatthehighermomentumscalebecausethecompositionofthe q = p T spectrumchangestofavorhighp T .Thedependenceof maybeunknown,but increasingthemomentumoftheprobedsampleallowsforvariationstobeobservedand changesintheabsolutescaleconstrainedtothatwhichiswithinreach. F.2ComparingDataandSimulationMethods ThecomparisonindatabetweenthebootstrapandMDTmethodswasdone withdatabeforethevertexconstraintwasappliedinthealignmentdiscussedin AppendixD.FigureF-4showsalargetwistinthetrackerinthebootstrapmethod. Thebootstrapmethodisfasterandsimplertoimplementbecuasethereisnoneedto validatesimulation.Thebootstrapmethodalsohasmorestatisticalpowernowthatthe deliveredluminosityishigherthanwhatisproducedbysimulation.TheMDTmethodis usedmostlyasaredundatcrosscheckincasealargebiasisobserved.Alargebiasis observedinFigureF-4,andthetwomethodsreturnthesameresult. Thebootstrapmethodcanalsoberunindependentlyonsimulationanddata. Independentchecksonsimulationgiveanadditionalvalidationonthemethodanda validationforsimulateddetectormisalignments.Withthebootstrapmethod,dataand simulationcanberunintheexactsamemannerandtheresultscanbecompared.In thecaseof 2012 simulation,thebootstrapmethodsuccessfullyspottedabuginthe misalignedsimulatedgeometrywherethemuonsystemalignmentwasnotmodied tobeconsistentwiththesimulatedtrackermisalignment.FigureF-5usesthea 3 TeV Z 0 resonanceasareferenceforhighp T events.Theleftpanelshows meausuredin simulationwiththetrackertrack;theamplitudeofthe is 0.05 c/TeV aroundzero. 162

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Therightpanelshows withthemuonsystem 1 includedinthet;theamplitudeof is 0.15 c/TeV aroundzero.Whenmeasuredindata,thereisnodifferencein when measuredbythetrackerorpickymuonts,asitwasshowninFigure6-21. F.3Uncertainties The 2 distributionthatariseswhenthescanacrossvaluesof tendstobejagged duetostatisticaluctuationsfromthisbeingabinnedshapecomparison.Tond ,the minimumofthe 2 distributionisinterpolatedbyttingitwithaneighthorderpolynomial smoothingfunction.Theminimumofthettedpolynomialisthettedbias, .The minimumofthepolynomialisveryclosetoparabolic,sotheerroron isgivenby: = s 2 f 00 F where f 00 isthesecondderivativeoftheeighth-orderpolynomialusedtointerpolate the 2 distribution,and ifthettedbias.Theparabolicerroriscomparedtothe MINOS errors. MINOS errorsarecreatedbyndingtheinterpolatedpositionswherethe 2 =1 .[119]Pulltestsareperformedwithsimulationfortheendpointt,wherethe MINOS andparabolicerrorsareapplied.FigureF-6showsthettedpulldistributions,and thedifferenceisnegligible. MINOS errorsarechosenfor becuasetheycanbemore generallyapplied. Theeffectofanon-zero onaresonancehasbeenshowntoincreaseinimpactas thetheoreticalresonancemassincreases.Onecriticalsystematictoevaluateifthere isanysystematicmismeasurementon asitincreases.Totestthis,aspectrumof constant areinjectedintosimulation.Pulltestsareperformedforeachinjected ,and thepullmeansandwidthsarereportedasafunctionoftheinjectedbiasinFigureF-7. Nosystematicmismeasurementisseenthatdependsonthemagnitudeof 1 Thepickymuontispresentedinthegure.Theglobalmuont,thatcontainsthe mostmuoninformation,givesthesameresult. 163

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Energylossinthematerialisexpectedtobeabout 0.15% higherfor + thanfor )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(becauseofslightlylargerionizationlosses[114].Theeffectisnegligibleonthe measurementof ;aconservativesystematicuncertaintyof 0.2% isapplied. Theendpointtisdominatedbystatisticaluncertainties.Astheavailabledataset increases,theprobeintotheabolutemomentumscaleincreasesaswelltomatchthe extendedreach.The Z 0 analysisdoesnotapplyacorrectiontotheabsolutemomentum scale.Therotationofthetrackerin ismodeledbysimulation,sonoadditional correctivesmearingisappliedtotheresolutionmodel.Theextentoftheobserved averagescalebiasindata 0.1 0.08 c/TeV isnotsolargeastoremovesensitivity toapeak,anditisclosetoconsistentwithnoscalebias.Inthmostpessimisticcase, thiscreatesa 2% shiftina 1 TeV resonance,whichiseasilycoveredbytheresolution functionsothiseffectisneglectedinthestatisticalinterpretation. 164

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FigureF-1.Modelofinjectingtwobiaseswithasmoothtransitioningcurvethat dependsonthetransversemomentum.Theinjectedmodelbiasstartswith a 2 =0.1 c/TeV bias.Aninectionpointisplacedatthemomentumscale of =150 GeV withatransitionwidth, =0.1 c/GeV ,thatendswithanal biasof 1 =0.5 c/TeV 165

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FigureF-2.Blackpointsrepresentthemeasuredbiaslabeledasaveragebiasasa functionoftheminimum p T labeledasmuon p T cutrequiredforeventsto enterintothet.Redlineshowstheappliedbias. FigureF-3.Pullmeanvs. p T cutofffor200pseudo-experiments 166

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FigureF-4.ComparisonindatawithbootstrapandMDTendpointmethods.Blackisthe bootstrapmethodlabeleddatabalancingandredistheMDTmethod labeledMCttodata. 167

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ABiasmeasuredinsimulationwiththetracker muont. BBiasmeasuredinsimulationwiththepickymuon t. FigureF-5.Measurementofthebiasintransversecurvature, ,in 2012 simulationwith thebootstrapmethod. AMINOSerrors. BParabolicerrors. FigureF-6.Pulldistributionsfor 200 toysimulationsusingMINOSerrorsandparabolic errors. 168

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Apullmean Bpullwidth FigureF-7.Pullmeansandwidthsfor400toyexperimentsasafunctionoftheinjected bias. 169

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[117]CMSCollaboration,AlignmentoftheCMSTrackerwithLargeHadronCollider Data,,awaitingapproval. [118]A.Bhardwaj,K.Ranjan,in 12thPisaMeetingonAdvancedDetectors [119]W.T.Eadie,etal., StatisticalMethodsinExperimentalPhysics North-Holland, 1971 175

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BIOGRAPHICALSKETCH TheodoreKypreoswasbornandraisedinFlorida.Inhighschool,hedeveloped apassionforplayingtheguitar.HewasacceptedintotheUniversityofNorthFlorida SchoolofMusictostudyjazzguitarbutquicklyfoundalargerpassionforscience. Hegraduatedsummacumlaude,majoringinphysicsandminoringinmathematics. HewasawardedUniversityHonorsforhisthesis,ABitangencyTheoremforCurves Immersedin C 2 .Forayear,hetaughtguitaratNiceMusicinJacksonville,Floridawhile workingasamusician.HethenenrolledatUniversityofFloridaforgraduateschool inphysics,wherehejoinedtheexperimentalhigh-energyphysicsgroupandlaterthe CMScollaborationunderthedirectionofthefreshlyhiredAssistantProfessorIvanFuri c, graduatingin2013. 176