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The Study of the Z Boson Transverse Momentum Spectrum Recorded by the Compact Muon Solenoid from 2010 Large Hadron Colli...

Permanent Link: http://ufdc.ufl.edu/UFE0043682/00001

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Title: The Study of the Z Boson Transverse Momentum Spectrum Recorded by the Compact Muon Solenoid from 2010 Large Hadron Collider Data
Physical Description: 1 online resource (186 p.)
Language: english
Creator: Gartner, Joseph A Iii
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

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: This note describes the full details of 2 studies of $Z^0$ bosons performed using the Compact Muon Solendoid detector at the Large Hadron Collider of proton on proton collisions with center of mass energy of 7 $TeV/C$. The first study searches for physics beyond the Standard Model by looking for excesses in production of $Z^0$ bosons by examining the $Z^0 p_{T}$ spectrum. As no excess is found, limits on new physics models are presented as a function of mass and free parameters. The second study focuses on a precision measurement of the $Z^0 p_{T}$ spectrum, and is compared to theoretical calculations for the purposes of testing high order QCD calculations in addition to probing the predictions of various tunes of the underlying event.
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 Joseph A Iii Gartner.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Acosta, Darin E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043682:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043682/00001

Material Information

Title: The Study of the Z Boson Transverse Momentum Spectrum Recorded by the Compact Muon Solenoid from 2010 Large Hadron Collider Data
Physical Description: 1 online resource (186 p.)
Language: english
Creator: Gartner, Joseph A Iii
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

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: This note describes the full details of 2 studies of $Z^0$ bosons performed using the Compact Muon Solendoid detector at the Large Hadron Collider of proton on proton collisions with center of mass energy of 7 $TeV/C$. The first study searches for physics beyond the Standard Model by looking for excesses in production of $Z^0$ bosons by examining the $Z^0 p_{T}$ spectrum. As no excess is found, limits on new physics models are presented as a function of mass and free parameters. The second study focuses on a precision measurement of the $Z^0 p_{T}$ spectrum, and is compared to theoretical calculations for the purposes of testing high order QCD calculations in addition to probing the predictions of various tunes of the underlying event.
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 Joseph A Iii Gartner.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Acosta, Darin E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043682:00001


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THESTUDYOFTHEZBOSONTRANSVERSEMOMENTUMSPECTRUM RECORDEDBYTHECOMPACTMUONSOLENOIDFROM2010LARGEHADRON COLLIDERDATA By JOSEPHA.GARTNERIII ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2011

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c 2011JosephA.GartnerIII 2

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ACKNOWLEDGMENTS Myeducationhasbeenalongjourneywhichhastakenmerstacrossthecountry andlateraroundtheworld.Iwouldliketothankmyparents,JosephandPeggy.They haveshownmeunconditionalsupportthroughthisentireprocess,andthereisno greaterrewardthantheirpraise.Iamindebtedtothemforlightingthesparkofcuriosity withinme,andinstillingmewithaworkethicneededtofulllthiscourseofstudy.I wouldberemiseifIdidnotalsothankmysister,Mary,whoservedasanexcellent modelofsuccesswhichItriedtofollowthroughmuchofmylife.Iwouldliketothank mygirlfriendRebecca,whocontendedwithmyspendingayearinFrancesoIcould participateintherstyearofdatatakingfortheLargeHadronCollider.Imustalsothank herforherpatienceandcareduringthelongroadofthisstudy. IwouldliketothankthescientistsIhavehadthechancetogaininstructionfrom. Chronologically,IwouldstartwithRichardHughesandBrianWineroftheOhioState University.Iamextremelygratefultobothofthemforintroducingmetothisgreateld, andshowingmethejoyofparticlephysics.IfIwouldn'thaveworkedforthemfor4years asanundergraduate,ImayhaveneverpursuedaPh.D.Frommyrstyearofcourse workattheUniversityofFloridaUF,IwouldliketothankRichardWoodard,notonly forhisinventionofthefunctionnamedafterhim,butforhispassionateandchallenging teachingstyle.IwouldliketothankmyPh.D.advisorDarinAcosta,whohasbeenboth agreatallyandmentoroverthelastyears.Hisinstructiveandstraightforwardmanner madehimapleasuretoworkwithandlearnfrom.InadditiontoDarin,IvanFuricgave largeamountsofinstructionandadvice,forwhichIamgrateful.Lastly,GianPieroDi GiovanniandKhristianKotov,thetwopost-docswhowere`downinthetrenches'with methroughmostofmygraduatecareerandweremycompanyonseverallongnights atwork.Ultimately,thelistofhighqualityindividualsatUFandtheEuropeanCenterfor NuclearResearchCERNaretoolongformetorecalleveryone,butsufcetosayIam 3

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gratefultotheUFgroupfortheopportunitiestheyfacilitatedandthegenerosityoftime thatwasuniversallyshowntome. Lastly,Icanthankmyfriendsbothinsideandoutsidetherealmofphysics.Ifeel veryblessedtohaveagoodnumberofpeoplewhogivemeperspective,keepme grounded,andwhenitisneededgivemeagoodlaugh.Specically,mybestfriendfrom ClevelandMikeMalone.FrommydaysonMaynardthereisErikJohnson,JasonStalter, andCarlSchultz.FromtheUFphysicsdepartmentthereisRonRemmington,Evan Donohugh,KyleThompson,andBobbyScurlock.Lastly,myfriendsfromtheGainesville Hogs,GageMiller,DavidHanson,KerriO'Mally,andAndrewLapatinatoonlynamea few.Iknowthelistislong,butyouhaveallkeptmehappyandactiveinsomeway,so thanks. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS..................................3 LISTOFTABLES......................................8 LISTOFFIGURES.....................................11 ABSTRACT.........................................17 CHAPTER 1THESTANDARDMODELANDSOMEPOSSIBLEEXTENSIONS.......18 1.1Introduction...................................18 1.2ParticleTypes..................................21 1.2.1Leptons.................................22 1.2.2Quarks..................................23 1.2.3GaugeBosons.............................25 1.3TheStandardModelLagrangian.......................26 1.4ProblemsintheStandardModel.......................28 1.5PrecisionMeasurementof Z 0 TransverseMomentum...........29 1.6StandardModelExtensionsProducingBoosted Z 0 .............31 1.6.1ExcitedQuarks.............................31 1.6.2OtherStandardModelExtensions..................35 2THELARGEHADRONCOLLIDERLHC.....................37 2.1HistoricalReview................................37 2.2LHCLayout...................................39 2.3LHCMainStorageRingDesignSpecication................40 2.42010LHCPerformance............................42 3THECOMPACTMUONSOLENOIDCMSDETECTOR.............45 3.1TheCoordinateSystem............................47 3.2TheInnerTrackingSystem..........................48 3.3TheElectromagneticCalorimeter.......................50 3.4TheHadronicCalorimeter...........................52 3.5TheSuperconductingMagnet.........................54 3.6TheMuonSystem...............................55 3.7TheCMSTriggerSystem...........................59 4OVERVIEWOFSTUDIES..............................63 4.1ExperimentalOverviewoftheSearchforNewPhysicsUsingBoosted Z 0 DecayingtoMuonPairs..........................63 4.2ExperimentalOverviewof d = dP T for Z 0 DecayingtoMuons.......65 5

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4.3OutlineofDocumentation...........................66 5EVENTSELECTION.................................69 5.1MuonIdentication...............................69 5.2MuonReconstruction.............................70 5.3MuonIdenticationTagandProbeEfciency................72 5.3.1TrackEfciency.............................72 5.3.2GlobalMuonIdenticationEfciency.................73 5.4Isolation.....................................73 5.4.1IsolationUsedinthe p T SpectrumMeasurement..........74 5.4.1.1RelativeCombinedIsolationEfciency...........74 5.4.2IsolationUsedintheSearchforNewPhysics............75 5.5TriggerEventSelection............................78 5.5.1HighLevelTriggerTagandProbeEfciency.............79 5.5.2ScaleFactors..............................81 5.6 Z + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(EventSelection..........................82 5.7MonteCarloAcceptanceandEfciency...................83 6DATATOSIMULATIONCOMPARISONS.....................88 6.1DataSamples,andCMSSpecicDetailsinProcessing..........88 6.2MonteCarloSamples.............................89 6.3 Z + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(SelectionVariablesDistributions.................89 6.4Mass,TransverseMomentumandRapidityDistributions..........90 6.5Summary....................................90 7METHODSOFBACKGROUNDESTIMATION..................95 7.1 t t BackgroundEstimationfrom e Events..................95 7.2QuantumChromoDynamicQCDBackgroundEstimationfromData..98 7.3DrellYan....................................102 7.4Summary....................................105 8SENSITIVITYTONEWPHYSICS.........................106 8.1ShapeoftheTransverseMomentumforthe q Models...........108 8.2SelectionEfciency..............................109 8.3Optimizingthe p T ThresholdsforCountingExperiments..........113 8.4SettingtheLimits................................115 8.4.1BackgroundandCorrespondingSystematicUncertainty......115 8.4.1.1Fittothe p T spectrumvaryingthetparameters.....116 8.4.1.2Stabilityofthetondata..................116 8.4.1.3Fittothe p T spectrumwithvariousparametrizations...117 8.4.1.4Finalbackgroundestimation................118 8.4.1.5Biasduetosignal......................119 6

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8.4.2DetectorAcceptanceandEfciencytoSignalandCorresponding Systematic...............................120 8.4.3IntegratedLuminosity.........................121 8.5ComputingtheLimits..............................123 9MEASUREMENTOFTHEZBOSONTRANSVERSEMOMENTUMSPECTRUM.........................................129 9.1Unfolding....................................129 9.1.1Theresponsematrix..........................130 9.1.2StatisticalTests.............................133 9.1.3DataDrivenEstimationofResolution.................135 9.1.4SmearingInducedBackground....................140 9.1.5UnfoldingSmearingfromFinalStateRadiationFSR.......142 9.1.6FinalResolutionUnfoldingMatrix...................143 9.1.7UnfoldingSummary..........................144 9.2SystematicEffects,Studies,andUncertainties...............144 9.2.1PDFUncertainties...........................144 9.2.2EfciencyCorrections.........................146 9.2.3BackgroundUncertainties.......................147 9.2.4UnfoldingUncertainties........................148 9.2.4.1Uncertaintyfromextractedresolutionparameters....148 9.2.4.2UncertaintyontheSpectrumShape............151 9.2.5Summary................................154 9.3FinalResults..................................154 9.3.1RestrictedAcceptance.........................155 9.3.2TotalCrossSection...........................156 9.4CombinedResults...............................156 9.5Conclusions...................................162 10CONCLUSIONS...................................165 APPENDIXA:THECATHODESTRIPCHAMBERTRACKFINDERCSCTF....166 A.1Introduction...................................166 A.2TheCSCTFEmulatorandDQM.......................172 BOPTIMIZINGTHE p T THRESHOLD........................178 BIOGRAPHICALSKETCH................................186 7

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LISTOFTABLES Table page 1-1Thethreegenerationofleptons...........................22 1-2Thethreegenerationofquarks...........................23 1-3TheKnownForceCarriers..............................25 2-1TheLHCBeamDesignParameters........................42 5-1Muonidenticationcriteria..............................70 5-2CumulativeTagandProbeefciencyforthemuontobeatrackermuon,a globalmuonandpassingallthemuonidselectionsandtobeisolatedisolationdenitioninEquation5...........................75 5-3HLTpath,associatedrunrangeofuse,andintegratedluminosityforthatrange.79 5-4Finalefciencyfactorsusedintheanalysis,obtainedusingthetagandprobe technique........................................81 5-5Looseselectionrequirementsformuonsinbothanalysis.............82 5-6Efciency, ,andacceptancetimesefciency,A ,asafunctionofthe Z 0 p T ..84 6-1DetailsofMonteCarlosimulationsamples.....................89 6-2DataMCeventscounting.MCisrescaledaccordingtotheproduction toan integratedluminosityof36pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .Theerroriscomputedas p N ..........94 7-1Fitresultsfromthetofthe t t shapeusingthefunctionfromEquation7...96 7-2Data-MCeventscountingfor 60 < M < 120 and p T > 30 GeV = c .MCis rescaledaccordingtotheproduction toanintegratedluminosityof36pb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 ..99 7-3ExpectednumberofdimuonscandidatesfromtheQCDdatadrivenestimationforseveral p T thresholds............................100 7-4Summaryofdata-drivenandMCestimatesofQCDbackground.........102 7-5Summaryofdata-drivenestimatesofQCDbackgroundforthe Z 0 p T binning denedinSection9.1................................102 7-6FitresultsfromthetoftheDrell-Yanshapeusingthefunction F x = A e )]TJ/F40 7.9701 Tf 6.587 0 Td [(B p x .........................................103 7-7FitresultsfromthetoftheDrell-Yanshapeusingthefunction F x = A e )]TJ/F40 7.9701 Tf 6.587 0 Td [(B p x .........................................104 8-1FitcoefcientsfortheGaugeInteraction q templatesforseveral q masses..110 8

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8-2FitcoefcientsfortheContactInteraction q templatesforseveral q masses..111 8-3Fitcoefcientsforthe Z 0 templatesforseveral Z 0 masses.............111 8-4Generatorefciencyofthe p T cut..........................112 8-5Generatorlevelacceptance p T > 20GeV/ c j j < 2.1.4,60GeV/ c 2 < m < 120GeV/ c 2 abovedifferent p T cuts.....................112 8-6Totalselectionefciency.Statisticalerroronanyofthenumbersinthetable doesn'texceed1%..................................112 8-7Bestperforming p T cuts GeV = c ..........................115 8-8Expectedbackgroundforseveralvaluesofthe p T cut GeV = c .........115 8-9FitresultsfromthetoftheDrell-Yanshapeusingthefunction F x = A e )]TJ/F40 7.9701 Tf 6.586 0 Td [(B p x ..........................................116 8-10Expectedbackgroundforseveralvaluesofthe p T cut GeV = c ..........116 8-11Expectedbackgroundforseveralvaluesofthe p T cut GeV = c ..........117 8-12 2 = NDFforthedefaulttfunctionandthethreealternatetfunctions.The tsandthe 2 = NDFevaluationsareperformedfor p T 2 [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200] GeV = c ....117 8-13Expectedbackgroundforseveralvaluesofthe p T cutforthedefaulttfunctionandthethreealternatetfunctions.......................118 8-14Expectedbackgroundforseveralvaluesofthe p T cutandrelativesystematic errorassignment....................................119 8-15Limitsonthecrosssectionofthebenchmarkmodelsassuming5.2%and11% uncertaintyontheluminosity.Thenumberrepresentsthevalueof *BR q qZ 0 *BR Z 0 ..................................123 8-16Feldman-Cousinslimitsonnumberofsignalevents................125 8-17Feldman-Cousinslimitsonthesignalcrosssection................126 9-1MuonresolutiononMC,comparisonofextractionmethod............138 9-2MuonresolutiononMC,parameterscorrespondingtoEquation9......138 9-3Acceptancetimesefciency,A ,systematicuncertaintiesandtheirpercentagevariationsasafunctionoftheZ p T .......................147 9-4SystematicerrorsasafunctionoftheZ p T resultingfromthevariationonthe A .Thevariationisgivenwithrespecttothe 1 d dP T inthefullacceptance...148 9

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9-5SystematicerrorsasafunctionoftheZ p T resultingfromthevariationonthe scalefactorsoftheefciency.Thevariationisgivenwithrespecttothe 1 d dP T intherestrictedacceptancedenition........................149 9-6SystematicerrorsasafunctionoftheZ p T resultingfromthe100%variation onthebackground.Thevariationisgivenwithrespecttothe 1 d dP T intherestrictedacceptancedenition............................151 9-7CompletedetailsonhowthedoubleGaussiantvaluesvarywiththerange ofthet........................................152 9-8ThedetailsoftheuctuationoftheVoigtian withthevariationofthetrange.153 9-9SystematicerrorsasafunctionoftheZ p T resultingfromthedifferentunfoldingmatricesobtainedfromthevariationsontheresolutionparameters.The variationisgivenwithrespecttothe 1 d dP T intherestrictedacceptancedenition...........................................153 9-10SystematicerrorsasafunctionoftheZ p T resultingfromthedifferentunfoldingmatricesduetothe p T shapevariationofthegeneratorlevel.Thevariationisgivenwithrespecttothe 1 d dP T intherestrictedacceptancedenition. .............................................155 9-11TotalsystematicerrorsasafunctionoftheZ p T ..................156 9-12 1 d dP T GeV = c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 intherestrictedacceptance.Errorsarestatisticalandsystematicsummedinquadrature.ThebinRangesarein GeV = c ,with 1 d dP T and it'serrorshavingunitsof GeV = c )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .........................159 A-1NumberofstripsandwiregroupsperchamberinvariousCSCstations.....168 10

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LISTOFFIGURES Figure page 1-1DiagramsillustratingNLOandNNLO Z 0 production................30 1-2Thebranchingfractionof q asafunctionof f s ...................32 1-3Thecrosssectiontimesbranchingratiofor q decaywitha q massof1.5TeV createdthroughquarkgluonfusionasafunctionofstrongcouplingconstant, f s .33 1-4Thecrosssectiontimesbranchingratioof q createdthroughquarkgluonfusionasafunctionofmass,formultiplevaluesofthestrongcouplingconstant.33 1-5Theproductionof q fromquarkgluonfusionleftandthroughcontactinteractionright......................................34 2-1BirdseyeviewoftheLHC,notingpointsofinterest.................37 2-2AneventdisplayofoneoftherstobservedcollisionsinCMS..........39 2-3ThecartoonrepresentationoftheLHC.......................40 2-4Thedeliveredintegratedluminositytothefourprimaryexperimentsduring the2010datatakingperiod..............................43 2-5Thepeakinstantaneousluminosityoverthe2010datatakingperiod.......44 3-1TheTransverseXYviewofCMS..........................46 3-2TheLongitudinalviewofCMS............................48 3-3ThelongitudinalviewoftheCMStracker......................49 3-4Theprocessesthatcreateelectromagneticshowers.Left:FeymanDiagram depictingbremsstrahlungradiation.Right:Pairproduction............50 3-5FitoftestbeamdataforECALresolutionperformance[49]............52 3-6Anillustrationofaprotonconvertingtoa + andaneutronthroughinelastic scatteringfromanuclei................................53 3-7MonteCarloresolutionperformanceforHCALjetenergyresolution[49].....54 3-8AphotographofmeinsidetheCMScavernduringtheinstallationperiodfeaturingtheDTsystemsilverandtheironreturnyokered............56 3-9AphotographofmestandinginfrontofCSCstation1ofthenegativeendcap,whilethediskwasstillaboveground......................57 3-10AnillustrationoftheinsideofaCSCchamber...................58 11

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3-11Inclusiveppproductioncrosssection........................60 3-12IllustrationoftheLevel1CMStriggersystem....................61 4-1Thedimuoninvariantmassspectrumbeforeleftandafterrightselection requirementsaremade................................64 5-1Themuon p T resolutionforvariousreconstructiontechniques..........71 5-2Tagandprobeefciencyforamuontobereconstructedinthetrackerasa functionofthestandaloneprobemuon p T leftand right...........73 5-3Tagandprobeefciencyforglobalmuonidenticationandtopassallthemuon IDkinematicselectionasafunctionofoftheprobemuon p T leftand right.74 5-4Data/MCmuontagandprobeefciencyfortheisolationcutasafunctionof theprobemuon p T leftand right........................75 5-5Left:Theoverallselectionefciencywithuncorrectedisolation.Right:The overallselectionefciencywithcorrectedisolation.................77 5-6Fractionofdimuoneventswithtwomuonsenteringthe0.3isolationconeof eachotherasafunctionofdimuon p T ........................77 5-7Distributionofthecorrectedisolationvariableforseveralmodelsofthenew physics.........................................78 5-8Tagandprobeefciencydistributionsasafunctionof respectivelyforthe9 GeV = c triggerthershold,fortherunrange[132440,144144]leftand[144115, 147195]right.....................................80 5-9Tagandprobeefciencydistributionsasafunctionof respectivelyfor11 leftand15right GeV = c triggerpaths.......................81 5-10Acceptancered,efciencygreenandproductofthetwoasafunctionof thegeneratorlevelpost-FSRdimuoncandidatestransversemomentumfor themeasurementleftandsearchright.....................83 5-11Theselectionefciencyforboosted Z 0 from q q + Z 0 forthequarkgluon fusionproductionmechanismfor q massesof 500,750,1000,1200 and 1500 GeV = c .85 5-12Theselectionefciencyforboosted Z 0 from q q + Z 0 forthecontactinteractionprodcutionmechanismfor q massesof 500,1000,1500, and 2000 GeV = c 2 .86 5-13Theselectionefciencyforboosted Z 0 from Z 0 H + Z 0 for Z 0 masses 500,1000,1500, and 1500 GeV = c 2 .........................87 6-1Left:Data-MCcomparisonforthenumberofvalidmuonhitsinthebarrel.Right: Data-MCcomparisonforthenumberofvalidmuonhitsintheendcap......90 12

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6-2Left:Data-MCcomparisonforthenumberofvalidpixelhits.Right:Data-MC comparisonforthenumberofvalidmuonsegments................91 6-3Left:Data-MCcomparisonforthenormalized 2 oftheglobalt.Right:DataMCcomparisonfortheimpactparameter......................91 6-4Data-MCcomparisonforthetrackisolation.....................92 6-5Data-MC Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(massspectrum.Left:logarithmicscaleandallMCcontributionsdisplayed.Right:logarithmicscaleandallMCcontributionsmerged.92 6-6Data-MC Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(transversemomentumspectrum.Left:logarithmicscale andallMCcontributionsdisplayed.Right:logarithmicscaleandallMCcontributionsmerged...................................93 6-7Data-MC Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(rapidityspectrum.Left:logarithmicscaleandallMC contributionsdisplayed.Right:logarithmicscaleandallMCcontributionsmerged.93 7-1 t t dimuon p T spectrumfromMCandit'staccordingtoEquation7.Left: thetisperformedovertherange0to240 GeV = c .Right:thetisperformed overtherange30to240 GeV = c ...........................96 7-2Left:Data-MC e oppositesignsmassspectrum.Right:Data-MC e oppositesigns p T spectrumfor 60 GeV = c 2 < M e < 120 GeV = c 2 ............97 7-3Data-MC Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(transversemomentumspectrumfor 60 < M < 120 and p T > 30 GeV = c ..................................98 7-4Data-MC e transversemomentumspectrumfor 60 GeV = c 2 < M e < 120 GeV = c 2 and p e T > 30 GeV = c ..................................99 7-5ClosuretestusingallMCsamplestopredicttheQCDbackgroundforsamesignandopposite-signdi-muons...........................101 7-6Data-DrivenQCDbackgroundpredictionandshapefromdata..........101 7-7Drell-Yandi-muonsMCtransversemomentumspectrumandrelativetaccordingtoEquation7................................103 7-8Drell-Yandi-muonsMCtransversemomentumspectrumandrelativetaccordingtoEquation7.Theentiredatasethasbeendividedinthreeequally sizedsub-dataset,eachttedseparately......................104 8-1Distributionofthetransversemomentumofthe Z 0 bosoninthe q decays. Gaugeproductionleftandcontactinteractionrightaredonefor M == 0.5,1.0, and 1.5 TeV = c 2 ...............................109 8-2Fulldecaywidthinunitsofmassofthe q asafunctionofthe m = ratio.....110 13

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8-3Distributionofthetransversemomentumofthe Z 0 bosoninthedecaysof Z 0 withmassof 0.5,1.0, and 1.5 TeV = c 2 ........................111 8-4Theacceptancetimesefciencyfordifferent q masses,for q producedvia contactinteractionwithstandardcouplings,contrastedbytheacceptance timesefciencyfor Z 0 throughstandardD.Y.production..............113 8-5Theacceptancetimesefciencyfordifferent q masses,for q producedthrough quark-gluon-fusionwithstandardcouplings,contrastedbytheacceptance timesefciencyfor Z 0 throughstandardD.Y.production..............114 8-6The p T dimuonspectrumcomparedtothedefaulttfunctionandthethree alternatechoices...................................118 8-7Expectedbackgroundforseveralvaluesofthe p T cutandrelativesystematic errorassignment....................................119 8-8Biasonthepredictedbackgroundeventsabovethethresoldof p T =350 GeV = c asafunctionofsignaleventsC.I. q ,m=0.5 TeV = c 2 ...............120 8-9The Z 0 peakpositionleftand Z 0 massresolutionrightmeasuredasthe widthofthe Z 0 peakontopofthenatural Z 0 width.................122 8-10Left:smoothinterpolationofthefoundlimitsonthecrosssection BRfrom Table8-15.Right:sameasleft,butwithoutbranchingof Z 0 + )]TJ/F20 11.9552 Tf 7.085 -4.338 Td [(......124 8-11Contoursofcompositenessscalevs. q massofthequarkgluonfusiontop andcontactinteractionbottom q productionmechanisms.Thevalueswhich areexcludedarebelowandtotheleftofthecurves................127 8-12Feldman-Cousinslimitsinnumberofsignaleventsfor36pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 and100pseudoexperiments.The3benchmarkmodelsareshown:gauge q productionleft, contact q productionmiddleand Z 0 right,allwith M =1.0 TeV = c 2 ......128 8-13ComparisonoftheFeldman-Cousinslimitsagainstlimitsfromthecounting experiment.......................................128 9-1The p T spectrumbeforeandafterthefulldetectorsimulation.Ontheleft thetwospectra,ontherightratioofthetwospectra..............129 9-2Theresponsematrix,astunedonMC.......................131 9-3Theinvertedresponsematrix............................132 9-4ClosuretestonMC,the 2 betweenthereconstructedandgeneratedis67, whilethecomparisonbetweenunfoldedandgeneratedis0.23..........132 9-5Therawdistributionofpulls,distributionsmearedbyaGaussianwith of0.8.134 14

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9-6TheGaussianprojectionofpulls,distributionsmearedbyaGaussianwith of0.8*BinWidth...................................134 9-7TheVoigtiantsofMC Z 0 massdistributionswithxed )]TJ/F20 11.9552 Tf 10.098 0 Td [(and m Z p 0 isthe valuefor inGeVand p 3 isthenormalizationfactor................137 9-8Thetruemuon p T resolutiononMC.........................137 9-9TheVoitiantsofthedata Z 0 masspeaks.Ingeneral,datashowsbetterresolutionthanwhatisobservedinMonteCarlo....................139 9-10TheclosuretestoftheMCsmearedmatrixappliedtoMCrecospectra.....140 9-11Thetruth,andsmearedspectraresultingfromthesmearingfunctiondescribed inEquation9.Ontheright,weincludetheclosuretestwiththegenerated unfoldingmatrix....................................141 9-12Left:Eventspassingbothrecoandtruthlevelcuts.Mid:Eventspassingreco butnottruthlevelcuts.Right:Scalefactorforremovingsmearinginduced background.......................................141 9-13Left:ResponseMatrixfromFSRunfolding.Right:InvertedResponseMatrix fromFSRunfolding..................................142 9-14TheresponsematrixfromdatatuneddetectorsmearingandpythiacalculatedFSRforboththelinearleftandlogrightzscale..............144 9-15Acceptancetimesefciency,A ,asafunctionoftheZ p T withtheassociatedvariationsobtainedwiththeModiedToleranceMethod...........146 9-16Left:percentagevariationsoftheA asafunctionoftheZ p T .Right:fractionalvariationsofthe 1 d dP T asafunctionoftheZ p T ...............146 9-17100%variationonthenumberoftotalbackgroundeventsredcomparedto therawdatacounting.................................150 9-18Thegeneratorlevel p T spectrumwithseveralstandardPythiaUEtunes.On theleftzoomintothelow p T rangeshownwithlineartsinthe[0.1] GeV/ c range.Ontherightseveralratiosofthespectrawithdifferenttunes.154 9-19SystematicerrorsasafunctionoftheZ p T .....................157 9-20Comparisonbetweenthe Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(differentialcrosssectionshapeagainst theP OWHEG predictionintherestrictedacceptance................158 9-21Comparisonbetweenstatisticalandsystematicerrorsassociatedtoeach p T bin.160 9-22Comparisonbetweenthe Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(differentialcrosssectionshapefrom dataagainsttheFEWZcalculationfor p T > 20 GeV = c intherestrictedacceptance..........................................161 15

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9-23CombinationofelectronandmuonchanneldatacomparedwithPOWHEG comparison.......................................161 9-24Thecomparisonofthelow q T spectrumtopredictionsmadefromvariousunderlyingeventtunes..................................162 9-25Thecomparisonofthehigh q T spectrumtopredictionsmadefromvarious perturbativeQCDcalculatorsatNLOandNNLOprecision............163 A-1TheCSCchambersmeasures and positionsatxed z ,providinginformationfortheCSCTFtocompute p T ........................166 A-2TheredlinesdenoteasingletriggersectoronME+2...............167 A-3AzoomedinphotographofaCSCchamber....................168 A-4AnillustrationoftheCSCtriggerchain.......................169 A-5AphotographofCSCTFprototypeboardsbeforeFPGAsareconnected....170 A-6AphotographofthefrontplaneoftheSPcrateonceallthewiringisconnected.171 A-7AblockillustrationoftheSPLogic..........................172 A-8AperformanceplotoftheCSCTFshowingproblemsinthelow region.....174 A-9AperformanceplotoftheCSCTF,depictingtheperformanceinthelow regionafterthexisimplemented...........................175 A-10Adatatoemulatorcomparisonoftrack assignment,showing100%agreement..........................................176 A-11Adatatoemulatorcomparisonplotofthetrackmode,showingwhichtypeof tracksarenotagreeduponbetweenthedataandemulator............177 B-1Signicanceasafunctionofsignalyieldforseveraldifferent p T cuts.Leftcolumn:gaugeproduction,centralcolumn:contactinteraction,rightcolumn: Z 0 models.Toprow:mass=0.5 TeV = c 2 ,middlerow:mass=1.0 TeV = c 2 ,bottomrow:mass=1.5 TeV = c 2 .............................178 16

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy THESTUDYOFTHEZBOSONTRANSVERSEMOMENTUMSPECTRUM RECORDEDBYTHECOMPACTMUONSOLENOIDFROM2010LARGEHADRON COLLIDERDATA By JosephA.GartnerIII December2011 Chair:DarinAcosta Major:Physics Thisdissertationdescribesthefulldetailsof2studiesof Z 0 bosonsperformed usingtheCompactMuonSolenoiddetectorattheLargeHadronColliderofproton onprotoncollisionswithcenterofmassenergyof 7 TeV .Therststudysearches forphysicsbeyondtheStandardModelbylookingforanexcessinproductionof Z 0 bosonsbyexaminingthe Z 0 p T spectrum.Asnoexcessisfound,limitsonnewphysics modelsarepresentedasafunctionofmassandotherfreeparameters.Thesecond studyfocusesonaprecisionmeasurementofthe Z 0 p T distribution,andiscompared totheoreticalcalculationsforthepurposesoftestinghighorderQCDcalculationsin additiontoprobingthepredictionsofvarioustunesoftheunderlyingevent. 17

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CHAPTER1 THESTANDARDMODELANDSOMEPOSSIBLEEXTENSIONS 1.1Introduction TheStandardModelSMisthenamegiventothecollectionoftheoriesdescribingtheinteractionsoffundamentalparticlesinnature.Theterm`fundamental particle'meansthatthereisnoknownstructurewithintheparticle[1].Thistermhas evolvedfromthetimesoftheplumpuddingmodeloftheatomtheorizedbyJ.J.Thomsom[2],tothediscoveryofnucleonsthroughscatteringexperimentsbyRutherfordand Chadwickintheearlypartofthe20thcentury[3];thestagewasthensetfortherapid developmentoverthenextcentury. AnimportantearlysteptowardsthecurrentmodelcamewiththebirthofQuantum MechanicswithEinstein'stheorythatenergycarriedbylightisdelieveredin`quanta'[4] asanexplanationforthephotoelectriceffect.Hecontinuedtodevelopthetheoryof thephotonoverthenextdecade,andina1916paperfromtheVerhandlungender DeutschenPhysikalischenGesellschaft[5]translated,ProceedingsoftheGerman PhysicalSociety,incorporatedndingsofspecialrelativity.TheobservationCompton scattering[6]in1924providedexperimentalevidenceofthephoton,resultinginthe ArthurComptontobeawardednobelprizeinphysicsin1927.ThisledtoPaulDirac's accuratepredictionsabouttransitionradiationbasedonaquantizedtheoryoftheelectromagneticeld[7].Asthetheorybecamemorewellunderstood,thefoundationsfor theformalismsusedtodaywereoutlinedinapaperbyEnricoFermiin1932[8].Problemsinthetheoryandtheirsolutionsledtodevelopmentoverthenext40years,theend resultwasatheorywhichcouldreproducetheprecisepredictionsofElectrodynamics, whileaccountingforthequantumbehaviorofeldsandparticles.Inthisway,thetheory isnamedQuantumElectroDynamicsQED. Atthesametime,nuclearphysicswasuncoveringthedynamicsofhowprotonsand neutronsinteracted.Thetheorywasquitepuzzling,asonewouldpredictthatpositively 18

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chargedprotonswouldrepeloneanother.WiththesuccessofQEDingoverning thedynamicsofchargedparticlesthroughtheexchangeofphotons,HidekiYukawa proposedatheoryinwhichnucleonsexchangedintermediaryparticlesinawayof holdingtogetherthenucleus.Hisproposalpredictedaspin0particleofmassaround 200MeV/ c 2 [9],andwiththediscoveryofthepion M 0 =134.97MeV/ c 2 thetheory wasthoughttobeagreatsuccess[10].Shortlyafterthediscoveryofpions,several additionalmesonswerediscovered,whichhadnotyetbeentheorized.Whilemanyof thenewhadronsdecayedthroughthestronginteractiondisplayingalifetimeofaround 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(23 s ,asmallportionweremuchlongerlived,withanaveragelifetimeof 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(10 s Theseparticlesweredenotedasstrangeparticlesasthebehaviorwasneitherpredicted orexplainedbyexistingtheory.Overthenextdecadesthelistofparticlesconsidered tobeelementaryincreasedataprolicrate.Atechnique,calledtheeightfoldway,of arrangingparticlesbasedoncertainpropertiesledtothepredictionofseveralnew particleswasdevelopedindependentlybyMurrayGell-MannandYuvalNe'eman[11]. Muchinthesamewayasthegeometricarrangementofelementsknownasthe periodictablereectspropertiesofelectroncouplings,theeightfoldwayledpeople tobelievethatthenewsetsofparticlesmayhaveinternalstructurethemselves.In 1963,Gell-MannandGeorgeZweigsuggestedtheexistenceofatypeofconstituent particlecomprisingthelargenumberofknownparticles[12].Gell-Manborrowedaterm `quark'fromtheJamesJoycenovel Finnegan'sWake ,andthenamestuck.Theonly problemwiththetheorywasthateverysearchforlonequarksrenderedanullresult. RichardFeymanarguedthatquarkswererealparticlesinthattheyhadpositionand momentum[13].Shortlyafterwards,datafromtheStanfordLinearAcceleratorCenter conrmedpredictionsmadebythequarkmodel[14],andthetheorywasconsidered valid. Thelastparallelthreadtopursuearethediscoveriesandtheoriessurrounding nucleardecay.Thelate19thandearly20thcenturiesbroughtaboutknowledgeof 19

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radiationforheavyelementssuchasuraniumandradium.WolfgangPauliproposeda particlewhichwouldbelighterthantheprotonandinteractsveryweaklyhisoriginal nameforthisparticlewastheneutron,butthenamewasawardedtothenucleon discoveredbyChadwickin1932.EnricoFermiindevelopingweakinteractiontheory renamedPauli'sparticlethe`neutrino'littleneutralone,andusedittoexplainthe decayofneutronsintoaproton,electron,plusmissingenergy.Thistheorypostulated that4fermionsinteractedatapoint,suchthattherewasnoparticleexchange[1]. AfterthesuccessofQED,theworkofSheldonGlashowproposedamodelfornuclear decaywhichinvolved3newvectorbosons,thoughttomediatetheweakforce[15].In addition,heincorporatedtheknownphoton,andbeganthemovementtowardsunifying theweakandelectromagneticforce.Thismovementwassupportedbytheworkof StevenWeinberg[16]andAbdusSalam[17];thetriowerejointlyrecognizedfortheir groundbreakingworkwiththeNobelPrizein1979.ThenewElectroweaktheoryused themathematicsofgrouptheorytodescribetheeldswiththeSUxUsymmetry groups,andemploysnewquantumnumberscalledtheweakhypercharge Y W and weakisospin T 3 ,whichrelatetoelectriccharge Q asdescribedinEquation1. Q = T 3 + Y W 2 TheSUgroupassociatedwiththreeWbosonswhicharerepresentedbySU2 doubletsforweakisospin,andtheUgroupcorrespondstothe B 0 bosonandthe Usingletofweakhypercharge.Inthisrepresentationtheobservedparticlestates arecomposedofthefundamentaleldsasfollows: W = 1 p 2 W 1 iW 2 Z =cos W W 3 -sin W B ,and A =sin W W 3 +cos W B where A istheelectromagneticeld.The rstevidenceofthetheorycamewiththeobservationofneutralcurrentsin1973from theGargameldetectorwhenmuonneutrinoswereobservedtocreatehadrons[18].The discoveryoftheW[19]andZ[20]bosonsin1983conrmedtheirtheories.Withthe 20

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discoveryofquarksandvectorbosons,thestrongandelectroweaktheorieswerewell established. 1 Thetwotheoriescombinetogivearobustalbeit,asofyetincomplete descriptionofnature. 1.2ParticleTypes Theknownfundamentalparticlescanbeeasilydividedinto3groups,calledforce carriers,quarks,andleptons.Thelattertwoaredifferenttypesoffermions,spin1/2 particlesthatobeythePauliexclusionprincipleandaregovernedbyFermi-Dirac statistics.Quarksaredistinctinthattheyaretheonlyknownparticlethathasfractional electriccharge.Additionallytheyareaffectedbythestrongnuclearforce,whichmeans theycarrycolorcharge.Leptons,ontheotherhand,donotparticipateinthestrong nuclearinteractionsandcarryintegerelectriccharge.Bothtypesoffermionsaredivided into3generations,consistingofapairofparticleswhosepropertiesaresymmetric acrossgenerationsthiswillbediscussedingreaterdetaillater.Thethirdtypeof particles,theforcecarriers,arebosons,spin1particlesobeyingBose-Einsteinstatistics, andgettheirnameastheyareassociatedwithaforce.Theforcesandtheirassociated particlesarethestrongforcemediatedbygluons,andtheeletro-weakforce whicharemediatedbythe W + W )]TJ/F20 11.9552 Tf 7.084 -4.339 Td [(, Z 0 ,and photon. InadditiontoalltheparticlesintheSM,theequationdescribingaparticle'stotalrelativisticenergyEquation1showstherelationshipbetweentheenergyofaparticle, E,andthemassandmomentummandprespectivelyofthatparticle.Immediately, onerealizesthattherearetwosolutionsforthisequation,thepositiveandnegative 1 TheinclusionofWandZmasstermscreatequadraticdivergencesthatcannotbe canceledthroughrenormalization;thatatheoryisrenormalizableisanaxiomofeld theory[21].Thesimplestsolutionistheinclusionofamassivescalareldtheorizedby PeterHiggs[22].Thecorrespondingparticle,calledtheHiggsBoson,hasnotyetbeen observed,andisdiscussedinSection1.4. 21

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energysolution.Thenegativeenergysolutionisinterpretedastheexistenceofantiparticles.Inthismanner,everyparticlelistedabovehasanassociatedantiparticle.In theinstanceofthe and Z 0 ,theparticleisitsownantiparticle.Theseparticleshavethe samemassandoppositechargeoftheirpositiveenergyconstituents. E 2 = p 2 c 2 + m 2 c 4 1.2.1Leptons Eachleptonicgenerationischaracterizedbyamassivechargedparticleandits associatednearmasslessneutralparticlecalledaneutrinonamedbyEnricoFermiin 1930,meaninglittleneutralone.ThenamesofthethreegenerationsarelistedinTable 1-1alongwithbasicpropertiesasreportedbytheParticleDataGroupPDG. Table1-1.Thethreegenerationofleptons Name Symbol Generation ElectricCharge P.D.G.Mass[26] Electron e e + 1 -1 0.511MeV/ c 2 ElectronNeutrino e e 1 0 < 225eV/ c 2 %CL Muon + 2 -1 105MeV/ c 2 MuonNeutrino 2 0 < 0.19MeV/ c 2 %CL Tauon + 3 -1 1.78GeV/ c 2 TauonNeutrino 3 0 < 18.2MeV/ c 2 %CL Therstthingthatonenotices,isthattheneutrinosdonothaveexactvalues assignedtotheirmass,butratherupperlimitsonhowlargetheirmassescouldbe. Thereasonforthisisthatneutrinosonlyinteractweaklyandcanpassthroughlarge volumesofmatterwithoutinteracting.Typically,neutrinosaredetectedindirectlyin theformofmissingenergyormomentum;infactthepredictionoftheneutrinowas motivatedbytheexistenceofmissingenergyinbetadecays.Experimentssuchas thosefoundattheLargeHadronColliderarenotwellsuitedforsuchmeasurements; however,dedicatedprogramsexisttostudythepropertiesofneutrinos.Examplesof theseareBooNE[23]usingneutrinobeamsfromaccelerators,Super-Kamiokande[24] 22

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whichusesatmosphericneutrinos,andDoubleChooz[25]usingneutrinosfromnuclear reactors. Thethreegenerationsofleptonshaveauniquenumberor`leptoncharge'whichis conservedinelectroweakinteractionsandisthesameforeachmemberofthesame generation.Theirantiparticlepairshavetheoppositeleptoncharge.Anillustrative exampleofthisiswhenamuondecaysintoanelectron,amuonneutrino,andan antielectronneutrino.Wepreservealeptonchargeof1,aswehaveapositivelepton chargefromboththemuonneutrinoandtheelectron,andanegativechargefromthe anti-leptonneutrino.Formostinteractions,theleptonavorisconserved,however,with thediscoveryofneutrinooscillationitispossibleforleptonavortobeviolatedinasmall numberofevents. 1.2.2Quarks Quarksarethefermionswhichcombinetoformhadrons.Theyaredistinctfrom leptonsbecausetheyparticipateinthestronginteraction.Somegeneralpropertiesof thequarksarelistedinTable1-2. Table1-2.Thethreegenerationofquarks Name Symbol Generation ElectricCharge P.D.G.Mass[26] Up u 1 +2/3 2.55 +0.75 )]TJ/F23 7.9701 Tf 6.586 0 Td [(1.05 MeV/ c 2 Down d 1 -1/3 5.04 +0.96 )]TJ/F23 7.9701 Tf 6.586 0 Td [(1.54 MeV/ c 2 Strange s 2 -1/3 105 +25 )]TJ/F23 7.9701 Tf 6.587 0 Td [(35 MeV/ c 2 Charm c 2 +2/3 1.27 +0.07 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.11 GeV/ c 2 Bottom b 3 -1/3 4.20 +0.17 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.07 GeV/ c 2 Top t 3 +2/3 171.3 1.1 1.2GeV/ c 2 Itisimportanttonotethat,likeneutrinos,quarksmassesarenotmeasureddirectly, andinfactthemethodfromwhichtheyareinferredisnotconsistent.Thereason thatquarkmassescannotbemeasureddirectlyisisolatedquarkshaveneverbeen observed.Asareactiontothis,QCDincorporatesthisandreferstothispropertyas connement.Quarksareboundtogetherbythestrongforce.Theforceswithwhich mostpeoplearemorefamiliararetheelectromagneticandgravitationalforce,bothof 23

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whichhaveamagnitudeinverselyproportionaltotheseparationofthetwoattracted bodies.Thestrongforce,however,hasagreatermagnitudeasthedistancebetween theparticlesincreases.Conversely,astheparticlesapproachsmallerseparation,the strengthoftheforcedecreases;thispropertyiscalledasymptoticfreedom. Quarkscarryunitcolorcharge,whicharecalledred,blue,orgreen,andtheir antiquarkscarrynegativecolorchargee.g.anti-red.Theselabelsdonotcorrespond tovisiblelight,butareratherbookkeepinglabelsthathaveobservableconsequences. Presently,onlycolorneutralstateshavebeendetected.Astateissaidtobecolor neutralifithasallthreecolors,orifithasthecombinationofacoloranditsanti-color. Thus,quarksarefoundineitherstatesof qqq q q q ,or q q .Inrealitythesestatesare heldtogetherbyamultitudeofgluons,photons,andvirtual q q pairs.Colorneutralstates consistingofmorethan3quarksforexample qqqq q havebeentheorizedbutasof yetnoevidenceexiststodetectsuchparticles.Thedynamicsofquarksandgluons interactioninthiswayisgiventhenameQuantumChromoDynamicsQCD. Statesconsistingof3quarksor3antiquarksarecalledbaryons.Twowellknown baryonsareprotonsandneutrons.Statesconsistingofaquarkantiquarkpairarecalled mesons.Ahistoricalintroductiontoparticlephysicsplacesmuchgreateremphasison theseparticlesasthequarkmodelcamewellafterthediscoveryofmanymesonsand baryonsandthemultitudeofexcitedstates.Sincetheexcitationoftheboundquark systemisobservedasadifferentinternalenergymeasuredasadifferentparticle mass,therearemoremesonsandbaryonsthanyouwouldexpectfromagiven combinationofquarks.Itshouldalsobenotedthattopquarkhasneverbeenseenina boundstate.Thereasonforthisisthatitistheonlyquarkwhichismoremassivethan theWboson,andhencecandecaytoarealWbosonandabquark,makingitslifetime tooshorttocreateaboundstate. 24

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Inadditiontocolorandelectriccharge,quarkshaveaquarknumberor'quark avorcharge'.Quarkavorchargeispreservedinboththestrongandelectromagnetic interaction,butcanbechangedintheweakinteractione.g. t b + W + 1.2.3GaugeBosons ThelastcollectionofparticlesaretheGaugeBosons.Gaugebosonsarenot dividedintogenerationsasarethefermions,butratherareassociatedwithaspecic force.Thisleadstothembeingreferredtoasforcecarriersattimes.Somegeneral propertiesoftheparticlescanbefoundinTable1-3 Table1-3.TheKnownForceCarriers Name AssociatedForce ElectricCharge P.D.G.Mass[26] photon Electromagnetic 0 0 W + Weak +1 80.398 0.025GeV/ c 2 W )]TJETq1 0 0 1 142.214 448.23 cm[]0 d 0 J 0.398 w 0 0 m 0 14.446 l SQBT/F20 11.9552 Tf 182.801 452.563 Td [(Weak -1 m W + -m W )]TJ/F20 11.9552 Tf 10.076 -0.299 Td [(=-0.2 0.6GeV/ c 2 Z o Weak 0 91.1876 0.0021GeV/ c 2 gluon g i Strong 0 0 The isperhapsthemoststoriedparticleintheentireSM.Thedebateoverthetrue natureoflightaspecicregionoftheelectromagneticfrequencyspectrumreachesas farbackasAristotle,andcenteredoverwhetherlightwasawaveoraparticle.Today, werecognizethe asthemediatoroftheelectromagneticforce.Theelectromagnetic forceisdescribedindetailbyquantumelectrodynamicsQED,andthuslythe s intrinsicpropertiesmass,spin,chargearewelldetermined.Additionally,QED,in particulartheconservationofglobalsymmetries,showsthatphotonsaretheirown antiparticles.TheelectromagneticforceiselegantlydescribedbyMaxwell'sequations, buttheseequationsdescribeelectrodynamicsonamacroscopicscale.QED,onthe otherhand,represents asaquantummechanicalparticle. Thegluonisthemediatorofthestronginteraction.Thestronginteractionholds togethernon-elementryparticlesmadeupofquarkstogether,mesonsandbaryons,in additiontoatomicnuclei.Thestrongforceissonamedbecauseofitsstrengthrelative totheotherknownforces,inparticularitsabilitytoholdtogethermultipleprotonswhich 25

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allcarrypositiveelectriccharge.Gluonsareinterestingbecausetheysimultaneously carrybothpositiveandnegativecolorchargeofsomevariety,whichisnecessaryfor colortobeconservedwhenaquarkemitsagluon.Toillustratethisprocess,consider aquarkwhichhasredcolorcharge.Ifthisquarkemitsagluonandchangesitscolor chargetogreen,theemittedgluonwillhaveared,anti-greencharge,suchthatbefore andaftertheemissionthenetcolorchargeisred.Becauseofthebookkeepinglabels ofthestronginteraction,theformalismwhichgovernsitsinteractionsiscalledQuantum ChromodynamicsQCD. The W + W )]TJ/F20 11.9552 Tf 7.084 -4.339 Td [(,and Z o areallmediatorsoftheweakforce.Theweakforceisso namedduetoitsstrengthrelativetothestrongandelectromagneticforce.Theweak forceiscommonlyassociatedwithradioactivity,butisalsoassociatedwiththedecay ofheavyelementaryparticles.The W + and W )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(aretheonlywaywhichafermioncan changeitsavor.Experimentshavepreviouslysearchedfor'avorchangingneutral currents' Z o whichchangefermiongeneration,butnoevidenceexiststosupportsuch theories. Theweakforceisalsotheonlyforcewhichallowsforparityviolation.Parityisa symmetrywhichremovesthedependanceofassumedconventionsfromthebehavior ofnature.Toenforceparity,weipthe3dimensionalaxissuchthatthesignofeach cartesiancoordinateisreversed.Parityviolationintheweakinteractionwasrst observedbyC.S.Wuin1956[27].Theexperimentputcobalt-60inastrongmagnetic eldsuchthattheirnuclearspinswereinalignment.Whenitwasobservedthatemitted -raystendedtobeantialignedwiththecobaltNuclei,itservedasdirectevidenceof parityviolation. 1.3TheStandardModelLagrangian ThepreviousdiscussionoftheSMhasbeenlargelyphenomenological,butthe theoryismuchmorethantheorganizationofparticlesandtheirproperties.Everyterm intheStandardModelrepresentsapossibleinteractionbetweenparticles.Eachterm 26

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intheLagrangianrepresentsapossiblevertexofinteractingparticles,anddescribes thestrengthofthiscoupling.TheLagrangianoftheknownSMparticlesisdepictedin Equation1. L = q i @ )]TJ/F25 11.9552 Tf 11.955 0 Td [( g s T a G a q )]TJ/F22 11.9552 Tf 13.151 8.088 Td [(1 4 G a G a + L i @ )]TJ/F39 11.9552 Tf 14.344 8.088 Td [(i 2 W )]TJ/F39 11.9552 Tf 13.151 8.088 Td [(g 0 2 B Y L + R i @ )]TJ/F39 11.9552 Tf 13.151 8.088 Td [(g 0 2 B Y R )]TJ/F22 11.9552 Tf 13.151 8.088 Td [(1 4 W W )]TJ/F22 11.9552 Tf 13.15 8.088 Td [(1 4 B B TherstlineofthisequationrepresentsinteractionsviaQCD,whichisrepresented bytheSUgroup.The q and q representthequarkcolortriplets. G a representthe gluonocteteld,and G a aregluoneldstrengthtensors.Thetermsdescribehow quarksandgluonsinteract.Thenext3linesshowtheSUxUrepresentationof theelectroweakcouplings,withoutsymmetrybreaking.Linestwoandthreeshowthe dynamicsofleftandrighthandedfermionsrespectively,with L representingtheleft handedfermiondoublet,and R representingtherighthandedfermionsinglet.The GaugebosonsweobservearesuperpositionstatesoftheWbosonthreevectorandthe Bboson.Thedistinctioncomesintheircouplingtotheweakisospininthecaseofthe WandtheweakhyperchargefortheB. Thedistinctionofthepropertiesofleftandrighthandedparticlesreferstothe propertyofchirality.ChiralityisthedeterminationofthehandednessofthePoincar e transformationwhichdescribesaparticle.Formasslessparticles,chiralityisthesame ashelicity,orthealignmentoftheparticlesspinwiththeirmomentum.Aparticlewho's spinprojectionisinthesamedirectionasitsmomentumissaidtohaverighthanded helicity.Aparticlewho'sspinprojectionisintheoppositedirectionofitsmomentum issaidtohavelefthandedhelicity.Itisimportanttoreiteratethatthesepropertiesare onlythesameformasslessparticles,becauseformassiveparticlesyouarealways abletoboosttoaframewheretheparticleistravelingintheoppositedirectionwithout changingthedirectionoftheparticlesspin,andthushelicityisaframedependent 27

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property.Chiralityisofparticularimportanceduetoapropertyoftheweakinteraction whichisthatitviolatestheconservationofparity.Assuch,onlylefthandedfermions righthandedanti-fermionsparticipateintheweakinteraction.Thisisofparticular importancewhenconsideringneutrinos,whichunderthistheoryarealwayslefthanded. 1.4ProblemsintheStandardModel ThelistedLagrangianEquation1isincompletegivenourcurrentexperimental knowledgeofparticles.Onereasonthisisso,isthatitdoesnotallowthe W + W )]TJ/F20 11.9552 Tf 7.084 -4.338 Td [(,and the Z 0 tohavemass.Thesimplestsolutiontothisproblemistheadditionofascalar eldreferredtoastheHiggseld.Bycouplingtothenon-zerovacuumexpectation valueoftheHiggseld,thevectorbosonscanbecomemassive.Findingevidenceof theHiggsbosonisaprimaryphysicsgoalofalloftheexperimentsattheLargeHadron ColliderSection2. Inadditiontotherequirementofanasofyetundiscoveredparticle,theStandard Modelhasotherproblematiccharacteristics:thegravitationalforceisnotdescribed bythismodel,measurementsoftheamountofmassintheuniversebasedon cosmologicalevidenceshowthatthereisadecitofbaryonicmatterintheuniverse; theStandardModelprovidesnodarkmattercandidate,thescaleoffundamental couplingsbetweenthegravitationalandweakforces,thePlanckscaleandthescale forelectroweaksymmetrybreaking,andthemasssplitsbetweentheneutrinomasses arewidelydifferingthisproblemisreferredtoasthehierarchyproblem,multiple parameterssuchastheHiggsmassandthechiralquarkmassphaseareconned althoughthereislittleunderlyingtheoreticalmotivationforsuchconnementthistypeof problemisreferredtoasane-tuningproblem. Toovercometheseproblems,theoristshaveconstructedawidevarietyofmodels thataimtoextendormodifythestandardmodel.Oneofthemoreprolicmodels,called SuperSymmetrySusy,forshort,isdiscussedinsection1.6.1.Susyhasbecomea widelystudiedtheoryasitsolvesthehierarchyandnetuningproblems,offersmultiple 28

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darkmattercandidates,anduniesthethreefundamentalforcesbymakingtheir couplingconstantsconvergeatthesamevalueatthegrandunicationscale.Other modelssuchasextradimensionssimilarlyaddressmultiplechallengestothestandard modelandarethesubjectofstudyformanyindividualsatCERNaswell. 1.5PrecisionMeasurementof Z 0 TransverseMomentum Inallhadroncolliders,itisassumedthatthebeamshavelowcrossinganglesand consequentlythecollidingprotonshave0netmomentumtransversetothebeamline p T .As p T mustbeconservedinallcollisions,any p T thata Z 0 isobservedtohave mustbebalancedbyaotherobjectswithequalandopposite p T .Themomentumofthe recoilingsystemisparticularlysensitivetoQCDinitialstateradiationISR,andsince Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(isaclean,easytoisolatesignal,themeasurementofthe Z 0 isparticularly usefulinmeasuringQCDISR. Thismeasurementhasbeenperformedpreviouslyondatacollectedfromthe TevatronattheFermiNationalAcceleratorLaboratorybymostrecentlytheD0[28] collaboration.Thestudyreachestoaround200 GeV = c in p T ,whilethehighercollision energyprovidedbytheLHCwillallowfortheextensionofthissearchtoseveralhundred GeV = c .ThismakesthisstudyanexcellentstudyofperturbativeQCDatahigher momentumtransfer Q 2 ,andisanimportantrststepinamorecomplexelectroweak programplannedfortheLHC[29].Anysignicantdeviationfromthesecalculations couldindicatenewphysics. Thevalueof Q denesourQCDrenormalizationscale.Ifcalculationstoallorders ofperturbativeQCDaretakenintoaccount,theresultsareindependentofthisscale; however,ourtheoreticalpredictionstakeonlynexttonexttoleadingordereffectsinto account[30].Additionally,asithasbeenexplainedthattheprotonisacomposite particle,anditstotalmomentumisthesumofitsconstituents;thescaleforthepartons momentumiscalledthefactorizationscale[31].Thedependanceuponthesescalesis highestatleadingandnexttoleadingorders,andcontributestotheoreticaluncertainty 29

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forperturbativecalcualtions.Additionally,Z+Jetsrepresentsanimportantbackground tomanyHiggsandbeyondstandardmodelsearches,soadetailedcharacterizationof thisspectrumisconsideredanimportantearlyphysicsgoalforCMS[32]. Whenconsideringthepredictionofthe Z 0 p T spectrum,itmaybeeasilydividedinto 2regions:theperturbativeandnon-perturbative.Perturbationtheoryisamathematical expansionforsmalltermswhereaproblemforwhichnosolutioncanbecalculated directlyiscalculatedbystartingwiththesolutiontoasimilarproblem,andadding modicationstothissolution.Thistypeofcalculationispossiblewhenconsideringthe scatteringofquarksoffoflownumbersofhighenergygluons.Inthisway,perturbative calculationsareabletopredictthehighendofthe Z 0 p T spectrum.Thebehavioris greatlyaffectedbynexttoleadingorderNLOandnexttonexttoleadingNNLO orderdiagrams[33],asdepictedinFigure1-1.Onlyrecentlycalculationscannow beperformedbyanalytictoolssuchasFEWZ[34],albeitinthecaseoftheNNLO calculationsextensivecomputingresourcesmustbedevoted. Figure1-1.DiagramsillustratingNLOandNNLO Z 0 production. Inthecaseoftheemittanceofmanysoftgluons,perturbationtheorybecomes impracticalforpredictingthedynamicsofparticleexchange.Thelow Z 0 p T regionis largelyshapedbymultiplesoftgluonexchange;thistypeofeffectisreferredtoasthe underlyingevent,andhasconsequencesforthepredictionofkinematicdistributionsof severalparticles.Inordertopredictthebehaviorofsoftgluonresummation,toolssuch 30

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asRESBOS[35]havebeendeveloped.Byperformingearlyprecisionmeasurements ofthe Z 0 p T ,importantfeedbackisprovidedforthepurposeofaccurateandreliable simulation. 1.6StandardModelExtensionsProducingBoosted Z 0 ThereareseveralextensionstotheStandardModelthatmanifestintheproduction of Z 0 withahightransversemomentum p T .Examplesofthesearequarkcompositeness[36],Susy[37],andnewgaugebosons[38]amongstseveralothers.Assuch, searchingforanexcessofboosted Z 0 becomesamodelindependentsearchfornew physics;thesearchcanresultindiscoveryindependentofthespecicmodel.Dueto itshigherpredictedcrosssection,intheearlydatatakingemphasisisplacedonthe discoveryandinthecasenoexcessisfound,exclusionofexcitedquarks. 1.6.1ExcitedQuarks Sincefermionsdemonstrategenerationalbehavior,itisanaturalsuppositionthat bothquarksandleptonshaveinternalstructureandthatthetwoparticletypesmight sharecommonconstituents,calledpreons.Muchlikeuniquebaryonsexistcomprised asexcitedcombinationsofquarks,onemaysupposethatexcitedquarkstateswould beaconsequenceofcompositequarks[36].Ithasbeendiscussedpreviouslythat multiplemesonstatescanbeobservedbytheexcitationofthequarksthatmakethem up.Similarly,ifquarksarecomposedofmultiplepreons,itisreasonabletoexpecttheir preonstoformnewstatesbytheexcitationoftheconstituents.Themodelforexcited quarks q hasthefollowingLagrangianasdescribedbyEquation1. L trans = 1 2 f R g s f s a 2 G a + gf 2 W + g 0 f 0 Y 2 B f L + h c Theterm describesthecompositenessscale.Thethreeterms, G a W and B describethecouplingstotheSU,SU,andUgaugeparticlesoftheStandard Modelrespectively.Thecouplings g s g and g 0 aretheStandardModelgaugecoupling 31

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Figure1-2.Thebranchingfractionof q asafunctionof f s strengths,andtheterms f s f ,and f 0 arescalefactors.Itisconventionaltoassumethat thescalefactorsareallunitaryi.e. f s = f = f 0 =1 ,butitisimportanttonotethatthis isnotnecessarilytrue[39].Whenthesescalefactorsarevaried,therearetwoeffects onemustconsider;thetotalnumberof q producedandthebranchingfractions,the probabilityofaparticletodecaythroughaparticularmode,ofthe q .Figure1-2depicts thebranchingfractionofthe q asafunctionofthestrongcouplingparameter f s Therstobservationworthnotingisthestrongtendencyfor q todecayto q + g underthestandardassumptionofthestrongcouplingparameters,andthatitis overtakenasthevalueof f s isreducedinprotononprotoncollisions.Thisisimportant whenconsideringthediscoverypotentialofalternativesearches,namelyasearchfor resonancesinjetsperformedatCMS[40].Anysearchinthischannelwillbothhave decreasedreachif f s islessthan1,bothinthatless q willbecreatedandthe q which arecreatedwilldecayintogluonslessfrequently.For q producedbyquarkgluonfusion anddecaying,thenetyieldisnotsosimple.Whilethenumberof q createdisless, theprobabilityofthe q decayinginto q + Z 0 increases;Figure1-3depictsthecross section*branchingfractionof q q + Z 0 q + + )]TJ/F20 11.9552 Tf 7.085 -4.338 Td [(,andcomparesittotheproduction 32

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of q q + g .Whilethedijetsearchappearstohavepoweruptolowvaluesof f s itisworthnotingthatthedijetbackgroundwillbequitelargewhencomparedtothe backgroundonewouldexpectfromlookingforboosted Z 0 Figure1-3.Thecrosssectiontimesbranchingratiofor q decaywitha q massof 1.5TeVcreatedthroughquarkgluonfusionasafunctionofstrongcoupling constant, f s Figure1-4.Thecrosssectiontimesbranchingratioof q createdthroughquarkgluon fusionasafunctionofmass,formultiplevaluesofthestrongcoupling constant. 33

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Inadditiontoproductionof q throughquark-bosoninteraction,thereisanadditionalmechanismwhichisnaturalforthismodelinvolvingtheforcewhichbindsthe preons.Weconsideritaneffective4pointinteractionasweexpecttherangeofthis forcetobeverysmall,andrefertothisasproductionthroughcontactinteractions.Productionthroughcontactinteractions q + q q + q isdenedbytheLagrangianin Equation1.ThedepictionofbothproductionmechanismsareshowninFigure1-5. Here, g 2 isafreeparameterwhichisordinarilysettobe 4 j isthefermioncurrent[36], and isthesamecompositenessscaleasdenedinEquation1. L contact = g 2 2 2 j j Figure1-5.Theproductionof q fromquarkgluonfusionleftandthroughcontact interactionright. Thisproductionmechanismisparticularlysuitedforasearchforboosted Z 0 ,due tothefactthatitscreationisindependentofthevalueofthegaugecouplings.Inthis way,asearchforboosted Z 0 becomesincreasinglysensitiveto q productionas f s decreases,includingavalueof f s =0 ,whichiscompletelyinaccessibleinthecase ofasearchfordijetresonances.Furthermore,astheCMSsearch[40]analyzesonly the2highest p T jetsperevent,itisreasonabletobelievetheyareinsensitivetothis productionevenathighervaluesof f s asthereisaroughly 2 3 chancethatoneofthe 34

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highest p T jetswillbefromtherecoilingquarkfromthe q production.Inthiscase, themostrelevantsearchforcomparisonwasexecutedatHERAacceleratorbytheH1 collaboration[41].HERAwasan ep collider,whichmeansthatthissearchassumed productionwasentirelythrough q + = Z 0 q .Initially,itisdifculttotellwhetherthis searchiscomparableastheH1searchassumesnocontactinteractionsexist,however duetotheir p s peakingat319GeV,itisfairtoassumethattheH1analysiscould exclude q onlyuptothismass.Itisalsoworthnoting,thattheincreaseinproduction duetocontactinteractionisoffsetbythestrongtendencyforthe q todecaythroughthe 4pointchanneli.e. q + q q + q q + q + q + q 1.6.2OtherStandardModelExtensions WhilethepriorityintheearlyLHCrunninghasfocusedonthe q decayingto Z 0 ideallythesearchwillbesensitivetomultiplemodelsasdiscussedinSection1.6.In Section8.1,wediscusstheexperimentalprocedureforcharacterizingthesignalone wouldexpectfromvariousphysicsmodels.Ultimately,itwasfoundthatinthecurrent integratedluminosityscenario,competitivelimitscanbesetupononlythe q model. Forthetimebeing,abriefdiscussionofafewothermodelsisstillappropriate.Thetwo othermodelsgivenseriousconsiderationwereheavyneutralgaugebosons Z 0 and Susy. The Z 0 existenceisanecessaryingredientinseveralincarnationsofphysicsbeyondtheStandardModel[42,43];notablyextraneutralvectorbosonsareaprediction ofgranduniedtheories,superstringtheories,andSusy.Whilethesemodelsdifferintheirconsequences,theparticlestheypredictmanifestasanarrow,highmass resonance.LimitsbytheCMS[38]dileptonresonancesearchexcludemassesupto 1140GeV.Thereisthepossibilityforthe Z 0 todecayto Z 0 +aHiggsboson,albeitthis wouldbeasmallbranchingfractionandtheutilityofasearchforboosted Z 0 isfurther reducedbythebranchingratioofthe Z 0 + )]TJ/F20 11.9552 Tf 7.085 -4.338 Td [(. 35

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SusyisaanotherwellmotivatedextensiontotheStandardModel.Susyisatheory inwhichallStandardModelparticlesarepairedwithamassivecounterpartorsuperpartnertoavoidquadraticdivergenceswhicharisefromtheinclusionofelementry scalarparticlestoaccountforvectorbosonmass[44,45].Thenamesupersymmetry isused,asthepairingcombinesfermionandbosonpartners.Susyintroducesmany degreesoffreedomtoremovethequadraticdivergenceofthescalareld,andas suchinmanifestsasmanyorderingsinthemassofthevarioussuper-partners.Gauge mediatedsupersymmetrybreakingGMSB,isaversionofSusyinwhichthelightest supersymmetricparticleLSPistheGoldstonefermionofsupersymmetrybreaking.In thismodel,ifthenexttolightestsuper-partnerNLSPisHiggslike,thentheproduction ofsupersymmetricparticleswillcreateacopiousamountof Z 0 36

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CHAPTER2 THELARGEHADRONCOLLIDERLHC TheLargeHadronColliderLHCisa27kmlongprotononprotoncolliderlocated underground,beneaththeborderofFranceandSwitzerland,justoutsideGenevasee Figure2-1.TheLHCwasdesignedfor14TeVcenterofmasscollisionsatapeak luminosityof10 34 cm )]TJ/F23 7.9701 Tf 6.586 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 pb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 persecond.Itisthehighestenergyhadron collidereverbuilt,surpassingitsdirectpredecessor,theTevatronatFermiNational AcceleratorCenterFNAL,inbothcategories.96TeV,3x10 32 cm )]TJ/F23 7.9701 Tf 6.586 0 Td [(2 s )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .Toachieve suchhighluminosity,theLHCdiffersfurtherfromtheTevatron,whichisaproton antiprotoncollider.TheLHCisthecurrentoperationalfocusoftheEuropeanCenterfor NuclearResearchCERN. Figure2-1.BirdseyeviewoftheLHC,notingpointsofinterest. 2.1HistoricalReview TherstapprovalfortheLHCcamefromCERNmanagementin1994whenthe projectwasproposedtooccurasa2phaseproject.Inthatproposal,theLHCwould havebeenoriginallyoperatedatacenterofmassenergyof10TeVstartingin2004, thenlaterbeupgradedtoa14TeVcollisionenergyforoperationin2008.Itwastobe 37

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aprotononprotoncollider,takingoverthebeamtunnelspreviouslyoccupiedbythe LargeElectron-PositronColliderLEP.Thisschedulewaslateramendedin1997when substantialfundingfromnon-membercountrieswassecured,representingthersttime thatamachineatCERNwasbuiltwithsubstantialportionsofmaterialsprovidedfrom nonmembercountries.Theamendmentdictatedthatthe10TeVtargetwouldbeforgone andthattheinitialconstructionwouldtargeta14TeVcollider.The1995publication oftheLHCConceptualDesignReportoutlinesthedesignofthemachinewhichhas remainedsignicantlyunchangedoverthedevelopmentoftheLHC[46]. TherstattempttocirculateprotonswasperformedonSeptember10,2008, withbeam1clockwiseasviewedfromabove.At10:25amGenevalocaltimethe LHCcompletedafullorbitduringwhichtimetheCompactMuonSolenoidCMSand otherexperimentsdetectedevidenceofbeamhalomuons.By3pmofthesameday, beam2counterclockwisehadcirculated.Overthennextday,theLHCcontinued withsinglebeamcirculationaswellasbeamsplashevents,whichinvolvesteering beamintothecollimatorsforthepurposeoftestingfailsafemechanisms,aswellas providinglargeamountsofsynchronizationdataforthevariousdetectors.Onthe14th ofSeptember,thebeamswerestoppedsothatservicetoapowersupplytoaportionof theacceleratorcouldbexed,anduponcompletiontheywouldrampupthemagnets andattemptacceleration.OnSeptember19,2008itisthoughtthatabadweldbetween 2superconductingmagnetscausedanelectricresistance.Thiscausedthejointto rapidlyheatupandthemagnetsystemtobecomeseverelydamaged.Theincident damagedordestroyedaround40superconductingdipolemagnets,withrepairstaking over1yeartocomplete. OnNovember21,2009theLHCrestarteditseffortstohaveafunctioningaccelerator.Overthecourseofroughly3hours,singlebeaminjectionsgraduallyprogressed untilbeam1circulated.Effortswerethenturnedtocirculatingbeam2,whichwas 38

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achievedshortlybeforemidnightofthesameday.Testsofsafetyanddiagnosticsystemscommencedoverthecourseofthenextfewdayswithoccasionalsinglebeam injections.OnNovember23,2009,bothbeamswereinjectedthenbroughtintocollisionsandevidenceoftherstcollisionsinCMSweredetected;aneventdisplayofone oftherstobservedcollisionsinCMScanbeseeninFigure2-2. Figure2-2.AneventdisplayofoneoftherstobservedcollisionsinCMS. 2.2LHCLayout TheLHCaccelerationofprotonsiscomprisedof5phases.Atthestartofthe process,hydrogengasisstrippedofitselectronsandfreeprotonsarethentakenfrom resttoanenergyof50MeVthrougha50mlonglinearacceleratorcalledtheLINAC2 Figure2-3,lowerleftcorner.Theprotonbeamistheninjectedtoacircularbooster whereitisacceleratedtoanenergyof1.4GeV.ThetheyarethenpassedtotheProton SynchrotronPS,acircularacceleratorwitharadiusof100m.There,theprotons areacceleratedtoanenergyof26GeV.Next,theprotonsareinjectedintotheSuper ProtonSynchrotronSPS,aroughly1kmradiuscircularaccelerator,wheretheyare broughtuptoanenergyof450GeV.Atthispoint,theprotonsareinjectedin2different directionstothemainstorageringoftheLHC. 39

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Figure2-3.ThecartoonrepresentationoftheLHC. 2.3LHCMainStorageRingDesignSpecication ThepurposeoftheLHCistoproducerarecollisioneventswithcenterofmass energy7TeVcurrentlywithinenvironmentsthatcanbestudiedandwellunderstood. Anyrelevantdiscoverywillneedtobestatisticallycompelling,hencetheLHCneedsto producemanyrepetitionsofrareevents.Wedene event tobeaneventcrosssection, thelikelihoodofaneventtooccur.Thenumberofrareevents, N event ,producedovera givenperiodoftime dt isthendenedequation2. N event = Z L t event dt With L t beingthetimedependentLHCluminosity.Luminosityisameasureofthe frequencyatwhichcollisionsoccur.Itisimportanttonotethatprotonsarenotinjected tothemachineasacontinuousstreamofparticles,butratheraccordingtoaprecise bunchstructure.Aprotonbunch,isjustacollectionofprotonswhichcirculateabout theLHCringinroughlythesamelocationatagiveninstant.ThedesignoftheLHCis suchthatprotonbunchescrossaxedpointalongtheringseparatedbyatleast25ns intervals.Thiswouldsumto40milliontimesinasecondhowever,thereareplanned 40

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gapsinthebunchstructure,sotherateofbunchesthatcrossesapointisslightlylower thanthis.Onecanpredicttheluminositygiventhepropertiesofthebunch;theseare thenumberofprotonsperbunch N p ,thenumberofprotonbunchesperbeam n b thefrequencyatwhichthebeamsrevolve f rev .Additionalfactorsincludethedensityof theprotonsinbothpositionandmomentumphasespace,calledbeamemittance n thegeometricluminosityreductionfactorduetothecrossingangleattheIP F ,the abilityofthequadrupolemagnetstofocusthebeamattheinteractionpoint,calledthe amplitudefunction ,andit'srelativisticboostfactor r .Theycombineasdescribed inequation2. L = N 2 p n b f rev r 4 n F Table2-1istakenfromtheLHCTechnicalDesignReport,andcontainsinformation aboutthebeamparametersbothatinjectionandpeakenergywhiletheLHCisinproton operation.TheseconditionsarepresentforCMSandtheotherhighluminositydetector ontheLHC,AToroidalLHCApparatusATLAS,whilethebeamhaslowerLuminosity forboththeLargeHadronColliderBeautyLHCb,andALargeIonColliderExperiment Alice.Theremaining2experiments,TotalCrossSection,ElasticScatteringand DiffractionDissociationTOTEMandLargeHadronColliderforwardLHCfshare interactionpointsIPswithCMSandATLAS,respectively.ForalayoutoftheLHCwith thedetectors,seeFigure2-3.TheLHCisalsocapableofproducingcollisionswith leadnuclei[47].Therearededicatedphysicsgroupsforheavyionphysicsaswellasa dedicateddetector;however,asitisnotthefocusofthispaper,detailsonthesesuch operationswillbeomitted[48]. Aspreviouslystated,thegoalofhighluminosityexcludestheuseofprotonon antiprotoncollisionsitwouldbeextremelydifculttoproduceasufcientnumber ofanti-protons.Thismeansthatthemainstorageringsconsistsof1,232opposite 41

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Table2-1.TheLHCBeamDesignParameters Parameter Units ValueatInjection ValueatPeakEnergy ProtonEnergy GeV 450 7000 Relativisticgamma r n/a 479.6 7461 Protonsperbunch N b n/a 1.15x10 11 1.15x10 11 Numberofbunches n b n/a 2808 2808 Revolutionfrequency f rev kHz 11.24 11.24 TransverseBeamEmmitance n mrad 3.5 3.75 RMSbunchlength [ Z ] cm 11.24 7.55 RMSbeamsizeatIP5 m 375.2 16.7 HalfCrossingAngleatIP5 c rad 160 142.5 dipolemagnetssharedbybothbeams,theonlyareacommontobothbeamsare theinteractionpointsofthedetectors,andtheinjectortothemainstoragering.Due tospatiallimitationsoftheLEPtunnel,thereisnotenoughroomtohouseseparate magnets.Hence,theLHCemploystwinboremagnetsthathousebothbeamlines.In ordertobendthehighlyenergeticbeams,thepeakmagneticeldis8.33Twhenthe protonsareat7TeV,whichisonlyavailablethroughsuperconductingtechnology.In additiontobendingmagnets,RFcavitiesareusedtogivethebeamselectromagnetic 'kicks',andthereforeboosttheprotonbeamsfromtheirinjectionenergytotheireventual collisionenergy. 2.42010LHCPerformance Inlightoftheincidentin2008,theLHCfavoredaslightlyconservativeluminosity scheduleofsystematicallyincreasingtheluminosity,byincreasingboththenumberof bunches,andtheprotonoccupancyperbunch.TheoperationoftheLHCforaperiodof timeiscalledall.Allstartswiththerampupperiod,inwhichprotonsareinjectedat thecorrectinterval,andthenacceleratedtotheireventualcollisionenergy.Overtime, theoccupancyperbunchdeteriorates,atwhichpointitbecomesnecessarytoperform abeamdump,theprocessofslowlysyphoningbunchesoffintoabsorbermaterial,so thatanewllcanbegin.Thelengthoftimeofallcanvarygreatly,buttypicallyall willlastforseveralhours.Theintegratedluminosityover2010isdepictedinFigure 42

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2-4.Forroughlytwothirdsoftheyear,thegainsinratedepictedinFigure2-5were marginal.Afteranextendedsummerdownperiod,duringwhichtimeessentialchecks wereperformed,theluminositybegantoincreaseandtherateofdatatakingincreased prolically.Bytheendofthe2010datatakingperiod,theLHChaddeliveredroughly50 pb totheCMSdetectortobeusedforanalysis. Figure2-4.Thedeliveredintegratedluminositytothefourprimaryexperimentsduring the2010datatakingperiod. 43

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Figure2-5.Thepeakinstantaneousluminosityoverthe2010datatakingperiod. 44

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CHAPTER3 THECOMPACTMUONSOLENOIDCMSDETECTOR Inchapter2,theLHCapparatuswasdiscussed.Asitwasexplained,thepurpose ofcreatingsuchahighluminosityenvironmentistostudyrareprocesses.Mostparticles thatweareinterestedin,forexamplethe Z 0 ,cannotbeobserveddirectly,butrather arereconstructedbythedetectionandmeasurementoftheirdecayproducts.The purposeoftheCompactMuonSolenoidistoidentifyparticlesbyuseofacombination ofdetectorelements,andmeasuretheirpropertiessuchthatdeductionscanbemade ontheunderlyingenvironmentwhichcreatedthem. TheCMSDetectordepictedinFigures3-1and3-2isthemostmassivedetector attheLHCweighinginat12,500tons,andis21.6mlong,by15mwideandhigh.CMS islocatedatLHCinteractionpoint5P5,seeFigure2-1100metersunderneaththe FrenchtownofCessy.CMShasacylindricalgeometry,andiscomprisedofconcentric detectorelementswhichareusedincombinationtoidentifyawiderangeofparticles andaccuratelyassignvaluestotheirpositionandmomentum.Ultimately,CMSis designedtoachievespecicphysicsgoals.TheCMSPhysicsTechnicalDesignReport[49]hasanorderedlistofphysicsgoals:tosearchfortheHiggsboson,tosearch forsupersymmetricparticles,tosearchfornewmassivevectorbosons,tondevidence ofextradimensions,tostudythepropertiesoftheStandardModel,andtostudythe interactionsofheavyions.Thephysicsgoalsdictatethedesignrequirementsofthe detector.Specically,itmusthaveexcellentresolutionofmomentumforallcharged particles.Furthermore,itmustbecapableofgoodmuonidenticationoveralargegeometricacceptance.Third,itmusthavegoodelectromagneticenergyresolutionforboth electronandphotonenergyresolution.Additionally,itmusthavegoodmissingenergy E miss T andjetenergyresolution.Lastly,itmusthavetheabilitytoresolvesecondary verticeslikethosecomingfrom 'sand b -jets. 45

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Figure3-1.TheTransverseXYviewofCMS. Figure3-1depictsatransversesliceofthecentralbarrelregion,andhighlights thedetectorelementsandhowtheyarecombinedtoprovideparticleidentication information.Theclosestdetectortotheinteractionpoint,theinnertrackerdiscussed indetailinsection3.2,isusedtoveryaccuratelymeasurethepositionofelectrically chargedparticlessuchaselectrons,muons,andchargedhadrons.Additionally,theuse ofpixeldetectionintheinnermostlayersprovidestheabilitytotagsecondaryvertices veryclosetothebeamlineresultingfromheavyavordecaysof c and b quarks. Electricallyneutralparticles,suchasneutralhadronsandphotons,cantraversethe trackervolumewithoutdetection.Thenextdetectorelementistheelectromagnetic calorimeterECAL,seesection3.3.ThepurposeoftheECAListoaccuratelymeasure theenergyofphotonsandelectrons.ThenextsystemistheHadronicCalorimeter HCAL,seesection3.4.TheHCALconsistsofalternatinglayersofbrassandplastic scintillators.ThepurposeoftheHCAListomeasuretheenergyofstronglyinteracting particlesthatarenotcontainedwithintheECAL.Duetothefactthatthenuclearcollision lengthismuchlongerthanradiationlengththeradiationlengthfortheCMSECAL 46

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crystalsis0.89cm,whiletheparticledatagroupliststhenuclearcollisionlengthof Copperas9.393cm[26],theHCALisaroughlytwiceasthickastheECAL.Thenext device,thesuperconductingsolenoidalmagnetseesection3.5providesthestrong magneticeldtobendchargeparticlesandallowformomentummeasurementsbased oncurvature.Theonlydetectorelementwhichliesprimarilyoutsideofthemagnetisthe muondetectionsystemsseesection3.6. Anadditionalmethodofdividingthedetectorisinregionsof .Figure3-2depictsa longitudinalsliceoftheCMSdetector,andthedetectorregionsarevisibleinregionsof .Thecentralregionsofthevarioussubsystems j j < 1.0isreferredtoasthebarrel region,wheretheforwardregionsofthedetectorareoftenreferredtoastheendcaps. Thefollowingsectionsaimtoillustratethethefunctionalityanddesignofthevarious subdetectorsofCMS.Thesectionswillmovefromtheinnermostdetector,andworkits wayoutward. 3.1TheCoordinateSystem Figure3-1depictsthedetectorlayoutinthebarrelregion.Theyaxispointsverticallyupward,whilethexaxispointsinwardwithrespecttotheLHCring.Thepositivez directionisthendeterminedtobeinthesamedirectionasthecounterclockwisebeam. Itisconvenienttousetheazimuthalangle, ,whichisdenedastheanglefromthe xaxisinthex-yplane,withthe+yaxishavinga valueof 2 .Thepolarangle isthe anglefromthe+zaxisintheplanedenedbythezaxisandanypointinthedetector volume.Wedonotusethis,however,as isnotinvariantunderLorentztransformations.AvariablewhichisinvariantunderLorentztransformationsistherapidity Y denedas Y = 1 2 ln E + p z c = E )]TJ/F39 11.9552 Tf 12.106 0 Td [(p z c .Whilethisvariablecanbeusedtodescribea particle'strajectory,itisdependentontheknowledgeoftheparticle'stotalenergy,andis notconvenientgeometrically.Insteaditisconventiontousethevariablepseudorapidity, denotedas ,where =-lntan[ /2]andinthelimitthat m = p issmall,thistermisequal 47

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to-ln j p j + p z = j p j)]TJ/F39 11.9552 Tf 18.843 0 Td [(p z .Inthelimitthattheparticleishighlyrelativistic,thesedenitionsarethesame,andwehaveavariablewhichisanalogoustoaLorenzinvariant quantityandstillhasageometricdenition.Additionally,itwillbeconvenienttousethe cylindricalcoordinate todescribevariousdetectorelements,althoughitisalmostnever referencedinthecontextofananalysis.Insteadof itiscommontousethevariable r theradiusinsphericalcoordinates. Figure3-2.TheLongitudinalviewofCMS. 3.2TheInnerTrackingSystem TheCMStrackerusessiliconpixelandmicrostripdetectorsdesignedtodetect chargedparticlesthattraversethedetectorvolume.Achargedparticlepassingthrough thesiliconseparateselectronsfromnucleicreatingnegativelychargedelectronsand positivelychargedions.Thesepositivelychargedionsarereferredtoaselectron holes,astheionsarexedwithinthelattice,however,theycancaptureelectronsfrom neighboringatoms.Inthisway,whilethepositiveionsarexedinspace,theelectron holesarefreetomove.Anelectriceldisinducedoverthevolumeofthesilicon,such 48

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thatfreeelectronswilldrifttowardpixelorstripimplants,andholeswilldriftinthe oppositedirection.Electricalreadoutsareusedtodetectthefreeelectronsandholes, andpositionassignmentscanbemadebasedontheparticularchannelsthatrecorded thesignals[10]. TheCMSTrackeriseasilydividedinto3sections.Listedfromtheinnermostto outermost,theyarethepixeltrackerPIX,thetrackerinnerbarrelTIB,andthetracker outerbarrelTOB.Forcoverageinthehigh regions j j > 1.0,therearethepixel endcap,thetrackerinnerdiskTID,andthetrackerendcapTEC. Thepixeldetectoremploys66millionsiliconpixelswithanareaof100x150 m 2 andisreadoutthrough16,000readoutchips.Inthebarrelregionthereare3pixel layerswith =4.4,7.3,and10.2cm,each53cmlong.Thepixelendcapcoversfrom6 to15cmin ata j z j =34.5and46.5cm.Inthe )]TJ/F25 11.9552 Tf 12.301 0 Td [( scheme,thespatialresolutionis roughly10 m. TheTIBiscomprisedofsiliconmicrostripsassmallas10cmx80 m.TheTIB extendsto j z j < 65cm,andhas4layerswhichextendfrom20 << 55cm.Ithas aspatialresolutionof23-34 minthe )]TJ/F25 11.9552 Tf 13.151 0 Td [( scheme.TheTOBismadeoflarger microstrips,withamaximumsizeof25cmx180 m.TheTOBismadeof6layers extendingfrom55 << 110cmand j z j < 110cm.Figure3-3depictsthetrackerwith coordinatesoverlaid. Figure3-3.ThelongitudinalviewoftheCMStracker. 49

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3.3TheElectromagneticCalorimeter TheECALsystemaimstomeasuretheenergyofphotonsandelectronsbyinducingelectromagneticshowers.Itdoessobyrelyingupon2physicsphenomena depictedinFigure3-4.Therst,calledbremsstrahlungradiation,occurswhenhigh energyelectronsinteractwiththeelectriceldofanucleusandaphotonisemittedas aresult.Thesecond,calledpairproduction,iswhenphotonsinteractwiththeelectric eldoftheatomicnucleusantoalesserextent,theelectriceldoftheelectronssurroundingthenucleus.Atlowerenergies,ionizationenergylossbecomesasignicant sourceofenergylossaswell.Itisworthnotingthatallchargedparticlesaresubjectto bremsstrahlungradiation,however,moremassiveparticlessuchasprotonsandmuons arelesslikelytoloseenergyinthiswaydiscussedlaterinthissection.Ascharged particlestraversetheECALvolume,theseprocesseswillrepeatresultinginalarge numberoflowerenergyphotons;thisphenomenaisreferredtoasanelectromagnetic shower. Figure3-4.Theprocessesthatcreateelectromagneticshowers.Left:FeymanDiagram depictingbremsstrahlungradiation.Right:Pairproduction. Fromtheresultingelectromagneticshower,theenergyfromthe 'saremeasured usingampliedphotodiodes.Anaturalquestiononewouldaskissincethisprocess isbasedontheelectromagneticinteraction,iswouldoneexpectchargedhadrons andmuonstoleavesignicantenergydepositsinthissystem.Toanswer,welookat thenatureofbremsstrahlungradiation.Equation3prescribestherelationofthe 50

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differentialradiationcrosssectionintegratedovermomentumtransfer d R d andthe massofarelativisticincidentparticleM[50].Here, d istheenergyofaemitted photoninaunitarea,and d isthefrequencyoftheemittedphoton. d R d 16 3 Z 2 e 2 c z 2 e 2 Mc 2 2 ln 00 EE 0 Mc 2 ~ Theimportantrelationshiptonoteisthatthistypeofradiationissuppressedbya factorof 1 M 2 ,hencewedonotexpectsignicantenergydepositsfrommuonsthemass ofthemuonis200timesgreaterthantheelectron,andaprotonisabout1000times themassoftheelectron.HadronsdoleavedepositsintheECAL,buttheunderlying physicsprocesscomesfromnuclearreactions,discussedingreaterdecalin3.4. MovingontothedesignoftheECAL,itistobehermeticandhomogeneous.The ECALiscomposedof61,200leadtungstatePbWO 4 crystalsforthebarrel,and14,648 crystalsfortheendcaps.Thepropertiesforwhichleadtungstatewaschosenareits shortradiationlengthallowingformaximalnumbersofinteractionsinarelativelysmall length 0 =0.89cmand2.2cmrespectively,itslightemissionspeed%ofthelight isemittedwithin25ns,anditsradiationhardnessupto10Mrad.Themaindrawback istherelativelylowlightyield, /MeVwhichrequirestheuseofphotodetectorsthat canoperateinamagneticeld.Therefore,siliconavalanchephotodiodesareusedin thebarrelregion,andvacuumphotodiodesareemployedintheendcaps. Theelectronbarrelhasaninner of129cm,andextendsto181cm.Thecrystals areorganizedintosupermodules,whichrunhalfthebarrellengthor0 < j j < 1.479. Thecrystalsaretiltedat3 o withrespecttotheprojectedlinefromthenominalvertex ofx=0,y=0,z=0.TheECALendcapscover1.479 < j j < 3.0andarecenteredatz =314cm.Thenormalizedenergyresolution E E oftheECALdecreaseswithenergy. ItsperformanceisdescribedinEquation3,attributingenergymismeasurementto stochasticenergylossS,noiseN,andaconstantterm. 51

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E E 2 = S p E 2 + N E + C 2 The E E oftheECALwasmeasuredindedicatedbeamtestsofcrystals.Figure35depictsitsmeasurement,whilereportingthevaluesfortheresolutiontermsaccording tothets.Onecanseethatforenergiestypicalofthoseexpectedofdaughterelectrons fromthedecayof Z 0 ,theelectronenergyresolutionisbetterthan1%. Figure3-5.FitoftestbeamdataforECALresolutionperformance[49]. 3.4TheHadronicCalorimeter TheHCALislocatedoutsideoftheECALandisusedtocontaintheshowerstypical ofhadronicinteractions.Hadronicenergylossfromradiativeeffectsaresuppresseddue toit'slargermassdiscussedpreviouslyinSection3.3,andfortypicalenergiesthe morerelevantformofenergylosscomesfromscatteringoffatomicnuclei.Ifahadron passesclosetothenucleiofanatomitcaninteractstrongly.Iftheincidenthadronisof sufcientlyhighenergy,thegluonwilldisassociateaconstituentquark.Asthequarks 52

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separate,itbecomesenergeticallyfavorablefornewmattertoformintheformofquark antiquarkpairs,almostentirelyintheformofpions + = u d )]TJ/F22 11.9552 Tf 10.806 -4.338 Td [(= d u and 0 = u u )]TJ/F40 7.9701 Tf 6.586 0 Td [(d d p 2 TheprocessisdepictedinFigure3-6.Duetothefactthathadronscantraversegreater distancesbeforeinteractinginthisway,theHCALissignicantlylargerthantheECAL. Figure3-6.Anillustrationofaprotonconvertingtoa + andaneutronthroughinelastic scatteringfromanuclei. WhentraversingmaterialintheECALandHCAL,chargedhadronsarecapableof creatinglightinscintillatingmaterialbyexcitingatomicmolecules.Themakeupofthe HCALtakesadvantageofthesefactsbyhavingalternatinglayersofplasticscintillators interwovenwithwavelengthshiftingbersforreadoutandbrassabsorberstoinduce hadronicshowering.Thewavelengthshiftingbersareattachedtolongerattenuation lengthclearbersoutsidethescintillatorwhichcarrieslighttothereadoutsystem.The readoutsystemconsistsofmulti-channelhybridphotodiodes. ThehadronbarreloftheHCALcovers-1.4 << 1.4.Itisdividedinto2half barrels,eachcomposedof18identical20 o wedgesin .Theouterandinnermostlayers oftheHCALaremadeofsteelforstructuralintegrity.Betweentheseare17layersof plasticscintillatorsinterspersedbetweenbrass,theinnermostofwhichisroughlytwice asthickastheresttohelpmeasureenergyoflowenergyshoweringparticlesfrom supportmaterialbetweentheECALandHCAL.IndividualHCALtileshavea x = 0.087x0.087andarefedtoasinglewavelengthshiftingber.TheHCALendcaphas 53

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onlybrassabsorptionplatesthebarrelhassomesteelforstructure,with19active scintillationlayers. ThestandardbywhichtheHCALismeasuredisit'sabilitytomeasureJetenergy and E miss T .Figure3-7depictsthemeasurementofjettransverseenergyresolutionasa functionofjettransverseenergyfor3regionsof Figure3-7.MonteCarloresolutionperformanceforHCALjetenergyresolution[49]. Anoteworthycharacteristicistheimprovementofjetenergyresolutionasafunction ofjetenergy.Theresolutionfor E miss T forQCDdijeteventsisthen E miss T p E T 3.5TheSuperconductingMagnet CMSissonamedbecauseitemploysasinglesuperconductingsolenoidalmagnet toprovidebendingpowerforboththeinnertrackingandoutermuondetectionsystems. Themagnethasadesignstrengthis4T,butiscurrentlyoperatedat3.8T.Themagneticeldcauseschargedparticlestobend,allowingmomentumassignmentpossible withthetrackingandmuonsystemsthroughthemeasurementofthecurvatureoftheir transversepath.Thestrengthofthemagnetisdictatedbytherequirementofunambiguouslydeterminingthesignofthechargeofmuonsupto 1TeV/cofmomentum.Due tothestrengthrequiredforthisbending,superconductingtechnologywasneededfor themagnettobepowerfulenough.Hence,theCMSmagnetusesliquidheliumforthe 54

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purposeofcooling.ThesolenoidislocatedoutsidetheHCALwithaninnerradiusof5.9 m,andisnearly13mlong,allowingfor2178turnsoftheNiobium-Titaniumsuperconductingalloy[51].Operatingatfullpower,themagnetcreates2.7GJofenergyinthe magneticeld. 3.6TheMuonSystem TheoutermostsystemofCMSisthemuondetectionsystemdocumentedbythe CMSMuonSystemTDR[52].Themuonsystemiscomprisedof3separatesystems ofdetection,inthebarreltherearethedrifttubechambersDTs,intheendcapthere arecathodestripchambersCSCs,bothofwhicharecomplementedbyresistiveplate chambersRPCs.BothCSCandDTsystemsaredividedinto4stationsofsuccessive planesofmuondetectionwiththeRPCsystemhaving6stationsinthebarreland3in theendcap.Thisallowsfortrackbuildingbystationtostationextrapolation.Themuon detectionchambersaremountedonirondiskswhichactasthereturnyokeforthe magnetseeFigure3-8.Themuonsystemshaveconsiderablylesschannelsthanthe innertrackingsystem,andcanprovideinformationforthelevel1triggerdiscussedin moredetailinsection3.7. Thebarreldetectoriscomprisedof250drifttubechambersintheregionof0 < j j < 1.2,withit'sinnermoststationat 4mandendingwith 7m.Themuon endcapconsistsof468CSCchambersintheregionof0.9 < j j < 2.4.Station1 has3ringsofchambersseeFigure3-9,whilestations2,3,and4have2.Dueto budgetlimitations,theouterringofstation4wasnotcompletedwithexceptiontoa smallnumberofchambersinoneendcap.Theresistiveplatechambersexistinboth thebarrelandendcapregionsupto j j < 1.6.Inthebarrelregion,theRPC'shave6 stations,2oneithersideoftherst2DTstations,and1ontheinnersideoftheouter DTstations.Intheendcaps,3stationsofRPCsexistontheouterringsofstation1,2, and3. 55

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Figure3-8.AphotographofmeinsidetheCMScavernduringtheinstallationperiod featuringtheDTsystemsilverandtheironreturnyokered. BoththeDTsandCSCsrelyonsimilarphenomenaforthedetectionofcharged particles.Bothdetectorsarelledwithgasseswhichwillionizewhentraversedbyahigh energychargedpartilcesAr-CO 2 fortheCSCsandAr-CO 2 -CF 4 fortheCSCsandhave anodewireswhichrunalonglinesroughlyparallelin fortheDTsandconstant inthe CSCs;theCSCsalsohavecathodestrips,forwhichtheyarenamedseeFigure3-10, whichareconstantin .Whenachargedparticletraversesthechamber,electronswill beejectedfromtheiratoms,causingthemtodrifttowardstheanodewires.Asthey gainmomentum,theybecomesufcientlyenergetictocausesecondaryionizations, andthroughsuccessiveinteractionscreateanavalancheofelectronswhichcausean electricalpulseontheanodewires.Sincethesewiresareatxedspatialcoordinates, andthedriftvelocitiesforgivengassesiswellmeasured,aspatialmeasurementis madewithhighaccuracy 100 m .IntheCSCs,thepositivelychargedionswill similarlydrifttowardsthecathodestripswhichrunroughlyparalleltolinesofconstant ,whicharecombinedwiththeadditionalmeasurementof madebythewires.The 56

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Figure3-9.AphotographofmestandinginfrontofCSCstation1ofthenegative endcap,whilethediskwasstillaboveground. RPC'soperateunderasimilarpremise.Insteadofwireanodes,theRPC'shaveplates ofopositelychargedgraphitecoatedBakelite,withcopperreadoutstrips. Theperformanceofthemuonsystemismeasuredforitsabilitytoperformit's intendedfunctions:muon p T assignment,identication,andtriggering.Themuon systemmeasuresthepositionofmuonsastheypassthroughthedetectorelementson atrajectory ~ s .Combiningknowledgeofpositionandthefactthatchargedparticlesbend inamagneticeld,therelationshipbetweenthecurvature d 2 ~ r ds 2 ,themomentumofa muon p ,andit'sunitlengthtangenttothetrajectory d ~ r ds ,isdescribedinEquation3. Here q isthechargeofthemuon,and B isthestrengthofthemagneticeld. 57

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Figure3-10.AnillustrationoftheinsideofaCSCchamber. d 2 ~ r ds 2 = q p d ~ r ds B r Thisparameterizationneglects3effects;theinhomogeneousBeld,theenergy lossofthemuonasittraversesthedetectorvolume,andmultiplescattering,allofwhich contributetoresolutioneffectsofmomentumdetermination.Despitethis,themagnetic eldandcombinepositionmeasurementofthetrackerandmuonsystemsprovidegood resolutionforalargerangeofmomentum.Thebasicformfortheassignmentof p T then simpliestoEquation3althoughmoresophisticatedformsexistwhichaimtotake secondordereffectsinplace. p T = A [ ] )]TJ/F39 11.9552 Tf 13.151 8.087 Td [(B [ ] 58

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In2008,astudywasreleasedoftheCMSmuonsystemperformance.Figure5-1, depictsthemuonsystemperformancefromthisnote.Inchapter9.1wedescribehow theprecisionmeasurementofthe Z 0 p T addressesresolutioneffects,andinsections 5.3,5.4,and5.5wedescribeourmeasurementofthemuontriggerandselection efciencyusingthetagandprobetechnique. 3.7TheCMSTriggerSystem TheLHCdesignluminosityleadstoabunchcrossingrateof40MHz,with 10 9 interactionspersecondseeFigure3-11.Currentlytherateatwhichinformationcan bewrittenislimitedto 10 2 eventspersecond,henceafactorof 10 7 eventsmustbe rejected.Thepurposeofareadouttriggeristoreducetheprolicamountsofdatatoa sizewhichcanbewrittentotapebyidentifyingsignaturesofsufcientlyrareoccurrence andusefulpurpose. Toperformsuchselectionsonthenumberofinteractionsused,CMSemploysa twoleveltrigger[53].Firstisthelevel-1triggerprocessorsforthemuonandcalorimeter systems.Thesystemisresponsibleforreducingtheratefromthe40MHzofbunch crossingsto100KHzarejectionrateof 10 4 ,withadecisiontimeof3.2 s andworks synchronouslywithLHCcollisions.TheLevel1triggeremployscustomelectronicswith quickreadoutcapability.Individualsubsystemsemploylocallogictoidentifysignatures ofhighenergyparticles,suchaslowcurvaturetrajectoriesthroughthemuonsystems andlargeenergydepositsinthecalorimeters.Thisinformationiscombinedbyregional triggersforthepurposeofquicklyidentifyinghighenergyparticlesandjetsbycombining informationacrosssubsystemsintolevel1triggerobjects;theprocessisillustratedin Figure3-12. TheUniversityofFlorida,alongwithRiceUniversity,developed,produced,and maintainsthelevel1triggeringsystemfortheCSCs,calledtheCSCtracknder CSCTF.ServiceworkontheCSCTFwasmyprimaryfocusfortherst2years workingwiththeUFgroup.ThetasksIundertookinvolvedmonitoringthehealthof 59

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Figure3-11.Inclusiveppproductioncrosssection. theCSCTFsystembyperformingMonteCarlostudiesontheofineemulator,and developingdataqualitymonitoringDQMtoolstoassestheonlinehealthofthesystem, includingthecomparisonoftheoutputofthehardwaretotheofineemulator.The detailsofwhichcanbefoundinAppendixA.1.Thepurposeofthissystemistoidentify muonsandquicklyassigna p T valuefortheglobalmuontrigger.Analogoussystems existfortheothermuonsystemsaswellastheECALandHCAL,andthedetected signatureofamuon,electron,photon,jets,ormissingenergyarecalledlevel1trigger objects.Oncelevel1triggerobjectsareformed,informationfromtheindividualmuon 60

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Figure3-12.IllustrationoftheLevel1CMStriggersystem. andcalorimetersystemsarecombinetoglobalmuonandcalorimetertriggers.Itisthe joboftheglobaltriggerstodecideifthesystemshouldbereadout. IfaL1acceptisissued,allofthedetectorchannelsarereadouttotheHighLevel TriggerHLT.ThejoboftheHLTTriggeristoanalyzeeventsandfurtherreducethe ratetonogreaterthan O 2 Hz.TheaverageprocessingtimefortheHLTis50ms, signicantlylargerthanthe100kHzprovidedbytheLevel1Trigger.Todoso,theHLT usesafarmof 10 4 processorcoresworkinginparallel,andthesystemscombineto haveanaverage10 sdecisiontime.TheHLTusesthefullprecisionofthemuonand calorimetersystems,aswellaspreviouslyunusedinformationfromthetracker,allowing forhigherefciencyandbetterratereduction.TheHLTissoftwarebased,whichhas severaladvantages.First,byavoidingthecostassociatedwithcustomelectronics,it isrelativelyinexpensive.Itcarriestheadditionaladvantageofbeingrelativelyexible asthetransitionfromoneluminosityperiodtothenextrequiressimplythatanew triggertableisloaded.Atriggertableisaseriesofsignaturesthataresufcientlyrare 61

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tomeritthereadoutofalldetectorchannels.Thelaststrongadvantageofthesoftware basedHLTisthatitcanoperateonofineanalysisobjects,makingcontributionfromall collaboratorspossible. Inaddition,theLevel1TriggerandHLTmaylookforacombinationofobjects acrosssubsystemssothatlowerthresholdson E T and p T maybeemployed.An exampleofthisistheuseofadoublemuontrigger.TherateatwhichCMSdetectshigh p T muonsincreaseswiththeLHCluminosity.Duetothelimitedbandwidthallocatedto muontriggers,thethresholdfortriggeringonsinglemuonsincreasedwiththeluminosity seeSection5.5.Whiletheluminositystayedsufcientlylowthatthethresholdwas stilladequatefortheuseoflower p T muons,atthedesignluminosityoftheLHCthe singlemuontriggerratewillbehighenoughsuchthattriggerscomingfroma 45 GeV muonthemomentumofamuonresultingfroma Z 0 with p T =0willbeprescaled 1 Thefrequencyofmultiplemuonsofhigh p T isconsiderablylower,however.Byrequiring thedetectionofmultiplemuons,calledadoublemuontrigger,theHLTcanlowerthe p T thresholdonbothmuons 2 .Whilenotemployedinthecontextofthesestudies,the increaseinLHCluminositywillmakemultipleobjecttriggersincreasinglyimportant. 1 Whenatriggerbecomesprescaled,thesystemisonlyreadoutonceforasetfrequencyoftheoccurrenceofaparticulartrigger.Thiswayoftriggeringisnotrecommendedforphysicsanalysis. 2 Anexamplefromthe2011datatakingperiodarehavingconcurrentunprescaled triggerthresholdsof30 GeV = c forsinglemuoneventsand17 GeV = c fordoublemuon events 62

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CHAPTER4 OVERVIEWOFSTUDIES Inthepreviouschapters,theconceptoftheStandardModelisintroduced,aswell asthemostrecentscienticinstrumentsusedtostudythismodel,theLHCandCMS. Insection1.5,wediscusstheaspectsofthestandardmodelthataretestedfromthe precisionstudyofthe Z 0 crosssectionasafunctionofit's p T d = dP T .Similarly,in section1.6,weintroduceextensionstothestandardmodelwhichcanbeobserved whenlookingforexcessesofboosted Z 0 .Thefollowingsectionsoutline2related studies,thedifferentialcrosssectionmeasurementofthe Z 0 andasearchfornew physicslookingforanexcessofboosted Z 0 .Thelastsectionwillincludeanoverviewof theremainderofthisdocument. 4.1ExperimentalOverviewoftheSearchforNewPhysicsUsingBoosted Z 0 DecayingtoMuonPairs Usingthe Z 0 P T spectrumasacandlefornewphysics,weapplycutstomaximize signalefciencywhilereducingbackground.Examplesofbackgroundsthatcancreate dimuonpairsarethedecayof t t pairs, W recoilingoffofjets,andlighterhadronic decaysreferredtoastheQCDbackground.Figure4-1showstheinvariantmass spectrumfordimuonpairsbeforeandaftercutsareapplied.Asyoucanseenotingthe logscalefortheYaxis,QCDistheprimarybackgroundbeforeselectionrequirements aremade.MuonscomingfromQCDdecaysareassociatedwithashowerofmany particlesincontrasttothemuonscomingfromthedecayofthe Z 0 .Muonscoming fromsuchdecaysareeasilyidentiedbythepresenceofmanyhighenergyparticles nearbythemwithinthedetector.Anabsenceoflargeenergyofnearbyparticlesis referredtoasisolation,andisakeyvariableintheidenticationofmuonscomingfrom thedecayof Z 0 63

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Figure4-1.Thedimuoninvariantmassspectrumbeforeleftandafterrightselection requirementsaremade. Withthesearchforboosted Z 0 however,thebackgroundofstandardDrell-Yan 1 productionisirreducible.Oneisthereforleftwitha p T spectrumofthe Z 0 whichis acombinationofstandardDYproductionandpossiblecontributionsofanomalously producedhigh p T Z 0 .Therearetwomethodsfordistinguishingthesignicanceofany deviationthatwereconsidered. Therstmethodistoexaminethetailofthedistributioninwhatwillbereferredto asa'cutandcount'technique.Todoso,oneextrapolatesbasedoneitherMonteCarlo simulationsordatadriventechniques,thenumberof Z 0 producedoveragivenvalueof p T .UsingMonteCarlobasedpredictionsofsignalmodels,onecanalsopredictyields ofsignaleventsforthesamecuts.If S isthenumberofpredictedsignalevents,and B isthenumberofbackgroundevents,selectinga p T thresholdforaparticularmodelis simplytomaximizethesignicance, d ,asdenedbyequation4. 1 TheDrell-Yanprocessoccurswiththeannihilationofaquarkandananti-quark, resultingintoaneutralintermediarybosoneithera or Z 0 ,whichthendecaysintoa leptonandananti-leptonofthethesameavor. 64

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d = S p B Onemayalternativelyoptimizeathresholdforsettingupperlimitsonthecross sectionforaparticularprocess.Inthiscase,onemustuse L ,asdenedbyequation 4. d = S p S + B Oncewedetermineourthresholdvalues,wecalculate p ,theprobabilitytoobserver N orlesseventsasaratioofthesignalplusbackgroundoverthebackgroundonly predictions.Onethenusemontecarlopredictionstogiveasignalcrosssectionwhich correspondstothep=0.95probabilityforthenewphysicsproduction.Analternative method,istoimplementashapettest.Inprincipal,thistestcanbeverysimilarin thatyoutaketheratioofprobabilitiesofasignalplusbackgroundtoabackgroundonly model.Thewaytheseanalysisdifferlargelyisthatthecutandcountmethodignoresthe portionofthe p T spectrumwhichispopulatedbytheDrell-Yanbackground.Intheend, theanalysisoptsforthecutandcountmethod,andwillbedicussedingreaterdetailin section8. 4.2ExperimentalOverviewof d = dP T for Z 0 DecayingtoMuons Tomeasurethe d = dP T Z 0 + )]TJ/F22 11.9552 Tf 7.084 -4.338 Td [( ,onestartswiththecutsonbothmuons andthedimuonpairtoisolatesignalfrombackground.Fromthere,theentiretyofthis studyisencapsulatedinequation4.Forthisstudy,itismostimportanttoreporta correctshaperatherthantheactualdifferentialcrosssectionhencetheterm 1 onthe lefthandside.Indoingso,systematicsstemmingfromtheuncertaintyininstantaneous luminositywillcancel. 65

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1 d dP i T Z = + )]TJ/F22 11.9552 Tf 7.085 -4.936 Td [(= A N Tot )]TJ/F39 11.9552 Tf 11.955 0 Td [(B Tot 1 i k R )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 ik N k )]TJ/F39 11.9552 Tf 11.955 0 Td [(B k A k Theavailable Z 0 p T spectrumisdividedintobinsasdictatedbystatisticsand detectorresolution.Startingfromtherighthandsideofeq.4,inthenumeratorwe havetheterm N k )]TJ/F39 11.9552 Tf 12.887 0 Td [(B k .Theterm N k ,isthetotalnumberofobservedeventswhich passselection.Weestimatebackgroundlevels B k basedonbothMonteCarlostudies anddatadriventechniques,andremovebackgroundbyabinbybinscalingthebin numberisdenotedbythesubscript k .Inthedenominator,weseetheterm A k Thistermrepresentthecorrectionsappliedtoaccountfordetectoracceptance A and efciency .Efciencycanbefurtherbrokendownintotrigger,reconstruction,and selectionefciencies.Againthesecorrectionsaredoneonabinbybinbasis.Thenext termis R )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ik ,andrepresentsunfoldingsmearingduetodetectorresolutionandnalstate radiation.Thenextterm i ,isthebinwidthoftheparticularbin,sothemeasurementis occupancyperGeV.Lastly,wenormalizetothetotalnumberofevents,accountingfor theaverageacceptanceandefciency.Thenalresultispresentedasacomparison tothetheorypredictionbeforenalstateradiationpre-fsrspectrum.Byaccounting removingdetectoreffects,thespectrumprovidesausefultooltocomparebothto previousexperimentsandtheoreticaltunestotheunderlyingeventandpartondensity functions. 4.3OutlineofDocumentation Theremainderofthenotewillproceedasfollows.Chapter5discussesthespecics ofidentifyingacleandimuonsamplefromprimarily Z 0 decay,andtheestimationof theefciencyofsuchselections.Chapter6thencomparesthedistributionsseenin dataoverthepredictionsofMonteCarloMCsimulation.Chapter7discussesthe datadrivenmethodsofestimatingthebackgroundcontributionstothesamplewhich passeseventselection.Thesethreechaptersareallcommonstepsinboththesearch 66

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forphysicsbeyondthestandardmodel,andthemeasurementofthe Z 0 p T spectrum. Thecontentsofthesechaptersarecommontoboththesearchforphysicsbeyondthe standardmodelandthe Z 0 p T spectrummeasurement.Inchapter8,wediscussthe stepsspecictotheboosted Z 0 search.InChapter9,wediscussstepsspecictothe characterizationofthe Z 0 p T spectrum. Itisimportanttonotethatthestudieswhichcomprisethisnotewereacollaborative effort,andassuch,portionsofthestudieswereexecutedbymycollaborators.Iwould liketohighlighttheaspectsofthetwoanalysisuponwhichmyeffortwasprimarilyfocused.InSection1.6,severalmodelswhichextendthestandardmodelwerediscussed. Ispentagooddealoftimeinvestigatingthediscoverypotentialofthevariousmodels, includingcharacterizingtheresulting Z 0 p T spectrumandcomparingthediscovery potentialtostudiesinalternativechannels.Ispentagoodamountoftimeunderstanding ourselectionefciencies,andinparticulardevelopedtheisolationmodicationforthe boostedZsearchdiscussedinSection5.4.2.ThismodicationcamedirectlyfromMC basedefciencyestimations,namelytheN-1methoddescribedinSection5.6.InChapter7,themethodsofbackgroundestimationarediscussed.Forthe2010versionsof theseanalysis,themethodswereappliedbyothers,however,inthefollowupsearches of2011Iimplementedthesamemethods,obtainingcompatibleresults.InChapter 8,themethodsoflimitsettingonexcitedquarksarediscussed.WhileItooktimeto understandthestatisticalmodelsused,Ididnotimplementthelimitsettingtoolsonthe 2010analysis.Forthe2011followup,Iprovidedthelimitsusingthe CL S techniquenot discussedinthisnote,butasimilartothemethodsdescribedinChapter8.Chapter9 istheworkwherealargepartofmyeffortwent.Theprocessofunfolding,includingthe datadrivencharacterizationofthemuon p T resolution,creatingcodestoinvertmatrices, anddoinganumberoftestsofthemethodweperformedexclusivelybyme.Additionally,allofthesystematicerrorsbasedonthismethodweremywork.Wepresentthe resultsofthecombinationofthedimuonanddielectronchannelattheendofChapter9, 67

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andagoodamountoftimewentintohelpingourcollaboratorsintheelectronchannel understandingthistechnique.IalsoincludemyworkontheCSCTFintheAppendix. 68

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CHAPTER5 EVENTSELECTION InthisSection,wereviewthemuonidenticationandtheeventselectioncriteriafor thesignatureofaZboson.WedonotobservetheZbosondirectly,butrather,select apairofmuonswithinvariantmassbetween60and120GeV.Thereareseveralother processeswhichcanproducethesamesignature;thusitbecomesnecessarytorene theeventselectiontodiscriminateagainstthedecayof t t pairs, W recoilingoffof jets,andthemoreprolicproductionofmuonsassociatedwiththeproductionoflighter quark-antiquarkpairproduction.Thelatterprocesshappenswithahugevarietyof processes,andthebackgroundassociatedwithitreferredtoastheQuantumChromo Dynamicbackground,or`QCD'forshort.Additionalbackgroundsuchas Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(and dibosonproductionalsocontribute,albeitatamuchsmallerrate. Thecontentsofthisthesisarelargelycenteredaround2studies:themeasurement ofthe Z 0 p T spectrum,andasearchfornewphysicslookingforresonancesinthe Z 0 p T spectrum.Forthetwostudiestheselectioncriteriaarelargelythesame,however, differencesdoexist.Inparticular,theisolationvariableusedisdifferent,andwillbe treatedseperatelyinSection5.4.Thedifferencesinthetwoselectionsarehighlighted inSection5.6.Severalplotsareshownformuonselectionandtriggerefciency. Theseguresaremadebasedontheselectionof Z 0 basedonthe p T spectrumshape measurement,unlessotherwisenoted,althoughthedifferencesinefcienciesbetween thetwoanalysisareverysmall.Additionally,itwillbehelpfultodeneshorthand notationtodesignateonestudyfromtheother,andwillusethehandles`measurement' and`search'assuch. 5.1MuonIdentication Therststepinidentifyingpairsofmuonsisidentifyinghighqualitysinglemuons. ThecompletesetofcriteriaarereportedinTable5.1. 69

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Table5-1.Muonidenticationcriteria. Cut Comment p T > 20 GeV/ c Selectprompthigh p T muons Muonreconstructedusingan Effectiveagainstdecay-inight insideoutandoutsidein punch-throughandaccidentalmatching extrapolation Numberoftrackerhits 10 Smallnumberofhitsgiveabad p T estimate;chosenvaluefromstudyin[54] Numberofpixelhits 1 Discardnon-promptmuons Atleast 2 chambersindifferent SimilarrequirementintheL1muon stationswithmatchingsegments triggerlogic Globalt 2 = NDF < 10 Requirereasonableglobaltquality Atleast 1 validmuonhit Makesurethatthetrackerandmuon associatedwiththeglobalmuon systemsinformationareconsistent j d xy j < 2 mm,where d xy isthe CheckconsistencywithIPhypothesis impactparameterw.r.t.ofinebeamspot andreducecosmicbackground Themotivationbehindthecutsaretohavewellmeasuredmuonswiththemost accuratepossible p T assignment.Additionally,wewanttodiscriminateagainstnonpromptmuons,ormuonswhichcomefromthedecayoflongerlivedparticlessuchasK orBmesons. 5.2MuonReconstruction CMSreconstructsmuonsusinganinnersilicontrackertracksmatchedtotracksin theoutermuonsystems.AnoteonmuonreconstructioninCMS[55]mostcompletely describesthissubject.Fromthesesystems,3classicationofmuonsarecreated:inner trackerextrapolatedtomuonhits,standaloneSTD,muonsystemonly,andglobal muonsGLB,combinedtrackerandmuonsystemfromoutside-inreconstruction.For theanalysiswerequirethatmuonsbebothglobalandtrackermuonsforthisanalysis. Thesemuonsfeatureaatandhighgreaterthan 95% muonreconstructionefciency formuonswith p T greaterthan10GeV/ c andashighas500GeV/ c Whilestandardreconstructionmethodsareeffectiveatassigning p T formuons ofuptoafewhundredGeV/ c ,itbecomeslesspreciseasthemuon p T reachesthe TeVscale.Tomosteffectivelycombinetrackerandmuonsysteminformation,several 70

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methodshavebeendeveloped.Thesemethodsaredescribedindetailinthe Z 'dimuon resonancesearch[56].Theyarethencombinedtoforma p T assignmentalgorithm referredtoasTune-PcolloquiallyreferredtoastheTeVmuoncocktail,orsimplythe cocktailreconstruction.Therelativeresolutionoftracker-only p T assignmentformuons ina p T rangefrom 200 )]TJ/F22 11.9552 Tf 12.365 0 Td [(2000 GeVisapproximately 7% ,andthemethodswhichform Tune-Phavearesolutionofaround 5% .Againof 2% issignicantgiventhescale, particularlywhenconsideringhowthemuonresolutioneffectsdimuoninvariantmass. Figure5-1displaystheRMSoftherelativeresidualforseveralreconstructionmethods studied.Itisclearthattrackeronlyreconstructionismuchbetterthantheglobalmuon reconstruction.Atlowmuon p T ,thereislittledifferencebetweenTune-Pandthetracker assignment,however,themethodsdivergeasthemuon p T approaches100GeV/ c Inthesearchforboosted Z 0 ,weareinterestedinhigh p T muonssignatures, weusetheTune-Preconstructionalgorithmforthemuontransversemomentum assignment.Itguaranteesrobustnessagainstttingfailuresanditindeedprovidesthe bestresolutionformuonathightransversemomentum p T > 200GeV/ c [57]. Figure5-1.Themuon p T resolutionforvariousreconstructiontechniques. 71

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5.3MuonIdenticationTagandProbeEfciency ThemuonidenticationIDefciencyismeasuredindataandcomparedtoMonte CarloMCpredictionsinordertounderstandifacorrectionisneeded.ThemuonID efciencyisdescribedbyequation5. ID = trk gbl j trk Y i i Here, trk isthetrackerTRKmuonefciency, gbl j trk istheglobalGLBmuon efciencygivenaTRKmuonwithitsselectioncutsexistsand i istheefciencyof eachoftheremainingselectioncriteriaappliedonTRKandGLBmuonsofthemuon identication. Themuonidefciencyisdeterminedusingthetag-and-probemethod[58]applied tomuonsfrom Z 0 decays.Forsuchstudies,theofciallysupportedpackageprovided byCMS[59]isused.Thetagmuonisobtainedbyapplyingallthekinematictight selectionsallthedetailsaregiveninSection5.6.Theprobemuondenitionvaries accordingtotheselectioncriterionunderinvestigation. 5.3.1TrackEfciency Theprobeisdenedasastandalonemuon,with 2 = NDF < 4 j j < 2.1 and p T > 7GeV/ c .Thetagandtheprobemuonsarerequiredtohaveoppositechargeandthe invariantmassofthestandalonedimuonsystemisrequiredtobe75GeV/ c 2 < M < 110GeV/ c 2 InFigure5-2thedataandMCcomparisonisshownforthetagmuontobereconstructedinthetrackerasafunctionofthemuonprobe p T and .Thecumulative efciencyisreportedinTable5-2.DataandMCreportcompatiblevaluesinsidethe statisticalerror. 72

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Figure5-2.Tagandprobeefciencyforamuontobereconstructedinthetrackerasa functionofthestandaloneprobemuon p T leftand right. 5.3.2GlobalMuonIdenticationEfciency Theprobeisdenedasatrackermuon,with j j < 2.1 and p T > 7GeV/ c .Thetag andtheprobemuonsarerequiredtohaveoppositechargeandtheinvariantmassofthe dimuonsystemisrequiredtobe75GeV/ c 2 < M < 110GeV/ c 2 InFigure5-3thedataandMCcomparisonisshownfortheGLBandallthekinematicselectioncriteria.ThecumulativeefciencyisreportedinTable5-2.DataandMC havevaluescompatibletoafewpercent. 5.4Isolation Isolationisakeyvariableinthereductionofbackgrounds.Isolationisameasurementoftheenergyofparticlesnearthemuoninquestion.The Z 0 decaystomuons suchthatthemuonsareisolated,whichcontraststheQCDbackgroundwheremuon productiontendstobeassociatedwithdecaysofstronglyinteractingparticles.As notedearlier,theisolationvariablesbetweenthe Z 0 p T measurementandthesearchfor boosted Z 0 aredifferent,andwillbetreatedseparately.Thetwoisolationvariableshave similarefciency,andthedivisioncomeslargelyfromthedesiretobecompliantwiththe standardselectiontechniquesofcomparablestudies. 73

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Figure5-3.Tagandprobeefciencyforglobalmuonidenticationandtopassallthe muonIDkinematicselectionasafunctionofoftheprobemuon p T leftand right. 5.4.1IsolationUsedinthe p T SpectrumMeasurement TheapproachtoisolationisidenticaltoReference[60].Bothmuonsarerequested topasstherelativecombinedisolationcut,denedin5. I rel comb = I HCAL + I TRK = p T < 0.15, Thedenitionofisolationvariablesforthesubsystemsare I HCAL = P E T HCAL and I TRK = P p T tracks Thesumsareperformedforobjectsfallingwithinacone R = p 2 + 2 < 0.3 aroundtheleptoncandidate.Theenergydepositsandthetrackassociatedtothe leptoncandidateareexcludedfromthesums. 5.4.1.1RelativeCombinedIsolationEfciency Theisolationefciencyisstudiedusingthetagandprobetechniqueandfound todependonthemuon p T .Thetagmuonhastheusualdenitiontopassallthetight kinematicselection.Theprobeisdenedasatrackermuon,with j j < 2.1 and p T > 7 GeV = c passingtheGLBandmuonidenticationselections.Thetagandtheprobe 74

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muonsarerequiredtohaveoppositechargeandtheinvariantmassofthedimuon systemisrequiredtobe75 < M < 110GeV/ c 2 InFigure5-4thedataandMCcomparisonisshownfortheisolationcut.The cumulativeefciencyisreportedinTable5-2.DataandMCreportvaluescompatible withinstatisticalerror. Figure5-4.Data/MCmuontagandprobeefciencyfortheisolationcutasafunctionof theprobemuon p T leftand right. Table5-2.CumulativeTagandProbeefciencyforthemuontobeatrackermuon,a globalmuonandpassingallthemuonidselectionsandtobeisolated isolationdenitioninEquation5. Variable Data MC isGbl+MuonId 0.9699 0.0015 0.9763 0.0004 isTracker 0.9983 0.0004 0.9952 0.0002 Isolation 0.9853 0.0012 0.9903 0.0003 5.4.2IsolationUsedintheSearchforNewPhysics Thesearchfornewphysicsusing Z 0 facesauniquesetofchallenges.Wewish touseasmuchofthedataavailable,andassuch,wechoosetoomittheuseofHCAL 75

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fromtheisolation. 1 Additionally,aswearelookingforthedecayproductsofanobject who'sboostislargewithrespecttoit'smass,theobjectcanbecloselyspacedin )]TJ/F25 11.9552 Tf 12.252 0 Td [( space.Inthisinstance,onemuonmayentertheisolationconeoftheother,requiringa correctiontotheconventionalisolationvariabletobemade.Weuseanabsolutetrack sum p T isolation,denedinEquation5. I trk = X R < 0.3 p i T )]TJ/F30 11.9552 Tf 11.956 28.095 Td [(8 > < > : P 2 T if R 1 2 < 0.3 andconventionalisolation > 0.9 P 2 T 0 otherwise Here p i T isthetransversemomentumofatrackinacone R < 0.3 andwith Z < 0.2 cmwithrespecttothemuontrack.Moreovertrackswithinaconeof R < 0.01 are excludedtoavoidincludingthemuontrackinthecounting. Thecorrectiontermisrelevantinthecaseofextremelyhighboost,thesecond muonfromthe Z 0 decaycanentertheisolationconeoftherstandtheconversewould inthisinstancebenecessarilytrue.InFigure5-5wecomparetheefciencycurves forcorrectedanduncorrectedisolation.Figure5-6showshowoftenthetwomuons comecloserthan dR = p 2 + 2 =0.3 asafunctionof p T ofthedimuonpair.Itis clearthatatathresholdof Z 0 p T 600GeV/ c intheefciencycurvethisbecomesa signicanteffect,andthecorrectionisjustied.InFigure5-7onecanseedistribution ofthemodiedisolationforseveralmodelsofthenewphysics,producingsuchboosted Z 0 s. 1 Foreveryrunperiod,dataiscertiedbyindividualsub-detectorsforerrorfreeoperationandreliabilityofdata.Duringtheinitialdatataking,someperiodsoccurredwhere individualsub-detectorshadhardwareerrors,whiletherestoftheCMSdetectorwas operatingerrorfree.Sincenootherpartofthemuon p T orpositionassignmentrelies ontheHCAL,itcanbedroppedwithoutanynegativeeffectsontheresolutionofthe muons. 76

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Figure5-5.Left:Theoverallselectionefciencywithuncorrectedisolation.Right:The overallselectionefciencywithcorrectedisolation. Figure5-6.Fractionofdimuoneventswithtwomuonsenteringthe0.3isolationconeof eachotherasafunctionofdimuon p T 77

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Figure5-7.Distributionofthecorrectedisolationvariableforseveralmodelsofthenew physics. 5.5TriggerEventSelection TheHighLevelTriggerHLTpathsusedtoselectdimuonschannelistheHLT MuX path,whereXisthelowestsinglemuontriggerthresholdwithoutprescaling.These triggersrequireatleastonemuoncandidatewith p T > X GeV/ c and j j < 2.5 .No selectioncriteriabasedonisolationisused. Duringthe2010collisiondatatakingperiod,theLHCcontinuouslyincreased theluminosity.Asaresult,severalHLTtriggersbecameprescaledovertheyear.For 78

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example,afterrun 147195 148058 HLT Mu9HLT Mu11startedbeingprescaled,thus weselecteventswithanincreasedthresholdforthesinglemuontriggerusedinthe analysis.InTable5-3weshowtherunrangesthethecorrespondingHLTpathsusedto selectdataforthatspecicrunrange. Table5-3.HLTpath,associatedrunrangeofuse,andintegratedluminosityforthat range. Time RunRange Trigger Integrated Efciency Period Threshold Luminosity GeV/ c pb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 1 132440 )]TJ/F22 11.9552 Tf 11.955 0 Td [(144114 9 3.18 0.880 0.008 2 144115 )]TJ/F22 11.9552 Tf 11.955 0 Td [(147195 9 5.06 0.914 0.005 3 147196 )]TJ/F22 11.9552 Tf 11.955 0 Td [(148058 11 9.47 0.922 0.004 4 148059 )]TJ/F22 11.9552 Tf 11.955 0 Td [(149442 15 18.44 0.924 0.003 Simulation 9 0.950 0.0008 5.5.1HighLevelTriggerTagandProbeEfciency AsusualtherststepisstudyingthetriggerefciencyandhowitcomparestoMC expectations. Wedeterminedthetriggerefciencyusingthetag-and-probemethod.Thetag muonisobtainedbyapplyingallthetightkinematicselectionswiththeadditional requestofthematchingtothetriggerobjectunderinvestigation.Theprobemuonis associatedifitpassesallthetightkinematiccriteria,butitisnotforcedtomatchthe triggerobjectatthisstage.Anadditionalcutonthedimuoninvariantmasstobe75 < M < 110GeV/ c 2 isapplied. TheMChasonlytheHLT Mu9simulationembedded,sofortheHLT Mu11and HLT Mu15 v1pathsweexplicitlyrequiretohavethe p T oftheonlinetriggerobjects abovethedesiredthreshold,butitdidnothaveanoticeableeffectontheMCestimations. Wesplitthedatasampleinto4runranges,accordingtothetechnicalstopsthat occurredinCMSeithersignicantchangesinefciencyinthe regionaround2.1 fromperiod1to2,orchangesinthetriggerduetoLuminosityincreasesfromrange 79

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2to3and3to4,seetable5-3:-144114HLTMu9,-147195 HLTMu9,-148058HLTMu11,-149442HLTMu15 v1.In Figures5-8and5-9thedataandMCcomparisonisshownforthethreedifferentpaths. Theefciencydropfor j j 2.1 iswellunderstood. 2 Inordertobeawayfromthe problematicregionwethereforerequiretheHLTmatchingonlyfor j j < 2.1 .Theoverall efcienciesintheregion j j < 2.1 bothondataandMCarereportedinTable5-3. Figure5-8.Tagandprobeefciencydistributionsasafunctionof respectivelyforthe9 GeV = c triggerthershold,fortherunrange[132440,144144]leftand [144115,147195]right. TheseHLTpathsareseededatLevel-1L1bythesameL1 SingleMu7.Thedata willbecorrectedbyatriggerefciencywhichwillresultfromtheweightedaverage basedontheluminosityofthethreeHLTthresholds.IntheselectioncriteriaSection5.6werequestoneofthetwoofinereconstructedmuonstomatchtheHLTmuon, 2 Thedropinefciencyistheresultofthestripstriple-gangingintheME11aendcapchambers.Theeffectismuonswhicharedetectedinthisregionareassigneda low`quality'avariabledescribinghowreliablethe p T assignmentis,anddonotpass requirementthatsinglemuonsfortheHLTtriggerbeofhighquality. 80

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Figure5-9.Tagandprobeefciencydistributionsasafunctionof respectivelyfor11 leftand15right GeV = c triggerpaths. thereforethetotalefciencyisgiveninequation5.Theaveragedimuontrigger efciencyondatais DATA HLT =0.993 0.005 .TheefciencyonMCis MC HLT =0.998 0.002 HLT + HLT )]TJ/F25 11.9552 Tf 11.955 0 Td [( HLT HLT =0.993 0.005. 5.5.2ScaleFactors DatafromthetagandprobeseemtoagreeratherwellwiththepureMCexpectations.Neverthelesstheagreementisnotperfect.Wethencomputeseveralscale factorswhichwillbeusedtocorrecttheefcienciesfromMCusedinthecalculationof thedifferentialcrosssection.InTable5-4wereportthescalefactorsforeachindividual efciency. Table5-4.Finalefciencyfactorsusedintheanalysis,obtainedusingthetagandprobe technique. Efciency Data/Simulation GLB + MuonId 0.991 0.001 Trk 1.0028 0.0004 Iso 0.998 0.001 HLT 0.996 0.005 81

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5.6 Z + )]TJ/F48 11.9552 Tf 10.408 -4.338 Td [(EventSelection Theselectionofthe Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(eventisachievedthroughaseriesofcutseither ontheindividualmuonsorthedimuonpair.Thisdocumentisbasedon2studies;while thestudiesbothaimtoexaminethe Z 0 p T spectrum,thedetailsoftheselectionare slightlydifferent.Section5.2describestheuseofTune-Pmuonreconstruction,which isemployedforthe p T assignmentforthesearchforanomalouslyproduced Z 0 ,but notforthecharacterizationofthe p T spectrum.Additionally,Section5.4highlightsthe variationbetweenthetwoisolationvariablesused.Forthedimuonpair,werequirethat bothmuonssatisfytheconditionsofbeing`loose'muons,aslistedinTable5-5. Table5-5.Looseselectionrequirementsformuonsinbothanalysis. CutforZ p T measurement Explanationofselection Searchfornewphysics differences p T > 20GeV/ c same j j < 2.4same Tracker&Globalreconstructionsame Numberoftrackerhit 11 Thenumberoftrackerhitswas increasedinthetotalcrosssection measurement[60].The Z 0 p T measurementincreasedto 11forconsistancyacrossthe2analysis. I rel comb < 0.15GeV I tkr < 10 SeeSection5.4 Inadditiontopassingthelooseselection,thereisatightmuoncriterionthat themuonhasan j j < 2.1andthatitsatisestherequirementsofTable5.1.The Z 0 p T measurementrequiresbothmuonstobetight,whilethesearchfornewphysics decayingto Z 0 requiresonly1tightmuonthisistobeconsistentwiththesearchfor Z 'decayingtodimuonpairs.Inbothcases,oneofthemuonspassingtightselection mustbematchedtotheHLTtrigger.Withthisitisintendedthatatleastoneofthe muonsmustmatchaLevel 3 triggerobjectringtheHLT MuXpathseeSection5.5. ThematchingissatisediftheL3objectisinsideaconeof R < 0.2 aroundthe ofinereconstructedmuonandtherelativetransversemomentumdifferencetobe 82

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p T = p T < 1 .Theadditionalcutplacedonthedimuonpairisthattheyhaveopposite charge,with60 < M < 120GeV/ c 2 Themethodtoreconstructmuontransversemomentumtrackerreconstruction algorithmforthemeasurementofthe Z 0 p T spectrum.Forthesearchfornewphysics, theTune-PalgorithmisusedseeSection5.2. 5.7MonteCarloAcceptanceandEfciency Thenalstepistodeterminetheefciencyofthechosenselectioncriteriaon the Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(MC.InFigure5-10weshowthedistributionfortheacceptance,the efciencyandtheproductofthetwousingtheDrell-YanMCdatasetusedinboth analysis. Theacceptanceisdenedastheprobabilityofdimuoncandidatestopass j j < 2.1 or2.1and2.4and p T > 20 GeV/ c and 60 < M < 120 GeV/ c 2 cutsongenerator levelleptons.TheMCshowsitincreasesastheZboson p T increases.Thisisexpected astheacceptanceisdrivenbythe selectionandthehigherthe Z 0 p T ,thehigherthe probabilitythatthetwomuonswillbeinthedetectorgeometricacceptance. Figure5-10.Acceptancered,efciencygreenandproductofthetwoasafunctionof thegeneratorlevelpost-FSRdimuoncandidatestransversemomentumfor themeasurementleftandsearchright 83

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InTable5-6weshowthevaluefortheacceptancetimesefciencyandforthe efciencyasafunctionof p T .TheerrorsarecomputedusingClopper-Pearson[61] abinomialcondenceintervalbasedonthecumulativeprobabilitiesofthebinomial distribution. Table5-6.Efciency, ,andacceptancetimesefciency,A ,asafunctionofthe Z 0 p T BinNumber Z 0 p T RangeGeV/ c Acc 1 0.0-2.5 0.9389 +0.0024 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0024 0.3512 +0.0029 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0029 2 2.5-5.0 0.9328 +0.0017 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0017 0.3471 +0.0019 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0019 3 5.0-7.5 0.9328 +0.0016 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0016 0.3632 +0.0019 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0019 4 7.5-10.0 0.9309 +0.0018 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0018 0.3723 +0.0022 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0022 5 10.0-12.5 0.9279 +0.0021 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0021 0.3768 +0.0025 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0025 6 12.5-15.0 0.9201 +0.0024 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0025 0.3806 +0.0028 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0028 7 15.0-17.5 0.9209 +0.0027 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0028 0.3829 +0.0032 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0031 8 17.5-20.0 0.9153 +0.0031 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0032 0.3868 +0.0035 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0035 9 20.0-30.0 0.9101 +0.0020 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0020 0.3848 +0.0022 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0022 10 30.0-40.0 0.9012 +0.0028 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0029 0.3974 +0.0031 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0031 11 40.0-50.0 0.9022 +0.0037 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0038 0.4070 +0.0041 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0041 12 50.0-70.0 0.9009 +0.0037 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0039 0.4189 +0.0042 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0042 13 70.0-90.0 0.9132 +0.0054 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0058 0.4280 +0.0066 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.0066 14 90.0-110.0 0.9035 +0.0085 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0092 0.437 +0.010 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.010 15 110.0-150.0 0.9199 +0.0086 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.0095 0.474 +0.012 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.012 16 150.0-190.0 0.935 +0.014 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.017 0.523 +0.022 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.022 17 190.0-250.0 0.868 +0.026 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.031 0.553 +0.032 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.032 18 250.0-600.0 0.904 +0.035 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.048 0.695 +0.050 )]TJ/F23 7.9701 Tf 6.586 0 Td [(0.054 Anotherwaytoinvestigatetheselectioncriteriaistoquantifytheefciencyofeach individualcutonthemodelswewanttoprobe.Themethodweemployisthesocalled N-1approach,asweapplyallthetightselectioncriteriaseeSection5.6,exceptthe oneweintendtostudy.Figures5-11,5-12,and5-13displaytheefciencyresulting fromtheN-1methodforboosted Z 0 comingfromboth q productionmechanisms Q.G.F.andC.I.andfromthe Z 0 channelfortheselectioncorrespondingtothesearch fornewphysics.Inallcases,requiringbothmuonstohavea p T greaterthan 20 GeV = c isconrmedtobethelargestsourceofinefciencyapproximately 7 )]TJ/F22 11.9552 Tf 12.154 0 Td [(16% .Afterthat, isolationisthenextsourceofinefciency,althoughitismuchsmaller. 84

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Figure5-11.Theselectionefciencyforboosted Z 0 from q q + Z 0 forthequark gluonfusionproductionmechanismfor q massesof 500,750,1000,1200 and 1500 GeV = c 85

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Figure5-12.Theselectionefciencyforboosted Z 0 from q q + Z 0 forthecontact interactionprodcutionmechanismfor q massesof 500,1000,1500, and 2000 GeV = c 2 86

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Figure5-13.Theselectionefciencyforboosted Z 0 from Z 0 H + Z 0 for Z 0 masses 500,1000,1500, and 1500 GeV = c 2 87

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CHAPTER6 DATATOSIMULATIONCOMPARISONS Asdiscussedinchapter2,theconditionsoftheLHCareconstantlyevolving,in particular,theinstantaneousluminosityprovidedbytheLHC.Inanefforttodeliverthe highestqualitydata,theconditionsunderwhichthedetectoroperatesiscontinually changing.Atperiodicintervals,thehardwareconditionsandthesoftwarewhich emulatesitarefrozensothataconsistentandstableframeworkexistsinwhichonecan performananalysis.TheDataandtheMCdatasetusedinthecurrentanalysishave beenprocessedusingversionCMSSW 3 8 6 patch1ofthereconstructionsoftware. 6.1DataSamples,andCMSSpecicDetailsinProcessing Datatakenoveraspecictimearegivena6digit`runnumber'sothatwhen referringtoaspecicperiodofdatataking,acommonconventionisused.Additionally, thereareseveralwaysofmeasuringhowthevariousdetectionelementsalign.The dataisreprocessedusingthemostuptodateknowledgeaboutthedetector,andthe reprocessingarenamedwiththedatathattheprocessofreprocessingthedatabegins on.Thecollisiondatasetsusedarefromrunnumbers136033-144114istheRun 2010ANovember4threprocessingofthedataandforrunnumbers145762-149442is theRun2010BNovember4threprocessing. Assessingthereliabilityofthedataforallsubsystemsistoolargeataskforasingle persontotakeon.Individualsubsystemsaretestedforeveryrun,andwithineach run,forthehealthofit'sdetectorelementsandelectronics.Thereportsarecompiled intoalistofrunswhicharecertiedasgoodforallsubsystemsandreportedintoan ofciallyprovidedlist,andweusethislisttoselectportionsofrunswhicharesuitable foranalysis.Additionally,weuseMonteCarlocongurationparametersforthedetector whicharethesameasthoseusedduringdatataking. 88

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6.2MonteCarloSamples Forthecomparisonbetweendataandsimulation,weusedseverallargeMC datasets.AllthesamplesarelistedinReference[62].Thesamplesofelectroweak processeswithZandWproductionareproducedwiththePOWHEGeventgenerator[6365]forboththegenerationandsimulationofnexttoleadingorderQCDinitial stateradiation.POWHEGisinterfacedwiththePythia[39]parton-showergenerator. QCDeventswithamuoninthenalstatearestudiedusingPythia.Eventsfrom t t + Jetsand W +Jetsarestudiedusingamatrix-elementbasedeventgeneratorcalled MADGRAPH[66].GeneratedeventsareprocessedthroughthefullGEANT4[67,68] detectorsimulation,triggeremulationandeventreconstructionchainoftheCMSexperiment.DetailsabouttheanalyzedsamplesarereportedinTable6.2. Table6-1.DetailsofMonteCarlosimulationsamples. Dataset Generator Production pb Kinematiccuts PDF Drell-Yan POWHEG 1614 M > 20 GeV = c CT10 t t +Jets MADGRAPH 156 nocuts CTEQ6L1 Inclusive QCD Pythia 84679.3 p T > 20 GeV = c CTEQ6L1 j j < 2.5 Z POWHEG 1614 M > 20 GeV = c 2 CT10 W +Jets MADGRAPH 24640 nocuts CTEQ6L1 t +Jets MADGRAPH 10.56 nocuts CTEQ6L1 WW MADGRAPH 27.79 nocuts CTEQ6L1 WZ MADGRAPH 10.4 nocuts CTEQ6L1 ZZ MADGRAPH 4.297 nocuts CTEQ6L1 6.3 Z + )]TJ/F48 11.9552 Tf 10.408 -4.338 Td [(SelectionVariablesDistributions Inthissectionwereportthedata-MCcomparisonforthevariablesusedinthe analysistoperformtheselection. FromFigure6-1toFigure6-4weshowthedistributionsofthereconstructionquality variablesforthemuonlegsofthe Z + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(candidatesusedinthesignalselection. Forthisstudythetightcutin j j < 2.1 isrelaxedupto j j < 2.4 .Dataareoverlaid overtheexpectedbackground,rescaledtotheluminosityofthedatasample.Allthe comparisonsshowagenerallygoodagreementbetweendataandMC,althoughthe 89

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distributionsseempulledlow.Thisisduetothesimulationssomewhatidealdetector description,whereinrealitythedetectormaycontaindeadchannelsorhaveelectronic malfunctions.Additionally,errorsintheestimationofintegratedluminosityandtoa lesserextenterrorsintheDrell-Yanproductioncrosssectioncancausediscrepancies intheintegralnumberofevents.Beneaththeoverlaiddistributionsarereportedthe differencesintheorytosimulationovertheerrorasreportedindata. Figure6-1.Left:Data-MCcomparisonforthenumberofvalidmuonhitsinthebarrel. Right:Data-MCcomparisonforthenumberofvalidmuonhitsintheendcap. 6.4Mass,TransverseMomentumandRapidityDistributions InFigure6-5weshowthe Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(massdistributionfromdataandMCfor eventspassingtheselectioncriteriadescribedinSection5.InFigure6-6wereportthe Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(transversemomentumdistributionfromdataandMC.FinallyinFigure6-7 theZrapiditydistributionispresented.TherawdataandMCeventscountingisreported inTable6.4.Thehighestdimuoncandidate p T is 618 GeV = c 6.5Summary Wecomparedthedatacorrespondingtoanintegratedluminosityof36pb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 withthe MCsimulation,properlyrescaledtotheluminosity.Thecomparisonshowsagenerally 90

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Figure6-2.Left:Data-MCcomparisonforthenumberofvalidpixelhits.Right:Data-MC comparisonforthenumberofvalidmuonsegments. Figure6-3.Left:Data-MCcomparisonforthenormalized 2 oftheglobalt.Right: Data-MCcomparisonfortheimpactparameter. 91

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Figure6-4.Data-MCcomparisonforthetrackisolation. Figure6-5.Data-MC Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(massspectrum.Left:logarithmicscaleandallMC contributionsdisplayed.Right:logarithmicscaleandallMCcontributions merged. 92

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Figure6-6.Data-MC Z + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(transversemomentumspectrum.Left:logarithmicscale andallMCcontributionsdisplayed.Right:logarithmicscaleandallMC contributionsmerged. Figure6-7.Data-MC Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(rapidityspectrum.Left:logarithmicscaleandallMC contributionsdisplayed.Right:logarithmicscaleandallMCcontributions merged. 93

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Table6-2.DataMCeventscounting.MCisrescaledaccordingtotheproduction toan integratedluminosityof36pb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 .Theerroriscomputedas p N NumberofEvents DATA 12370 111 Z = + )]TJETq1 0 0 1 294.935 644.583 cm[]0 d 0 J 0.398 w 0 0 m 0 14.446 l SQBT/F22 11.9552 Tf 316.189 648.917 Td [(11908 109 t t +Jets 18.4 4.3 W+Jets 0.47 0.69 QCD 4.5 2.1 Z = + )]TJETq1 0 0 1 294.935 585.206 cm[]0 d 0 J 0.398 w 0 0 m 0 14.446 l SQBT/F22 11.9552 Tf 322.117 589.539 Td [(15.5 3.9 t+W 1.2 1.1 WW 2.5 1.6 WZ 5.9 2.4 ZZ 4.7 2.2 goodagreementforthephysicsobservableofinterest, Z 0 mass, Z 0 transversemomentumand Z 0 rapidityaswellasforthevariablesusedtodenethesignalselection. Theobservedgoodagreementbetweenthedataandthepredictionconrmsthatthe StandardModelexpectationsandthedetectorperformancearewellunderstood.The highest p T eventfoundindatais 618 GeV = c Inthenextsectionwearegoingtoinvestigatebetterthedifferentsourcesof backgroundandwheneverpossibleestimatetheminadata-drivenfashion. 94

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CHAPTER7 METHODSOFBACKGROUNDESTIMATION Inthissectionwereviewthetwomostsignicantsourcesofbackground, t t and QCDdijetproduction,usingdata-driventechniquesfortheestimationoftheircontribution. t t canproducepromptisolatedmuonsthroughthedecayof t t W + bW )]TJ/F22 11.9552 Tf 10.501 -1.682 Td [( b + b )]TJ/F25 11.9552 Tf 10.408 -4.338 Td [( b .WhilemostmuonsassociatedwithQCDareassociatedwiththeproductionofjetsandwillthereforebeexcludedthroughisolationrequirements,thecross sectionforQCDissohighthattherareinstanceofisolateddimuonpairscanoccur. AdditionallyahugevarietyofQCDprocessesthatexist,makingitisimpossibletosufcientlysimulateallpossibilities;itisnecessarytoexaminethisbackgroundinadata drivenmanner.Alltheremainingsourcesofbackgroundaregoingtobeextractedusing theMCsamplesdiscussedinSection6. 7.1 t t BackgroundEstimationfrom e Events Asvisiblefromthe + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(transversemomentumdistributionfromFigure6-6,the t t eventsarethemostimportantsourceofbackgroundcontributingtothe Z 0 p T tail p T > 30 GeV = c .Wetthe t t shapewiththefunctioninEquation7,sothatwehave apredictionfortheshapeofthepotentialcontaminationfrom t t inoursample. F x = N e )]TJ/F40 7.9701 Tf 6.586 0 Td [(A x M )]TJ/F39 11.9552 Tf 11.955 0 Td [(x 2 ,where x = p T Thechosenfunctionalformseemstowelldescribethedimuonstransversemomentumspectrumabove30GeV/c,whilettingtotheentiredistributionbelow240GeV seemstoprovidedapoorerdescriptionbetween100-200 GeV = c .Thetoverlaidon theMCexpectationisshowninFigure7-1whiletheresultsfromthetarereportedin Table7.1. Themethodweusetoestimatethe t t backgroundisbasedupontheonedevelopedbythehighenergyelectronphysicsHEEPgroupandextensivelydiscussedin Reference[69].Theideaistoestimatethe t t contributionbycountingthenumberof 95

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Figure7-1. t t dimuon p T spectrumfromMCandit'staccordingtoEquation7.Left: thetisperformedovertherange0to240 GeV = c .Right:thetis performedovertherange30to240 GeV = c Table7-1.Fitresultsfromthetofthe t t shapeusingthefunctionfromEquation7. Parameter FitResult p T < 240 GeV = c FitResult p T 2 [30,240] GeV = c N 0.00026 0.00001 0.00049 0.00007 A 0.0498 0.0005 0.054 0.0001 M )]TJ/F22 11.9552 Tf 9.298 0 Td [(3.01 0.45 6.0 1.9 eventswherethetwo W bosonsdecayindifferentleptonavors, e and .Thekinematicsareidenticaltothe + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(decayandinprinciple,aftercorrectingfordifferencesin acceptanceandselectionsbetweenthemuonandtheelectron,thenumberofselected t t e shouldbetwicethenumberof t t + )]TJ/F20 11.9552 Tf 7.085 -4.338 Td [(,thusreducingtheuncertaintyon the t t backgroundestimate,describedinEquation7. N rec + )]TJ/F22 11.9552 Tf 10.073 0.795 Td [(= 1 2 A + )]TJETq1 0 0 1 282.851 204.018 cm[]0 d 0 J 0.478 w 0 0 m 44.005 0 l SQBT/F39 11.9552 Tf 282.851 192.828 Td [(A e C N rec e InEquation7, A istheacceptancetimetheselectionefcienciesforthe and e channels, C = 1 1+ R isacorrectionfactorand R isthefractionalcontaminationof the e 96

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The e eventselectionisperformedwithatightselectioncriteriaformuons describedinSection5,with j j < 2.1 andelectronscomingfromHEEPselection describedinReferences[70,71]. InFigure7-2weshowtheinvariantmassandtransversemomentumdistributions fortheoppositesignelectronandmuoncombinationsinthecollisionseventsfor 60 GeV = c 2 < M e < 120 GeV = c 2 .ThedataandMChaveagoodagreement,butwe arestilldominatedbythestatisticalerror. Figure7-2.Left:Data-MC e oppositesignsmassspectrum.Right:Data-MC e oppositesigns p T spectrumfor 60 GeV = c 2 < M e < 120 GeV = c 2 Withthecurrentamountofdata,however,itissufcienttousejusttheratio N rec = N rec e from t t simulationasthetotalcorrectionfactor,withoutworryingabout thedifferentcontaminationratesorratiosofacceptancestimesefcienciesforthevarioussmallercontributionstothe e spectrum.Thisfactorisindeedfoundtobeafunction oftransversemomentum,butfor p T thresholdsof30,50,and70 GeV = c itisroughly constantat0.63. Asmoredatacomesinandthestatisticalerrorstartstobesmallerthanthe systematicerrorincurredfromusingjustthe t t correctionfactor,wewillbegintoinclude theeffectofthedifferentcontaminationandacceptancetimesefciencyratios.Infact, 97

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asvisibleinFigure7-3,abovea p T thresholdofaround30 GeV = c andextendingto around200 GeV = c ,themostrelevantnonDrell-Yanbackgroundcontributionseemsto bethe t t .TheexpectedMCcontributionsfromsimplerawcountingofdimuonevents arereportedinTable7-2andareabout14.7,10.3,and6.2eventsforthe p T thresholds of30,50,and70 GeV = c .Thenumberofcollisioneventssurvivingtheselectioncriteria for e )]TJ/F25 11.9552 Tf 13.029 0 Td [( eventsare29,16,and7eventsrespectively.InFigure7-4wereportthe data/MCcomparisonforthe p T ofthe e distributionfor p e T > 30 GeV = c .Asweassume C =1 andusingtheratioof0.63.62,0.63,theexpectednumberofbackground eventsis 18.1.9,4.4;thisresultiscompatiblewiththepureMCexpectation.Asthe amountofstatisticsfromthe t t MCismuchhigherthanwhatthedatacanprovide,we willusetheeventsfromMCforthenalbackgroundsubtraction. Figure7-3.Data-MC Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(transversemomentumspectrumfor 60 < M < 120 and p T > 30 GeV = c 7.2QuantumChromoDynamicQCDBackgroundEstimationfromData Anadditionalbackgroundwhichisimportanttomeasureindataisthatcoming fromQCD.Thepoorestimationofsuchabackgroundcouldleadtolesseffectivesignal identication,orinthecasewherenosignalisseen,constraintheeffectivenessoflimit setting.Ontheotherhand,thegenerationofsuchabackgroundiscomputationally 98

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Table7-2.Data-MCeventscountingfor 60 < M < 120 and p T > 30 GeV = c .MCis rescaledaccordingtotheproduction toanintegratedluminosityof36pb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 NumberofEvents DATA 2027 45 Z + )]TJETq1 0 0 1 286.281 644.583 cm[]0 d 0 J 0.398 w 0 0 m 0 14.446 l SQBT/F22 11.9552 Tf 313.812 648.917 Td [(1959 44 t t +Jets 14.7 3.8 W+Jets 0.23 0.48 QCD 0.22 0.47 Z + )]TJETq1 0 0 1 286.281 585.206 cm[]0 d 0 J 0.398 w 0 0 m 0 14.446 l SQBT/F22 11.9552 Tf 316.602 589.539 Td [(1.7 1.3 Figure7-4.Data-MC e transversemomentumspectrumfor 60 GeV = c 2 < M e < 120 GeV = c 2 and p e T > 30 GeV = c expensiveandhardtoreproduceallitsfeaturesaccurately.Thereforeweattemptto estimateitscontributiontothetotalbackgroundinadata-drivenfashion. ThemethodforestimatingtheQCDbackgroundinthe Z 0 p T spectrumemploysthe re-weightingoftheanti-isolateddi-muonspectrumandisoutlinedinReference[56].The methodaimstodiscovertheprobabilityofamuoncomingfromQCDtopassisolation requirements.Tostart,oneusesasampleofexclusivesinglemuonevents,astheyare expectedtobepopulatedlargelythroughQCD,althoughsignicantcontaminationwill exist.Weusethissampletocreateaprobabilitymappingasafunctionofmuon and p T thatamuonpassesisolationrequirements. 99

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Table7-3.ExpectednumberofdimuonscandidatesfromtheQCDdatadriven estimationforseveral p T thresholds. predmethod all p T p T > 70 GeV = c p T > 200 GeV = c data-drivenos 0.91 0.047 0.00 0.000 0.00 0.000 trueMCos 0.93 0.149 0.00 0.000 0.00 0.000 data-drivenss 0.41 0.038 0.00 0.000 0.00 0.000 MCss 0.67 0.169 0.00 0.000 0.00 0.000 Onceonehasadata-drivenpdffortheprobabilityofamuontobeisolated.One thenmustaccountfortheprobabilityagain,asafunctionof & p T ofamuontocome fromQCD.Startingfromasampleofanti-isolatedmuons N a ,onemaypredictthenumberofcorrelatingisolatedmuonsamplefromQCD N Iso QCD accordingtoEquation7. Theprogresstionfromthersttosecondlineowsnaturallybymultiplyingbyafactorof 1 N Tot ,thetotalnumberofsinglemuon. N Iso QCD = P Iso QCD j p T N Iso N a N a = P iso j p T P iso j p T P Iso QCD j p T N a = p T N a Theresultisaformulationoftheweightofasinglenon-isolatedmuontocorrelateto anisolatedQCDmuon.Onemayapplythisweighttodimuoneventssimplybynding theproductofthetwoterms.Theterm P Iso QCD j p T isderivedusingMonteCarlo toestimatethecontaminationofthesinglemuon p T spectrumfrom W +Jets, t t ,and Z 0 + )]TJ/F20 11.9552 Tf 7.085 -4.339 Td [(. Thenextstepistotesttheshapethatispredictedbyapplyingthisscalefactor tothesamesigndimuonspectrum.InFigure7-5weshowtheclosuretestwherewe comparethetrueisolateddi-muonMCwiththepredictedre-weighted Z 0 p T usingall backgroundsofMC.TheestimatednumberofeventsaregiveninTable7-3. 100

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Figure7-5.ClosuretestusingallMCsamplestopredicttheQCDbackgroundfor same-signandopposite-signdi-muons. Figure7-6.Data-DrivenQCDbackgroundpredictionandshapefromdata. SeeingthattheclosuretestinMCgivesgoodagreementwithlimitedMCstats andimprovesstatisticsonthetails,wemovetoapplyingthisestimateonthedatain Figure7-6withtheexpectedeventestimatesinTable7-4.Theonlynumberwehave tousefromMConthedataistheestimatedcontaminationofotherbackgroundsinthe QCD. 101

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Table7-4.Summaryofdata-drivenandMCestimatesofQCDbackground. predmethod all Z 0 p T Z 0 p T > 70 GeV = c Zp T > 200 GeV c data-drivenos 45.98 3.048 0.27 0.085 0.00 0.000 MCos 39.86 6.408 0.00 0.000 0.00 0.000 data-drivenss 24.62 2.297 0.07 0.039 0.00 0.000 MCss 28.91 7.263 0.00 0.000 0.00 0.000 Table7-5.Summaryofdata-drivenestimatesofQCDbackgroundforthe Z 0 p T binning denedinSection9.1. BinNumber BinRange GeV = c NumberofQCDevents/binwidth 1 0.0-2.5 0.350 0.101 2 2.5-5.0 0.515 0.112 3 5.0-7.5 0.457 0.108 4 7.5-10.0 0.471 0.105 5 10.0-12.5 0.467 0.100 6 12.5-15.0 0.491 0.096 7 15.0-17.5 0.302 0.075 8 17.5-20.0 0.451 0.097 9 20.0-30.0 0.612 0.103 10 30.0-40.0 0.220 0.063 11 40.0-50.0 0.131 0.049 12 50.0-70.0 0.075 0.030 13 70.0-90.0 0.041 0.022 14 90.0-110.0 0.021 0.021 15 110.0-150.0 0.000 0.000 16 150.0-190.0 0.000 0.000 17 190.0-250.0 0.000 0.000 18 250.0-600.0 0.000 0.000 InTable7-5wereportthedata-drivenestimationfortheQCDbackgroundforthe Z 0 p T binningdenedinSection9.1. 7.3DrellYan Whensearchingfornewphysicsdecayingtoboosted Z 0 ,thedominantbackground contributiontothe Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(massandtransversemomentumtailsistheDrell-Yan continuum.Toestimatethisbackground,weassumethespectrumfallssmoothlyin p T .Wethereforetthespectrumwithacontinuousfunctionoutsideoftheregionof interestandextrapolatetotheareawestudy.Particularattentionwillhavetobegiven 102

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tothecorrectunderstandingoftheshapeandeventsizeandapropersystematicerror evaluationwillhavetobetakenintoaccount. WettheDrell-Yanshapewiththefollowingfunctionalform: F x = A e )]TJ/F40 7.9701 Tf 6.587 0 Td [(B p x ,where x = p T ThetoverlaidontheMCexpectationisshowninFigure7-7.Equation7seems towelldescribetheDrell-YanfunctionalformfromthePOWHEGMCforatransverse momentumspectrumabove 50 GeV = c .TheresultsfromthetarereportedinTable7-6. Figure7-7.Drell-Yandi-muonsMCtransversemomentumspectrumandrelativet accordingtoEquation7. Table7-6.FitresultsfromthetoftheDrell-Yanshapeusingthefunction F x = A e )]TJ/F40 7.9701 Tf 6.587 0 Td [(B p x Parameter FitResult A 2.17 0.12 B 0.715 0.006 Inordertostudythestabilityofthechosentfunction,wesplittheDrell-YanMC sampleinthreeequallysizedsub-datasetsandperformatoneachindividualone. Thettedparametersarecompatibleinsidetheirstatisticalerror.Thetfunctions 103

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overlayedtothedataarereportedinFigure7-8andthettedparametersarecompared inTable7-7. Figure7-8.Drell-Yandi-muonsMCtransversemomentumspectrumandrelativet accordingtoEquation7.Theentiredatasethasbeendividedinthree equallysizedsub-dataset,eachttedseparately. Table7-7.FitresultsfromthetoftheDrell-Yanshapeusingthefunction F x = A e )]TJ/F40 7.9701 Tf 6.587 0 Td [(B p x Parameter 1 st sub-dataset 2 nd sub-dataset 3 rd sub-dataset A 2.44 0.23 2.18 0.21 2.24 0.20 B 0.726 0.011 0.713 0.011 0.717 0.010 104

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7.4Summary Westudiedinmoredetailthetwomostsignicantsourcesofbackgroundtothe DrellYanspectrum: t t andQCD.Theircontributionshavebeenestimatedwithdatadrivenmethods.TheremainingsourcesofbackgroundwillbeextractedbytheMC samples.Concerningthe t t ,aftercheckingcompatibilitybetweendataandMC,we nallydecidedtostillusethehigherMCsampleforthenalestimation.AlltheMC estimationsarerescaledtorecordedluminosityof36pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 .TheQCDrepresents theonlyexception.SinceitisadifcultbackgroundtoevaluateusingpureMC,its estimationisobtainedinadata-drivenfashion. Additionally,weconsidertheDrellYanspectrumitselfasthemostsignicant backgroundwhenconsideringsourcesofnewphysics,suchasthedecayofexcited quarks.Wedescribethespectrumasafunctionof p T usingequation7,Thetis thenttedforstabilitybynotingthevariationofthefunctionparameterswhentherange ofthetisaltered.Ultimately,thesevariationswillenterintothesystematicerrorofthe limitsetting. 105

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CHAPTER8 SENSITIVITYTONEWPHYSICS Fromtheanalysisofthedataweobservegoodagreementbetweenthedataand thepredictionfromtheStandardModel.AsnoclearevidenceofphysicsbeyondtheSM wasfound,wecalculatetheupperlimitonthecrosssectiontimesbranchingfractionof thebenchmarkprocessesofnewphysics.Themodelwechoosetofocusonisexcited quarks.AsreportedinSection1.6.1,thismodelpotentiallyyieldshigh Z 0 production rates.Itallowsonetosetmeaningfulconstraintsontheparameterspaceofthemodel withtheavailableintegratedluminosity.Whileothermodelswerediscussed,theydonot predictsufcientyieldstosetmeaningfullimitsonthisdataset.Westartbydeningthe functionaltemplatesofourbenchmarkmodelsandcalculateupperlimitsontheircross sectionusingasimplecountingexperimentandusingashapediscriminationtechnique asawayofveryifyingourresults. Asanaside,itisimpossibletocontinuewithoutintroducingthetwoprevailing schoolsofthoughtonstatisticaltreatmentofcondenceintervals,Bayesianandfrequentist.TheiruseinhighenergyphysicsareoutlinedthoroughlybythePDGstatistics guidelines[72].Bothtechniqueshaveuniquestrengthsandweaknesses,however,in manyinstancesgivesimilarresults.Theinterpretationofafrequentistprobabilityisthe frequencyoftheoutcomeofarepeatableexperiment.Frequentistcondenceintervals areconstructedtocoverthetruevalueoftheparameterwithaspecicprobability.The Bayesianprobabilityisinterpretedasadegreeofbelief,sometimescalledthesubjective probability.Bayesianintervalsrequireapriorp.d.f.asinputparameterstotheircalculations,andinthiswayyouinsertpriorbeliefabouttheoutcomeintotheresultoftencited asthemainstrengthandweaknessofBayesianstatistics. Themethodoflimitsettingusingacountingexperimentiswellsuitedforsearching forresonancesinthetailsofdistributions.Thecondencelimitssetinthiswayare consistentwiththeCousins-Highlandmethod[73].Inthismethod,thecentralvalues 106

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forthelimitsarefrequentistinterpretations,whiletheweightedvariationofthenuisance parametersmaketheinterpretationofthecondenceintervalBaysian.Inthismethod,a p T thresholdforthe Z 0 issetwhichmaximizessignicancediscussedinSection8.3. Onceathresholdisset,theratioofPoissonprobabilitiesistakenforthesignalplus backgroundoverthesignalmodel,asdescribedinEquation8. = P n k =0 P k ; + b P n k =0 P k ; b where P i ; j = j i e )]TJ/F40 7.9701 Tf 6.587 0 Td [(j i InEquation8, n isthenumberofobservedeventsabovethethreshold, is thenumberofeventspredictedbytheory,and b isthenumberofeventspredictedby background. isthecondencelimit,andhenceavalueforavalueof thatgivesa valueof0.95for ThesecondmethodusedforlimitsettingisreferredtoastheFeldman-Cousins F.C.technique[74].Incontrasttothecutandcountlimit,thecondenceintervals obtainedinthistechniqueareofapurefrequentistinterpretation.Additionallytheratio usedinthistechniqueareoftheLikelyhoodofshapets,andbecauseofthisthetechniqueissensitivetosignalinareasofgreaterbackgroundduetoshapedescrimination. ThetsobtainedinSection8.1akeyinputtothelimitsettingproceedure.Thismethod usestheratioofLikelihoods R ,asdenedinEquation8,fortheshapeobservedin datatobeofthetestedhypothesismodel,overthemodelofbesttforeachvariationof thenumberofperbinobservedevents.ThecentralvalueforF.C.limitsisobtainedby ndingthemaximumvalueof R R = L n j L n j best 107

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InEquation8 L n j isthelikelihoodofthesignalplusbackgroundshape giventheobserveddataandthepredictedvaluefor presumablythisisthecross section,takenfrompythiacalculations. L n j best isthevaluewhichgivesthemaximal likelihoodfortheshapecomparisonbetweendataandthesignalplusbackground model.CondenceintervalsareproducedbyrankingvaluesofRforvariousvaluesof n theperbinyieldsofdata,andadding L n j untilthedesiredintervalisachieved. Theuseofcomplimentarytechniquesisgoodbecausetheinsensitivityofone techniquewillbeexposedbytheother,althoughtheresultsconvergeintheinstance oflowbackgroundexpectation,andadditionallyshieldstheanalysisfromanyofthe shortcomingsofeitherstatisticalschoolofthought.Whileitisthoughtthatforthe purposeofthisanalysis,theresultsshouldagreewell,itispossiblethatdifferencesmay ariseduetothefactthattheF.C.canmakeshapediscriminationsthatthecutandcount methodlacks. 8.1ShapeoftheTransverseMomentumforthe q Models Therststepforexaminingnewphysicspotentialischaracterizingtheshapeof the Z 0 p T spectrum.Figure8-1showsthedistributionofthetransversemomentum ofthe Z 0 bosonforthreescenariosofthe q mass:0.5,1.0,and1.5 TeV = c 2 .The fullchainofthedetectorsimulationandanalysisselectionwasapplied.Couplingsin the q modeldonotchangethedistributionofthetransversemomentumofthe Z 0 bosonfor q createdthroughgaugeproduction,butinsteadaffecttheproductionrate. Therefore,allofthe q couplingsaretakenequal: f = f 0 = f s =1 .P YTHIA produces q viagaugeproduction,soit'snearlyatrestinthetransverseplanewithalloftheinitial momentuminthedirectionofbeam.Contactinteractionproductionalwaysresultsina pairofobjects,aquarkanda q .Althoughthesystemofobjectsisnearlyatrestinthe transverseplane,the q itselfmaybesomewhatboostedinthissystem.Thataccounts forthedifferenceinshapeofthe Z 0 p T inthegaugeandcontactinteractionproductions, depictedinFigure8-1. 108

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Figure8-1.Distributionofthetransversemomentumofthe Z 0 bosoninthe q decays. Gaugeproductionleftandcontactinteractionrightaredonefor M ==0.5,1.0, and 1.5 TeV = c 2 Thefullwidthofthe q resonancestronglydependsonthe m = ratioseetheright panelofFigure8-2.At m = =1.2 the q widthmayaddsmearingtothe Z 0 transverse momentumspectrumupto20%ofthemass,shownintherightpanelFigure8-1. Unlessotherwisestated,fortherestofthisstudyweassume m = Distributionsofthe Z 0 transversemomentumfor3 Z 0 models Z 0 massof0.5,1.0, and1.5 TeV = c 2 isshowninFigure8-3.Thefullchainofthedetectorsimulationand analysisselectionwasapplied. WetallofthepotentialsignaldistributionsusingamodiedCauchyfunction Equation8. f q T = A B + exp C q T )]TJ/F39 11.9552 Tf 11.956 0 Td [(D + E q T )]TJ/F39 11.9552 Tf 11.955 0 Td [(D 2 TheresultingfunctionaltemplatesPDFsareusedforthelimitsetting,whichwe discussinthefollowingsections.ThetparameterscanbefoundinTables8-1,8-2, and8-3. 8.2SelectionEfciency Theselectioncriteriaweapplyreducethenumberofpotentialsignaleventsthat wecouldobserveinthedata.Thereforeitisimportantweestimatethisefciencyby usingdetectorsimulationfortheseveraldifferentsamplesofthe q .Westudythe 109

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Figure8-2.Fulldecaywidthinunitsofmassofthe q asafunctionofthe m = ratio. Table8-1.FitcoefcientsfortheGaugeInteraction q templatesforseveral q masses. Model Massof q TeV = c 2 0.5 1.0 1.5 2 = ndf 109.3/35 133.7/52 168.2/76 A 10.9 2.6 878.9 570.1 1819 1144 B -0.10 0.03 2.7 2.2 12.9 8.2 C 0.02 0.001 .2 0.2 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(2 .5 0.2 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 D 366.4 0.9 459 12.5 639.1 10.6 E .1 1.0 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(6 .6 1.9 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(4 .2 2.8 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(4 acceptancetimestheefciencyfordifferentmodels,whicharechosentocoverawide rangeofpossible q scenarios.Wevarythe M q aswellasgenerateeventswithcontact interactionorquarkgluonfusionandcomparetheacceptanceandefciencywith respecttotheStandardModel Z 0 bosonproduction. 110

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Figure8-3.Distributionofthetransversemomentumofthe Z 0 bosoninthedecaysof Z 0 withmassof 0.5,1.0, and 1.5 TeV = c 2 Table8-2.FitcoefcientsfortheContactInteraction q templatesforseveral q masses. Model Massof q TeV = c 2 0.5 1.0 1.5 2 = ndf 218.8/76 225.7/87 176.8/92 A .44 0.0 10 5 .7 1.3 10 6 .78 1.6 10 6 B .35 0.0 10 3 .4 1.1 10 4 .81 1.6 10 5 C 8.8 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3 2.47 -3.4 0.2 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 -2.5 0.5 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 D 234.9 0. 401.7 4.7 559. 5.7 E .8 0.09 10 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2 0.48 0.38 0.21 0.42 Table8-3.Fitcoefcientsforthe Z 0 templatesforseveral Z 0 masses. Model Massof Z 0 TeV = c 2 0.5 1.0 1.5 2 = ndf 31.2/29 77.86/70 78.51/94 A 296.4 423.0 611.2 403.6 567.3 686.3 B 2.634 4.683 3.666 2.917 10.93 14.32 C .652 1.443 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(2 .031 0.345 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(2 .028 0.391 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(2 D 220. 9.5 468.1 8.1 687.8 17.7 E .2 3.5 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(3 .0 5.1 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(4 .3 7.0 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(4 Figures8-4and8-5showtheresultingacceptancetimesefciencyasafunction ofthe Z 0 transversemomentum,respectivelyforcontactinteractionandquark-gluonfusion.ThedistributionsarecomparedtotheStandardModelDrell-YanMC. 111

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InTable8-4,8-5,and8.2thevaluesfortheacceptanceandefciencyforthe different p T cutsarereported. Table8-4.Generatorefciencyofthe p T cut. p T cut Efciencyforcontact q ,m TeV = c 2 Efciencyforgauge q ,m TeV = c 2 GeV = c 2 m=0.5 m=1.0 m=1.5 m=2.0 m=0.5 m=1.0 m=1.5 200 66.4% 90.5% 95.8% 97.4% 52.4% 91.2% 95.8% 250 55.3% 84.2% 93.3% 95.8% 14% 86.2% 93.4% 300 45% 76.5% 90.5% 94.3% 5% 78.9% 90.5% 350 37% 68.3% 86.4% 92.5% 3% 68.6% 86.4% 400 30% 58.8% 82.6% 90.8% 1% 55.5% 82.6% 450 24% 50.0% 77.2% 88.0% 1% 37.4% 77.2% 500 19% 42.1% 69.9% 85.0% 0% 12.8% 69.9% Table8-5.Generatorlevelacceptance p T > 20GeV/ c j j < 2.1.4, 60GeV/ c 2 < m < 120GeV/ c 2 abovedifferent p T cuts. p T cut Acceptanceforcontact q ,m TeV = c 2 Acceptanceforgauge q ,m TeV = c 2 GeV = c 2 m=0.5 m=1.0 m=1.5 m=2.0 m=0.5 m=1.0 m=1.5 200 86.8% 88.4% 91.0% 91.8% 81.7% 88.0% 90.2% 250 88.0% 89.5% 91.5% 92.4% 85% 88.6% 90.6% 300 88.9% 90.2% 92.1% 92.8% 88% 89.3% 90.7% 350 89.7% 91.0% 92.6% 93.0% 91% 89.7% 91.1% 400 90.2% 91.8% 93.0% 93.3% 95% 90.1% 91.4% 450 90.0% 92.2% 93.3% 93.3% 100% 91.0% 91.9% 500 90.5% 92.3% 93.7% 94.3% 100% 92% 92.1% Table8-6.Totalselectionefciency.Statisticalerroronanyofthenumbersinthetable doesn'texceed1%. p T cut Acc Effforcontact q ,m TeV = c 2 Acc Effforgauge q ,m TeV = c 2 GeV = c 2 m=0.5 m=1.0 m=1.5 m=2.0 m=0.5 m=1.0 m=1.5 200 49.6% 66.4% 64.0% 57.6% 38.3% 73.5% 69.0% 250 40.1% 62.1% 62.3% 56.7% 11.0% 69.5% 66.9% 300 33.1% 56.2% 60.4% 55.8% 4.0% 63.7% 64.9% 350 26.9% 49.5% 57.3% 54.4% 2.2% 54.8% 61.9% 400 21.3% 41.9% 53.8% 52.9% 1.2% 43.3% 58.5% 450 16.5% 35.0% 49.0% 50.6% 0.7% 28.0% 54.6% 500 12.5% 28.0% 43.9% 48.2% 0.4% 12.2% 48.5% 112

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Figure8-4.Theacceptancetimesefciencyfordifferent q masses,for q producedvia contactinteractionwithstandardcouplings,contrastedbytheacceptance timesefciencyfor Z 0 throughstandardD.Y.production. 8.3Optimizingthe p T ThresholdsforCountingExperiments Wesetlimitsonthebenchmarkmodelsofnewphysicsusingthebackground predictionandactualeventcountsaboveacertain p T threshold.The p T thresholdisoptimizedtogivethebestexpectedlimitonecancheckinAppendixBthatoptimizationof theconventialsignicancegivesverysimilar p T thresholds.Thesetof p T thresholds correspondingtothebestexpectedlimitsisgivenintheTable8-7. 113

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Figure8-5.Theacceptancetimesefciencyfordifferent q masses,for q produced throughquark-gluon-fusionwithstandardcouplings,contrastedbythe acceptancetimesefciencyfor Z 0 throughstandardD.Y.production. 114

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Table8-7.Bestperforming p T cuts GeV = c Mass TeV = c 2 0.5 1.0 1.5 Contact q production 350 400 400 Gauge q production 200 350 400 8.4SettingtheLimits Wesetlimitsusingthestandardcountingexperimenttechnique.Thatmethodis wellsuitedforthehighmassresonances,thatyieldmostofeventsinthebackground freeregion.Wecounteventsabovethecertain p T thresholdandcalculatethe 95% C.L. upperlimitonthecrosssectionassumingPoissonstatisticsfortheobservedyield.We alsocalculateFeldman-Cousins[74]typelimitsasacrosscheck. Thestatisticaltoolsrequireonetodeneuncertaintiesontheirinputs.Theusual inputsareintegratedluminosity,efciencytosignal,andexpectedbackgroundyield. Theuncertaintiesontheseparametersarediscussedaspartoftheanalysissystematic errors. 8.4.1BackgroundandCorrespondingSystematicUncertainty AwaytoestimatetheamountofDrell-Yanbackgroundinthesignalregion p T > 200 GeV = c istodirectlytthedata,butinsteadofperformingsuchtinthewhole p T spectrum,werelyontheparametersestimationintheregionwithhigherstatistics, p T 2 [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200] GeV = c ,andpropagatethettothesignalregion. ThedefaulttfunctionusedistheonederivedfromMCstudiesreportedinSection7.3,Equation7.InTable8-8wereportthecomparisonbetweentheexpected numberobtainedintegratingthetperfomedfor p T 2 [50 )]TJ/F22 11.9552 Tf 12.558 0 Td [(200] GeV = c andthedata countingforseveral p T thresholds. Table8-8.Expectedbackgroundforseveralvaluesofthe p T cut GeV = c p T cut GeV = c > 200 > 250 > 300 > 350 > 400 > 450 > 500 DataCounting 16 9 5 1 1 1 1 FitExtrapolation 19.5 7.3 3.0 1.3 0.57 0.26 0.11 115

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InTable8-9weshowthetparametersobtainedondatausingEq7inthe p T 2 [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200] GeV = c Table8-9.FitresultsfromthetoftheDrell-Yanshapeusingthefunction F x = A e )]TJ/F40 7.9701 Tf 6.587 0 Td [(B p x Parameter FitResult A 18242 3200 B 0.65 0.020 8.4.1.1Fittothe p T spectrumvaryingthetparameters Therstsystematiceffectweevaluatecomesfromthevarianceofthebackground tparameters.Wevariedtheparametersinsidetheerrorobtainedfromthetand usedthemaximumdifferencetoassignasystematicerrortotheDrell-Yanbackground evaluation. InTable8-10wereportthecomparisonbetweenthepredictednumberofDrell-Yan eventsfordifferentrangesofthedimuon p T usedtoperformthet. Table8-10.Expectedbackgroundforseveralvaluesofthe p T cut GeV = c p T cut GeV = c > 200 > 250 > 300 > 350 > 400 > 450 > 500 DataCounting 16 9 5 1 1 1 1 DefaultFitParameters 19.5 7.3 3.0 1.3 0.57 0.26 0.11 Parameters+1 16.7 6.1 2.4 1.0 0.44 0.19 0.08 Parameters-1 22.0 8.5 3.6 1.6 0.72 0.33 0.14 8.4.1.2Stabilityofthetondata AsecondchecktoperformisthestabilityoftheDrell-Yanbackgroundestimationin thesignalregion.Inordertocheckforit,weperformedthetbyvaryingthe p T rangefor thetdetermination. InTable8-11wereportthecomparisonbetweenthepredictednumberofDrell-Yan eventsfordifferentrangesofthedimuon p T usedtoperformthet.Thenumberof eventsestimationsareconsistent,butweassignasystematicerrortothedefaultdatadrivenestimationusingthemaximumdifferencebetweenthedefaultchoiceforthe p T range, p T 2 [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200] GeV = c ,andtheotherwindows. 116

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Table8-11.Expectedbackgroundforseveralvaluesofthe p T cut GeV = c p T cut GeV = c > 200 > 250 > 300 > 350 > 400 > 450 > 500 DataCounting 16 9 5 1 1 1 1 FitExtrapolation [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200] GeV = c 19.5 7.3 3.0 1.3 0.57 0.26 0.11 FitExtrapolation [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(150] GeV = c 21.6 8.3 3.5 1.5 0.68 0.31 0.13 FitExtrapolation [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(175] GeV = c 21.1 8.1 3.3 1.5 0.66 0.30 0.13 8.4.1.3Fittothe p T spectrumwithvariousparametrizations Asourdefaultchoiceforthetfunctionisnotmotivatedbyphysicsreasons,we probedseveralotherparametrizations.InFigure8-6weshowthe p T distributionofthe dimuonpairswithfourdifferentparametrizations:thedefaultfunctionwith2parameters andthreealternatets,therstwith4parametersandtheotherwith3parameters,as describedinequation8. F p T = A e )]TJ/F40 7.9701 Tf 6.587 0 Td [(B p p T ,DefaultChoice = A )]TJ/F40 7.9701 Tf 13.573 5.112 Td [(p T p s B p T p s C + ln p T p s ,AlternateFitB = A )]TJ/F40 7.9701 Tf 13.572 5.112 Td [(p T p s B p C T ,AlternateFitC = A B + p T C ,AlternateFitD Alltchoicesgiveagood 2 = NDFasreportedinTable8-12. Table8-12. 2 = NDFforthedefaulttfunctionandthethreealternatetfunctions.The tsandthe 2 = NDFevaluationsareperformedfor p T 2 [50 )]TJ/F22 11.9552 Tf 11.955 0 Td [(200] GeV = c FitFunction 2 = NDF Prob default 30.24 = 40 89.17% AlternateFitB 29.57 = 38 86.23% AlternateFitC 29.61 = 39 88.59% AlternateFitD 29.54 = 39 88.76% 117

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Figure8-6.The p T dimuonspectrumcomparedtothedefaulttfunctionandthethree alternatechoices. InTable8-13weshowthepredictednumberofDrell-Yaneventsfordifferentt functionin p T 2 [50 )]TJ/F22 11.9552 Tf 12.485 0 Td [(200] GeV = c .Weassignasystematicerrorstothedefaultdatadrivenestimationusingthemaximumdifferencebetweenthedefaulttestimationand theotheralternatetfunctions. Table8-13.Expectedbackgroundforseveralvaluesofthe p T cutforthedefaultt functionandthethreealternatetfunctions. p T cut GeV = c > 200 > 250 > 300 > 350 > 400 > 450 > 500 DataCounting 16 9 5 1 1 1 1 DefaultFunction 19.5 7.3 3.0 1.3 0.57 0.26 0.11 AlternateFitB 9.9 2.2 0.5 0.1 0.02 0.01 0.001 AlternateFitB 11.2 2.8 0.7 0.2 0.05 0.01 0.003 AlternateFitD 13.5 4.3 1.5 0.6 0.23 0.10 0.04 8.4.1.4Finalbackgroundestimation Inconclusion,weevaluatedthenumberofDrell-Yaneventsinthesignalregion, byextrapolatingthetfromEquation7performedfor p T 2 [50 )]TJ/F22 11.9552 Tf 12.661 0 Td [(200] GeV = c .We assignedseveralsystematicerrorbyvaryingthetparameters,changingthe p T range forthetandusingseveralalternatetfunctions.Thenalestimationisreportedin Table8-14andvisuallyshowninFigure8-7. 118

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Table8-14.Expectedbackgroundforseveralvaluesofthe p T cutandrelative systematicerrorassignment. p T cut GeV = c > 200 > 250 > 300 > 350 > 400 > 450 > 500 FitPars. 2.5 1.2 0.6 0.3 0.15 0.07 0.03 Ranges 2.1 1.0 0.5 0.2 0.11 0.05 0.02 FitFunctions 9.6 5.1 2.5 1.2 0.55 0.25 0.11 FinalEstimation 19.5 10.1 7.3 5.3 3.0 2.6 1.3 0.58 0.57 0.26 0.27 0.11 0.12 DataCounting 16 9 5 1 1 1 1 Figure8-7.Expectedbackgroundforseveralvaluesofthe p T cutandrelativesystematic errorassignment. 8.4.1.5Biasduetosignal Thepresenceofrealsignalmaybiasourbackgroundestimateasthetstarts absorbingsomeofsingaleventsthatendedupinthettingregion.Wechecktheimpact ofthiseffectonthesensitivityofthesearchinaseriesofpseudoexperiments.Each pseudoexperimentsimulates36pb )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 ofbackgroundandacertainsignalyieldup to200signaleventswereprobed.Ineverypseudoexperimentthenumberofsignal eventsaswellasthenumberofbackgroundeventsuctuatesasPoissonaround therequestedyields.Fittingthe p T distribution,wecalculatethenumberofexpected 119

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backgroundeventsaboveacertain p T threshold.Wevarythesignalyield,andthe expectedbackgroundduetottingisaveragedover1Kpseudoexperimentsand comparedtotheaverageDrell-Yanbackgroundabovethesamethreshold.Figure8-8 showsanexampleplotofthe q ofm=0.5 TeV = c 2 inC.I.productionthelowes q massmodelischosenbecauseitgivesthehighestfeedtothetingregion.Onecan seethattheeffectislinearandratherweak:200injectedsignaleventsaddonly 0.6 backgroundeventsabove350 GeV = c tothetpredictionwhichisstillwithinthe systematicuncertaintythatweassigntotheprediction. Figure8-8.Biasonthepredictedbackgroundeventsabovethethresoldof p T =350 GeV = c asafunctionofsignaleventsC.I. q ,m=0.5 TeV = c 2 8.4.2DetectorAcceptanceandEfciencytoSignalandCorrespondingSystematic Thegeometricacceptanceofthedetectorcanbecalculatedforeachspecicmodel ofthesignalandthebackground,whichisonlylimitedbytheuncertaintiesontheParton DistributionFunctions.Forthisstudywerelyontheresultfrominclusive Z 0 and W crosssectionsmeasurements[60]andassigna2%atuncertaintyontheacceptance. 120

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ForDrell-YanproductionthisnumberismostlydrivenbythePDFuncertaintyonthe Z 0 occupancyinhighrapidityregions.Incaseofthecentrallyboosted Z 0 bosonsthe populationofthehighrapidityregionsdiminishesandthecorrespondinguncertainty decreases.Anothersourceofuncertaintyistherenormalizationandfactorizationscale assumptions,whicharealsoexpectedtodecreaseforhighmomentumtransfersand highboosts.Thus,2%isaconservativeestimate. AsonecanseeinSection5.7Figures5-11,5-12,and5-13,theleadingsource ofinefciency 10%isduetothecutof 20 GeV = c onmuon p T .Uncertaintyofthis inefciencyisdirectlyrelatedtotheperformanceofthemuonmomentumreconstruction. If,forexample,themuonmomentumscaleisnotproperlymodeledbythedetector simulation,theefciencycalculationwillbesystematicallyoffsetfromtheactualdetector efciency.Thus,wecomparedthemuonmomentumscaleandresolutionindata andintheMonteCarlo.FromtheresultsinFigure8-9onecanidentifythemaximum discrepancybetweendataandMonteCarlotobe 0.4% forthemomentumscaleand 25% forthe Z 0 massresolutionwhichisassumedtobeequaltothemuonmomentum resolutionmoredetailsinsection9.1..Correctingthemuonmomentumscaleby varyingthe p T cutleadstoa 0.1% changeintheefciencyforallofthemodels. Correctingthemuon p T resolutionby 25% towardsthetruevaluegains 0.6 )]TJ/F22 11.9552 Tf 12.83 0 Td [(1.3% efciencydependingonthemodel.Wetakeaconservative 1.5% atuncertaintyfor theefciencyofallofthemodels. Foreachmodeltheresultinguncertaintyontheefciency acceptanceisevaluatedasasquaresumofthestatisticaluncertaintyfromTable8.2,andthesystematic errorof 2% acceptance 1.5% muonkinematiccut. 8.4.3IntegratedLuminosity Oneofthelargestsourcesofsystematicuncertaintiesisuncertaintyontheintegratedluminosity.The2010estimatedaccuracyontheluminositymeasurementis 11% [75]thishasbeenimprovedsincethetimeofthisanalysis.Onecanfactoroutthis 121

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Figure8-9.The Z 0 peakpositionleftand Z 0 massresolutionrightmeasuredasthe widthofthe Z 0 peakontopofthenatural Z 0 width. typeofuncertaintyusingnormalizationtosomewellknownStandardModelprocess. Weusethe Z 0 productionasourstandardcandleandrecyclesomeoftheresultsofthe inclusiveDrell-YanMassanalysis[60].TheNNLOpredictionfor Z 0 productioninthefull acceptancecalculatedintheVBTFanalysisis 0.97 0.04 nb 60 < M < 120 GeV = c TheacceptanceoftheVBTFselectiontwotightmuons,trackerbasedisolationcutat 3 GeV = c is 0.3977 0.0048 .Efciencyoftheselectionisabsorbedinthesimultaneous twhichtreatsthetotalnumberofeventsandefciencyofeveryselectioncriterion asthetparameters.WendtheMonteCarloefciencyis 0.948 .ApplyingtheVBTF selectionwecount 12500 eventsinourdatasample.Thatcorrespondsto 34.18 pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 integratedluminosityusingtheNNLOcrosssection.The 5.2% uncertaintyonthisnumberisasquaresumof 4% uncertaintyonthetheoreticalcrosssection, 1% statistical 122

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uncertaintyonthenumberofselectedevents, 1.2% ofacceptanceaccuracy,and 3% uncertaintyontheMonteCarloefciency. 1 8.5ComputingtheLimits Themachineryofcalculatingalimitinacountingexperimentiswelldeveloped. 2 TheexpectedandactuallimitscanbefoundinTable8-15. Table8-15.Limitsonthecrosssectionofthebenchmarkmodelsassuming5.2%and 11%uncertaintyontheluminosity.Thenumberrepresentsthevalueof *BR q qZ 0 *BR Z 0 Mass Limitspbfor L =5.2% Limitspbfor L =11% GeV = c 2 expected found expected found contact q production 0.5 0.676 0.618 0.683 0.625 1.0 0.372 0.428 0.376 0.433 1.5 0.317 0.364 0.320 0.368 2.0 0.360 0.414 0.346 0.418 gauge q production 0.5 2.095 1.735 2.127 1.760 1.0 0.305 0.280 0.309 0.283 1.5 0.198 0.228 0.200 0.230 Forthe q weusethelimitsonthecrosssectioninTable8-15andtranslatethem intocontoursinthespaceofsomeoftheparametersofthegaugeandcontactmodels. Asthelimitdependsonthemassof q ,weinterpolateitwithacontinuousfunction f m = A + B = m + C = m 2 seeFigure8-10.Then,foreverypointofmasswend valuesof and f s ,whichresultinthecrosssectionwithin 10 )]TJ/F23 7.9701 Tf 6.586 0 Td [(3 pbaroundthelimit. 1 UncertaintyontheMonteCarloefciencyisconservativelytakenasasquaresum ofthevariationsofalloftheN-1efcienciesfromthebaselineefciency.Theonlyuncertaintyontheefciencyofthemuon p T cutwastreateddifferentlyinthesum.We recycledourpreviousresultandtookitasaconservative 1.5% uncertainty. 2 WeuseanofcialCMStoolvalidatedbyCMS,the cl95cms.C macro,designedto calculateBayesiancondenceintervalsonPoissonstatistics. 123

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Finally,weinterpolatethepointsintheparameterspacewiththepolynomialsanddraw acontinuouscontour. Figure8-10.Left:smoothinterpolationofthefoundlimitsonthecrosssection BR fromTable8-15.Right:sameasleft,butwithoutbranchingof Z 0 + )]TJ/F20 11.9552 Tf 7.085 -4.338 Td [(. InFigure8-11wereportthenalupperlimitcontoursinthe M q and planefor differentassumptionsofthestrongcoupling, f s ,incontactinteractionandquarkgluon fusionproductionmodels.Underthestandardassumptionsfortheparameters M q = f = f 0 = f s =1 ourlimitstranslateinto M q < 911 GeV = c 2 forthegauge q production and M q < 1115 GeV = c 2 forproductionviacontactinteraction. AccordingtoPythiathecrosssection branchingfractionofthe Z 0 H + Z 0 processisontheorderof fb .Thus,settinglimitsonthisspecicprocessisnotfeasible withthecurrentintegratedluminosity. Asacrosscheck,weadditionallycomputeFeldman-Cousinstypelimits.Table816summarizesFeldman-Cousinstypeupperlimitsonthenumberofsignalevents calculatedwith36pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ofdata.ItiscomparedtothemedianandtheRMSoflimitsin 100pseudoexperimentsofbackground-onlymodel.TheluminosityandDrell-Yanslope areleftasnuisanceparameterstothet. 124

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Table8-16.Feldman-Cousinslimitsonnumberofsignalevents. Mass Limits ] events GeV = c 2 median RMS found contact q production 0.5 5.6 3.6 11.1 1.0 3.5 1.9 6.35 1.5 2.7 1.2 5.05 gauge q production 0.5 10.4 4.3 9.1 1.0 3.9 1.8 6.05 1.5 3.0 1.0 4.95 Z 0 production 0.5 10.2 4.7 7.5 1.0 2.7 1.7 5.55 1.5 2.4 0.9 4.55 Figure8-12showssomeoftheFeldman-Cousinstypeupperlimitssuperimposed ontopoflimitsof100pseudoexperimentsofbackground-onlymodel. Thelimitonthenumberofsignaleventshastobepropagatedintothelimitonthe crosssectionofthemodel.Wedothisstepusingthestandardformula,whichlinks numberofeventsandcrosssectionasdescribedinEquation8. N signal = L BR A InEquation8theterm BR identiesthecrosssection branchingfraction andtheterm A istheacceptancetimesselectionefciency.Weusethesame formulatopropagatetheuncertaintiesassuming11%uncertaintyfortheluminosity, RMSfromTableforthe N signal ,and2% 1.5% stat err factorsforthe A .Table8-17 showsthecrosssectionandthetotaluncertainty.Theresultinglimittreatedascross section+uncertainty.Themajorcontributiontotheuncertaintyobviouslycomesfrom statistics.Ifonechangesuncertaintyontheluminosityto5.2%amoreaggressive uncertaintyontheluminosityuncertainty,thenumbersinthetablechangeby 0.01pb. Figure8-13comparesresultsofFeldman-Cousinstechniquewithresultsfromthe 125

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countingexperiment.TheshapediscriminatingFeldman-Cousinstechniquegives betterperformanceinthelow q massscenarioswheresignalandbackgroundoverlap. Although,forthehighmass q thelimitsconvergewhenfeweventsareobserved. Table8-17.Feldman-Cousinslimitsonthesignalcrosssection. Mass Limitspb GeV = c 2 contact q production gauge q production 0.5 0.45 0.15 0.36 0.18 1.0 0.26 0.09 0.22 0.07 1.5 0.22 0.06 0.20 0.05 126

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Figure8-11.Contoursofcompositenessscalevs. q massofthequarkgluonfusion topandcontactinteractionbottom q productionmechanisms.The valueswhichareexcludedarebelowandtotheleftofthecurves. 127

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Figure8-12.Feldman-Cousinslimitsinnumberofsignaleventsfor36pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 and100 pseudo-experiments.The3benchmarkmodelsareshown:gauge q productionleft,contact q productionmiddleand Z 0 right,allwith M =1.0 TeV = c 2 Figure8-13.ComparisonoftheFeldman-Cousinslimitsagainstlimitsfromthecounting experiment. 128

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CHAPTER9 MEASUREMENTOFTHEZBOSONTRANSVERSEMOMENTUMSPECTRUM Insection4.2,anoverviewofthemeasurementofthe Z 0 p T spectrumispresented. Inthischapter,wediscusstheremainderofthestepsexclusivetothisanalysis,specicallyunfoldingfordetectorresolution.Wethenestimatesystematicresults,andpresent acomparisonofthedatatothepredictionsofMonteCarloSimulation. 9.1Unfolding The p T resolutionofthemuonsdirectlyeffectsthe p T ofthe Z 0 ,andasaresult, someeventsfrombin i ofthetrue p T spectrumendupinadifferentbin j ofthe measuredone.Theeffectbecomesparticularlypronouncedinthelow p T portionofthe spectrum,withbinsizesthatarecomparabletotheresolution.Figure9-1comparesthe p T spectrumbeforeandafterthefulldetectorsimulation. Figure9-1.The p T spectrumbeforeandafterthefulldetectorsimulation.Ontheleft thetwospectra,ontherightratioofthetwospectra. Weunfoldthemuonmomentumresolutionfromthe Zp T spectrumusingastandardunfoldingtechnique,describedindetailin[76].Inanutshell,thistechnique instructsonetoconstructaresponsematrix R ij ,whichdescribestheprobabilityofan 129

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eventtomovefrombin i true p T tobin j measured p T .Theunfoldingisreducedto solvingalinearmatrixEquation9. x measured j = X i R ij x true i Inthisinstance,wehavethe p T spectrummeasuredindataand R ij depictstheZ p T resolutionofthedetector.Ifthebinningissufcientlycoarseseesection9.1.2,it ispossibletoinvert R ij resultinginEquation9andhaveerrorsreportedinEquation 9. x true i = X j R )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ij x measured j 2 i = X j R )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ij 2 x measured j 9.1.1Theresponsematrix Theresponsematrix, R ij ,isconstructedusingthedetectorsimulation.Ifwe dene v i tobethevectorofoccupanciesinbinsoftrue p T and u j tothemeasured p T spectrum,thentheeffectsofdetectorresolutionaretohaveeventsexistinbin v k 1 and u k 2 suchthat k 1 6 = k 2 .Tollthevectors u j and v j oneexaminesthefulldetector simulationoutputandappliesallthetriggerandeventselection.Afterthis,foreverypair ofmuonswhichpassselection,apairofgeneratorlevelmuonswhicharegeometrically closesttothethereconstructedmuonsarerecorded.Inaddition, R ij islledasa2Darrayindexedbythebinsoftrueandreconstructed Z 0 p T respectively.Onceall eventsareconsidered,columnsarenormalizedtothenumberofevents.Intheend, Equation9,describestherelationshipbetween v i u j ,and R ij u j = X i R ij v i 130

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Moresimply, R ij isaprobabilityofamuonpairwith p T inbinimigratingtoareconstructed p T binj.Figure9-2depictstheresponsematrixtrainedondirectcomparison ofMCtruthandreco.WhenexaminingthisResponseMatrix,itisimportanttonotethe valueofthediagonalelements.Thechoiceofbinningisdeterminedentirelybythebin tobinspilloverdepictedinthismatrix.Itisimportantthatthebintobinspilloverisno higherthat30%,ortheuncertaintyduetounfoldingwillbecomeverylargeadditionally, thevalueofthemeasurementbecomesquestionable. Figure9-2.Theresponsematrix,astunedonMC Fromhere,Gauss-Jordaneliminationisemployedtoinvertthematrixdepictedin Figure9-3.Weareleftwithamappingfromthemeasured p T spectrumtotheunfolded p T spectrum. Thereareseveralclosuretestswhichweperformtoensureproceduralcorrectness. Therstoftheseistoapplytheresultinginvertedresponsematrixontheoriginalsamplethesameevents.Ifyouhavedonetheunfoldingprocedurecorrectly,theresulting p T spectrumshouldagreewiththegeneratorlevelspectrumtowithinerrors.Figure9-4 depictssuchanapplication,andasonecansee,theunfoldingisexecutedproperly.One alsoobservesanincreaseintheerror,anaturalconsequenceofunfolding. 131

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Figure9-3.Theinvertedresponsematrix Figure9-4.ClosuretestonMC,the 2 betweenthereconstructedandgeneratedis67, whilethecomparisonbetweenunfoldedandgeneratedis0.23. 132

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9.1.2StatisticalTests Itisimportantwhenchoosingbinsizethatbintobincorrelationisminimizedby choosingappropriatelylargebinning.Whilemakingtheseselections,webalance thisneedtokeepbinsizeslargeagainstthedesiretohavenegranularityinthe measurementofthespectrum.Theprocessofpulltestsaddressesthisimportantpoint. Ourpulltestofthematrixunfoldingprocedureisatwostepprocedure.InStep 1,asetoftoyMC,calledthetrainingsample,isgeneratedsuchthateverybinhas equaloccupancyandthedistributionwithinthebinisat.Thedataisthensmeared byaGaussianwitha thatisaxedfractionofthebinwidth.Aresponsematrixis constructedusingthisdataandtheprocessofinversionisapplied.Inthesecondstep, asecondsetofdata,calledthetestsample,isgeneratedunderthesameconditionsof thetrainingsample.Thisdataissmearedusingthesamefunctionfromrststep.The invertedresponsematrixtrainedinsteponeisthenappliedtothespectrumwhichis smearedinstep2.Iftheoccupancyforbinjforgeneratedspectruminstep2is g j and theunfoldedspectrumfromsteptwois u j witherror u j asdenedinEquation9,then thevalueofthepull, p j isdenedinEquation9. p j = g j )]TJ/F39 11.9552 Tf 11.956 0 Td [(u j u j Steps1and2arethenrepeatedthousandsoftimes,untilasmoothdistributionof pullscanbeconstructedwithineachbin.Figure9-5showstherawdistributionofpulls forasmearingGaussianwitha of80%ofthebinwidth.Theonlywayinwhichthe spectrumismanipulatedisthatsimilarlytohowwecannotmeasurea Z 0 p T lessthan0, wedonotallowforspillovertothe0thbin,andsimilarly,wedisallowoverowfromthe 18thbin. OnecanthentaketheprojectionofeachbinandtitwithaGaussian.Thet valuesshoulddescribeaGaussianwithameanof0,andasigmaof1.Figure9-6 133

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Figure9-5.Therawdistributionofpulls,distributionsmearedbyaGaussianwith of 0.8 depictsthebinbybintparametersforthepulltestfromabove.Thepointsdepictthe meanvalueoftheGaussian,whiletheerrorbarsarethesigma. Figure9-6.TheGaussianprojectionofpulls,distributionsmearedbyaGaussianwith of0.8*BinWidth Thefactthatthedistributionshavecentersconsistentwith0and 'sof1demonstratethatstatisticallywecorrecttheresolutionbythecorrectamount,andtheerror assignedareofthecorrectmagnitude. 134

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9.1.3DataDrivenEstimationofResolution WhilegreatefforthasbeenmadetomakethedataandMCconsistent,itisimportanttocrosschecktheresolutionof p T basedondatadriventechniques.Ifonecan extractadatadrivenestimationforthemuon p T resolution,onecansmeargenerator leveldata,andconstructaresponsematrixbasedonthisresolutionobtainedfromdata. Fortherststep,weconsiderhowtoextractthemuon p T resolutionfromdata. Firstconsiderthemethodofmeasuringthe p T resolutionofindividualmuonsby theadditionalbroadeningbeyondtheknownBreit-Wigner Z 0 masspeak.Assumethat therewehaveameasuredmassforthe Z 0 of m rec ,andamasscomingfromthetrue underlyingdistributionof m true .Similarlywehavemuonswhichareusedtoreconstruct the Z 0 with p true and p rec .Thenthedeviationfromthetruevalueforbothmassand momentumwillbe m and p suchthat m rec = m true + m and p rec = p true + p Therelationshipbetween m rec andthe2muon's p rec isgivenignoringmuonmassby Equation9. m = p 2 p 1 p 2 )]TJ/F39 11.9552 Tf 11.955 0 Td [(cos [ ]= f p 1 p 2 m 2 = @ f @ p 1 p 1 2 + @ f @ p 2 p 2 2 = )]TJ/F39 11.9552 Tf 11.955 0 Td [(cos [ ] 2 p 1 p 2 2 + p 2 p 1 2 2 p 1 p 2 )]TJ/F39 11.9552 Tf 11.955 0 Td [(cos [ ] m m = s p 1 2 p 1 2 + p 2 2 p 2 2 Wethenaveragingovermanyeventssuchthat p 1 2 p 1 = p 2 2 p 2 ,andweareleftwiththe workingansatzabouttherelationshipbetweenthemassofthe Z 0 m andthe p T ofthe muonswhicharereconstructedasthedecayproductsofthe Z 0 peakaredepictedin Equation9. m m = p T p T 135

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Thereconstructedmasspeakofthe Z 0 canbetwithaVoigtianfunctiona Breit-WignerconvolutedbyaGaussian,Equation9.TodothisonMC,werst xtheGaussian tobe0,andextractthetrueBreit-Wignerparametersfromtting thegeneratorlevelmassspectrum.WethenxtheBreit-Wignertotheparameters extractedfromthetruthtsandallowtheGaussian todescribetheresolutionofthe masspeak. Z 1 dx G x B W m )]TJ/F39 11.9552 Tf 11.955 0 Td [(x ,, M 0 Forthebaselinerangeofthist,wechoosetogofromthemasspeak 3 where weapproximate tobe1.5GeVfortheDTandoverlapregions,and2.5fortheCSC region.Sinceweanticipatetheresolutiontovarywithincreasing ,wedividethe acceptanceregioninto3distinctregions,thosecoveredbytheDTs,theOverlapregion, andtheCSCsofthemuonsystemwhichcorrespondto j j valuesof0-0.9,0.9-1.2, and1.2-2.1respectively.Itisthenpossibletoclassifythedecayofthe Z 0 into6distinct categoriesbaseduponthereconstructed valuesofthedecaymuons.TheMCbased tsforall Z 0 p T rangesareshowinFigure9-7. Itisthenusefultotesttheansatzbycomparinginsimulationtheextractedresolutionparameterstothoseextractedfromadirectdeterminationofthe p T resolution usingthetrueversusreconstructedvalues.Figure9-8depictsthedirect p T resolution fromMC.WetthedirectresolutionfunctionwithadoubletheGaussiandescribedin Equation9. N 0 f 12 G m 1 1 + )]TJ/F39 11.9552 Tf 11.955 0 Td [(f 12 G m 2 2 Table9-1depictsthecomparisonofthetwomethods.TheVoigtianmethodappears toextracttheresolutioninreasonableagreementwiththedirectdeterminationintheDT region,however,itdoesnotseemtoconsistentlyworkinthehigherregionsof .The 136

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Figure9-7.TheVoigtiantsofMC Z 0 massdistributionswithxed )]TJ/F20 11.9552 Tf 10.098 0 Td [(and m Z p 0 isthe valuefor inGeVand p 3 isthenormalizationfactor. Figure9-8.Thetruemuon p T resolutiononMC. 137

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additionalcomplicationisthatthe p T resolutionofindividualmuonsisnotwelltbya singleGaussian,duetolargetails. Table9-1.MuonresolutiononMC,comparisonofextractionmethod Region Voigtian,MC% Directt,MC% Voigtian,Data% DT 1.487 1.538 1.107 Overlap 1.517 1.945 1.387 CSC 2.629 2.975 2.807 Aftercarefulconsideration,itisdecidedtousethefulldoubleGaussianvalueforthe muon p T resolution.Thismethodallowsforthetailstobebettermodeled.Inadditionto dividingtheresolutionintoregionsof ,wealsodivideinto3regionsofmuon p T aswell. Theregionsofmuon p T arefrom20-40,40-50,andabove50GeV.Table9-2showsthe valuesforthedoubleGaussiantsofMCwextheGaussianCentersto0. Table9-2.MuonresolutiononMC,parameterscorrespondingtoEquation99 Region 1 2 f 12 DT,Low p T 0.01369 0.0500 0.9817 Overlap,Low p T 0.0181 0.05486 0.9734 CSC,Low p T 0.02259 0.06477 0.8819 DT,Mid p T 0.01597 0.05114 0.9812 Overlap,Mid p T 0.01993 0.06021 0.9725 CSC,Mid p T 0.02573 0.07575 0.8854 DT,High p T 0.0198 0.0598 0.9787 Overlap,High p T 0.02206 0.0500 0.9294 CSC,High p T 0.02997 0.08225 0.8622 Weadjusttothedifferencesin p T resolutionfromdatatoMCbycomparingthe valuesoftheVoigtiantsbetweendataandMC,Equation9.Bydividingthe ofthe dataVoigtiantbythe oftheMCVoigtiant,weconstructascalefactorbywhichthe directlyextractedresolutionparametersarescaled:Figure9-9depictstheVoigtiantsof themasspeakindata. R D MC = Voigt ., Data Voigt ., MC 138

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Figure9-9.TheVoitiantsofthedata Z 0 masspeaks.Ingeneral,datashowsbetter resolutionthanwhatisobservedinMonteCarlo. Atthispoint,wecanalsoperformaclosuretestofourabilitytosmearthedata consistently.Here,wecreateaninvertedresolutionmatrixobtainedbysmearing generatorleveldatabasedontheMCtruthextractedresolutionfunction.Fromthe samespectrum,weunfoldrecoleveldatathenewlyformedunfoldingmatrix.Figure910depictstheresultofthisclosuretest.Onecanobservethattheresultingunfolded spectrumisconsistentwithinstatisticalerrorofthetruthlevelspectrum.Thisclosure testconvincesusthatsmearinggeneratorleveldatawithamuon p T resolutionwhichis consistentwiththereconstruction. ThenalprocessistotrainamatrixbasedonthescaledMCts.Wehavedouble Gaussianparameters, f 12 1 ,and 2 whichallvarywiththe p T and ofthemuon,and anextracted R D MC whichdependsonlyonmuon .Equation9and9describes 139

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Figure9-10.TheclosuretestoftheMCsmearedmatrixappliedtoMCrecospectra. thenalmuonsmearingfunctionusingtheseparametersinadditiontoarandomly generatedvalue x 2 [0,1 p smear T = p true T + x f 12 G R D MC 1 + )]TJ/F25 11.9552 Tf 9.932 0 Td [( x f 12 G R D MC 2 x f 12 = f 1 if x f 12 0 if x > f 12 Figure9-11depictsasampleofonehundredmillionsimulated Z 0 todimuonevents smearedwiththisresolutionfunction. 9.1.4SmearingInducedBackground Thereexiststhepossibilityofthemuon p T orthe Z 0 masstobereconstructed withintheacceptanceregion,whereinactualitythetrueparametersareoutsideof it.Sincewepresentdatainalimitedacceptanceregion,theseeventsconstitutea background.Usingthedatatunedresolutionsmearing,wederiveaprobabilityofan eventtobesmearedintotheacceptanceregionfromoutsideofitasafunctionof Z 0 p T .Figure9-12depictstheeventswhichpassreconstructioncutsandtruthlevel 140

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Figure9-11.Thetruth,andsmearedspectraresultingfromthesmearingfunction describedinEquation9.Ontheright,weincludetheclosuretestwith thegeneratedunfoldingmatrix. acceptance,thosewhichpassreconstructioncutsbutnottruthlevelacceptance,and theirratio.Wescaleourobserveddataspectrumbythisscaleandconsiderthistobe thebackgroundfromsmearing. Figure9-12.Left:Eventspassingbothrecoandtruthlevelcuts.Mid:Eventspassing recobutnottruthlevelcuts.Right:Scalefactorforremovingsmearing inducedbackground. 141

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9.1.5UnfoldingSmearingfromFinalStateRadiationFSR Anothereffectwhichdistortsthedistributionof p T ofthe Z 0 isQEDnalstate radiation.Weaccountforthisdistortionusingthesametechniqueofmatrixinversion. Settinguptheresponsematrixisastraightforwardmappingfromnalstatemuonsto the Z 0 candidate p T .Wetheninvertthematrixandapplytoourmeasuredspectrum aftercorrectionsforefcienciesandacceptanceinthecaseofweextrapolatebeyond thelimitedacceptanceregionhavebeenapplied.Forclarity,theresponsematrix whichaccountsforFSRwillbereferredtoas F ij soasnottobeconfusedwith R ij theresponsematrixfromdetectorresolution.Figure9-13displaystheresponseand invertedresponsematrixforFSR. M Figure9-13.Left:ResponseMatrixfromFSRunfolding.Right:InvertedResponse MatrixfromFSRunfolding. Theonlywaywhichthistechniquediffersfromtheoriginalunfoldingprocessisthe assignmentoferrors.Equation9describestheperbinerrorfromtheunfolding,given thevaluesof x measured j areuncorrelated.Whenweaimtounfoldthenewspectrum,the spectrumforFSR,weknowthatbinsarecorrelated.Wemustaccountforthisbyusing acovariancematrix.Ifwedene M x tobethecovariancematrixoftheobservedevents, 142

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thenEquation9describesit'selements,with ij beingthedeltafunctionifi 6 = j,1if i=j. M x ij = ij measured i measured j Amoregeneralcovariancematrixhasoffdiagonaltermswhichdescribecorrelation betweenbins.Wecanthenformourcovariancematrixonthedetectorresolution unfoldedspectrum, M R ,asdenedbyEquation9. M r ij = X k X p F )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ki M x kp F )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 pj WethencalculateerrorsaccordingtoEquation9 2 i = X j X k F )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 ij M x jk F )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 ik 9.1.6FinalResolutionUnfoldingMatrix WithourresolutionandFSRunderstood,wenowconstructasinglematrixto accountsimultaneouslyfortheeffectsofFSR,efciency,anddetectorresolution. Startingwithgeneratorlevelmuonsfromasampleofonehundredmillion Z 0 todimuon events,acceptancecutsarethenappliedonsmeareddimuonpairssothatonlythose eventsinlimitedacceptancespaceareconsidered.Efciencycutsdevelopedinsection 5areappliedasafunctionofindividualmuon p T .Themuonsarethensmearedasaby Equation9tosimulatedetectorresolution.Thenalresponsematrixisconstructed asdescribedpreviouslyandareleftwithamatrixdescribingthemigrationofapreFSR Z 0 p T spectrumtoa Z 0 p T resolutionasmeasuredindata.Figure9-14depictsthenal baselineunfoldingmatrix,includingabintoaccountforpotentialoverowbinnumber 19inFigure9-14. 143

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Figure9-14.Theresponsematrixfromdatatuneddetectorsmearingandpythia calculatedFSRforboththelinearleftandlogrightzscale. 9.1.7UnfoldingSummary Inthissection,theconceptofaresponsematrixisintroducedasatoolforunfolding smearingfromdetectorresolutionandQEDnalstateradiation.Itisdemonstratedthat themachineryforimplementingthematrixinversiontechniquecancorrectlyunfolda spectrumwithconsistentresolution.Pulltestsareperformedtodemonstratethatthis methodisstatisticallysound.Finally,themethodofconstructingaresolutionmatrixon resolutionmeasuredindataisoutlined. 9.2SystematicEffects,Studies,andUncertainties InthisSectionwedescribetheproceduresusedtoassignsystematicerrorstoour nalmeasurement. 9.2.1PDFUncertainties Themeasurementofthetransversemomentumdifferential Z 0 crosssectionhas beenperformedrelyingonaMCgeneratedwiththeNLOMCgeneratorPOWHEGand thepartondistributionfunctionPDFCT10[77].DifferencesinthePDFmayaffectthe nalresult.Thusweevaluatethecontributionofthesystematicuncertaintiesonthe acceptancetimestheefciencyduetorecommendedmodicationofthePDFvariations. 144

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Thestudypresentedhereisbasedonthecompletesetofrecommendedvariations oftheCT10providedbytheLHAPDFpackageversion5.8.9[78].Simulatedevents arereweightedatthehardscatteringlevelusingmodiedPDFsets.Theeffectonthe acceptanceandefciencyforthecrosssectionmeasurementcanbethenstudied. Toevaluatethesystematcuncertaintiesbin-by-binweusetheModifedTolerance Method[79]wherethevariationsonaphysicsobservableXareobtainedfromthe Equation9. X + max = v u u t N X i =1 [ max X + i )]TJ/F39 11.9552 Tf 11.955 0 Td [(X 0 X )]TJ/F40 7.9701 Tf -1.591 -8.277 Td [(i )]TJ/F39 11.9552 Tf 11.955 0 Td [(X 0 ,0] 2 X )]TJ/F40 7.9701 Tf -1.59 -7.891 Td [(max = v u u t N X i =1 [ max X 0 )]TJ/F39 11.9552 Tf 11.955 0 Td [(X + i X 0 )]TJ/F39 11.9552 Tf 11.955 0 Td [(X )]TJ/F40 7.9701 Tf -1.59 -8.277 Td [(i ,0] 2 InthecaseunderstudyXistheacceptancetimesefciencyasstudiedinSection5 and N =26 forthecurrentCT10implementation[78]. X 0 correspondstothenominal PDFand X i arethereweightedvaluesinducedbythePDFvariations.Infactthe LHAPDFversionprovidesasetof26independentvectors,eachavailableforpositive andnegativedirections,toprobethephasespaceoftheCT10variations. InFigure9-15andinTable9-3wereportthemodicationontheacceptancetimes theefciencyandthepercentagevariationsasafunctionoftheZbosontransverse momentum.ThechosenbinningistheonerecommendedinSection9.1. Thesystematicerrorisdeterminedbyusingthemaximumandminimumvariation A curvestocorrect d dP T .Thissystematicerrorisassignedonlywhenmeasuring thedifferentialshapeinthefullacceptance.ThevaluesarereportedinTable9-4. ComparedinFigure9-16isthecomparisonbetweenthevariationinducedonthe acceptancetimesefciencybythePDFandthesystematicerrorontheshape.Although 145

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Figure9-15.Acceptancetimesefciency,A ,asafunctionoftheZ p T withthe associatedvariationsobtainedwiththeModiedToleranceMethod. thevariationsintheacceptancetimesefciencyvarybetween2.0%to3.7%,the variationsontheshapeareingeneralofoneorderofmagnitudesmaller. Figure9-16.Left:percentagevariationsoftheA asafunctionoftheZ p T .Right: fractionalvariationsofthe 1 d dP T asafunctionoftheZ p T 9.2.2EfciencyCorrections TheselectioncriteriahavebeendescribedinSection5.FromtheplotinFigure5-10wecanconcludethattheefciencynotbeingcompletelyatasafunctionof 146

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Table9-3.Acceptancetimesefciency,A ,systematicuncertaintiesandtheir percentagevariationsasafunctionoftheZ p T BinNumber Z p T Range GeV = c Acc Variation% 1 0.0-2.5 0.3512 +0.013 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.013 +3.7 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.7 2 2.5-5.0 0.3471 +0.013 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.012 +3.6 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.5 3 5.0-7.5 0.3632 +0.014 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.013 +3.7 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.6 4 7.5-10.0 0.3727 +0.014 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.013 +3.6 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.5 5 10.0-12.5 0.3768 +0.013 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.013 +3.4 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.4 6 12.5-15.0 0.3806 +0.013 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.013 +3.4 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.4 7 15.0-17.5 0.3829 +0.013 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.013 +3.3 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.3 8 17.5-20.0 0.3868 +0.013 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.012 +3.3 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.2 9 20.0-30.0 0.3848 +0.013 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.012 +3.2 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.1 10 30.0-40.0 0.3974 +0.012 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.012 +3.0 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.0 11 40.0-50.0 0.4070 +0.011 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.011 +2.7 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2.7 12 50.0-70.0 0.4189 +0.011 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.011 +2.5 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2.5 13 70.0-90.0 0.4280 +0.010 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.010 +2.2 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2.2 14 90.0-110.0 0.4369 +0.009 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.009 +2.1 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2.1 15 110.0-150.0 0.4735 +0.009 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.010 +2.0 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2.1 16 150.0-190.0 0.5227 +0.011 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.011 +2.1 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2.1 17 190.0-250.0 0.5531 +0.012 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.012 +2.2 )]TJ/F23 7.9701 Tf 6.587 0 Td [(2.2 18 250.0-600.0 0.6947 +0.022 )]TJ/F23 7.9701 Tf 6.587 0 Td [(0.026 +3.2 )]TJ/F23 7.9701 Tf 6.587 0 Td [(3.8 dimuons p T affectstheshapeofthespectrumitself.Inthenalcalculationwecorrect theMCefciencyusingthescalefactorsreportedinTable5-4.Thesecorrectionsare providedwithanerror. Weassignasystematicerrorbyincreasingdecreasingsimultaneouslyallthescale factorsbyonesigmawhilekeepingthenormalization 1 xedtothenominalvalue,i.e. weapplythevariedscalefactorsonlyto d dP T .TheerrorsareshowninTable9-5. 9.2.3BackgroundUncertainties Theuncertaintyonthebackgroundestimationisanotherpossiblesourceof systematicerror.Toaccountforitinthenalresult,wewillvarytheestimatedvalueof thetotalbackgroundby100%. InFigure9-17wereportthesystematicvariationinducedbya100%misknowledge onthetotalbackgroundcontributionandcomparetotherawcountingofthedata 147

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Table9-4.SystematicerrorsasafunctionoftheZ p T resultingfromthevariationonthe A .Thevariationisgivenwithrespecttothe 1 d dP T inthefullacceptance. Bin Z p T 1 d dP T FullAcc. Pos.Error Neg.Error GeV/ c GeV/ c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 GeV/ c )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 GeV/ c )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 1 0.0-2.5 0.03485 +0.00012 -0.00011 2 2.5-5.0 0.06491 +0.00013 -0.00010 3 5.0-7.5 0.05718 +0.00019 -0.00021 4 7.5-10.0 0.039452 +0.000070 -0.000076 5 10.0-12.5 0.034921 +0.000019 -0.000017 6 12.5-15.0 0.0267837 +0.0000058 -0.000009 7 15.0-17.5 0.0217625 +0.0000014 -0.000012 8 17.5-20.0 0.016025 +0.000022 -0.000025 9 20.0-30.0 0.010969 +0.000019 -0.000021 10 30.0-40.0 0.005817 +0.000024 -0.000024 11 40.0-50.0 0.003182 +0.000021 -0.000021 12 50.0-70.0 0.001517 +0.000013 -0.000013 13 70.0-90.0 0.0006750 +0.0000079 -0.0000073 14 90.0-110.0 0.0004101 +0.0000054 -0.0000051 15 110.0-150.0 0.0001414 +0.0000020 -0.0000018 16 150.0-190.0 0.00005149 +0.00000066 -0.00000059 17 190.0-250.0 0.00000745 +0.00000009 -0.00000010 18 250.0-600.0 0.000001180 +0.000000002 -0.000000006 accordingthebinningdiscussedinSection9.1.InTable9-6wereportthesystematic errorduetothebackgrounduncertaintiesforeachbinin p T 9.2.4UnfoldingUncertainties Theprocessofunfoldingcanbelogicallydividedinto2steps:extractingtheparameterswhichwesmearthegeneratorleveldatawith,andtrainingtheresponsematrix basedonthisresolution.Eachstephaspotentialsourcesofsystematicuncertainly, whichwewillconsiderinorder. 9.2.4.1Uncertaintyfromextractedresolutionparameters Therstsourceofsystematicuncertaintyfromunfoldingisextractingtheparametersfromthe R D MC f 12 1 ,and 2 forEquation9.Thelatter3formfromrather stabletsoftheMCdirect p T resolutionmeasurement. R D MC ,isbasedonsimilarly stableMCVoigtiant,andaVoigtiantofthedatamasspeakwhichislessstabledue 148

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Table9-5.SystematicerrorsasafunctionoftheZ p T resultingfromthevariationonthe scalefactorsoftheefciency.Thevariationisgivenwithrespecttothe 1 d dP T intherestrictedacceptancedenition. Bin Z p T 1 d dP T Res.Acc. Pos.Error Neg.Error GeV/ c GeV/ c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 GeV/ c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 GeV/ c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 1 0.0-2.5 0.03209 +0.00032 -0.00032 2 2.5-5.0 0.05886 +0.00058 -0.00058 3 5.0-7.5 0.05505 +0.00055 -0.00054 4 7.5-10.0 0.03903 +0.00039 -0.00038 5 10.0-12.5 0.03493 +0.00035 -0.00034 6 12.5-15.0 0.02741 +0.00027 -0.00027 7 15.0-17.5 0.02227 +0.00022 -0.00022 8 17.5-20.0 0.01680 +0.00017 -0.00016 9 20.0-30.0 0.01140 +0.00011 -0.00011 10 30.0-40.0 0.006320 +0.000063 -0.000062 11 40.0-50.0 0.003529 +0.000035 -0.000035 12 50.0-70.0 0.001737 +0.000017 -0.000017 13 70.0-90.0 0.0007762 +0.0000077 -0.0000076 14 90.0-110.0 0.0004865 +0.0000048 -0.0000048 15 110.0-150.0 0.0001790 +0.0000018 -0.0000018 16 150.0-190.0 0.00007087 +0.00000070 -0.00000069 17 190.0-250.0 0.00001172 +0.00000012 -0.00000011 18 250.0-600.0 0.00000224 +0.00000002 -0.00000002 tocomparativelylimitedstatistics.Totestthestabilityofthets,wevarytherangeofthe tsfrom3* downto2andupto4.Forthedoublegaussianparameters,thevaluesvary onlyslightlyanditisexpectedthattheirvariationshouldhaveaverylimitedeffectonthe totaluncertainty.Table9-7summarizesthevarianceintheparametersforthedouble Gaussianparameters. ThenumbersfromtherationoftheVoigtianparametersvaryinamorecomplicated way.Thewidervariationofthetseessomeparametersincreaseandothersdecrease. Table9-8summarizesthevarianceintheseparameters. Toquantifythenetsystematiceffect,wetakefourvariationsofthebaselineparameters.Twoofthesevariationsarethosewhichmaximizethenetsmearingofthedouble Gaussiansmearingparametersmaximizes 1 2 andminimizes f 12 andminimizenet smearing,minimize 1 2 andmaximize f 12 .Thisvariationrepresentsthemaximaland 149

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Figure9-17.100%variationonthenumberoftotalbackgroundeventsredcompared totherawdatacounting. minimalerrorofthetvaluesobtained.Thesecondvariationinvolvesmaximizingand minimizing R D MC .Thevariationsinthetsondatatonotfollowthesameuctuation, thereforthemostconservativeestimateofthesystematicvariationfromthisnumber comesfromcombinationoftwidthsthatmaximizeandminimizetheseratiose.g.the minimaluctuationfortheCSCscalingcomesfromtheratioofthe2 dataVoigtianand the4 MCVoigtian. Takingthe4parametervariationscenarios,weduplicatetheprocessofresponse matrixgenerationandinversionasdescribedinsection6.4.Itisthenpossibletodirectly observetheeffectofthisvariationontheunfolding.Ultimatelywendthesystematic uncertaintyintroducedbythevariationoftheseparameterstobesmallwhencompared tostatisticaluncertainty. Foreachvariationunderstudyweobtainanewresponsematrix.Wethenuseit torepeatthewholemeasurementprocedureandobtainanewdifferential p T shape spectrum.Thenalsystematicerrorisdeterminedfromthelargestdeviationwith respecttothenominal p T shapespectrum.ThevaluesarereportedinTable9-9. 150

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Table9-6.SystematicerrorsasafunctionoftheZ p T resultingfromthe100%variation onthebackground.Thevariationisgivenwithrespecttothe 1 d dP T inthe restrictedacceptancedenition. Bin Z p T GeV = c 1 d dP T GeV = c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 Res.Acc. Syst.Error GeV = c )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 1 0.0-2.5 0.03209 0.00012 2 2.5-5.0 0.05886 0.00023 3 5.0-7.5 0.05505 0.00018 4 7.5-10.0 0.039028 0.000092 5 10.0-12.5 0.034926 0.000084 6 12.5-15.0 0.027413 0.000051 7 15.0-17.5 0.022268 0.000035 8 17.5-20.0 0.016796 0.000016 9 20.0-30.0 0.0113951 0.0000091 10 30.0-40.0 0.006320 0.000023 11 40.0-50.0 0.003530 0.000026 12 50.0-70.0 0.001737 0.000026 13 70.0-90.0 0.000776 0.000021 14 90.0-110.0 0.000487 0.000011 15 110.0-150.0 0.0001790 0.0000035 16 150.0-190.0 0.00007087 0.00000079 17 190.0-250.0 0.00001172 0.00000021 18 250.0-600.0 0.00000224 0.00000001 9.2.4.2UncertaintyontheSpectrumShape Oneofthemainconcernsoftheunfoldingprocedureisthattheresponsematrixis constructedforaspecicspectrumshapeintheMonteCarlo,andthenitisappliedto unfoldtheunknownandmaybedifferentspectrumfromthedata.Inordertoestimate thiseffectwechoosetoreweighttheMonteCarlospectrumtofewvariousshapesand repeattheunfoldingforeachspectrumshapeindependently. Thelowest p T dynamics p T < 1.5GeV/ c islargelydrivenbythephasespace ofthecylindricalcoordinates p T p Z .Thesteplinearraiseofthespectruminthat regionisasimplehandletoprobethesystematicuncertaintyoftheunfoldingwherethe detectorresolutiondistortsthespectrumatmost.WeusePythiaandgenerateDrell-Yan eventswithseveralstandardUnderlyingEventtunes Z 2 100Mevents, ProQ 20 10Mevents, D 6 T CW 900 ,and X 2 1Mevents.AsonecanseeinFigure9-18 151

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Table9-7.CompletedetailsonhowthedoubleGaussiantvaluesvarywiththerangeof thet p T Region 1 2 f 12 3 Fit DT,Low 0.01369 0.0500 0.9817 Overlap,Low 0.0181 0.05486 0.9734 CSC,Low 0.02259 0.06477 0.8819 DT,Mid 0.01597 0.05114 0.9812 Overlap,Mid 0.01993 0.06021 0.9725 CSC,Mid 0.02573 0.07575 0.8854 DT,High 0.0198 0.0598 0.9787 Overlap,High 0.02206 0.0500 0.9294 CSC,High 0.02997 0.08225 0.8622 2 Fit DT,Low 0.0136 0.04449 0.9785 Overlap,Low 0.01782 0.05448 0.9675 CSC,Low 0.02185 0.05919 0.8548 DT,Mid 0.01591 0.04546 0.9788 Overlap,Mid 0.01957 0.05701 0.9643 CSC,Mid 0.02486 0.07314 0.8627 DT,High 0.01968 0.05701 0.9759 Overlap,High 0.02204 0.05926 0.9399 CSC,High 0.02817 0.06741 0.7932 4 Fit DT,Low 0.01379 0.05896 0.9851 Overlap,Low 0.01829 0.06452 0.9796 CSC,Low 0.02336 0.07575 0.9094 DT,Mid 0.01606 0.06078 0.9844 Overlap,Mid 0.02014 0.07059 0.9785 CSC,Mid 0.02641 0.08879 0.9086 DT,High 0.01993 0.07067 0.9826 Overlap,High 0.02306 0.07781 0.9708 CSC,High 0.03049 0.09004 0.8802 variousUEtunesatrstfollowthesimplelinearlawwiththesameslopewithin 5% uncertainty. AnotheradditionalcheckontopofusingthedifferentP YTHIA tunesistoalso reweighttheMonteCarlosmearedspectrumtomatchthereconstructeddataspectrum. Againwerepeattheunfoldingprocedureindependentlyandobtainanotherresponse matrixtoevaluteasystematicerror. 152

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Table9-8.ThedetailsoftheuctuationoftheVoigtian withthevariationofthet range. FitSample 2 t 3 tbaseline 4 t MC,DT 1.351 1.33 1.361 MC,Over 1.366 1.354 1.419 MC,CSC 2.437 2.694 2.701 Data,DT 1.009 0.944 0.9936 Data,Over 1.265 1.037 1.235 Data,CSC 2.635 2.609 2.624 Table9-9.SystematicerrorsasafunctionoftheZ p T resultingfromthedifferent unfoldingmatricesobtainedfromthevariationsontheresolutionparameters. Thevariationisgivenwithrespecttothe 1 d dP T intherestrictedacceptance denition. Bin Z p T GeV/c 1 d dP T GeV = c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 Res.Acc. Syst.Error GeV = c )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 1 0.0-2.5 0.03209 0.00020 2 2.5-5.0 0.058861 0.000069 3 5.0-7.5 0.055049 0.000096 4 7.5-10.0 0.03903 0.00020 5 10.0-12.5 0.034926 0.000049 6 12.5-15.0 0.027413 0.000082 7 15.0-17.5 0.022268 0.000049 8 17.5-20.0 0.016796 0.000091 9 20.0-30.0 0.011395 0.000050 10 30.0-40.0 0.006320 0.000014 11 40.0-50.0 0.003529 0.000011 12 50.0-70.0 0.001737 0.000011 13 70.0-90.0 0.0007761 0.0000056 14 90.0-110.0 0.00048649 0.00000035 15 110.0-150.0 0.0001790 0.0000014 16 150.0-190.0 0.00007087 0.00000016 17 190.0-250.0 0.00001172 0.00000058 18 250.0-600.0 0.00000224 0.00000001 Thenalsystematicerrorduetothe p T spectrumshapeisobtainedbymeasuring thedifferenceofthenominaldifferential p T shapemeasurement-obtainedfromthe Z 2 tune-withrespecttothemeasurementfromtheadditionalP YTHIA underlyingevent tunesandthereweightonthedata.Thelargestdeviationamongallwillbeusedin assigningthesystematicerror.ThevaluesarereportedinTable9-10. 153

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Figure9-18.Thegeneratorlevel p T spectrumwithseveralstandardPythiaUEtunes. Ontheleftzoomintothelow p T rangeshownwithlineartsinthe [0.1]GeV/ c range.Ontherightseveralratiosofthespectrawith differenttunes. 9.2.5Summary InthisSectionwedescribedthedifferentsourcesofsystematicerrorassociatedto themeasurementoftheshapeofthecrosssectionforthe Z + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(asafunctionof theZbosontransversemomentum. Inconclusionweassignasystematicerrorsduetopartondensityfunctionuncertainties,efciencyscalefactors,backgroundestimation,paramtersofthedata-driven unfolding,and p T spectrumshapeusedfortheresponsematrixconstruction.InTable9-11andinFigure9-19wesummarizetotalsourceofsystematicerror,obtainedby summinginquadraturethesingleeffectcontributions. 9.3FinalResults Wenallyextracttheshapeofthedifferentialcrosssectionfor Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(asa functionofthetransversemomentumaccordingtoEquation4. Wethencomparethedifferentialcrosssectionmeasurementwithourbaseline MCgenerator-P OWHEG -andthecurvesfromanalyticalcalculatorssuchasFully ExclusiveW,ZProductionFEWZsoftwares[80]. 154

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Table9-10.SystematicerrorsasafunctionoftheZ p T resultingfromthedifferent unfoldingmatricesduetothe p T shapevariationofthegeneratorlevel.The variationisgivenwithrespecttothe 1 d dP T intherestrictedacceptance denition. Bin Z p T GeV = c 1 d dP T GeV = c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 Res.Acc. Syst.Error GeV = c )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 1 0.0-2.5 0.03209 0.00020 2 2.5-5.0 0.05886 0.00038 3 5.0-7.5 0.05505 0.00041 4 7.5-10.0 0.03903 0.00029 5 10.0-12.5 0.03493 0.00030 6 12.5-15.0 0.02741 0.00043 7 15.0-17.5 0.02227 0.00038 8 17.5-20.0 0.01680 0.00031 9 20.0-30.0 0.01140 0.00014 10 30.0-40.0 0.006320 0.000020 11 40.0-50.0 0.003530 0.000019 12 50.0-70.0 0.001737 0.000015 13 70.0-90.0 0.0007761 0.0000099 14 90.0-110.0 0.0004865 0.0000088 15 110.0-150.0 0.0001790 0.0000029 16 150.0-190.0 0.0000709 0.0000020 17 190.0-250.0 0.00001172 0.00000087 18 250.0-600.0 0.00000224 0.00000008 9.3.1RestrictedAcceptance InFigure9-20wecomparethemeasureddifferentialcrosssectionshapeagainst thepredictionfromtheCMSbaselineDrell-YanMCgenerator,P OWHEG .Thedatapoints arereportedinTable9-12withthestatisticalandthesystematicerrorssummedin quadrature.Thedatapointsaswellastheanalyticalcalculationsarepresentedinthe restrictedacceptancedenedbytheselectioncriteriamoredetailsinSection5.7. ThestatisticalandsystematicerrorarealsoshowninFigure9-21intermof fractionalcontributionwithrespecttothemeasuredvalueineach p T bin. InFigure9-22wealsocomparethemeasureddifferentialcrosssectionshape againsttheFEWZcalculationsatNexttotheLeadingOrderNLOandNextNexttothe LeadingOrderNNLOfora Z 0 + )]TJ/F39 11.9552 Tf 7.085 -4.339 Td [(p T > 20 GeV = c .Forthiscomparisonthe integrationusedtothenormalizethedifferentialcrosssectionstartsat p T > 20 GeV = c 155

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Table9-11.TotalsystematicerrorsasafunctionoftheZ p T Bin Z p T GeV = c Pos.Syst.Error GeV = c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 Neg.Syst.Error GeV = c )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 1 0.0-2.5 0.00046 -0.00045 2 2.5-5.0 0.00075 -0.00074 3 5.0-7.5 0.00073 -0.00074 4 7.5-10.0 0.00053 -0.00053 5 10.0-12.5 0.00047 -0.00047 6 12.5-15.0 0.00052 -0.00052 7 15.0-17.5 0.00045 -0.00045 8 17.5-20.0 0.00036 -0.00036 9 20.0-30.0 0.00019 -0.00019 10 30.0-40.0 0.000075 -0.000074 11 40.0-50.0 0.000053 -0.000053 12 50.0-70.0 0.000039 -0.000039 13 70.0-90.0 0.000026 -0.000026 14 90.0-110.0 0.000016 -0.000016 15 110.0-150.0 0.0000054 -0.0000054 16 150.0-190.0 0.0000024 -0.0000024 17 190.0-250.0 0.0000011 -0.0000011 18 250.0-600.0 0.00000008 -0.00000008 Thedatapointsarereportedwiththestatisticalandthesystematicerrorssummedin quadrature. 9.3.2TotalCrossSection Oneimportantchecktovalidateouracceptancemeasurementistocomputethe totalcrosssectionforthe Z = + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(process.WeusethefollowingEquation9, where R Ldt is36pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 Tot = N Tot )]TJ/F39 11.9552 Tf 11.955 0 Td [(B Tot A R Ldt Theresultweobtainis Tot =0.9459 0.0088 stat.nbwhichiscompatiblewiththe latestofcialresultfromCMS[60], 0.924 0.031 stat. 0.022 syst. 0.102 lumi.nb. 9.4CombinedResults Thepredictionsmadeabouttheshapeofthe Z 0 p T spectrumareindependentof thedecaychannelofthe Z 0 .Henceforthonecaneffectivelydoublethestatisticsofthis 156

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Figure9-19.SystematicerrorsasafunctionoftheZ p T measurementbycombiningtheresults[81]ofameasurementofthe Z 0 e + e )]TJ/F39 11.9552 Tf 7.084 -4.339 Td [(p T spectrum[82].Oneimportantnoteiswhencombiningwithothergroups,agreedupon conventionsmustbereached;onallplotsforthecombinedresultitwasagreeduponto refertothe p T ofthe Z 0 as q T toavoidconfusionwithlepton p T .Forboththeanalysis usingmuonsandelectronstheresultsarepresentedinthelimitedacceptancephase space.Systematicuncertainties,backgroundestimation,andunfoldingareconsistent betweenthetwoanalysis.ThedetailsofhowtheresultsarecombineareinReference [83].Theinitialcombination,alongwithit'scomparisontoPOWHEGinterfacedwith PythiaisshowninFigure9-23. Toextractphysicscomparison,wethenturnourattentiontothedistinctendsof thespectrum.Atlow Z 0 p T ,ourcomparisontovarioustunesoftheunderlyingeventare depictedinFigure9-24.`Tunesoftheunderlyingevent'describesetsofparameters whicharematchedtoseveralquantitiesaimedtobepredictedbynon-perturbativeQCD. Thetunesweseeinthis,andpreviouscomparisonsareProQ20[84],Perguia2011[85], 157

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Figure9-20.Comparisonbetweenthe Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(differentialcrosssectionshape againsttheP OWHEG predictionintherestrictedacceptance. andZ2tune[86].BestagreementisfoundbetweentheZ2tuneanddata,witha 2 = NDOF =9.4 = 8 .TheProQ20performedsimilarlywellwitha 2 = NDOF =13.3 = 8 ThePerugia2011tunewasthelessaccuratewitha 2 = NDOF =48.4 = 8 andthe PYTHIA+POWEGgenerationwasworstwitha 2 = NDOF =76.3 = 8 2 aretakeninto accountusingfullcovariancematrices.TheseresultsprovidevalidationtotheZ2tune 158

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Table9-12. 1 d dP T GeV = c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 intherestrictedacceptance.Errorsarestatisticaland systematicsummedinquadrature.ThebinRangesarein GeV = c ,with 1 d dP T andit'serrorshavingunitsof GeV = c )]TJ/F23 7.9701 Tf 6.587 0 Td [(1 .. Bin Range 1 d dP T Res.Acc. Pos.Error Neg.Error 1 0-2.5 0.0321 +0.0014 -0.0014 2 2.5-5 0.0589 +0.0021 -0.0021 3 5-7.5 0.0551 +0.0020 -0.0020 4 7.5-10 0.0390 +0.0018 -0.0018 5 10-12.5 0.0349 +0.0016 -0.0016 6 12.5-15 0.0274 +0.0015 -0.0015 7 15-17.5 0.0223 +0.0014 -0.0014 8 17.5-20 0.0168 +0.0012 -0.0012 9 20-30 0.01140 +0.00041 -0.00041 10 30-40 0.00632 +0.00028 -0.00028 11 40-50 0.00353 +0.00021 -0.00021 12 50-70 0.00174 +0.00010 -0.00010 13 70-90 0.000776 +0.000071 -0.000071 14 90-110 0.000487 +0.000055 -0.000055 15 110-150 0.000179 +0.000022 -0.000022 16 150-190 0.000071 +0.000014 -0.000014 17 190-250 0.0000117 +0.0000051 -0.0000051 18 250-600 0.00000224 +0.00000078 -0.00000078 withahighQ 2 processthatisquitedifferentthentheminimum-biaseventsonwhichthe Z2tunewasformed. Theshapeofthehighendofthe Z 0 p T spectrumisdominatedbyeffectsattributed toperturbativeQCD.InFigure9-25,onecanobservethecomparisonbetweenthe FEWZNLOandNNLOpredictions,aswellasthepredictionsofthePOWHEGNLO calculatorfor Z 0 p T > 20 GeV = c .Inthisgure,predictionswereeachnormalizedtotheir ownpredictedtotalcross-section.Ofthetwobestperformers,FEWZNNLOperformed slightlyworsewitha 2 = NDOF =30.5 = 9 Inadditiontocomparisontotheory,wecompareourresultstothosequoted byotherexperiments.TheD0study[28]discussedinSection1.5comparesfor Z 0 p T > 30 GeV = c tothecalculationsofRESBOStoNLOprecision.Similarlythis studyreportsanoveralldecitinthetotalcrosssectionatNLO.For Z 0 p T < 30 GeV = c 159

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Figure9-21.Comparisonbetweenstatisticalandsystematicerrorsassociatedtoeach p T bin. theycomparetoseveralTunesoftheunderlyingevent.Theyreportthebestagreement oftheunderlyingeventmodeltoPerugia6,butnotethatthetunewaspartiallycreated ontheelectronmeasurement;theynotethattheonlytuneoftheunderlyingeventthat doesnotmatchdatawithintheoryuncertaintyisunderlyingeventtuneD6.Thesetunes areallpredecessorsofthetunesusedforouranalysis,butitisinterestingtonotethat theP2011ofourcomparisontheworstperforminghasit'srootsinthePerugia6tune oftheD0analysis. AnadditionalstudyworthcomparingtowasthesimultaneousstudybyATLAS[87] ofthe Z 0 p T ,onalmosttheidenticaldatasamplesize.Forhigh Z 0 p T ,thisstudyalso comparestothepredictionsofFEWSatNNLOprecision.Whiletheirsearchdoesnot extendtothesamehigh p T ,itisclearthatthesamefeaturesareobservedinthetwo comparisons.ThesearethatFEWZatNLOprecisiongreatlyunderrepresentsthetotal crosssection,thatFEWZatNNLOunderrepresentsthespectrumaround100 GeV = c 160

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Figure9-22.Comparisonbetweenthe Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.338 Td [(differentialcrosssectionshapefrom dataagainsttheFEWZcalculationfor p T > 20 GeV = c intherestricted acceptance. Figure9-23.CombinationofelectronandmuonchanneldatacomparedwithPOWHEG comparison. 161

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Figure9-24.Thecomparisonofthelow q T spectrumtopredictionsmadefromvarious underlyingeventtunes. thereexcessextendslower,andthataround150 GeV = c thepredictionofFEWZat NNLOovertakestheresultsindata.Insteadofvaryingthetuneoftheunderlyingevent withaxedgenerator,theychoosetotestthepredictionsofvariousgenerators.They notethattheSHERPA[88]generatorhasthelowest 2 /NDOF. 9.5Conclusions Insummary,wepresentedthemeasurementofthenormalizedZ = + )]TJ/F20 11.9552 Tf 7.084 -4.339 Td [(+X crosssectionasafunctionofthedimuontransversemomentum.Thisisthersttime thismeasurementhasbeenperformedatCMS.Theresultshavebeenobtainedusinga sampleofabout36pb )]TJ/F23 7.9701 Tf 6.586 0 Td [(1 gatheredbytheCMSexperimentat p 7 TeV = c .Wecompared 162

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Figure9-25.Thecomparisonofthehigh q T spectrumtopredictionsmadefromvarious perturbativeQCDcalculatorsatNLOandNNLOprecision. themeasuredspectrumagainstanalyticalpredictions.Infactanaccuratedescription ofthelowandhigh p T regionsisessentialinpredictingtheproductionratesandthe kinematicsandthisresultinanimportantinputfortuningthetheoreticalcalculations. Further,theseresultsarecombinedwiththecomparablemeasurementof Z 0 decayingtoelectronpairs.Inthisway,weperformthebestpossiblemeasurement ofthe Z 0 p T spectrumwiththegivenvolumeofdata.Thecombinedresultsareagain comparedwithseveralmodelsofboththeunderlyingeventandpredictionsmade byperturbativeQCD.Bestperformingmodelsareidentiedinbothinstanceswitha 163

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2 comparison,andthedataprovidesinformationtotheoristsforthemostaccurate possiblepredictionsinthefuture. 164

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CHAPTER10 CONCLUSIONS TherstyearofLHCdatatakingprovidedaninterestingsampleforscienticstudy. Particularly,thedatasethadarobustcollectionof Z 0 + )]TJ/F20 11.9552 Tf 10.408 -4.339 Td [(candidates,allowing forthestudyofthe p T spectrum.Thestudyofthe p T spectrumtookondifferentforms. Specically,newphysicsmodelsdecayingto Z 0 weretested,andinitialsearches resultedinanullresult.Inthecaseoftheexcitedquarkmodel,thelackofexcesswas sufcienttosetcompetitivelimitsonaninterestingportionofphasespacepreviously untestedbyotherexperiments. Next,thepredictionsoftheStandardModelweretested.The Z 0 p T spectrum allowedvarioustunesfortheunderlyingeventtobeprobed,andprovidesfeedbackfor futureimprovementstobemade.Additionally,thehighendofthe p T spectrumprovided atestofperturbativeQCDandresultswerecomparedtothepredictionsofboththe POWHEGandFEWZcalculators.Thesecomparisonsalsoprovideimportantfeedback totheoristssuchthatthemostaccuratepossiblepredictionscanbemade. Thesestudiesrepresentonlytheinitialsearchesinwhatpromisestobearich physicsprogramcomingfromtheLHCexperiments.Aslargervolumesofdatabecome available,furthertestsshouldprobedeeperintoourunderstandingoftheStandard Model,andstarttheformationoftheinevitablenextsetofmysteriesthatnaturewill presentoureld. 165

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APPENDIXA:THECATHODESTRIPCHAMBERTRACKFINDERCSCTF A.1Introduction TheCSCTrackFinderCSCTFisthepieceofhardwareresponsibleforforming level1triggersfromsuccessivedetectionsofchargedparticlewithintheCSCs.By makingsuccessive3Dmeasurementsinaknownmagneticeld,thetrackndercan measurethebendingduetothemagneticforce,andfromthereassigna p T valueto themuonseegureA-1.TheUniversityofFlorida,alongwithotheruniversities,is responsiblefortheoperationsoftheCSCTFespeciallytheSectorProcessor;this coversalargearrayoftasks,suchasonlineoperations,maintenance,studieson performance,andupgrades.Inthisappendix,thedetailsofthetrackndersystemand monitoringtoolsareprovided. FigureA-1.TheCSCchambersmeasures and positionsatxed z ,providing informationfortheCSCTFtocompute p T TheCSCTFusesinformationfromsuccessiveCSCchambers.TheCSC'sare organizedbythetheirdistancefromthecenterofthedetector;eachdiskisnumbered withlabelmuonendcapME 1-4,e.g.thediskclosesttodetectorcenterwitha + z coordinateisME+1.Inadditiontoplanesordisks,theCSCsarealsoarranged byconcentricrings.ME1has3rings,andME2-4havetwo;withtheexceptionthat themajorityofthechambersoftheouterringofME4donotexist.TheringsofaCSC 166

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diskarenumberafteraslashfromlowtohighgoingoutwarde.g.theinnermostringof ME+1isreferredtoasME+1/1,theoutermostisME+1/3.Thechambersintheouter ringsofME2-4andalltheringsofMEhavechamberswhichprovide10 o ofcoverage in ,whiletheinnerringsofME2-4have20 o coverage.InallstationsbutME 1/3, chambersoverlapandthereforealternatingchambersareoffsetinthe z coordinate withrespecttooneanother.TheCSCsystemisdividedinto6triggersectorsper endcapseegureA-2.Atriggersectorisa60 o with1 o overlapperslicein ofthe endcap,startingat15 o offsetfrom =0.Inthisway,eachtriggersectoroverlapswiththe neighboringsectorby 1 o [52]. FigureA-2.TheredlinesdenoteasingletriggersectoronME+2 WhenachargeparticlepassesthroughtheCSC,asignaliscreatedontheanode wiresandcathodestripsasdescribedinsection3.6,whichresultsinameasurable voltageonboth.AnodeFrontEndBoardsAFEBswhicharelocatedonthefrontplane oftheCSCchambersseegureA-3,silverboxesonthelefthandsideofthechamber andCathodeFrontEndBoardsCFEBsareresponsibleforconvertinggaussianvoltage readingsintodigitalsignalsofstripandwirehits.BoththeAFEBsandCFEBsreadinto 167

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theTriggerMotherBoardlocatedontheperipheralcratesjustbesidetheCMSdetector volume.BothAFEBsandCFEBshave96inputchannelsor16perstrip/wirelayer. ThismeansthenumberofAFEBsandCFEBsrangefrom3-7and4-8perchamber, respectively. Parameter ME1/1 ME1/2 ME1/3 ME2/1 ME3/1 ME4/1 ME234/2 WireChannelsperplane 48 48 48 112 96 96 64 StripChannelsperplane 2x64 80 64 80 80 80 80 TableA-1.NumberofstripsandwiregroupsperchamberinvariousCSCstations. FigureA-3.AzoomedinphotographofaCSCchamber. TheTMBcombinesinformationaboutstripandwiresignalstoformlocalcharged tracksLCTs.AnLCTisadataobjectcorrespondingtothepassageofacharged particlethroughaCSCchamber.Itcarriesstripandwireinformation,aswellastime, local bendwithinthechamber,andthequalityofthesegmentbasedonthenumber stripandwirehits.ThisinformationisthenpassedalongtotheMuonPortCardMPC, alongwiththeinformationfrom8additionalTMBsfromthesamestation.TheMPCthen 168

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sortstheLCTsbasedonquality,andsendthehighest3or6inthecaseofME1,as ME1has2MPCs,totheCSCTFSectorProcessorSP.Theentiretriggerchainis illustratedingureA-4. FigureA-4.AnillustrationoftheCSCtriggerchain. ThesectorprocessorSPisthepieceofelectronichardwarewhichperformsthe taskoftransformingLCTsintomuontracksandlevel1triggercandidatesseegures A-5&A-6.TherstpartoftheprocessiscompletedbytheSectorReceiverLookUp TableSRLUTs.TheSRLUTsareresponsiblefortranslatingstripandwireinformation oftheLCTsrstintoalocal withinthechamberandthentoaglobal and within thesectorthroughtheimplementationoftunedlookuptables.Global isa12bit integersuchthatithas0.015 o precision,andglobal is7bitswhichleadsto0.0125 unitprecision.Additionally,theSPusesinformationfromtheDTsystemfortrack ndinginthe regionfrom0.9to1.2.Forthisregion,thereareLUTswhichtranslateDT informationtoCSCcoordinates.TheseLUTsarephysicallylocatedontheDTTF,and 169

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similarlytheCSCTFcontainsLUTswhichtranslateCSCinformationtoDTTFformat. WerefertotheLUTwhichtranslatesDTinformationtotheCSCTFformatastheDT Receiver. FigureA-5.AphotographofCSCTFprototypeboardsbeforeFPGAsareconnected. Afterthis,LCTinformationispassedtotheSPcore,whichperformsthetrack ndingfunctionsoftheSP.Therststepintheprocessusesextrapolationunits,which considerthechangein and ofallpossibleLCTcombinations.IfLCTsfallwithin userdenedwindows,thentheextrapolationisconsideredgood,andtheLCTswillbe includedfortheformationofatrack.Asdiscussedinsection2,thedesignoftheLHC callsforcollisionsatarateofonceevery25ns.ThisisthenthetimetheSPelectronics hasbetweenlockingdata,andtheunitoftimensisreferredtoabunchcrossing BX.OnefeatureoftheSPisthatithastheabilitytorecoveroutoftimeLCTsthrougha functioncalledtheBunchCrossingAnalyzerBXA.TheBXAstoresLCTsfor2BX,and 170

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FigureA-6.AphotographofthefrontplaneoftheSPcrateonceallthewiringis connected. performsthefunctionoftheextrapolationunitfor 2BX.Aftervariousextrapolations aredeemedvalid,tracksareassembledusingthebestcombinationofstations.Once tracksareassembled,valuesfor and forthetrackareassigned,aswellasacharge ofthemuonbasedonthesignofthetrackscurvature.Additionally,a4bitnumbercalled themodeofthetrackisassigned,whichencodeswhichstation-to-stationextrapolations areusedtoformthetrack.Italsohas8bitsforthe 12 betweentherstandsecond 171

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stationused,anda4bit 23 fortheextrapolationforthesecondtothirdstation.Inthe instancewhereall4stationshavehits,thestationswiththe3hitsmostconsistenttoa goodextrapolationareused.Afterthis,tracksarepassedto p T LUTsPTLUTs,which areusedtoassignrank.Rankisacombinationquality,a2bitwordwhichdescribeshow wellthecurvatureismeasuredandwhatthe p T bitsofthetrack.Thesevaluesare assignedbasedondatatunedLUTswhichtakeintoaccountmode, 12 23 ,and TheentireprocessisillustratedingureA-7. FigureA-7.AblockillustrationoftheSPLogic. Aftertracksarefound,theyaresenttotheMuonSorter,whichcovertsthele formattotheGMTinputandselectsthebestcandidatesbasedonrank.TheMuon sorterthensendsregionalcandidatestotheGMT,whereit'slogicthendecidesonwhich muonstoselectfortheglobaltrigger. A.2TheCSCTFEmulatorandDQM Itisessentialformakingunbiasdecistionsaboutanalysiscutsthattheresponseof theCMSdetectorcanbepreciselyreproducedforallpossiblephysicssignals.Sothat simulationisconsistentwithupgradesmadetologic,everygroupwhichhashardware responsibilitiesmustprovidenotonlythehardware,butsoftwarewhichemulatesthe 172

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functionalityofthehardware.TheUniversityofFloridamaintainstheemulatorforthe CSCTF.Theemulatorisrunastwoprocesses;therstprocessimplementsthelogic ofthesectorprocessorwhilethesecondimplementsthelogicofthemuonsorter.The sectorprocessorslogiccanbedescribedas2pieces,theSPwrapperandcore.The logicofthecorereplicatesexactlythelogicoftheFPGAsontheSectorprocessor boards.ThecoreslogicisautomaticallygeneratedC++code,andisresponsiblefor associatinghitsfromsuccessivestations,anddeterminingthechangein fromstationto-station.Thewrapperimplementsthelogicofthesectorreceiverlookuptables SRLUTs,theCSCDTrecievers, p T lookuptablesPTLUTs,andpassestheLCTsto thecoreinthetimeorderedway. Theparametersthatareusedtobenchmarktheperformanceofthetracknder aretheefciencyandresolution.Efciencyisanumberwhichdescribestheprobability offormingaCSCtriggergivenamuonofsufcientmomentumhaspassedthrough thesystem.Resolutionisthemeasureofhowpreciselyvariablesaremeasured.In bothinstancesweusebothinformationfromtruthlevelMCandtracknderoutputs toquantifytheseproducts.Thevalueofanemulatorthatreproducesthehardware's logicistheabilitytoaccuratelypredicttheeffectsofchangesinlogictotheemulator andtomonitorforfailuresintheelectroniccomponents.FigureA-8depictsthetrack ndersefciencyfordetectingtracksofall3qualitythresholdsasafunctionof ;inthis instance,itdisplaysadecitintheregionbetween0.9and1.2forhighqualitytrack assignment. Byplottingefciencyasafunctionof ,itallowsustoidentifyquicklywhichaspects oftrackndingcouldbegoingawry.Inthisinstance,thefactthattheinefciencywas occurringintheoverlapregionpointedtocommunicationproblemsbetweentheDTTF andCSCTF.Thisisbecausetoassignaqualityofgreaterthan1toatrackintheoverlap region,aDTstubmustbeincludedat j j 0.9atrackmusthaveanLCTinME1for qualitygreaterthan1.Thisevidenceshedlighttothefactamethodwhichordered 173

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FigureA-8.AperformanceplotoftheCSCTFshowingproblemsinthelow region. DTsegmentshadbeenimproperlycodedintheemulator.Oncethexhadbeen implemented,thelow efciencywasrestoredtoit'sfullperformance,asdepictedin gureA-9. Aswehavestated,thepurposeoftheemulatoristomakepredictionsaboutthe operationofthehardware.AstheCSCTFiscomprisedofofhardware,discrepancies canarisebetweenit'sfunctionandthefunctionoftheemulatorifelectronicfaultsoccur. Toensurethatthehardwareandemulatorareoperatedunderpreciselythesame conditions,aseriesofchecksareperformedtoensureconsistentoperationofthetwo. ThesechecksarepartofthedataqualitymonitoringDQMpackageswhicharerun onlineandarereferredtoasdata-emulatorDEchecks.DQMisoneofseveralonline operationsthatoccurtoensurethatallcomponentsofCMSareinproperworkingorder sothattheresultsoftherunareanalysisqualitydata.ForDQMandotherchecks,there areonlineshifters;peoplewhoactivelymonitortheperformanceofthesystemsbothby 174

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FigureA-9.AperformanceplotoftheCSCTF,depictingtheperformanceinthelow regionafterthexisimplemented. visuallymonitoringperformanceplots,andbyfollowinguponautomaticallygenerated checks.Ifanyerroroccurs,thereisusuallyinstructionsfortheonlineshiftertoreturn thesystemtoworkingorder.Intheinstanceofaproblemoutsidethescopeofthese instructions,oncallshiftersarecontactedandsubsystemexpertsarebroughtinto addressanyremainingproblems. TheconceptbehindtheDEchecksarestraightforward.Foreveryeventwhichis readout,theLCTswhicharesenttothetracknderbytheMPCaresavedasapart oftheeventrecord.Theemulatoriswritteninamannersuchthatonlinedatacanbe unpackedtheprocedureofconvertingbinaryelectronicsignalstotheofineformat andreadinbytheCSCTFemulation.Thisprocessisdoneonthey,andtheresults forvariousquantitiesarecomparedbetweentheCSCTFemulationandhardware. 175

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FigureA-10depictsascreenshotofonesuchvariablewhenthereisperfectagreement betweenthedataandemulator. FigureA-10.Adatatoemulatorcomparisonoftrack assignment,showing100% agreement. Initially,thereweresomecomplicationingettingthe100%agreementnecessary fordatatomatchthehardwareoperation.Bycheckingallthepossibleinternalvariables oftheCSCTF,wecanidentifymalignantproblemsbyclassifyingthetypesoferrors encountered.FigureA-11depictsonesuchproblem.Thisplotshowstracksbeinglisted asdifferentcombinationsofstationsbetweenthedataandemulator.Thisindicates thatoneoftheparameterspassedtothecoreinthehardwarewasdifferentthanthat passedtothecorebythesoftware,andtherefore,adisagreementarose.Disagreementssuchasthesearenowcircumventedasthesystemdynamicallyacquiresthe softwarecongurationforthecorebyreadingoutadatabasewrittenbythehardware conguration. 176

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FigureA-11.Adatatoemulatorcomparisonplotofthetrackmode,showingwhichtype oftracksarenotagreeduponbetweenthedataandemulator. 177

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APPENDIXB OPTIMIZINGTHE P T THRESHOLD FigureB-1.Signicanceasafunctionofsignalyieldforseveraldifferent p T cuts.Left column:gaugeproduction,centralcolumn:contactinteraction,rightcolumn: Z 0 models.Toprow:mass=0.5 TeV = c 2 ,middlerow:mass=1.0 TeV = c 2 bottomrow:mass=1.5 TeV = c 2 178

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BIOGRAPHICALSKETCH JosephAnthonyGartnerIIIwasborninCleveland,Ohioin1984.Hestartedschool intheeasternsuburbofMentorwhereheenjoyedmathandscience.Healsodeveloped passionsforsportsandmusic,andhascontinuedtobeactiveinbothpursuits.In2002, hebeganhisenrollmentatTheOhioStateUniversitypursuingamajorinphysics. Duringhisrstyear,hebeganperformingresearchundertheadvisementofRichard HughesandBrianWinerfortheColliderDetectoratFermilabcollaboration.During thistime,hedevelopedagreatenjoymentfortheeld,anddecidedtopursuehis Ph.D.In2006,hereceivedhisBachelorofScience.HeenrolledattheUniversityof Floridainthejointmasters/Ph.D.programinthefallof2006.Inthesummerof2007, hebeganperformingresearchundertheadvisementofDarinAcosta.In2008,he receivedhismasterdegreefromtheUniversityofFlorida.From2007through2011, heperformedresearchfocusingontheendcaplevel1triggerfortheCompactMuon Solenoidexperiment,thesearchfornewphysicsdecayingtohighlyboostedZbosons, andthecharacterizationoftheZtransversemomentumspectrum.Joeisknownforhis directnatureandhissenseofhumor. 186