Measurement of the Underlying Event Activity in Proton Proton Collisions at the LHC using the Leading Tracks

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Title:
Measurement of the Underlying Event Activity in Proton Proton Collisions at the LHC using the Leading Tracks
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Zakaria, Mohammed
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Doctorate ( Ph.D.)
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University of Florida
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Physics
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FIELD,RICHARD D
Committee Co-Chair:
SIKIVIE,PIERRE
Committee Members:
FURIC,IVAN KRESIMIR
ACOSTA,DARIN E
GREGORY,FRED G

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accelerators -- cms -- detectors -- lhc -- physics -- qcd
Physics -- Dissertations, Academic -- UF
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Abstract:
A measurement of the activity accompanying the hard collision is performed in proton-proton collisions at two center of mass energies of 0.9 TeV and 7 TeV at CMS. The direction of the track with the highest transverse momentum is used to divide the azimuthial plane to three regions: “Toward”, “Away”, and “Transverse”. The data are corrected to the hadronic level and compared with several Monte Carlo Generators. The results are compared with other experiments at the LHC and the Tevatron. These results can be used to add further constrains on the Monte-Carlo generators. It will also enable us to give better predictions for hadronic collisions at higher energies.
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by Mohammed Zakaria.
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Thesis (Ph.D.)--University of Florida, 2013.
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Adviser: FIELD,RICHARD D.
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Co-adviser: SIKIVIE,PIERRE.
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MEASUREMENTOFTHEUNDERLYINGEVENTACTIVITYINPPCOLLISIONSATTHELHCUSINGTHELEADINGTRACKSByMOHAMMEDZAKARIAADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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c2013MohammedZakaria 2

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Thisworkisdedicatedtomydad,forhisvisionandunlimitedsupport. 3

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ACKNOWLEDGMENTS IamverythankfulforallthehelpIhavereceivedinlearningaboutthephysicsandtheresearchtoolsneededtowritethisdissertation.ThankstomyadviserRickFieldforhistrust,encouragement,andsupportthroughouttheseyears.ManythanksgotoIvanFuric,DarinAcosta,KevinBurkett,PaoloBartalini,LucaMucibillo,andAndreaLucarounifortheirsupportandinspirationinvariousformsgiventhroughoutthisjourney,Iamindeepgratitudetothedepthoftheirknowledgeaswelltotheirgivingspirit.Manythankstomylifepartner,JustynaDobrowoloska,forherloveandsupportthroughthechallengesofbuildingareasonablebalancebetweenworkandotheraspectsoflife.Thanksgoestomyfamilyandfriendsfortheirfaithandencouragement.Inparticular,IwouldliketothankMarwanSuheimat,alivingproofofafriendshipthatsurviveslarge(4dimensional,spacelike)displacement.AspecialthanksgoestoRashidHamdan,adearfriendandroom-mateforhisgreatcompanyandfriendship. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTIONTOPARTICLEPHYSICS .................... 12 1.1Overview .................................... 12 1.2TheStandardModel .............................. 12 1.3TheRoleofQCD ................................ 13 2HADRONICCOLLISIONS .............................. 18 2.1Overview .................................... 18 2.2TypesofHadronicInteractions ........................ 18 2.3PartonDistributionFunctions ......................... 19 2.4QCDCalculationsUsingMCGenerators ................... 21 2.4.1TheFixedOrderMethod ........................ 21 2.4.2ThePartonShoweringMethod .................... 22 2.5TheUnderlyingEvent ............................. 23 2.5.1StudyingtheUEinMCGenerators .................. 29 2.5.2FundamentalsofTuning ........................ 32 3THECOLLIDERANDTHEDETECTOR ...................... 34 3.1TheLargeHadronCollider .......................... 34 3.2TheCompactMuonSolenoid ......................... 37 3.2.1TheSuperconductingMagnet ..................... 37 3.2.2TheTracker ............................... 38 3.2.2.1Pixeltracker ......................... 38 3.2.2.2Siliconstriptracker ...................... 39 3.3Calorimeters .................................. 40 3.3.1TheElectomagneticCalorimeter ................... 40 3.3.2TheHadronicCalorimeter ....................... 41 3.4ForwardDetectors ............................... 43 3.4.1CentauroandStrangeObjectResearch ............... 43 3.4.2ZeroDegreeCalorimeter ........................ 43 3.5TheMuonSystem ............................... 43 3.6Triggers ..................................... 44 3.6.1Level1Triggers ............................. 45 5

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3.6.2HighLevelTriggers ........................... 45 4TRACKINGATCMS ................................. 47 4.1TrackReconstruction .............................. 47 4.2TrackQuality .................................. 49 4.3PrimaryVertexReconstruction ........................ 50 4.3.1VertexFinding .............................. 50 4.3.2VertexFitting .............................. 51 4.4TrackSelectionfortheUEAnalysisandEfciencies ............ 51 4.4.1TrackCuts ................................ 52 4.4.2TransverseMomentumUncertainty .................. 54 5THEUEANALYSISSTRATEGY .......................... 55 5.1Overview .................................... 55 5.2TriggeringStrategy ............................... 55 5.3DataandMCSamples ............................. 59 5.4EventandTrackSelection ........................... 60 5.5Monte-CarloSamples ............................. 64 6ANALYSISRESULTS ................................ 66 6.1Hard-scaleDependenceat7TeVand0.9TeV ............... 66 6.2TheUEintheToward,AwayandTransverseRegions ........... 67 6.3TheMaximumandMinimumTransverseRegions .............. 70 6.4AveragepT ................................... 73 6.5TheRatiooftheObservablesatTwoCenter-of-MassEnergies ...... 75 6.6ComparisonwithOtherExperiments ..................... 75 6.7EnergyScanoftheUE ............................. 78 6.8Conclusions ................................... 89 APPENDIX AUNFOLDING ..................................... 91 BTHECROSS-SECTIONFORMPI ......................... 92 CSANITYCHECKPLOTS ............................... 94 DSYSTEMATICUNCERTAINTY ........................... 96 REFERENCES ....................................... 97 BIOGRAPHICALSKETCH ................................ 101 6

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LISTOFTABLES Table page 2-1Theapproximatecrosssectionforvariousprotonprotoninteractions ...... 19 3-1ThedifferentsystemsusedtoacceleratehadronsattheLHC .......... 34 5-1TablelistingthetriggerbinsusedfortheBSCandBPTXtriggers. ........ 57 5-2Thenumberofeventssurvivingdifferenteventselectioncriteriaat0.9TeV. .. 62 5-3Thenumberofeventssurvivingdifferenteventselectioncriteriaat7TeV. ... 62 5-4Differentparametervaluesforthe3usedPYTHIA6tunes. ............ 65 D-1Themainsourcesofsystematicuncertainty .................... 96 7

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LISTOFFIGURES Figure page 1-1Summaryofknownfundamentalparticlesaccordingtothestandardmodel. .. 16 1-2TheQCDcouplingatdifferentscalesQ. ...................... 17 2-1LOPDFfortheprotonaccordingtoMSTWmodelattwoenergyscales. .... 20 2-2AschematicdiagramshowingtheUEinahadroncollision. ........... 24 2-3Aschematicrepresentationfortwoprotonspassingbyinaperipheralcollision,andtwoprotonsinvolvedinaheadoncollision. .................. 27 2-4Thecrosssectionobtainedwith2!2leadingordercalculationvsthetotalcrosssection. ..................................... 28 2-5ThechargedparticlemultiplicityforfewphasespaceregionsusingdifferentMPIschemes. .................................... 30 2-6Thechargedparticlemultiplicityforfewphasespaceregionsusingdifferentmatterdistributionandcolorcorrelationschemes. ................ 31 3-1AschematicdiagramfortheLHCchainofacceleration. ............. 35 3-2AdiagramshowingthelayoutoftheLHC. ..................... 36 3-3AdiagramofCMS,showingitsmaindetectingsystems. ............. 38 3-4AlongitudinalsectionviewofthetrackingsystematCMS. ............ 39 3-5AlongitudinalviewofaquadrantofCMS,showingtheECALsystem. ..... 41 3-6AlongitudinalviewofaquadrantofCMS,showingtheHCALsystem. ..... 42 3-7ThelayoutofonequarteroftheCMSmuonsystem ............... 44 3-8AnoverviewofCMSLevel-1triggers. ....................... 46 4-1Theefciencyandbackgroundcontributionforthethreetrackselectioncriteria. 53 4-2Thefractionoftracksvs.(pT)=pTat0.9TeV ................... 54 5-1BSCtriggerefciencyvstheleadingtrackmomentumat0.9TeV. ........ 58 5-2Thedifferenceinthezaxisbetweenthevertexandthebeamspot. ....... 61 5-3d0=(d0)anddz=(dz)at7TeV. .......................... 63 6-1The)]TJ /F5 11.955 Tf 11.96 0 Td[(phasespacedivisionschemewithrespecttotheleadingtrack ... 66 8

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6-2TheaveragechargemultiplicityasafunctionoftheleadingtrackpTinthetransverseregionat7TeV. ............................. 67 6-3Theaveragechargemultiplicityasafunctionoftheleadingtrack,fortheTowardandawayregions,atTeV .............................. 68 6-4TheaverageTransversemomentumsumasafunctionoftheleadingtrackpTintheTransverseregionat7TeV. ......................... 71 6-5TheaverageTransversemomentumsumasafunctionoftheleadinggtrack,fortheTowardandAwayregions,at7TeV ..................... 72 6-6TheaveragechargemultiplicityasafunctionoftheleadingtrackpTintheTransverseregionat0.9TeV. ............................ 73 6-7Theaveragechargemultiplicityasafunctionoftheleadinggtrack,fortheTowardandAwayregions,at0.9TeV ............................ 74 6-8TheaverageTransversemomentumsumasafunctionoftheleadingtrackpTintheTransverseregionat0.9TeV. ........................ 75 6-9Theaveragescalarmomentumsumasafunctionoftheleadinggtrack,fortheTowardandAwayregions,at0.9TeV ..................... 76 6-10TheaveragechargemultiplicityasafunctionoftheleadingtrackpTinthemaximumandminimumTransverseregionat7TeV. ............... 77 6-11ThedifferenceinaveragechargemultiplicityasafunctionoftheleadingtrackpTintheTransverseregionat7TeV. ........................ 78 6-12TheaveragescalarmomentumsumasafunctionoftheleadingtrackpTinthemaximumandminimumTransverseregionat7TeV. ............. 79 6-13TheDiffinaveragescalarmomentumsumasafunctionoftheleadingtrackpTintheTransverseregionat7TeV. ........................ 80 6-14TheaveragechargemultiplicityasafunctionoftheleadingtrackpTinthemaximumandminimumTransverseregionat0.9TeV. .............. 81 6-15TheDiffinaveragechargemultiplicityasafunctionoftheleadingtrackpTintheTransverseregionat0.9TeV. .......................... 82 6-16TheaveragescalarmomentumsumasafunctionoftheleadingtrackpTinthemaximumandminimumTransverseregionat0.9TeV. ............ 83 6-17TheDiffinaveragescalarmomentumsumasafunctionoftheleadingtrackpTintheTransverseregionat0.9TeV. ....................... 84 6-18TheaverageTransversemomentumasafunctionoftheleadingtrackpTat7TeV ......................................... 84 9

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6-19TheaverageTransversemomentumasafunctionoftheleadingtrackpTat0.9TeV ........................................ 85 6-20TheaveragechargemultiplicityandscalarmomentumsumasafunctionoftheleadingtrackpTintheTransverseregionat7TeVand0.9TeV ....... 86 6-21TheaveragechargemultiplicityandtheTransversemomentumsumasafunctionoftheleadingtrackforbothCMSandALICE ................... 87 6-22Thehadronicactivityatfourcenter-of-massenergiesintheTransverseregionandthemaxregion .................................. 88 6-23Thehadronicactivityatfourcenter-of-massenergiesintheminregionandthedifferenceintheactivitybetweenmaxandmin ................ 89 A-1TheratiooftheMCof(PYTHIA6,tuneZ1)simulationofthedetector(SIM)leveloverthegenerator(GEN)levelforthetwoobservables ........... 91 C-1pT,anddistributionsforthereconstructedtracksat7TeV .......... 94 C-2Sanitycheckplotsforeventreconstruction. .................... 95 10

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyMEASUREMENTOFTHEUNDERLYINGEVENTACTIVITYINPPCOLLISIONSATTHELHCUSINGTHELEADINGTRACKSByMohammedZakariaDecember2013Chair:RichardFieldMajor:PhysicsAmeasurementoftheactivityaccompanyingthehardcollisionisperformedinproton-protoncollisionsattwocenterofmassenergiesof0.9TeVand7TeVatCMS.Thedirectionofthetrackwiththehighesttransversemomentumisusedtodividetheazimuthalplanetothreeregions:Toward,Away,andTransverse.ThedataarecorrectedtothehadroniclevelandcomparedwithtwoMonte-CarloGeneratortunes.TheresultsarecomparedwithotherexperimentsattheLHCandtheTevatron.TheseresultscanbeusedtoaddfurtherconstrainsontheMonte-Carlogeneratorsusedtosimulatethesecollisions.ItwillalsoenableustogivebetterpredictionsforhadroniccollisionsatthehigherenergiestheLHCisplanningtoreachinthefuture. 11

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CHAPTER1INTRODUCTIONTOPARTICLEPHYSICS 1.1OverviewParticlephysicsseekstounderstandthefundamentalelementsofouruniverse,andtheforcesbetweenthem.Throughoutthepasttwocenturies,scienceachievedagoodsuccessinthistaskbystudyingthecomponentsofmatter.Afterestablishingthatallchemicalelementsaremadeofnucleiandelectrons,effortswenttostudyingthecomponentsofthesenuclei.Bythe'30softhelastcentury,twonuclearcomponentswereidentied:ProtonsandNeutrons.Thenextlevelwasunveiledinthe'50sandthe'60swiththediscoveryofquarksandgluonsasthebuildingblocksofthephysicalworldasweunderstandit.Duringthesediscoveries,wefoundmoreparticlesthatareconsideredfundamental.Theseparticles,knownasleptons,donothaveaninternalstructureaccordingtoourcurrentobservations,asisthecasewithquarksandgluons. 1.2TheStandardModelMostofourknowledgeaboutthesubatomicworldisorganizedwithinaframeworkcalledthestandardmodel(Figure 1-1 ).Thismodelassumesthatallcurrentlyknownparticlesandforcescanbetracedtobuildingblocksandforcecarriers.Thebuildingblocksconsistof6differentquarksand6differentleptons,andthereare4forcecarriers(ignoringgravitonsandcolorcharge)thatfacilitatetheinteractionbetweenthesebuildingblocks.Thestandardmodelassumesthatallfundamentalinteractionsareinvariantunderlocalgaugetransformations.Thatis,theLagrangianfortheseinteractionsisinvariantundertransformationscorrespondingtoconservedquantities.Thestandardmodelshowssimilaritiesbetweenthedifferentforcecarriers(photons,ZandWbosons,andgluons),thestandardmodelalsopresentsaprogramtounifytheseforcecarriersinonegrandtheory,wherethereisonelargergaugesymmetrygroupthataccountsfortheknownforces.Consequently,forceunicationassumesthatthecouplingconstantsfortheseforceswillbecomeequalathighenoughenergies.Themostrecentmajor 12

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stepinthisprogramwastheestablishmentoftheelectro-weakunication.Thecurrentunderstandingoftheelectro-weaksymmetryrequirestheexistenceofaspin1bosonknownastheHiggsboson.Thediscoveryofthisparticlewasoneofthemaingoalsofparticlephysicsforthelast4decades.Theexpectedmassofthisparticle,tobefoundafteraseriesofexperimentstobemorethan100GeV,madeitnecessarytobuildparticleacceleratorsonanunprecedentedscale.TheLargeHadronCollider(LHC)wasdesignedandbuiltwiththepurposeofscanningtheTeVenergydomaintodiscovertheHiggsboson.Thistargetwasreachedinthesummerof2012[ 1 ],provingthevalidityofthestandardmodelandtheforceunicationapproach. 1.3TheRoleofQCDMostofthecollisionsattheLHCaredominatedbythestrongforce,whicharisesduetointeractionsbetweenthequarksandthegluons(collectivelyknownaspartons,ahistorictermcoinedbyR.Feynmanthatisusedtodescribethestructerlessconstituentsofhadrons[ 2 ])ofthecollidinghadrons.Itwasfoundfromlepton-nucleonscatteringexperimentsthattheproton,ratherthanbeingapointobject,isanextendedobjectlledwithmanypoint-likeparticles.Byvaryingtheleptonicprobeandthetargetnucleon,itwasfoundthatthreeofthesepointparticleshavespin1/2,theseareknownasthevalencequarks.Itwasalsofoundthattherearemanypointparticlesthatexistforashortperiodoftimeasavorneutralpairsknownastheseaquarks.Thepointstructureofthesepartonswasdeducedfromthefactthattheformfactorsassociatedwiththemdependsonlyondimensionlessquantities,andnotonphysicalquantitiessuchasQ2,apropertyknownastheBjorkenscaling.Thepartonicmodelcanbefurtherrenedbyaccountingforthefactthatquarksandgluonsneedtohave3extradegreesoffreedomtoaccounttoPauli'sexclusionprincipleinthe++particle,where3leptonhavethesamequantumnumbers.Itshouldalsobetakenunderconsiderationthatquarksandgluonscanemitgluonsbeforeorafterthe 13

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interactionswiththeprobinglepton.ThiswillaffecttheBjorkenscalingandtheshapeoftheresultingspectrum.Addingthe3extradegreesoffreedom(referredtoascolors)bringsustothetheoryofQuantumChromodynamics(QCD).ThetheoryofQCDhasanumberofsimilaritiestoQuantumElectrodynamics(QED).Forexample,electronscarrytheQEDcharge,andquarkscarrytheQCDcharge,knownascolorcharge.However,thereare3kindsofcolorchargeversusonlyonekindofelectriccharge.ThereisonlyoneforcecarrierinQED;i.e.thephoton,whichhasnoelectricchargeattachedtoit.InQCD,gluonscarrythecolorchargeandtheyarenotcolorneutral.AnotherdifferencebetweenQEDandQCDisinthecouplingconstantforeachtheory.ThelagrangianofQCDisgivenby:L=Xq q,a(i@ab)]TJ /F3 11.955 Tf 11.96 0 Td[(gstCabAC)]TJ /F3 11.955 Tf 11.95 0 Td[(mqab) q,b)]TJ /F3 11.955 Tf 13.15 8.09 Td[(1 4FAFA, (1)where q,aarequark-eldspinorsforaquarkwithavorq,massmqandcolorindexa.ThetermACcorrespondstothegluoneldandCrunsfrom1to8tocoverthe8gluons.TermtCabrepresentsthe8matricesthatarethegeneratorsfortheSU(3)QCDgroup.gsisthecouplingconstant(s=g2s 4)andFAistheeldtensor.InQCD,thecouplingconstant(s)isafunctionofarenormalizationscaleR:2Rds d2R=(s)=)]TJ /F3 11.955 Tf 9.3 0 Td[((b02s+b13s+...), (1)whereisnegativetoaccountforasymptoticfreedom.ThecoefcientsbiaregivenforthecouplingofaneffectivetheorythatcountsonlyquarksmuchlighterthanR.Ignoringbuttherstterm,wegetasolutionfors:s(2R)=(b0ln(2R=2)))]TJ /F4 7.97 Tf 6.59 0 Td[(1. (1) 14

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Thecouplingconstantapproacheszeroathighmomentumscale(leadingtoasymptoticfreedom,wherethepartonsactasiftheywerefreeparticlesathighpT,contrarytoQED),anditblowsupatsmallscales(whichexplainswhynosinglepartonscanobserved),andinbetweenitevolvesfastwithscale[ 3 ],seeFigure 1-2 .SimilarscaledependenceischaracteristicofmanyQCDrelatedobservablessuchaspartondistributionfunctions,tobediscussedbrieyintheChapter2.ManyofQCDprocessescanbecalculatedusingtechniquesusedinQED,providedthatthecouplingconstantisreplacedwiththestrongcouplingandthatdifferentcolorcombinationsareaccountedfor.ThisperturbativeapproachisvalidonlyforlargeQ2,whichimpliesasmallvaluefors.Forlargevaluesofstheconnementisnotwellunderstood.ItisveryimportanttohaveagoodunderstandingofQCD,andtobeabletoreproduceQCDeffectsaccuratelyinourmodelsinordertocarryoutanyanalysisattheLHC,asQCDisoneofthemainsourcesofbackground.Achievingthislevelofunderstandingrequiresustostudyandmodelthepartofthecollisionsthatdoesnotparticipateinthehardscattering,whichisknownastheunderlyingevent.Thiscomponentoftheeventaffectsmanyoftheobjectsreconstructedbythedetectorsuchasjetenergiesandtransversemomentaaswellasisolationcriteria,especiallyforthetrackingsystems. 15

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Figure1-1. Summaryofknownfundamentalparticlesaccordingtothestandardmodel[ 4 ]. 16

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Figure1-2. TheQCDcouplingatdifferentscalesQ[ 5 ]. 17

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CHAPTER2HADRONICCOLLISIONS 2.1OverviewInChapter2,abriefdiscussionofvariousaspectsofhadronhadroncollisionsispesented.Firstwediscussthetypesofhadronicinteractions,andthecomputationalapproachesusedtoanalyzesuchcomplicatedprocesses.Inparticular,oneoftheMCgeneratorsusedtosimulatehadroniccollisionswillbediscussed,andtheroletheUEeventplaysinthispicture.WewillconcludewithadiscussionontuningMCgenerators. 2.2TypesofHadronicInteractionsProtonprotoncollisionshavetwomajorclasses:Elasticcollisions,wherethetwointeractingprotonsleavetheinteractionpointasprotonsafterexchangingphotons.ThesecondclassisInelasticcollisions,wherethenatureofatleastoneofthetwoprotonschangesduetotheexchangeofforcecarriers.InelasticcollisionsarethemainfocusoftheexperimentalinvestigationattheLHC.Inelasticcollisionscanbedividedintothreegroups: SingleDiffractive(SD),whereonlyoneofthetwoprotonslosesitsstructureduetotheexchangeofapomeron(i.e.acolorsingletexchange). DoubleDiffractive(DD),wherebothprotonslosetheirstructurethroughtheexhangeofpomerons. NonDiffractive(ND),wherebothprotonsinteractthroughweakandstronginteractions,andlosetheirstructure.InthisworkwewillfocusonlyonstudyingNDevents.ThevaluesofthecrosssectionsarelistedinTable 2-1 1. 1Anotherpossibilityiscalledcentraldiffraction,wheretheoutputistwoprotonswithextraparticles.Ithasamuchsmallercrosssectionthatitcanbeignoredinthisdiscussion. 18

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Table2-1. Theapproximatecrosssectionforvariousprotonprotoninteractions.ThevaluesarelistedatTeVcollisions[ 6 ]. Interactiontypecrosssectionvalue[mb] SD14.9DD9ND49.9 Themaineventinanon-diffractivecollisionisa2!2scatteringbetweenonepartonfromeachhadron.ThishappenswithinthesizeofthehadronandcanbecalculatedusingperturbativeQCD.SeeTable1inreference[ 7 ]fortheresults.Inadditiontothisprocess,thereareotherpartonicinteractionsthatarecollectivelycalledtheunderlyingevent.Thehardcomponentoftheeventcanbecalculatedusingthefactorizationmethod[ 8 ],wherewecanrelatetheinteractionatthepartonlevelwiththehadronicactivityseenatthedetector.(AB!cd)=XabcdZdxadxbfa=A(xa,2F)fb=B(xb,2F)^abcd(2s,2R), (2)whereaandbrunoverallquarks,anti-quarksandgluons.fa=A(fb=B)arethepartondensityfunctionsthatgivetheprobabilityofhavingparton`a'carryingfractionxa(xb)oftheprotonmomentumatscale2Fknownasthefactorizationscale.Itservestobridgebetweentheperturbativequantitiessuchas^andnonperturbativequantitiessuchasPDFs[ 9 ]and2R,whichisknownasthenormalizationscale. 2.3PartonDistributionFunctionsPartondistributionfunctions(PDF)arearesultofhadronsbeingcompositeobjects.Theycanbeextractedfromstructurefunctions,ameasurablephysicsquantity,withinthelimitsofaspecicfactorizationschemei.e:Orderbyorderintheperturbationexpansion.Attheleadingorder,PDFshavethesimpleinterpretationofbeingthepartonicdistributionofthehadroninmomentumspace.TheyarerelatedtothestructurefunctionF2usingthefollowingformula: 19

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F2(x,Q2)=Xie2ixfi(x,Q2). (2) Figure2-1. PDFtoLOfortheprotonaccordingtoMSTWmodelattwoenergyscales[ 10 ]. ManyaspectsofPDFsarestillunderstudy,suchasPDFbehavioratlowxregions,PDFuncertainties,andhowtousetheminconjunctionwithparton-showerMCcodes,seereference[ 9 ]foramoredetaileddiscussion.TherearemanymodelsavailableforPDFsbasedonthemethodsusedtoparametrizethedata.OneexampleisshowninFigure 2-1 .Determiningtheproton'sPDFsinvolvesdatafromvariousexperiments,somewithdirectsensitivitytoquarkssuchasDeepInelasticScattering(DIS),theotherwith 20

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indirectsensitivitytogluonssuchasDISenergyevolution,andotherexperimentswithdirectsensitivitytobothquarksandgluonssuchasjetdata[ 3 ]. 2.4QCDCalculationsUsingMCGeneratorsTherearetwogeneralmethodstoevaluateEquation( 2 ):Therstonereliesonperformingthecalculationsforaxednumberofperturbativeordersforthepartoniccrosssection,thesecondoneusesQCDMCmodelstogeneratepartonicshowers. 2.4.1TheFixedOrderMethodLeadingOrder(LO)MCgeneratorssuchasALPGEN[ 11 ]andMADGRAPH[ 12 ]usetreeleveldiagrams,thencarrytheintegrationoverthedesiredphasespaceandcalculatethesquaredmatrixelementsforeachpartonicsubprocess.Thislevelofcalculationscanaccountreasonablyfor2!6-8processes(twoparticlesinteractingtoproduceupto6to8particles).Thenextlevelofcalculations,knownastheNextLeadingOrder(NLO)leveladdsonelooptotheFeynmandiagramsusedinthecalculations,astepthataddstheadditionaltaskofregularization(i.e.gettingridoftheinnitiesassociatedwiththeemissionofsoftgluonsbyintegratingtheloopmomentaover4-dimensionsratherthan4).Afterthatthereisaneedtoaccountforthefactthatthephysicalcutsintroducedinarealexperimentarein4dimensions.Thestandardmethodistointroducesuitablecountertermsthatdonotaffectinfrared(IR)safeobservables.Thesetermswillcancelallcollinearandsoftdivergencesandcanbeintegratedanalyticallyinthe4-space.NLOordercalculationsareverylengthyandconsumelargeCPUresources.Mostoftheavailablemodelscover2!3-5processes.TheNexttoNextLeadingOrder(NNLO)levelsuffersthesameproblemthatNLOcalculationshave.Butthistimewearedealingwithtwosoftandtwocollineardivergencesinthediagrams.Thesubtractionprocedureisthusmorecomplicatedandwehaveroutinesthatonlydealwith2!1levelcalculationsforhadronicinteractions. 21

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2.4.2ThePartonShoweringMethodThesecondmethoddependsontryingtore-interpretthedivergencesobservedintherstapproach(IRandcollineardivergences)physically.Therststepistocalculatetheprobabilityofapartontoradiateagluonabovesometransversescale.ToaLOthiscanbewrittenas[ 3 ]:P(emissionabovekT)')]TJ /F3 11.955 Tf 23.12 8.09 Td[(2sCF ZdE EZd (E)]TJ /F3 11.955 Tf 11.95 0 Td[(kT), (2)WherePistheprobabilityofemittingagluonwithatransversemomentumabovekT,sisthestrongcouplingconstantandisrelatedtotheprobabilityofaQCDemitting/absorbingagluon,andCRisthecolorfactor,whichisdirectlyrelatedtothestrengthofthecouplingbetweentwodifferentcolorstatesthroughasinglegluonexchange.Subtractingthepreviousresultfromonegivesustheprobabilityofnothavingagluonemission.Atthesoftandthecollinearlimit,thisresultcanbeexpandedtoallorders:P(noemissionabovekT)(kT,Q)'exp[)]TJ /F3 11.955 Tf 10.5 8.08 Td[(2sCF ZdE EZd (E)]TJ /F3 11.955 Tf 11.95 0 Td[(kT)], (2)theterm(kT,Q)isasimpliedversionoftheSudakovfactor[ 13 ],wereweassumedstobeconstantandtookitoutoftheintegral,andusedahardcollinearradiationtermdE=Einsteadofafullcollinearsplittingfunction.TheSudakovformfactorallowsustocalculatethedistributionofthetransversemomentumkT1ofthegluonwiththelargesttransversemomentuminthehadronicevent:dP dkT1=d dkT1(kT,Q). (2) 22

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ThisleadstotheMCpart;wecantakearandomnumberrfromauniformdistributionboundbetween0and1tobetheSudakovfactor,thensolvetheEquation( 2 )forkT1.Thisgivesusagluoninadditiontotheinitialstateofthesystem.WerepeattheproceduretogenerateagluonwithkT2
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Figure2-2. AschematicdiagramshowingtheUEinahadroncollision[ 19 ].Theupperpanelrepresentthehardest2)]TJ /F3 11.955 Tf 11.95 0 Td[(2interaction,thesecondpanelshowsISRandFSRinblueandgreen.Thethirdpanelshowsthecombinedeffectoftheprevioustwopanelsaswellasadditioalpartonicinteractions. 24

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TheadditionofMPIleadstothepossibilityofobservingextraparton-partoninteractions.Theadditionaljetsarereferredtoasminijets.Thesejetshavethepropertyofformingback-to-backpairs,comparedtojetsfrombremsstrahlungthatarealignedwiththedirectionoftheparentpartons.ThisextraactivityismoreobservableatlowpTandgivessignicantcontributiontothecolorowandscatteringenergyoftheevent.ThisisobservedinthedetectorasanincreaseinmultiplicityandET,andasacontributiontothebreak-upofthebeamremnantsintheforwarddirection.TherstMCmodelforMPIwasproposedinthelate80's[ 20 ].Themainpremisebehinditwastoviewtheinteractinghadronsasabeamofincomingpartons.Thescenarioofmorethanoneinteractingpartoncanthenbetreatedprobabilistically.Thisinteractionwillalsochangethecolorowofthewholesystem.Quantitatively,havingMPIthataremostlysoftinscalemeansthatthe^t-channelisalmostonshellandthusthepartoniccrosssectionbehavesroughlyas:d^/^dt ^t2^dp2T ^p4T. (2)Weintegratethecrosssectionfromacut-offvaluetothecenterofmassenergyusingtheleadingorder2!2matrixwithPDFsincluded.TheresultisshowninFigure 2-4 anditshowsthecrosssectionforthissimpleMPImodelexceedingthetotalcrosssectionfortheregionsofpTbelow5GeV/c[ 21 ].Thiscanbeexplainedbyrecallingthefactthatwhilethetotalinteractioncrosssectioncountsaneventasone,the2!2crosssectionmightcountitmorethanonceduetoMPI.Hence,wecanrelatethetwocrosssections:2!2(pTmin)=hni(pTmin)tot, (2)andtheprobabilityofhavingnumbernofinteractionsinoneeventisgivenby: 25

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}n(pTmin)=[hni(pTmin)]nexp[hni](pTmin) n!. (2)Thismathematicalapproachcanbefurtherrenedbyimposingmomentumconservation,sothatpartonswillnotusemoremomentumthanwhattheparenthadronhad.ThisservestosuppressthelargedivergenceaspTgoestozero.Onealsohastoconsidercolorscreening.Thatis,atlowpTthewavelengthoftheexchangedpartonbecomeslargerthanthetypicalcolor-anticolorseparationdistance,anditsresolvingpowerisreducedtoseeingthecoloraveragechargethatvanishesaspTgoestozero,effectivelygivinganIRcut-offfortheinteraction.Thisscalecanbeestimatedusingthefollowingapproximation:pTmin'~ rp0.2GeV.fm 0.7fm0.3GeVQCD. (2)Inreality,thevalueobtainedinEquation( 2 )isabittoosmall.InMCmodelsthisnumberiseffectivelysetasaparametetthatcanbeinsertedtoEquation( 2 )asastepfunction(asisdoneinHERWIG)orasasmoothfunctionasinEquation( 2 )toregularizethedivergencefurther(asisthecaseinSHERPAandPYTHIA).Thisparametercanbeenergydependentandisoneofthekeyparameterstoconsiderwhenexploringnewenergyregions.HigherenergiesmeanthatPDFscanbeexploredatsmallerxvalues(asshowninFigure 2-1 ),wherethenumberofpartonsdrasticallyincreasesandtheybecomemorepacked;i.e.smallercolorscreeningdistance.Thisleadstoamajorconcernregardingtheuncertaintiesintheenergyandthexscalingofthecut-offwhenextrapolatingbetweendifferentcolliderenergies[ 9 ].OneofthemainfeaturesoftheUEistheso-called`pedestaleffect';theobservationthathardinteractionsappeartobeaccompaniedwithmuchhigherUEactivitythaneventswithnohardinteractions.Thisisinterpretedintermsoftheimpactparameter 26

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ofthecollidinghadrons[ 22 ],wherehavingahardscatteringmeansthattheimpactparameterissmallenoughthatmorepartonsareengagedatasmallerxaswell.Thustheabilitytodescribebothtypesofcollisions(calledcentralandperipheralcollisions,seeFigure 2-3 )dependsonthequalityofthemodelsoftheimpactparameterdependence.SpecialattentionisgivenwheninterpretingtheresultsofthezerobinofthePoissondistribution,whichcorrespondstoanimpactparameterlargerthanthediameterofthehadron(noNDinteractions).ForMCmodelsthatdescribetheentireinelasticandnon-diffractivecross-section,thisbinissimplyignoredasitrepresentsdiffractiveorelasticscatteringthataremodeledseparately.ForMCmodelsthatarerestrictedtohardinelasticevents,thiscanbereinterpretedasthefractionofthetotalinelasticcross-sectionthathasnohardinteractions. Figure2-3. Aschematicrepresentationfortwoprotonspassingbyverticallyinaperipheralcollision,wheretheimpactparameterislargeenoughthatonlythesoftpartoftheprotonsisinvolvedinthecollision(left)andtwoprotonsinvolvedinaheadoncollision,wheretheimpactparameterismallthatthecoreoftheprotonsparticipatesinthecollision(right)[ 22 ]. s(p2T)dp2T p4T!s(p2T0+p2T)dp2T (p2T0+p2T)2. (2)FurtherenhancementstotheMPImodelincludeshoweringthepartonsinvolvedinthisactivityandperturbativerescattering.Whiletheshoweringoftheoutputfollowssimilarpatternasfor2!2scatteringprocess,theshoweringofpartonsbeforeenteringtheMPIinteractionregionraisesquestionsonhowtocorrelatemulti-partondensity, 27

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Figure2-4. Thecrosssectionobtainedwith2!2leadingordercalculationvsthetotalcrosssection(thehorizontalline)usingseveralPDFmodels[ 21 ]. whichisatopicofongoingresearch.Perturbativerescatteringoccurswhenpartonsareallowedtodoseveralinteractions,whichisalsoanactivelineofresearch[ 23 ].IntroducingtheMPItothesystemaddschallengestohadronizationmodels,sinceithastocolorneutralizedifferentcolorsystems(beamremnants,aswellastheprimaryinteraction)thatareseparatedintherapidityspace.ManyoftheIRsensitivevariables(hadronmultiplicitiesandhadronspectra,forexample)dependcruciallyonthesecorrelationsincolorspace.Todate,thereisalargeuncertaintyonhowtoaddressthismatterwhichisreectedinthesubstantialamountofvariationbetweendifferentMCmodels. 28

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2.5.1StudyingtheUEinMCGeneratorsThemainfeatureofthepartonshoweringMCmodelsistheirabilitytoprovideacompleteanddetailedpictureofthecollidernalstate[ 24 ].Thelevelofaccuracydependsonthechosenprocess(themoreinclusivetheprocessis,thebettertheMCdescriptionwillbe)andthelevelofdetailthesimulationcontains.ThisisobviousfromtheimprovementobservedwithintheMCgeneratorsasbettertheoreticalmodelsbecomeavailable;forexample,includingmatchinghigherordermatrixelementsandbetternon-perturbativemodels.Italsodependsonconstrainingthefreeparametersofthesemodelsusingdata,aprocessknownasgeneratortuning.Asanexample,wewilldiscusssomeofthetunningaspectsofoneoftheknownMCgenerators:PYTHIA6.4.InthisclassofMCgenerators,auniedapproachisadoptedinmodelingallinelasticandNDevents[ 24 ].Thatis,theminimumbias(MB)eventisconsideredasasoftlimitcaseofdijetproductionandtheUEeventsaccompanyingit,withnochangeinmodelsbetweenthetwo.TherearemanyparametersassociatedwiththeregularizationoftheMPIcrosssection: TheInfraredRegularizationscale:AswasexplainedearlierandinEquation( 2 ),theparameterpT0setsthescaleforthecolorscreeningeffectandiscalledtheinfraredregularizationscale.InPYTHIA,itissettohaveapowerlowfunctionofcenterofmassenergy:pT0(p s)=PARP(82).p s PARP(89)PARP(90), (2)wherePARP(82),PARP(89),PARP(90)arePYTHIAparametersthatcanbetuned:PARP(82)setsthevalueofpT0atthechosencenterofmassenergyasdeterminedbyPARP(89),PARP(90)determineshowsteepthechangeofpT0iswithasthecenterofmassenergychanges,seeFigure 2-5 TheTransverseMassDistribution:Anotherimportantaspectfortuningistheshapeoftheprotonmatterdistribution.ThisstemsfromthefactthattheamountofMPIinteractionsinagivencollisionisproportionaltotheamountofmatteroverlapbetweenthecollidingbeamparticles.Thatis,thesmallertheimpactparameterbis,themoreMPIactivityistobeexpectedasisdemonstratedbyFigure 2-3 .Iftheprotonstructureisuniform,thedifferencebetweenperipheralandcentralcollisionswillbesmall.Ontheotherhand,astronglypeakeddistributioncanmake 29

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Figure2-5. ThechargedparticlemultiplicityforfewphasespaceregionsusingdifferentMPIschemes[ 24 ]. theactivityincentralcollisionsmuchhigherthaninperipheralones.Thematterdistributionismodeledaccordingtothefollowing:D(b)/exp()]TJ /F3 11.955 Tf 9.29 0 Td[(bd), (2)wherethepowerdisafreeparameterwhoserangeisnormallytakentobefromd=1(exponential,representingaverypeakedstructure)tod=2(Gaussian,representingasmoothstructure).Notethatthenormalizationofthisdistributionisxedtounity.Notealsothatbisgiveninanarbitraryunit;sincetheonlydimensionfulquantityisthetotalcrosssection,thebshapedoesnotaffectthetotalcrosssectionatallinthistypeofmodel,andonlythedimensionlessratiob=appearsintheexplicitcalculations.Thepower,d,appearsastheparameterPARP(83)inPYTHIA.Itisnotassumedtochangewithenergy:d(p s)=PARP(83). (2) 30

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Figure2-6. Thechargedparticlemultiplicityforfewphasespaceregionsusingdifferentmatterdistributionandcolorcorrelationschemes[ 24 ]. Inotherwords,theIRregularizationtermaffectstheaverageactivity,andthetransversemassdistributiontermcontrolsthedeviationfromthisaverageforperipheralandcentralcollisions[ 24 ].Itwasfoundfromdatathattheoverlapfunctionisclosertoagaussian[ 24 ]. ColorReconnectionStrength:MPIcorrespondtooneormorecolorexchangesbetweenthepartonsthatgivesacolorneutralnalstateatthehidronizationphase.InPYTHIAthisisdone,asmentionedearlier,throughtheLundstringmodel.Inparticular,weassumethatalarge,colorneutral,stringthatrepresentstheunstablestategetsbrokenintosmallerstringsthatarecolorneutralaswell.SuchscenarioseemsnecessarytoaccountfortheincreaseofmeanpTtrackmultiplicityinminimumbiasevents[ 24 ].TheparametrizationoftheLundmodelisaccomplishedwiththestringinteractionstrength(R),andissetbyPARP(78).Thelargertheparameteris,theharderthepTspectrumwillbe. 31

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2.5.2FundamentalsofTuningDuetothelargenumberofparametersavailableincurrentMCgenerators,thereisaneedforaframeworktoautomatethetuningprocedure.Therehavebeen3mainapproachestowardMCtuninginthelastcoupleofdecades: Manualtuning:WhereanexperteyeadjustsfewselectedparametersoftheMCtotthebehaviorrequired.Suchmanualapproachrequiresasignicantinsighttowardsthealgorithmicresponsetoparameterchoices,whichcanbedevelopedthroughexperience.Itisintrinsicallyslowasitinvolvesmanyiterationsofparameterchoicesbeforegettingareasonableoutputwithsatisfyingstatistics.Atypicaltuningeffortnormallycomprisesofadjustingonlyfewparametersandobservingfewplotsforresponsiveness.Foreachnewgenerator,thereisaneedtostartthelearningprocessfromscratch.Despiteallthat,manualtuningstillmaintainsstrongpresenceamongtheMCcommunity.Infact,mostofthetunespremieredinpreviousCompactMuonSolenoid(CMS)UEanalyseshadmanualtunessuchastunesZ1andD6T. BruteForcetuning:WhichcoversanyapproachaimingatdividingtheparameterspacetopointsandrunningtheMCgeneratorateachoneofthem.Theproblemswithsuchapproachareobvious;selectingonlyfewparameterswith,say,10pointseachwillrequirethousandsandthousandsofMCruns.Eventhen,thesamplinggranularitymightmaskanymeaningfulresults.Anothermethodwithinthisstrategyistorelyonthebest2t.Alsohinderedbythelimitedscalewecancoverandthelackofwaystoimprovehebestt,ortodistinguishbetweenlocalandglobalminima. Parametrization-basedtuning:Thisstrategydependsonparametrizingthegeneratorbehavior,wherewetthepolynomialtothegeneratorresponseofeachobservablebintoacertainelementoftheparametervector.Oncethisisdone,weconstructagoodnessoftfunctionandminimizeit.Theresultisaparametervectorthatshould,inprinciple,beabletopredictthebestdescriptionofthetunningdatathegeneratorcanprovide.Thiscanbedoneinaconsiderablyshortertimecomparedtotheprevioustwoapproaches.TuneZ2,introducedinourresults,usedthethirdapproach.ThiswasdoneusingthePROFESSOR[ 25 ]tunningframework,whichreliesonconstructingfastanalyticmodelsofthegeneratorbyanalysingitsresponsetoshiftsintheparameterspace.ThecomparisontoexperimentaldataisdoneviaRivet[ 26 ]analysistool.ThetunewasbasedonttingtheproleplotsforCMSanalysisthatusedtheleadingtrack-jettostudy 32

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theUEatCMS[ 27 ].Onlytwoparametersweretuned:PARP(90)andPARP(82),andallproleplotsweregivenequalweightforthetwocenter-of-massenergies. 33

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CHAPTER3THECOLLIDERANDTHEDETECTOR 3.1TheLargeHadronColliderTheLHCistheworld'shighestenergycollider.Thehighestenergyproton-protoncollisionshavereachedthevalueof4TeVperbeamprotonin2012andisexpectedtoreach13TeVwhenitresumesoperationsin2015.Therunningprotonsintheringformabeamcurrentofapproximately0.58A.Thetwoprotonbeamsruninseparatepipesexceptatinteractionsegmentsof120mateachinteractionpoint.Thiswouldleadtoaround30head-oncollisionsateachsegment.Thecolliderrepresentsthelastlinkinasystemofsmalleraccelerators.Eachacceleratorrisestheenergyofthebeamuntilitreachesthenextstage.Table 3-1 listsvariousacceleratorsystemsusedtoreachtheTeVenergyscaleattheLHC. Table3-1. ThedifferentsystemsusedtoacceleratehadronsattheLHC. KineticEnergyoftheprotonAccelerator 50MeVLinac21.4GeVPSBooster25GeVPS450GeVSPS7TeV(planned)LHC TheLHCringismadeofeightarcs.Eacharccontains154dipolebindingmagnets.Connectingthearcsareinsertionpointsthatconsistofalongstraightsectionwithatransitionregionateachend,calledthedispersionsuppressors.Theexactlayoutofthestraightsectiondependsontheinsertionpointspecicuse:Physics,injection,beamdumping,orbeamcleaning.SincethegoaloftheLHCistoproduceprocessesrarelyobservedinnatureatunprecededenergies,themostimportantparametersarethebeamenergyandthenumberofinterestingevents.Thisisexpressedthroughtherelationbetweenthenumberofeventsandtheluminosity: 34

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Figure3-1. AschematicdiagramfortheLHCchainofacceleration[ 28 ]. Nevent=Levent, (3)whereListheintegratedluminosityandisthecrosssectionfortheprocessunderinvestigation.Theluminositydependsonthebeamparametersandcanbewritten,assumingaGaussianbeamdistribution,as[ 29 ]:L=N2bnbfrevr 4nF, (3) 35

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Figure3-2. AdiagramshowingthelayoutoftheLHC[ 30 ]. whereNbisthenumberofhadronsperbunchfromonebeam,nbisthenumberofbunchesineachbeam,frevtherevolutionfrequency,ristherelativisticgammafactor,nisthetransversenormalizedemittance,istheopticalbetafunctionattheinteractionpoint,andFisthegeometryluminosityreductionfactor[ 29 ]:F= 1+cz 2!)]TJ /F9 5.978 Tf 7.78 3.26 Td[(1 2, (3)wherecisthecrossingangleattheinteractionpoint,zisthebunchlengthand=p nisthermsofthebeamsizeatIP.TheLHCaimstodeliverluminosityoftheorderof1034cm)]TJ /F4 7.97 Tf 6.59 0 Td[(2s)]TJ /F4 7.97 Tf 6.59 0 Td[(1atCMSandATLAS,with2808bunchesandbunchspacingof 36

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25ns,themaximumacceptablevaluefornis3.75mandthebeamdynamicsaswellasthemechanicalaperturesetsthelimitonthenumberofparticlesperbunchtobe1.15x1011. 3.2TheCompactMuonSolenoidCMSisoneofthemajorexperimentsthatutilizetheLHCbeam.Itsmainfeatureisthe3.8Tsuperconductingmagneticsolenoid.Thesolenoidsurroundsthetrackingsystemandthecalorimetricsystemsandimmersesthemwithitsuniformmagneticeld.Thereturningyokecontainsthemuondetectionsystem.Eachofthedetectorsystemscanbeimaginedasacylinderwithabarrelparalleltothebeamline,plustwocapsontheends.Thisdesignensuresalmostafullangularcoverage,asshowninFigure 3-3 .Theconventionalcoordinatesystemplacesthepointoforiginattheinteractionpoint.Thex-axisisparalleltotheEarth'ssurfaceandpointstowardtheLHC'scenter.They-axispointsupward,andthez-axisisparalleltothebeamline.Theazimuthalangle()ismeasuredinthex-yplanewithrespecttothex-axis.Thepolarangle()ismeasuredinthez-yplanewithrespecttothez-axis.Forconvenienceisreplacedwithpseudo-rapidity(),whichisdenedas:=)]TJ /F3 11.955 Tf 9.3 0 Td[(lntan 2, (3)BelowwelistthemajorcomponentsofCMSwithabriefdescriptionofeachpart: 3.2.1TheSuperconductingMagnetThemagnetprovidesastronganduniformmagneticeldformomentummeasurementatCMS.Themagneticcoiloperatesat4.5Kusingliquidhelium.Theironyokesecuresareturningeldofabout2T,withalargebendingpowerforaccuratemomentumresolutionforthemuons.Atfullcurrent,2.6GJofenergyisstoredinthesystem. 37

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Figure3-3. AdiagramofCMS,showingitsmaindetectingsystems[ 31 ]. 3.2.2TheTrackerTheCMStrackerisconstructedtomeasurechargedparticlestrajectoriesaccurately.Itwasdesignedtogiveanexcellentspatialresolutionforalloutgoingchargedparticlesfromtheinteractionregion.Duetothenatureofthebeam,thetrackershouldcombineagoodspatialresolutionwithhighperformanceintermsofvertexreconstruction.Thisneedstobedonewithminimummaterialbudgettoreduceeffectssuchasmultiplescatteringandbremsstrahlung.Thetrackerismadeoftwosubsystems:Thepixeltrackerandthesiliconstripes.Abriefdescriptionisgivenforbothsystemsbelow: 3.2.2.1PixeltrackerThepixeldetectoristheclosesttrackersystemtotheinteractionpoint.Itcoversaregionofjj<2.5andisorganizedintheformof3coaxialbarrelsthatare53cmlongwithradii4.4,7.3and10.2cm.Thecapsarecoveredbytwodisksoneachsideatz=34.5and46.5cm.Theyaredividedintopixels,eachhasanareaof100150m2givingaround44millionchannels.Attheend-caps,thepixelsarerotatedby20to 38

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improvehitresolution.Thepixeldetectorisabletoprovidesinglepointhitswithaspatialresolutionofabout10minther)]TJ /F5 11.955 Tf 11.96 0 Td[(spaceand15)]TJ /F3 11.955 Tf 11.95 0 Td[(20minthezdirection. 3.2.2.2SiliconstriptrackerTheSiliconStripTrackeristheouterpartofthesilicontracker.Itcoversthepseudorapidityregionjj<2.5,whereradiationlevelsandtrackdensityarereasonabletooperatesilicondetectors.Thestriptrackerisdividedtofoursubsections:TheTrackerOuterBarrel(TOB),theTrackerInnerBarrel(TIB),theTrackerInnerDisk(TID),andtheTrackerEndCaps(TEC).Eachsubsectionhaslayersofmodules,whereeachmodulecontainsasetofsiliconstripsensors.Thedimensionsofthestripsvarybetween117mm64mmfortheinnermodulesand190mm96mmfortheouterones. Figure3-4. AlongitudinalsectionviewofthetrackingsystematCMS[ 32 ]. Theresolutionofthetrackingsystemisaround1)]TJ /F3 11.955 Tf 12.22 0 Td[(2%inpTatpT=100GeV.Themainfactorthatreducestheresolutionismultiplescattering.At=0,thereisasmalldecreaseinefciencyduetothegapsinthepixelladders. 39

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3.3CalorimetersCalorimetersareanimportantdetectionsystemusedformeasuringtheenergyandpositionofaparticlebyitstotalabsorption[ 33 ].Calorimeterscanbeclassiedaccordingtotheirstructure:homogeneousorsampling.AhomogeneouscalorimetercanbeusedtodetectphotonsbyCerenkovradiationemittedbye+e-pairscreatedintheCoulombeldsofthenuclei.Alternatively,asamplingcalorimetercanbeconstructedfromseparatelayersofanabsorberanddetector.CMShasbothtypesofcalorimeters:thehomogeneousoneiscalledTheElectromagneticCalorimeter(ECAL),andthesamplingoneisreferredtoasTheHadronicCalorimeter(HCAL). 3.3.1TheElectomagneticCalorimeterTheElectromagneticCalorimeter(ECAL)isoneofthecalorimetricsystemsofCMS.Itisdesignedtomeasurephotonandelectronenergiesaccurately.ItismadefromLead-Tungestatescintillatingcrystals(PbWO4).Thereare61200crystalsinthebarrelreagionand14648attheendcaps.ThecrystalsatthebarrelhaveatotalradiationlengthofX=25.8X0and22mm22mmfrontalcrosssection.ThecollectionofthelightisperformedwithsiliconAvalanchePhotoDiodes(APD).Attheendcaps,thecrystalshave24.7mm24.7mmfrontalcrosssectionwithasmallerradiationlengthX=24.7X0,inordertobalancetheexistanceofthepre-showersysteminfrontoftheendcaps(1.65
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Figure3-5. AlongitudinalviewofaquadrantofCMS,showingtheECALsystem[ 34 ]. TheNinthesecondtermrefersisproportionaltophoto-electricirregularitiesalongsidethecrystals,andCisaconstanttermaffectedbyelectronicnoiseandpile-up.Equation( 3 )isvalidupto500GeV.Afterthat,theshowerleakagefromtherearofthecalorimeterbecomestoosignicantandthisparametrizationoftheresolutionisnolongeraccurate. 3.3.2TheHadronicCalorimeterTheHadronicCalorimeterneedstofullltwoconditionsinitsdesign:itneedstopossessenoughdensityandthicknesstocontainthehadronicshower,anditshouldnotbemadewithferromagneticmaterialssinceitisplacedinsidethesuperconductingmagnet.HCALismadefromasamplingcalorimeterwitha3.7mmplasticscintillatoralternatedwitha5cmthickbrassplateabsorber.SimilartoECAL,theHCALbarrelcoverstheregionofjj<1.48andtheendcapcovers1.48
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quartzandsteelandknownastheHF,seeFigure 3-6 .TheenergyresolutionofHCALis: Figure3-6. AlongitudinalviewofaquadrantofCMS,showingtheHCALsystem[ 32 ]. E E2=140.2% p E2+(4.7%)2. (3)Thersttermrepresentsthestochasticuctuationinthesignal.Thesecondtermisfoructuationsoftheshoweraccompanyingthesignal.IntheHCAL,theresolutiongetssensiblyworseforjjlargerthan1.4.Thisismainlyduetheinactivematerialinthedetector(i.e.servicecables).Theperformanceoftheforwardcalorimeter(HF)canbedividedintohadronicandelectormagneticcomponents:E E2hadronic=182% p E2+(9%)2, (3) 42

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E E2electromagnetic=138% p E2+(5%)2. (3) 3.4ForwardDetectors 3.4.1CentauroandStrangeObjectResearchTheCentauroandStrangeObjectResearch(CASTOR)isaquartz-tungstensamplingcalorimeterinstalledat14.4mfromtheinteractionpoint.Itcovers5.2
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Figure3-7. ThelayoutofonequarteroftheCMSmuonsystem[ 34 ]. spatialresolution.TheyareusedmainlytocomplementDTandCSCmeasurementsandtoidentifybunchcrossings.UsingthemuonsysteminconjunctionwiththetrackingsystemhelpsinimprovingthemomentumresolutionbyanorderofmagnitudeforbothregionsoflowpT(wheretracksareaffectedbymultipleCoulombscattering),andhighpT(wherethesagittaofthemuontrackcanbemeasuredbeforeandafterthesolenoid). 3.6TriggersAtriggersystemaimstoacceptallusefuleventsandtorejectmostbackgrounds.ThisiscrucialatanexperimentsuchastheLHC,wherethebeamfrequencyis400MHz.Suchhighfrequencyleavesonly25nsfordatareadoutandprocessing.Itistechnicallychallengingtoreadout,makeadecisionabouttheevent,andstorethelargeamountofdataatthisrate;nottomentionselectingthesignalsthatarerelevantto 44

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theevent.Thesolutionistopipethedatatoastrongprocessingsystemthattakesfewmicrosecondstomakethedecisiontoaccepttheeventornot.Suchselectionprocessrequiresagoodtiggeringstrategythatmaximizeseventswithdiscoverypotential.ThetriggersystematCMShastwostages:Levelonetriggers(L1)andHighleveltriggers(HLT): 3.6.1Level1TriggersALevel1triggerisdesignedtoperformveryfastaccept/rejectdecisions.L1triggerdecisionisbasedoncalorimetertowersandmuonchamberinformationonly.Thisreducestherateofdatato10kHz.Afterthat,thereare3layersofincreasingcomplexityofL1triggers:local(suchascalorimetertowers),regional(combinationsoflocaltriggers),andglobal(whichperformscalculationsforvariablessuchasjetsandtotaltransverseenergyETsum.Seediagram 3-8 formoredetailsofL1triggeringstratefyatCMS. 3.6.2HighLevelTriggersTheHighLevelTriggerisasoftwaresystemimplementedinaclusterofcommercialprocessorsatCMS.Itperformsthereadoutofthefront-endelectronicsforeventsacceptedatL1-trigger.ThereisnolimitationonthenumberofvirtualtriggerlevelsortothealgorithmsemployedexcepttheCPUtime.AtCMS,theHLTtriggerstrategyisthetraditionalmulti-leveltriggersystems,wheretheselectionprocessisoptimizedbyrejectinguninterestingeventsasquicklyaspossible.Withthisinmind,eachtriggerpathconsistsofasequenceofsoftwaremoduleswithincreasingcomplexityandphysicssophistication.Eachmodulefulllsawelldenedtasksuchasreconstruction,intermediatetriggerdecisionsorthenaltriggerdecisionforthatpath.AftertheHLTtheeventratewillbeintheorderof100Hz,whichismanageablewithinthecurrentstorageresourcesatCMS. 45

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Figure3-8. AnoverviewofCMSLevel-1triggers[ 34 ]. 46

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CHAPTER4TRACKINGATCMSCMSseesaneventasalargeamountofelectronicsignalsinitssystems.Thenextstepisprocessingthisinformationtoreconstructtheparticleshistoryafterthecollision.Sincethisanalysisdependsmostlyontracks,itisbettingtointroducethebasicsoftrackreconstructioninCMSinsomedetail. 4.1TrackReconstructionTrackreconstructionistraditionallydividedintotwoseparatesubtasks:trackndingandtracktting[ 35 ].Trackndingistheprocessofdeterminingthesubsetofmeasurementsinthetrackingsystemthatbelongstothesametrack.Trackttingextrapolatesthemeasurementsfromthetrackndingstagetoestimateasetparametersthatidentiesthetrack.Additionally,thequalityofthetrackcandidatesisevaluatedatthisphaseandadecisionismadeifitshouldbeacceptedasarealtrackornot.Thisdivisionbetweentrackttingandtrackndinglasteduntilthe'80s,whenKalmanlter[ 36 ]wasinvented.Itcanbeviewedasastatisticallyoptimalrenementoftrackfollowing[ 37 ].Generallyspeaking,atrackatanygivensurfaceofthedetectorcanbedescribedby5trackparameters:2forposition,2fordirection,andoneforcurvatureormomentum,alsoknownasthestatevectorofthesystem.AKalmanlterconsistsofaseriesofalternatingpredictonandltersteps.Inthepredictionstep,thestatevectorisextrapolatedtothenextdetectorsurface.Inthelterstep,theextrapolatedstatevectorisupdatedbytakingaweightedmeanofthemeasurement.ShortlyaftertheinventionoftheKalmanlter,itwasrealizedthatthisprocedurecanbeusedforbothtrackndingandtracktting.Duetotheuniformmagneticeld 47

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atCMS,theoutgoingchargedparticlesfromthepointofinteractionwillbemovinginahelicalpath.The5parametersusedbyCMStodescribesuchpathare1: pT,thetransversemomentum. cot()=pz=pT,thedipanglethatcomplementstheanglebetween~pand~pT. ,theazimuthalangleofthemomentumvectorattheimpactpoint. d0anddz,thetransverseandlongitudinaldistancewithrespecttothenominalvertex.Theyaresettohavetheclosestdistancetoit.TheQualityofthetracksisgivenintermsof2ofthetrackt,thenumberofdegreesoffreedomofthet,thenumberofhitsnusedinthet,andbythenumberofgapsinthemeasurementsequencenlosthits.ThefollowingsummarizesthegeneralstepsfortrackreconstructioninCMS[ 35 ]: Seedgeneration,wheretheseedconsistsoffewmeasurements,mostlyinthepixelpartofthetracker. Localtrackndingbeginningfromaseed.AttheLHCthisisdonethroughalgorithmsbasedongeneralizedversionsofKalmanlter. Tracktting,whichinvolvesproceduressuchasremovingtrackcandidatesthathavetoomanycommonmeasurements(trajectorycleaning).ForexampleGaussian-sumlter(GSF)isusedforelectrontracktting. Post-processing;retting,ambiguityresolution,etc.Itisworthmentioningthatthemuonsystemhasadedicatedstrategytohandleitstracks.Thisisbecauseithasareducedmagenticeldthatisgenerallynotaswellbehavedastheeldinthecentralregion,itisimportanttoaccountforthepassageofmuonsthroughmorematerial.CMSusescombinatorialKalmanlterformuontracking. 1Thisisnottheonlychoicetodescribeatrack,Forexampleonecanuse:q=p,dx=dz,dy=dz,(x,y)andsign(z)touniquelyidentifyatrack 48

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4.2TrackQualityAftertheprocessofttingthetracksandparameterizingthem,thetrackingsoftwareneedstodeterminethelevelittruststhatthesetrackscorrespondtophysicaltracks.Theresultofsuchtestisgivenintermsoftrackquality.Thetracksthathavelowvalueofqualityareconsideredfakeorghosttracks.Thecriteriaappliedinrejectingghosttracksare[ 38 ]: 2=n. d0,thetrackdistancefromthebeamspot. ThetrackztothepositionclosesttoHLTprimaryvertex. Thed0=d0whered0isthemeasurederrorinthetransversebeamspotpostion. Thez=dzlongitudinalcompatibilitywiththeclosestHLTvertex.Inordertoadaptthetrackqualitycutstotheexpectedtrackresolutionforthevertexassociation,theresolutionsonthetrackmeasuredd0anddzhavebeenparametrizedas:(d0,dz)(pT)=a+b pT[GeV=c], (4)whereaandbarecongurableparametersthatcanbesettothenominalvaluesa=30mandb=100mortightenedtoreducethefakerateatlowpT:Thedependenciesoftheoptimalcutswiththetracknlayers(numberoflayerscrossed),pTandhavebeenapproximatedwiththefollowingformulas: 2=n<0nlayers. jd0j<(1nlayers)x1d0(pT). jzj<(2nlayers)x2dz(pT). jd0j=d0<(3nlayers)x3. jzj=dz<(4nlayers)x4. 49

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Wherei,xj(withi,j2f1,2,3,4garecongurableparameters).CMS[ 38 ]hasadoptedfewtrackselectionscenariostosupressfaketrackswhilekeepinghighefciency.CMScollaborationhasimplementedthreedifferentthresholds:loose,tightandhighPurity.Therstcollectionoftracksareallthetracksreconstructedfromthealgorithmoftracking.Tightselectionandhighpurityselectiononlydifferinimpactparametercuts,thelatterisstricterduetodifferentparametrizationsinEquation( 4 ),forhighPuritytheadoptedoptionwasa=30mandb=10m.Inthefollowing,westudyhowchargedparticlesproducedwithpseudorapiditieswithinthetrackercoverage(jj<2.5)andtransversemomentapTabove0.5GeV=ccanbereconstructedandqualiedasahighpuritytrack.InordertoincreasetheperformanceofCMStracking,Iterativetrackingisappliedinselectingthetracks.Afterremovinghitsusedinthepreviousiteration,whereanewseedandtrackingparametersareusedineachiteration.Inthe5iterations,therearechangesintheseedinglayer(pixeltriples,doublet,orothercombinationsincludingthestriptracker),pT,d0,anddz. 4.3PrimaryVertexReconstructionOncetracksarereconstructed,dedicatedalgorithmsareappliedtoestimatetheprimaryvertexposition.Thisprocess,knownasvertexreconstruction,typicallyinvolvestwosteps:Vertexnding,whereclustersoftracksoriginatingfromthesamevertexaregroupedtogetherasvertexcandidates,andvertextting,wherethepositionoftheprimaryvertexiscomputed. 4.3.1VertexFindingTospeed-uptheprimaryvertexndingprocess,pixeltracksfrompixelhittripletscanbeusedtoefcientlyndthevertexpositions.Inoff-lineanalyses,wheretimingisnotanissue,thefullinformationofthereconstructedtracksandtheircorrespondingcovariancematricesareused.Thisoff-linemethod[ 39 ]startswithapreselectioncutbasedontheimpactparametersignicanced0=d0.Thiscutrejectssecondaryvertices 50

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andfaketracks,andreducesthecomputationtime.Inasecondstep,theselectedtracksareextrapolatedtothebeamline,andgroupedaccordingtotheirseparationinthezdirectioninordertoformprimaryvertexcandidates.Alimitissetonthemaximumseparationinzbetweenthetwosuccessivegroupoftrackstothesameprimaryvertexcandidate.Eventually,thereconstructedprimaryverticesaresortedindecreasingorderofhardness,denedbythescalarsumofthetansversemomentumofeachtracksquared.Ni=1(pTi)2. (4) 4.3.2VertexFittingThesetoftracksassociatedwiththeprimaryvertexttingalgorithmsareusedtocomputethebestestimateofthevertexparameterssuchasitspositionandcovariancematrix,aswellasindicatorsofthetquality[ 40 ].VertexttinginCMSisperformedusingastatisticalmethodknownastheAdaptiveVertexFitter[ 40 ].Itisconsideredsuperiortoleast-squareKalmanltersduetoitsbetterhandlingwithmis-associatedtracks(outliers).Intheadaptivevertext,eachtrackattachedtoavertexisassignedatrackweightbetween0and1basedonitscompatibilitywiththecommonvertex.Thetrackswithlargerdistancetothevertexpositionaredown-weightedsignicantly,whichmakesthealgorithmrobustagainstoutliers.Thenumberofdegreesoffreedomisdenedas2Tracksnwi)]TJ /F3 11.955 Tf 12.03 0 Td[(3,wherewiistheweightofithtrack.Itisthusstronglycorrelatedtothenumberoftrackscompatiblewiththeprimaryinteractionregion.Consequently,thenumberofdegreesoffreedomofthevertexcanbeusedtoselectrealproton-protoninteractions. 4.4TrackSelectionfortheUEAnalysisandEfcienciesThetrackselectioncriteriafollowsthestrategyemployedbypreviousUEanalysesatCMS[ 27 ].TomeasuretheUE,weneedtondthetracksassociatedwithp-p 51

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collisions(i.e.primarytracks).Thisstrategytriestominimizealltrackscomingfromsecondaryinteractionandfaketracks.Inadditiontothiscriteria,thereshouldbeemphasisongoodtrackresolution.ThisisbecausemostofalltheobservableswillbepresentedasafunctionofpToftheleadingtrack.Atrackisconsideredprimaryifithasc<1.Reconstructionefciencyisestimatedbycomparingthemtoassociatedhitsthatmatchthehitsexpectedfromachargedparticlepassagevstheclustersreconstructedinadetector.Atrackisconsideredassociatedifthesharedhitsaremorethan75%.Inordertoquantifytheperformanceofatrackndingalgorithm,aMCsimulationofatracksample,whereallthetracksarelabeled,isused.WeusetheefciencyPtomeasureit.Itisdenedasthenumberofassociatedtracksthealgorithmcannddividedbythetotalnumberofsimulatedprimarytracks.Tobeofrealuse,efciencyneedstobeaccompaniedwiththepurityPpofthesampleofthefoundtracks,whichisthenumberofassociatedtrackswiththecorrectlabeldividedbythetotalnumberofselectedtracks.Efciencyismoreimportantthanpurity,sinceanearperfecttrackwithfewwronghitscanverylikelybecorrected,whileatracknotfoundduringthetracksearchislostforever[ 37 ].Studyingefciencyinrealdataismuchmoredifcult,anditusuallyinvolvesscanninganeventsamplevisuallyorusingindependentsourcessuchasscintillators.SeeFigure 4-1 forthesevaluesfortheusedtrackingalgorithm,thedifferentMClabelsrepresentdifferenttrackcuts,atopicofthenextsection. 4.4.1TrackCutsToselecttheprimarytrackinoursample,asetofcutshavebeenintroduced: jj<0.8, pT>0.5GeV=c, d0(vtx) d0<3, dz(vtx) dz<3. 52

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Thelasttwocutsareusedtoselectthetracksassociatedtoaprimaryvertex.Ontopofthebaseselection,somequalitycutsarerequiredtoreducethefakecontributionandtorejecttrackswithpoormomentummeasurement.Threeselectionchoicesaredeveloped: UE1:baseselectionwithHighPurityand(pT) pT<10%, UE2:baseselectionwithNlayers4(theminimumnumberofstriplayerscrossedbytracks),Npixellayers2(minimumnumberofpixellayers)and(pT) pT<5%, UE5:baseselectionwithHighPurityand(pT) pT<5%,UE5ischosenasreferencewhileUE1andUE2areusedasacross-check.TheonlydifferencebetweenUE1andUE5istheloosercuton(pT)=pT,whileUE2doesnotusethehighpurityquality,butinsteadreliesontheminimumnumberofcrossedlayers.TheperformanceoftheUE5selection Figure4-1. Theefciencyandbackgroundcontributionforthethreetrackselectioncriteria[ 41 ]. TheleftpanelofFigure 4-1 showstheefciency,P,tobecloseto90%inthecentralregion,droppingto75%forjj<2,andintherightpanelofFigure 4-1 weobservethebackgroundcontribution.Asexpectedthedegradationinefciencyandtheincreaseinthefakeratearecorrelated,inthetransitionbarrel-endcapregionsofthe 53

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tracker,whichischaracterizedbyalargermaterialbudget.Theresultisanincreaseoftheprobabilityofinelasticnuclearinteractionsoftheprimaryparticles,whichconvertsthemtotwoormoresecondaryparticles.The3%ofnon-primarytrackspassingtheselectionareattributedtocombinatorialbackground(2%)andsecondarytracks(1%)resultingfromKSanddecay[ 27 ]. 4.4.2TransverseMomentumUncertaintyAsitwasexplainedearlier,thereisaneedtoseektrackswithasmuchprecisionaspossible,bearinginmindnottotightentheselectioncriteriatothelimitofeliminatingmanygoodtracks.Figure 4-2 showsthevariable(pT)=pTfordataanddifferentMonteCarlomodels.Intheplot,thesecondbumpisduetoprimaryparticlescreatinglesshits(i.e.electron-holepairs)thanexpectedbecauseofnuclearinteractionsordecays.Inparticular,thesetrackshavehitsinthepixeldetectoronly,givingawrongestimationsofthetransversemomentum. Figure4-2. Thefractionoftracksvs.(pT)=pTat0.9TeV[ 41 ]. similarresultswereobservedfor7TeV[ 42 ]. 54

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CHAPTER5THEUEANALYSISSTRATEGY 5.1OverviewInChapter5wewilllistthedatasamplesusedintheanalysisandbrieydescribethemethodsappliedinextractingtheeventsdeemedusefulfortheUEstudiesfromthebackground.Thesemethodsareeitherappliedduringdataacquisitionsuchastriggering,orafterthedatahavebeenstored,suchaseventselection.BothwillbediscussedaswellastheMCsamplesthatwereusedindetectorstudies. 5.2TriggeringStrategyThedatastreamingoutoftheCMSdetectorneedstobesplitintodatasetstotakeadvantageoftheparallelCMScomputingmodelfordataprocessing.EachsetiscalledaPrimaryDataset(PD)[ 43 ].TheusedPDsarebasedonZeroBiasandMinimumbiastriggercongurations: TheZeroBiasPDisbasedontheBeamPick-upTimingeXperiment(BPTX)[ 44 ].ThissystemisdesignedtoprovidepreciseinformationregardingthetimingoftheLHCbeam.Ithasatimeresolutionoftheorderof210)]TJ /F4 7.97 Tf 6.59 0 Td[(10s[ 44 ]. TheMinimumBiasPDisbasedontheBeamScintillationCounter(BSC).Itmeasurestherelativeratesofbackgroundparticlesandcollisionproducts,bothenteringandexitingCMS.Itisstationed10.86metersawayfromtheinteractionpointfrombothendswithtimeresolutionoftheorderof3ns[ 45 ].InTable 5-1 thetechnicaltriggerbitsdealingwithBPTXandBSCarereported.Atriggerstrategywithhighefciencywithcollisioneventswasneeded,itdependsonthefollowingtriggerbits: Bit40:itrequiresacoincidenceinsidea20nswindowbetweentwoBSCstationswithatleastonehitineachstation. Bit41:itrequiresacoincidencewithin20nsbetweenthetwoBSCstationswithatleasttwohitsineachstation. Bits36,37,38,39(thebeamhalotriggers):theyrequirehitsinbothBSCstationstobeseparatedintimeby7320ns,correspondingtothetimeofightbetweenthetwoBSCstations. 55

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Itisalsorequiredtohavethebeampresent(bit0),indicatingalledbunchfrombothbeamscrossingtheinteractionpointatthesametimebasedonthecorrespondingBPTXsignal.Thetriggerrequestedisacombinationofthebitsdescribedabove:0\40\!(36[37[38[39). (5) 56

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Table5-1. TablelistingthetriggerbinsusedfortheBSCandBPTXtriggers. BinTriggerTriggerNameTriggerDetails 0BPTXL1TechBPTXplusANDminusBPTX+andBPTX)]TJ /F3 11.955 Tf -493.16 -14.44 Td[(32BSCL1TechBSCminBiasinnerthreshold1BSCminbias:hits+zside>=1andhits)]TJ /F3 11.955 Tf 11.96 0 Td[(zside>=133BSCL1TechBSCminBiasinnerthreshold2BSCminbias:hits+zside>=2andhits)]TJ /F3 11.955 Tf 11.96 0 Td[(zside>=234BSCL1TechBSCminBiasORBSCOR:thereisatleastonehit,anywhereintheBSC35BSCL1TechBSCHighMultiplicityBSChighmultiplicity:allcoincides36BSCL1TechBSChalobeam2innerBSChalo:beam2inner37BSCL1TechBSChalobeam2outerBSChalo:beam2outer38BSCL1TechBSChalobeam1innerBSChalo:beam1inner39BSCL1TechBSChalobeam1outerBSChalo:beam1outer40BSCL1TechBSCminBiasthreshold1BSCminbias:hits+zside>=1andhits)]TJ /F3 11.955 Tf 11.96 0 Td[(zside>=141BSCL1TechBSCminBiasthreshold2BSCminbias:hits+zside>=2andhits)]TJ /F3 11.955 Tf 11.96 0 Td[(zside>=242BSCL1TechBSCsplashbeam1BSCsplashtrigger:beam1,threshold=2;innerringhitson)]TJ /F3 11.955 Tf 11.95 0 Td[(zside>=243BSCL1TechBSCsplashbeam2BSCsplashtrigger:beam2,threshold=2;innerringhitson+zside>=2 57

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InthisanalysisitisimportanttodetermineifthetriggerefciencyiscompatiblebetweendataanddifferentMCmodels.TheefciencyofthetriggerhasbeencomputedwitheventcandidatestakenfromtheZeroBiassample.TheeventselectioncorrespondingtothisanalysisisrequiredtohaveatleastonehighpuritytrackwithpTabove0.5GeV/cinthetrackeracceptanceregionjj<2.Thetriggerefciencyisdenedastheratioofthenumberofeventsthatpasstheeventselectionandrethetriggeroverthenumberofeventsthatpasstheeventselection. Figure5-1. BSCtriggerefciencyvstheleadingtrackmomentumat0.9TeV[ 41 ]. Figure 5-1 showsthattheMCefciencyoftheBSCtriggerselectionagreeswellwiththeefciencyderivedfromtheZeroBiasdata.Theefciencyiscloseto%95fora 58

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trackpT>2GeV=c.ThereisagoodagreementbetweenthedataandthereferenceMCsimulation.Similartriggerchoicesareimplementedat7TeV,withthesamePDconvention:ZeroBiasPDthatdependsontheBPTXtrigger,andMinimumBiasPDthatusestheBSCtrigger.For7TeV,thefollowingMinimumBiasbitshavebeenused: Bit40. Bits36,37,38,39. Bits42(43),BSCsplashtriggerforbeam1(2).Thethresholdissetat2,askingforinnerringhits.Thelogicimplementedconsideringthenumberingschemeover-reportedisthefollowing:0\40\!(36[37[38[39)\!((42\!43)[!(43\!42)). (5)Bits42and43werenotavailableintherstcollisionsat900GeV,theyallowustoimprovetheselectionoftruecollisionbetweenthebeams.Ouranalysisisbasedonthefollowingruns: Pre-1E29(Runs132440-135807):1PD 1E29(Runs135808-140041):8PDs 1E30(Runs140042-141949):9PDsThetriggeringstrategywasmodiedduetocodemigration(fromCMSSW 3 5 XtoCMSSW 3 6 X),therewasashifttousingHLTtrigger:HLT MinBiasPixel SingleTrackisapplied,wherewerequiretheexistenceofatlestonetrackinthepixeldetectorwithpT>=0.2GeV.ThistriggerisseededbyL1 BscMinBiasOr BptxPlusOrMinus(Thatisringeitherbit0orbit40).Thispathmaintainsthehighefciencyoftherstchoice. 5.3DataandMCSamplesThisanalysisusesdatasamplescoveringtwocenterofmassenergies: 59

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0.9TeVdatasamplecollectedin2009.Thedatasampleusedhas11.0Moftriggeredevents,foranintegratedluminosityofabout1b)]TJ /F4 7.97 Tf 6.58 0 Td[(1.Thefollowingdatasamplewasused: MinimumBias/Commissioning10-Jun14thReReco-v1/RECO 7TeVdatasample,ThedatausedinthisanalysishavebeentakenfromMarchtoMayof2010.Theanalyseddatacorrespondtoanamountof1nb)]TJ /F4 7.97 Tf 6.59 0 Td[(1ofintegratedluminosity.Duetothelimitedpre-scalingoftheMinimumBiastriggerthiscorrespondtoatotalstatisticsof28.5Meventstriggered.Thedataat7TeVhave4differentsamples(namedfrom1to4).TheycorrespondtoslightlydifferentrunningconditionsattheLHC.Thefollowingdatasamplesareused: DatasetI:/MinimumBias/Commissioning10 Jun14thReReco-v1/RECO DatasetII:/MinimumBias/Run2010A Jun14thReReco-v2/RECO DatasetIII:/MinimumBias/Run2010A Jul16thReReco-v1/RECO DatasetIV:/MinimumBias/Run2010A PromptReco-v4/RECOAsfortheMCsamples,therearetworequireddistinctions:MCsamplesthatrepresentsthehadronicactivityatthegenerator(GEN)levelonly,i.e.theoutputofsimulatingthephysicalprocessesofproton-protoncollisions.AndtheMCsamplesthatrepresentthephysicalprocessafterpassingadetectorsimulation(SIM).WhilewecaneasilygenerateGENsamplesprivately,theproductionofSIMsamplesismorerestrictedandweonlyusedofciallyapprovedCMSsamples: MinBias-TuneZ1-900GeV-pythia6/Summer10-START36-V10A-v1 MinBias-TuneD6T-900GeV-pythia6/Summer10-START36-V10A-v1 MinBias-TuneD6T-7TeV-pythia6/Summer10-START36-V10-SP10-v1 MinBias-TuneZ1-7TeV-pythia6/Summer10-START36-V10-TP-v1Thesesamplesareusedforexperimentalprocedurevalidation,andtocorrectthedatatothegeneratorlevel.TheamountofMCsamplesavailablevariesbetweendifferenttunes,buttheyareallabove10Meventslevel,thusprovidingenoughstatistics. 5.4EventandTrackSelectionAfterpassingthroughthetriggerphase,aneventneedstosurviveasetofcriteriadesignedtorejectbackgroundevents.Abeamscrapinglterisappliedtothetriggeredevents.Thenwerequireonlyoneprimaryvertextobeamongtheselectedevents.Thisvertexneedstobevalid(i.e.itshouldhavedifferentcoordinatesthanthebeamspot). 60

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Thecaseofvertexsplittingwasinspectedanditwasfoundnottogiveanysignicantbiasintheanalysisresults[ 42 ].Thevertexshouldhaveatleast5degreesoffreedomandshouldbewithin10cmfromthezdirectionofthebeamspot,asshowninFigure 5-2 thiscutiswithin3ofthegaussiantaverage.Tables 5-2 and 5-3 showthepercentageofeventsthatsurvivetheapplicationofeachoneoftheselectioncriteria.TheyalsoshowthepercentageofthesurvivingeventsforoneoftheMCtuensusedinthisanalysis. Figure5-2. Thedifferenceinthezaxisbetweenthevertexandthebeamspot. Furtherqualitycontrolswithtightercutswereneededtoreducethebackgroundcomingfromvarioussources,foreachselectedeventthereconstructedtrackcollectionneedstobecleanedupfromundesiredtracks,namelysecondarytracks(tracksresultingfromthedecayofunstableparticles)andcombinatorialbackground(fake 61

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Table5-2. Thenumberofeventssurvivingdifferenteventselectioncriteriaat0.9TeV. EventSelectionDataMC(Z1) Triggered11.0x106100%+1validPrimaryVertex91.6%90.5%+(+/-10cm)vertexwindow86.7%89.7%+vertexndoflargerthan485.6%83.2% Table5-3. Thenumberofeventssurvivingdifferenteventselectioncriteriaat7TeV. EventSelectionDataIDataIIDataIIIDataIVMC(Z1) Triggered18.7x10633.2x1032.7x10611.4x1069.5x106+1validPrimaryVertex95.3%95.8%95.8%95.9%93.8%+(+/-10cm)vertexwindow99.6%99.3%89.3%88.3%99.6%+vertexndoflargerthan490.7%90.6%90.7%90.7%87.6% trackscomingfromerroneousreconstructionofatrackfromsegmentsthatbelongtoothertracks).Thecutsappliedare: pT>0.5GeV=c. jj<0.8. TrackQuality:HighPurityselectionand(pT)=pT<0.05. Secondariesremoval,non-primaryparticlesresultingfromdecaysofsecondaryinteractionhavelargeimpactparameterwithrespecttothebeamaxisandarenotassociatedwiththepositionoftheeventvertex. thelongitudinalimpactparametersignicanced(vtx)0=d0<3. thetransverseimpactparametersignicanced(vtx)z=dz<3.Thedistributionsofd(vtx)0=d0andd(vtx)z=dzareshowninFigure 5-3 .Cuttingonthesignicanceoftheimpactparameterhasbeenpreferredwithrespecttheselectionontheabsolutevalueofthesamequantity.Theformerdistributionhaveamoreuniformbehaviourwithrespecttothelatterone.Thethresholdshavebeenchosenasacompromisebetweenahighprimaryparticleselectionefciencyandlowfakeratecontamination,asdescribedinChapter3.ThersttwoparameterswereadoptedinordertoremovesomeoftheminimumbiascomponentandtocomparewithvariousotherexperimentssuchasALICEandCDF,whichhaveasmallerrange.Furtherstudiesaboutthetrackingqualityisgiveninappendix 62

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Figure5-3. d0=(d0)(upperleftpanel),dz=(dz)(uperrightpanel)andtherelativepTuncertaintyat7TeV. 63

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5.5Monte-CarloSamplesTheMCeventgeneratormainlyusedinthisstudyisPythia6.420,ithasbeenthemaingeneratoreusedinCMSanalysesfortherstfewyearsofbeamusage,thereisaslowmigrationtothenewerversionPythia8.AswementionedinChapter2,generatorsofthissorthaveanumberoffreeparameterswhichmustbetunedtodescribetheexperimentaldataaccurately.HereweconcentrateontheparametersdescribingtheMPI,theirevolutionasafunctionofthecentre-of-massenergyisdescribedbyEquation( 2 ).TherstsuccessfultuneathadronmachineswasTuneAdevelopedbytheCDFcollaboration,primarilybyttingUEdata.Startingfromthistunequitelargenumbertuneshavebeendevelopedintherecentyears.Themainfeaturesofthetunesusedare: TuneD6TwasthereferencetunefortheCMSCollaborationwhentheLHCstarted.ItwasbasedonCDFrunIIresultsanditadoptedtheCTEQ6LPDFs.ItusedthevirtualityshowerandtheMPImodeldevelopedinPYTHIA6.2. TuneZ1wastherstCMSUEtune.UsingMinimumBiasATLAStune(AMBTI),R.FieldsetthePDFtoCTEQ5LandttedPARP(82)andPARP(90)totCMSUEdataat7TeVand0.9TeV. TuneZ2*wasbasedonaretoftuneZ2(asuccessoroftuneD6T,witharetusingCMSUEdatainconjunctionwithCTEQ6LasthePDF)usingtheresultsofthemostrecentunderlyingeventanalysisfromCMS[ 27 ].ThetwasdoneusingPROFESSOR. 64

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Table5-4. Differentparametervaluesforthe3usedPYTHIA6tunes. ParameterD6TZ1Z2* PDFCTEQ6LCTEQ5LCTEQ6LMSTP(81)12121PARP(82)1.83871.9321.921PARP(83)0.50.3560.356PARP(84)0.40.6510.651PARP(85)10.90.9PARP(86)10.950.95PARP(89)1.961.81.8PARP(90)0.160.2750.227PARP(62)1.251.0251.025PARP(64)0.21.01.0PARP(67)2.51.01.0PARP(91)2.12.02.0PARP(93)15.010.010.0 65

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CHAPTER6ANALYSISRESULTSTheUEisassociatedwiththehadronicactivitynotincludedinthehardest2-2scattering.TheobservablesusedtoquantifysuchactivityarethechargedparticlemultiplicityNchandthescalarsumofthetransversemomentapTforthechargedparticles.Thesetwoquantitiesareusuallydividedbytheappropriate)]TJ /F5 11.955 Tf 12.3 0 Td[(areaofthecoveredregion.OtherquantitiescanbederivedfromthesetwovariablestotesttheMCmodelsfurther.InordertoaccountfortheenergydependenceoftheUE,theseobservablesarepresentedattwocenterofmassenergies:7TeVand0.9TeV.TheyarepresentedasafunctionoftheleadingtrackpT,whichsetsthescaleforthehardcomponentoftheinteraction.PredictionsfromdifferentMCmodelsarepresentedtocomparewiththecorrecteddata. 6.1Hard-scaleDependenceat7TeVand0.9TeVThissectionpresentstheNchandpTdensitiesat3distinct)]TJ /F5 11.955 Tf 12.12 0 Td[(regions:Toward,Transverse,andAway.Theseregionsaredividedwithrespecttothedirectionoftheleadingtrack,asdemonstratedinFigure 6-1 Figure6-1. The)]TJ /F5 11.955 Tf 11.95 0 Td[(phasespacedivisionschemewithrespecttotheleadingtrack. 66

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6.2TheUEintheToward,AwayandTransverseRegionsFigure 6-2 showstheaveragemultiplicityinthetransverseregiondividedbythephasespacearea(()=0.8x4=3)asafunctionofthehardesttrack.Thehorizontalerrorbarsindicatethebinsize,whichtendstoincreaseaswereachhighervaluesoftheleadingtracktransversemomentumduetorebinning.Therearetwoerrorbarsateachdatapoint:Theinnererrorbarsindicatetheamountofstatisticaluncertaintyaffectingthatpoint.Theoutererrorbars,whichrepresentthestatisticalandsystematicuncertaintyaddedinquadrature.Thisconventionwillapplyinallourresults,exceptforthecommonplots,wherethehorizontalerrorbarsareomittedforclarity. Figure6-2. TheaveragechargemultiplicityasafunctionoftheleadingtrackpTinthetransverseregionat7TeV(right),andtheratiooftheMCoverData(left). InFigure 6-2 ,twodistinctivefeaturescanbeseen:ArapidriseforregionswithpTlessorequalto5GeV/c.Thisismainlyattributedtotheincreaseofmultiplepartoninteractionactivity[ 46 ],thatcorrespondstomorecentralizedcollisions(Figure 2-3 ).Theraiseisfollowedbyaregionofplateauwherethemultiplicityreachesroughlyaconstantvaluethatincreasesslowly.Thisslightincreaseisassociatedwiththeincreaseofradiativecontributions,thechangeofenergyandfragmentationscale. 67

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Figure6-3. Theaveragechargemultiplicityasafunctionoftheleadingtrack,fortheToward(upperleftpanel)andawayregions(lowerleftpanel),at7TeV.AndtheratiooftheMCcurvesoverthedataforthesame)]TJ /F5 11.955 Tf 11.95 0 Td[(region. 68

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AttherightpanelofFigure 6-2 ,theratiooftheMCgeneratorsareshownandusedtocomparewiththecorrecteddata.There,thesystematicuncertaintyisshownintheinner(green)bandsandthetotaluncertainty(again,statisticalandsystematicuncertaintyareaddedinquadrature)isshowninthegrayband.Weseethatthetunes(Z1andZ2)seemtogiveaverygoodqualitativedescriptionofthedata(rightpanel).However,whencomparingtheratios,itisclearthatbothtunesseemtoovershootthehadronicactivityinthetransverseregionattheperipheralcollisionsregion.Thisismainlyduetocontributionfromdiffraction.Z2seemstohavelesserdeviationfromthedataatverylowvaluesoftheleadingtrackmomentum.Attheotherendofthespectrum,thequalityoftheMCtunesseemtodecreaseasthestatisticaluncertaintyincreases.Thetransverseregionisconsideredtheleastcomplicatedamongtheotherregionsunderconsiderationinthisstudy.ThehadronicactivityissensitivetoBBRandtoMPI.AsimilarpatternisobservedfortheTowardandAwayNchdensity(Figure 6-3 );however,itisclearthattheactivityatthecentralizedregionincreaseatahigherratewithrespecttopToftheleadingtrackcomparedtotheTransverseregion.ThisisduetoISRandFSRcontributionfromthejetsintheTowardandAwayregions.Bothtunesgiveagoodqualitativedescriptionofthedata;however,theypredictmuchhighermultiplicityatthelowvaluesoftheleadingtrackpT.Attheotherextreme,theyalsogiveareducedaccuracy(muchworsefortheAwayregionwherethetunesseemtooverestimatethehadronicactivity)duetostatisticaluctuations.TheTowardisacomplicatedregiontomodel.ItissensitivetofragmentationanditreceivescontributionsfromBBR,MPI,andISR.Theawayregionisconsideredevenmorecomplicated.Itdependsiftheaway-jetliesoutsidethejj<0.8cutornot.Iftheaway-jetisoutsidethecut,theregionrecievescontributionsfromtheaway-jet,BBR,MPI,ISR,FSR,andPDF.Thelastfactoremergesfromthecontributionofthe2-2 69

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subprocessesinvolved(thetypeofpartonsinvolved).ThislevelofcomplicationmakesitdifcultfortheMCmodelstosimulatethedataaccurately.ThesecondobservableusedtostudythehadronicactivityisthescalarsumfortheTransversemomentumpT.Figures 6-4 ,and 6-5 showthebehaviorofthisobservableasafunctionoftheleadingtrackTransversemomentum.pTplotshavethesamegeneralfeaturesasNchforthethreephasespaceregions.ThesimilarityoftheMCpredictionsisvisible;i.e.goodqualitativeagreement,andpooragreementatthequalitativescaleattheperipheralregionduetodiffractioncontamination.Wealsoobservesomedeviationatthehighendofthespectrumthatcontainslowerstatistics,itisobservedthattheMCpredictionsaremuchworseattheAwayregion.Similarstudiesareperformedat0.9TeV.Figures 6-6 and 6-7 showthechargemultiplicitybehaviourwithrespecttotheleadingtrack.ThequalitativefeaturesarewellrepresentedbytheMCmodels.ThequalitativefeaturesareimprovedandaremuchclosertothedatafortheperipheralregionfortuneZ2,whiletuneZ1showsasimilardivergencetotheoneshownat7TeV.ThesamecanbesaidfortheTowardandAwayregions,withtheAwayregionshowingahigheractivityforthechargemultiplicityforbothtunes.ForpTat0.9TeV,tuneZ2givesamuchbetterquantitativedescriptionofthedataatthesoftcollisionsregion,whileZ1showsdivergencefromdataatpTfortheleadingtrackgetslower. 6.3TheMaximumandMinimumTransverseRegionsTherearefurtherconstrainsthatcanbeimposedonthe)]TJ /F5 11.955 Tf 12.15 0 Td[(space.Forinstance,theTransverseregioncanbedividedintotwoequalregions:oneofthemcontainingmorehadronicactivitycalledthemaximum(max)region,andtheotherregionwillbecalledtheminimum(min)region.Themaxregionhasahigherprobabilityofcontainingathirdjet.Bothregionsreceivecontributionsfrommultiplepartoninteractionsandbeambeamremnants.ThemaxregionsensitivetomanyfactorsjustliketheTowardandAway 70

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Figure6-4. TheaverageTransversemomentumsumasafunctionoftheleadingtrackpTintheTransverseregionat7TeV(right),andtheratiooftheMCoverData(left). regions,whiletheminregionismoresensitivetoMPIandBBRinparticular.Wecanalsostudythedifferencebetweenthetworegionsforbothobservables(dif),whichismoresensitivetoISRandFSR.Thedifferencebetweenthetworegionsissensitivetothenalstateradiation.Figures 6-10 and 6-12 showtheaveragemultiplicityproleplotsatthemax(NchMaxandpTMax)andmin(NchMinandpTMin)regions.WeseeanexcellentagreementfortheNchMaxthroughoutthespectrum,exceptfortherstfewbins.ForNchMin,wenoticeagoodagreementbetweentheMCandthedata,exceptforthetwoextremesofthespectrum.TheagreementisbetterforNchMaxcomparedtoNchMin.AsimilarpatternisobservedforpTmaxandpTmin.Thesamesectorwasstudiedfor0.9TeVcenterofmassenergy.There,agoodagreementisalsonoticed(notasgoodasthecaseofNchMaxat7TeV)forbothobservables,withthebiggestdiscrepancybeingreportedatthelowestandhighestbins.SeeFigures 6-14 and 6-16 71

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Figure6-5. TheaverageTransversemomentumasafunctionoftheleadingtrack,fortheToward(upperleftpanel)andAwayregions(lowerleftpanel),atTeV.TheratiooftheMCcurvesoverthedataforthesame)]TJ /F5 11.955 Tf 11.96 0 Td[(regionsareshownintherightpanel. 72

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Figure6-6. TheaveragechargemultiplicityasafunctionoftheleadingtrackpTintheTransverseregionat0.9TeV(right),andtheratiooftheMCoverData(left). Figures 6-11 and 6-13 showsthedifferenceoftheUEactivitybetweentheMaxandMinregionsforNchandpTat7TeV.ThereisanexcellentoverallagreementbetweenthetwoMCtunesandthedata,withtheexceptionoftherstfewbins.ThequalityoftheMCdescriptiondeterioratesforbothobservablesat0.9TeV,ascanbeseeninFigures 6-15 and 6-17 6.4AveragepTThenextsetofobservablesareconstructedfromtakingtheratiosoftheobservablesmeasuredpreviouslyattheTransverseregion:ThebinbybinratioofpToverNch.ThisobservablereliesmostlyontheshapeofthepTspectrumemergingfromMPI,thislinksittocolorconnectionschemes.Figure 6-18 showstheAvepTplotsat7TeV.Hereweseethetwotunesgivinganalmostidenticalvalueoftheactivitythroughoutthespectrum.Whencomparedtodata,theybothtendtoundershootthevaluepredictedbythedataatallregionsexceptthelowestpTvaluesoftheleadingtrack.For0.9TeV(Figure 6-19 )thetwoMCtunesshowidenticalpredictionsatlowpT.However,tuneZ2startsshowingslightlyhighervalues 73

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Figure6-7. Theaveragechargemultiplicityasafunctionoftheleadingtrack,fortheToward(upperleftpanel)andAwayregions(lowerleftpanel),at0.9TeV.AndtheratiooftheMCcurvesoverthedataforthesame)]TJ /F5 11.955 Tf 11.96 0 Td[(regions. 74

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Figure6-8. TheaverageTransversemomentumsumasafunctionoftheleadingtrackpTintheTransverseregionat0.9TeV(right),andtheratiooftheMCoverData(left). atthehighendofthespectrum.Bothtunes,however,showabetteragreementwiththedatathanin7TeV. 6.5TheRatiooftheObservablesatTwoCenter-of-MassEnergiesThenextsetofplotsshowstheaveragechargemultiplicityandpTforthetwoenergiesstudied.(asshowninFigure 6-20 ).Hereweseethetwotunestendtoagreewiththedatabehavior.Albeitthereisalargedivergenceattherstbinanditshowslessactivityatthehigherendofthespectrum. 6.6ComparisonwithOtherExperimentsTheresultsoftheUEanalysisarecomparedwiththendingsofALICE[ 47 ],oneoftheothermajorexperimentsattheLHC.Figure 6-21 showsthesimilarityofthendingsofbothcollaborationsatthetwocenter-of-massenergylevels.CMSresultsextendtolargervaluesofpTmaxduetobetterstatistics. 75

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Figure6-9. Theaveragescalarmomentumasafunctionoftheleadingtrack,fortheToward(upperleftpanel)andAwayregions(lowerleftpanel),at0.9TeV.AndtheratiooftheMCcurvesoverthedataforthesameeta-phiregions. 76

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Figure6-10. TheaveragechargemultiplicityasafunctionoftheleadingtrackpTinthemaximum(upperleft)andminimum(lowerleft)Transverseregionat7TeV,andtheratiooftheMCoverData(right). 77

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Figure6-11. ThedifferenceintheaveragechargemultiplicityasafunctionoftheleadingtrackpTbetweenthemaximumandminimumTransverseregionsat7TeV(left),andtheratiooftheMCoverData(right). 6.7EnergyScanoftheUETakingsimilarmeasurementsforthehadronicactivityatthephasespaceregionsmentionedaboveatdifferentcenter-of-massenergiesgivesagreatopportunitytostudytheenergydependenceofthevariousfactorscontributingtotheUE.ThiscanbeseenfromFigures 6-22 and 6-23 .ThisenergyscanisobtainedbycombiningtheresultsobtainedabovefromCMSwiththeresultsobtainbyCDFattwocenter-of-massenergiesthathavenotbeenexploredbytheLHC:0.3TeVand1.96TeV[ 48 ]. 78

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Figure6-12. TheaveragescalarmomentumsumasafunctionoftheleadingtrackpTinthemaximum(upperleft)andminimum(lowerleft)Transverseregionat7TeV,andtheratiooftheMCoverData(right). 79

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Figure6-13. ThedifferenceintheaveragescalarmomentumsumasafunctionoftheleadingtrackpTbetweenthemaximumandminimumTransverseregionsat7TeV(left),andtheratiooftheMCoverData(right). 80

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Figure6-14. TheaveragechargemultiplicityasafunctionoftheleadingtrackpTinthemaximum(upperleft)andminimum(lowerleft)Transverseregionat0.9TeV,andtheratiooftheMCoverData(right). 81

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Figure6-15. ThedifferenceintheaveragechargemultiplicityasafunctionoftheleadingtrackpTbetweenthemaximumandminimumTransverseregionsat0.9TeV(left),andtheratiooftheMCoverData(right). 82

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Figure6-16. TheaveragescalarmomentumsumasafunctionoftheleadingtrackpTinthemaximum(upperleft)andminimum(lowerleft)Transverseregionat0.9TeV,andtheratiooftheMCoverData(right). 83

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Figure6-17. ThedifferenceintheaveragescalarmomentumsumasafunctionoftheleadingtrackpTbetweenthemaximumandminimumTransverseregionsat0.9TeV(left),andtheratiooftheMCoverData(right). Figure6-18. TheaverageTransversemomentumasafunctionoftheleadingtrackpTat7TeVintheTransverseregion. 84

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Figure6-19. TheaverageTransversemomentumasafunctionoftheleadingtrackpTat0.9TeVintheTransverseregion. 85

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Figure6-20. Theaveragechargemultiplicity(upperleft)andscalarmomentumsum(upperright)asafunctionoftheleadingtrackpTintheTransverseregionat7TeVand0.9TeV.Theratioofthesameobservablesatthetwocenterofmassenergies. 86

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Figure6-21. TheaveragechargemultiplicityandtheTransversemomentumsumasafunctionoftheleadingtrackforCMSandALICE. 87

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Figure6-22. Thehadronicactivityatfourcenter-of-massenergiesintheTransverseregionandthemaxregion. 88

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Figure6-23. Thehadronicactivityatfourcenter-of-massenergiesintheminregionandthedifferenceintheactivitybetweenmaxandmin. 6.8Conclusions ThehadronicactivityassociatedwiththeUEhasbeenstudiedat7TeVand0.9TeVatCMS.Thetwochosenobservables,NchandpT,havebeenstudiedinvarious)]TJ /F5 11.955 Tf 11.96 0 Td[(regionsthatemphasizedifferentcontributionstotheUEdynamics. TwotunesthatbelongtotheMCgeneratorPYTHIA6.4arecomparedtodata.TuneZ1,thelasttuneproducedinCMSusingmanualtuning,andtuneZ2thersttuneproducedbyCMSusingPROFESSOR.Thereisageneralsuccessforboth 89

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tunestosimulatethedataatthequalitativelevel.However,thereisstillroomforimprovementatthequantitativelevel,especiallyatthelowvaluesofleadingtrackpT. TuneZ2givescloseresultstotuneZ1.ItperformsbetterforobservablepTinmostregions,particularlyatthelowleadingtrackpTvalues. Theresultsobtainedwerecomparedwiththeresultsofotherexperimentsatthesamecenter-of-massenergy.Wheretheresultsseemtoagree,withbetterstatisticsobtainedbyCMSthatenablesexploringregionswithlargerleadingtrackpT. Theresults,alongsideresultsfromCDF,formbasistostudythehadronicactivityinvarious)]TJ /F5 11.955 Tf 12.06 0 Td[(regionsatfourdifferentcenter-of-massenergies.ThisformsbasistoparametrizetheenergydependenceforeachUEcomponentmoreaccuratelyforfuturetunes. 90

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APPENDIXAUNFOLDINGUnfoldingistheprocedureusedtocorrectforanybiasintroducedtotheobservableduetoexperimentallimitation(reconstruction,selectioncriteria,andphysicallimitsetc.).Thegoalofunfoldingistorestoretheobservabletotruthorgeneratorlevelspectrumthatismeasuredwithanidealdetectorandaninniteeventstatistics.Whileunfoldingisnotessentialforadiscoveryorientedanalysis,itisimportantwhenthedistributionitselfisregardedasthesetofparametersofinterest,asisthecasewiththeUE.Inthisanalysis,wesettheconditionofhavingatleastonechargedtrackwithintherequiredcuts(pT>0.5GeV=candjj<0.8)todeneaneventatthegeneratorlevel.Themethodofchoiceisthebin-by-binmethod.Themainadvantageisitssimplicityandthetransparencyoftheprocedurewhilebincorrelationisconsidereditsmaindrawback.Itisstillusedinmanyanalysesinvariouscollaborations.Inthisanalysisweusetheratiooftheobservable(NchandpTproleplots)atthegeneratoroverthedetectorlevelforaMCtune(Z1)tocorrecttheData.SimilarprocedurewasperformedforMCtuneD6TandtheresultingdistributionswereclosetotheGENlevelobtaineddirectlyfromtheMC. FigureA-1. TheratiooftheMCof(PYTHIA6,tuneZ1)simulationofthedetector(SIM)leveloverthegenerator(GEN)levelforthetwoobservables:at7TeV(leftpanel)andat0.9TeV(rightpanel). 91

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APPENDIXBTHECROSS-SECTIONFORMPIWestartwithEquation( 2 ).Fromthatwecanwritethedifferentialcross-sectionas:d(AB!cd) dp2T=XabcdZdxadxbfa=A(xa,2F)fb=B(xb,2F)^abcd(2,R) dp2T, (B)whered^ dp2T=d^ d^t2s ^s21 q 1)]TJ /F4 7.97 Tf 13.15 6.48 Td[(4p2T ^s, (B)atsmallscatteringangles,tgoestozero,andthet-channeldominates.Inthiscasethedifferencebetweenquarkandgluoninteractionsareduetotheircolorfactors:^gg:^qg:^qq=9 4:1:4 9, (B)Thefactorscanbeobtainedfromthegluon-gluon(CA=3)andgluon-quark(TF=1 2),afterincludingcolor-averagefactors:1 N2)]TJ /F4 7.97 Tf 6.59 0 Td[(1=1 8forthegluonand1 N=1 3forthequark.ints=4ZpTmindp2T1Z4pT2=sdxa1Z4pT2=sxadxb9 22s(p2T) ^s2q 1)]TJ /F4 7.97 Tf 13.15 6.48 Td[(4p2T ^sF(xA,p2T)F(xB,p2T)f(^u ^t), (B)d^ dp2T=82s(p2T) 9p4T, (B) 92

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F(x,Q2)=g(x,Q2)+9 4i[qi(x,Q2)+qi(x,Q2)], (B)int(pTmin)=s=4ZpTmind^ dp2Tdp2T/1 p2Tmin, (B) 93

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APPENDIXCSANITYCHECKPLOTSFurthersanitychecksareshowninFigures C-1 and C-2 .AgoodmatchbetweentheMCandthedataisobservedinallthepanels,whichrepresentfundamentaltrackingvariables. FigureC-1. pT,anddistributionsforthereconstructedtracksat7TeV.TheunformityoftheanddistributionsandthesuccessoftheMCtosimulatethedataaccuratelyindicateagoodleveloftrackreconstructionquality. 94

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FigureC-2. Sanitycheckplotsforeventreconstruction:TheleftpanelshowsthenumberofofineverticesreconstructedfordataandMC.Firstbininthisplotcorrespondstotheeventsinwhichnovertexisreconstructed.Therightpanelshowsthendofdistributionoftherealverteces. 95

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APPENDIXDSYSTEMATICUNCERTAINTYThesimulationpredictionisaffectedbyinaccuraciesindetectororbeamconditionmodeling,soweestimatedetectorlevelsystematicuncertaintiesbyconcentratingontheDATA/MCratiooftheobservables.Thesystematicuncertaintyassociatedisevaluatedfromtheresidualswithrespecttoareferencedistribution:residuals=(A)]TJ /F3 11.955 Tf 12.02 0 Td[(B)=A,whereAisthereferenceandBisthesource.Inadditiontothedirectevaluationithasalsobeenconsideredanadditionalsafetymargin.Thesafetymarginisintroducedtotakeintoaccountthebinbybinuctuations,avoidingthattheeffectinbinswithlowstatisticsisunderestimatedbythets.Theconsideredsourcesofdetectorlevelsystematicuncertaintiesarethefollowing: RECOtoGENcorrection. Pile-upcontamination(comprisingalltheeffectsofhighluminosityruns). Vertexselection. Tracking. Trackselectionandtrackcuts.Table D-1 summarizesthesystematicuncertaintyvaluesforthecontributionsmentionedabove.Theinvestigatedsourcesofuncertaintiesarelargelyindependentfromeachother,justifyingthequadraturesumofthedifferentcontributions. TableD-1. Themainsourcesofsystematicuncertainty. Observabletrackingtrackbg.vtxpile-upp dz2+d02MCtotal(%)sel.cont.sel.model 7TeV1.021.40.80.80.72.82.03.61.041.10.81.20.72.32.03.7 0.9TeV1.340.70.81.501.80.93.01.420.70.81.501.80.92.8 96

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BIOGRAPHICALSKETCH MohammedKhattabZakariawasbornin1982inKuwaitcity,Kuwait.In2000,hejoinedtheUniversityofJordanmajoringinphysics.In2004hegraduatedwithhonorsandjoinedthephysicsprogramatCreightonUniversity.Hereceivedanawardforoutstandingscholarshipuponthecompletionofhismaster'sdegreein2007.Laterinthesameyear,MohammedjoinedthephysicsprogramattheUniversityofFlorida.Mohammedworkedasateachingassistantfortherst2yearsatthephysicsdepartmentandhewasawardedtheWayneBomstadIIawardforbeingthedistinguishedteachingassistantoftheyear2008.In2009,MohammedstartedworkingasaresearchassistantforhisadviserRickField.Mohammedwasinvolvedinstudyingtheunderlyingeventactivityassociatedwithproton-protoncollisionsattheLHC.HewasinvolvedinthedataanalysisatCMSandtheMonteCarlomodelingofthephenomena.Duringhisyearsofgraduatework,MohammedwastherecipientoftheUniversityResearchAssociationfellowshipthatenablehimtomovetoFermilabtopursuehiswork.Mohammedwasalsotherecipientof2LPCsummerfellowshipsatthesamefacility.MohammedreceivedhisPh.D.inthefallof2013. 101