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Fragmentation of Jets Produced in Proton-Antiproton Collisions at s**(1/2)=1.96-TeV

Permanent Link: http://ufdc.ufl.edu/UFE0021500/00001

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Title: Fragmentation of Jets Produced in Proton-Antiproton Collisions at s**(1/2)=1.96-TeV
Physical Description: 1 online resource (122 p.)
Language: english
Creator: Jindariani, Sergo Robert
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

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

Notes

Abstract: We present the first measurement of two-particle momentum correlations in jets produced in proton-antiproton collisions at center of mass energy of 1.96 TeV. A comparison of the experimental data to theoretical predictions obtained for partons within the framework of resummed perturbative QCD (Next-to-Leading Log Approximation) shows that the predicted parton momentum correlations survive the hadronization stage of jet fragmentation and are present at the hadron level. We also present the measurement of the intrinsic transverse momenta of particles with respect to jet axis. Experimental data is compared to the theoretical predictions obtained for partons within the framework of Modified Leading Log Approximation and Next-to-Modified Leading Log Approximation, and shows good agreement in the range of validity of the theoretical predictions. The results of both measurements indicate that the perturbative stage of the jet formation must be dominant and give further support to the hypothesis of Local Parton-Hadron Duality.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sergo Robert Jindariani.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Korytov, Andrey.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2017-12-31

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021500:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021500/00001

Material Information

Title: Fragmentation of Jets Produced in Proton-Antiproton Collisions at s**(1/2)=1.96-TeV
Physical Description: 1 online resource (122 p.)
Language: english
Creator: Jindariani, Sergo Robert
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

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

Notes

Abstract: We present the first measurement of two-particle momentum correlations in jets produced in proton-antiproton collisions at center of mass energy of 1.96 TeV. A comparison of the experimental data to theoretical predictions obtained for partons within the framework of resummed perturbative QCD (Next-to-Leading Log Approximation) shows that the predicted parton momentum correlations survive the hadronization stage of jet fragmentation and are present at the hadron level. We also present the measurement of the intrinsic transverse momenta of particles with respect to jet axis. Experimental data is compared to the theoretical predictions obtained for partons within the framework of Modified Leading Log Approximation and Next-to-Modified Leading Log Approximation, and shows good agreement in the range of validity of the theoretical predictions. The results of both measurements indicate that the perturbative stage of the jet formation must be dominant and give further support to the hypothesis of Local Parton-Hadron Duality.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sergo Robert Jindariani.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Korytov, Andrey.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2017-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021500:00001


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Countlesspeoplehavecontributed,directlyandindirectly,tothesuccessofthiswork.Withouttheireortsthisdissertationcouldnothavebeencompleted.HereImentionthoseofthem,whohavemostinuencedmywork.Ithankmyadvisor,Prof.AndreyKorytovforhispatienceandtolerance,hissupportandhisfriendship,andforconvincingmetoattendUniversityofFloridaintherstplace.IappreciateAndrey'sguidance,especiallythebroadviewhegavemeoftheparticlephysicsgenerally.HealsoinsistedthatIgavemanypublicpresentations,whichhelpedmetoconquermyfearofpublicspeaking.IalsothankRichardField,RegisLefevre,MaryConvery,KenichiHatakeyamaandJoeyHustonfortheirhelpduringdierentstagesofthiswork.IamalsothankfultoJayDittmann,KarenByrumandKojiTerashi,membersofthe\godparent"committeeformyanalysis,fortheirtimeandeortinthepreparationofdraftstobepublishedinphysicsjournals.Ithankmyfriendandocemate,LesterPinera,withwhomIsharedaCDFoceforthreeyears.Hisfriendshipandsupporthelpedmetogetthroughthetougheststagesofmygraduateschool.Iverymuchenjoyedoureverydayconversationsonvarioustopicsandlearnedalotfromhim.IalsothankmyoldfriendYuriOksuzianforhishelpandfriendship,whichstartedbackinhighschoolandcontinuestoday.IamgratefultoSashaPronko,whotaughtmehowtodoanexperimentalanalysisandhelpedmealotduringtheearlystageofit.Ialsolearnedfromhimthatitisveryimportanttosetagoalandworkhardtoachieveit.IwanttothankProf.JacoboKonigsberg,theleaderoftheUniversityofFloridaHighEnergyPhysicsGroupandCDFco-spokesperson,forhissupport.IalsoappreciatetheopportunitytobeapartoftheUniversityofFloridaHighEnergyPhysicsGroup.ItwasapleasuretoworkwithsuchgreatcolleaguesasSergeiKlimenko,AlexanderSukhanov,SongMingWang,RobertoRossin,NathanGoldschmidt,ValentinNeculaandGeorge 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 13 CHAPTER 1INTRODUCTION .................................. 14 1.1StandardModelofElementaryParticles ................... 15 1.2QuantumChromodynamics .......................... 17 1.3StructureofQCDEvents ............................ 19 2JETFRAGMENTATION .............................. 23 2.1MotivationandPhenomenology ........................ 23 2.2SoftGluonResummations ........................... 24 2.3LocalParton-HadronDuality ......................... 26 2.4TheoreticalPredictionsandPastMeasurements ............... 27 2.4.1MeanParticleMultiplicities ...................... 27 2.4.2MomentumDistributions ........................ 28 2.4.3Two-particleMomentumCorrelations ................. 29 2.4.4ThekTDistributions .......................... 32 2.4.5MixingQuarkandGluonJets ..................... 33 3EXPERIMENTALAPPARATUS .......................... 43 3.1Accelerator ................................... 44 3.1.1ProtonSource .............................. 44 3.1.2MainInjector .............................. 45 3.1.3AntiprotonSource ............................ 46 3.1.4Tevatron ................................. 47 3.2TheCDFIIDetector .............................. 48 3.2.1TrackingandVertexingSystems .................... 50 3.2.2Calorimetry ............................... 53 3.2.3OtherSystems .............................. 55 3.2.4TriggerSystemandDataAcquisition ................. 58 3.2.5GoodRunRequirements ........................ 60 3.3JetReconstruction ............................... 60 3.3.1JetClustering .............................. 61 3.3.2JetCorrections ............................. 62 3.4MonteCarloGeneratorsandDetectorSimulation .............. 64 6

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............................ 64 3.4.2CDFSimulation ............................. 65 4ANALYSISOFTHEDATA ............................. 76 4.1Two-particleMomentumCorrelations ..................... 76 4.1.1DataSamples .............................. 76 4.1.2EventSelection ............................. 77 4.1.3TrackQualityRequirements ...................... 78 4.1.4UnderlyingEventBackgroundSubtraction .............. 80 4.1.5SystematicUncertainties ........................ 81 4.1.6EectofTrackingIneciency ..................... 83 4.1.7NeutralParticles ............................ 83 4.1.8Heavyavorjets ............................. 84 4.1.9ResonanceDecays ............................ 84 4.2ThekTDistributions .............................. 84 4.2.1DataSamples .............................. 84 4.2.2UnderlyingEventBackgroundSubtraction .............. 85 4.2.3EectofTrackingIneciency ..................... 85 5RESULTS ....................................... 91 5.1Two-particleMomentumCorrelations ..................... 91 5.1.1NLLAFitstoData ........................... 91 5.1.2ComparisontoMonteCarlo ...................... 93 5.2ThekTDistributions .............................. 93 5.2.1ComparisontoMLLAandNMLLApredictions ............ 93 5.2.2ComparisontoMonteCarlo ...................... 94 6CONCLUSIONS ................................... 111 APPENDIX AINCLUSIVEMOMENTUMDISTRIBUTIONSOFPARTICLESINJETS ... 113 REFERENCES ....................................... 117 BIOGRAPHICALSKETCH ................................ 121 7

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Table page 1-1Summaryofquarkproperties. ............................ 22 1-2Summaryofleptonproperties. ............................ 22 1-3SummaryofgaugebosonpropertiesoftheStandardModel. ........... 22 3-1SummaryofthecurrentTevatronperformancecharacteristics. .......... 67 3-2SummaryofquantitiescharacterizingCDFcalorimetry. .............. 67 4-1Measurementofmomentumcorrelations:dijetmassbinsboundaries,averageinvariantdijetmasshMjjiandnumberofeventsineachbinaftertheeventselectioncuts. .......................................... 86 4-2Thez,evaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. .................................... 86 4-3Theresolutionoftheimpactparameter,d0,evaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. ............... 87 4-4Summaryofthesystematicuncertaintiesofthecorrelationparametersc0,c1andc2forthedijetmassbinwithQ=50GeV. .................. 90 4-5MeasurementofthekTdistributions:dijetmassbinsboundaries,averageinvariantdijetmasshMjjiandnumberofeventsineachbinaftertheeventselectioncuts. 90 5-1Summaryofthecorrelationparametersc0,c1andc2measuredinsevendijetmassbins.Therstuncertaintyisstatistical,thesecondoneissystematic. ... 95 8

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Figure page 2-1Acartoondescriptionofthedierentlevelsofajetevent.Thepartonlevelisthestatebeforepartonshadronize,intheorythisstageofaneventcanbedescribedbythepQCDcalculations.Thehadronlevelisthestateafterhadronization.Thetransition(hadronization)isusuallydescribedusingphenomenologicalmodels,andismostlyunexplored.Thedetectorlevelisaresultoftheeventasreportedbythedetector. .................................... 35 2-2Inclusivemultiplicityofchargedparticleswithincones0.168,0.280and0.466indijetevents.Dataerrorsarecompletelydominatedbycorrelatedsystematicerrors.FitforpossibleoverallnormalizationtoHerwigv5.6predictions,yieldsN=0:890:05.Theleveloftheerrorsdoesnotallowtoclaimthedierencesignicant.Herwigpredictionswerescaledbyafactor0.89andareshownontheplot(lines). .................................... 36 2-3NLLAinclusivepartonmomentumdistributionsforQ=19;50;120GeVandQe=230MeVascalculatedbyC.P.FongandB.R.Webber. .......... 36 2-4Inclusivemomentumdistributionofchargedparticleswithinrestrictedcones0.466indijeteventsttedwithMLLAlimitingspectrum.DijetmassMjj=378GeV. .......................................... 37 2-5TheNLLApatronmomentumcorrelationfunctioncalculatedforagluonjet,Q=50GeVandQe=230MeVascalculatedbyC.P.FongandB.R.Webber. 38 2-6The3-dimentionalmomentumcorrelationdistributionasmeasuredbytheOPALcollaboration(top).Alsoshownaresixnarrowbands(bottom)forwhichcorrelationindataiscomparedtotheanalyticalpQCDpredictions. ............. 39 2-7ComparisonoftheOPALdatatoanalyticalQCDcalculations.Thethreesolidcurvesrepresentthenext-to-leadingQCDcalculationsforthreevaluesofQeff,1000MeV(highest),255MeV(middle),and50MeV(lowest).ThedashedlinesindicatetheleadingorderQCDcalculationsforQeff=250MeV. ........ 40 2-8InclusivekTdistributionofchargedparticlesaspredictedbytheresultsoftheMLLAcalculations.Thedependenceofthepredictionsonjetenergyscaleisshown. ......................................... 41 2-9InclusivekTdistributionofchargedparticlesaspredictedbytheresultsoftheMLLAandNMLLAcalculations.A)Thedependenceofthepredictionsonjetorigin,quarkorgluon,(top),andB)valueofpartonshowercutoQeff(bottom)isshown. ........................................ 42 9

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......... 67 3-2TheprotonandantiprotonbeamstructureattheTevatron.Eachbeamisdividedintothree\trains"separatedbytheabortgap.Eachtraincontains12bunchesofprotonsorantiprotons.Thetimeseparationbetweenconsequentbunchesis396ns. ......................................... 68 3-3ThetotalintegratedluminositydeliveredbytheTevatronfromthebeginningofRunIIwhichstartedinApril2001.Theliveluminosity,whichexcludesintegratedluminosityduringallthedetectordead-timesisalsoshown. ........... 68 3-4Theschematiccross-sectionviewoftheCDFdetector. .............. 69 3-5Theschematicr{zviewofonequadrantoftheCDFtrackingsystem.Itscomponents:CentralOuterTracker(COT)andthesilicondetectors:Layer00(L00),SiliconVertexDetector(SVX),andIntermediateSiliconLayers(ISL)areshown. .... 70 3-6TransverseviewofthenominalcelllayoutforCOTsuperlayer2.Thearrowshowstheradialdirection.Theelectriceldisroughlyperpendiculartotheeldpanels.Themagneticeldisperpendiculartotheplane.Theanglebetweenwire-planeofthecentralcellandtheradialdirectionis35 71 3-71=6thoftheCOTeastendplate.Shownarethewire-planeslotsgroupedintoeightsuperlayers. ................................... 71 3-8SVXbulkheaddesign.Placementofladdersisshownintwoadjacentwedges. 72 3-9Schematicpictureofonequadrantoftheplugcalorimeterincludingtheelectromagneticandhadronicparts.Theplugcalorimeterhasfull2coverageandextendsto1:1
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................... 86 4-2Thezdistribtuionsfortracksreconstructedwithdierenttrackreconstructionalgorithms.Thedataarettoasumoftwo\Gaussians"todeterminethewidth,z,ofthedistributions,usedintheeventselection. ............... 87 4-3Theimpactparameterdistribtuionsfortracksreconstructedwithdierenttrackreconstructionalgorithms.Thedataarettoasumoftwo\Gaussians"todeterminethewidth,d0,ofthedistributions,usedintheeventselection. ......... 88 4-4IllustrationofthedistanceRconvfromthebeamlinetothepointwheretheconversionoccurred.Here,d0istheimpactparameter. .................... 88 4-5MonteCarlotrackmultiplicityinjetsbeforeandafterapplyingtrackqualitycuts.ThedistributionsareforthedijetmassbinwithQ=50GeV.Particlesarecountedwithinaconeofopeninganglec=0:5radians.CDFSimreferstothefullCDFdatasimulation. ............................ 89 4-6InclusivemomentumdistributionsofMonteCarlotracksinjetsbeforeandafterapplyingtrackqualitycuts.ThedistributionsareforthedijetmassbinwithQ=50GeV.Particlesarecountedwithinaconeofopeninganglec=0:5radians.CDFSimreferstothefullCDFdatasimulation. ............. 89 4-7Illustrationofthedenitionofcomplementarycones.Theunlabeledarrowsaretheaxesoftheconescomplementarytojets1and2 ................ 90 5-1Two-particlemomentumcorrelationsinjetsintherestrictedconeofsizec=0:5radiansfordijetmassbinwithQ=19GeV(top).Centraldiagonalproles1=2(middle)and1=2(bottom)ofthedistributionsareshown.ThecorrelationindataiscomparedtothatoftheoryascalculatedbyC.P.FongandB.R.WebberforQe=180MeVandascalculatedbyR.Perez-RamosforQe=230MeV. ................................... 96 5-2SameasinFig. 5-1 forQ=27GeV. ........................ 97 5-3SameasinFig. 5-1 forQ=37GeV. ........................ 98 5-4SameasinFig. 5-1 forQ=50GeV. ........................ 99 5-5SameasinFig. 5-1 forQ=68GeV. ........................ 100 5-6SameasinFig. 5-1 forQ=90GeV. ........................ 101 5-7SameasinFig. 5-1 forQ=119GeV. ........................ 102 11

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............ 103 5-9Hadron-leveltwo-particlemomentumcorrelationsinjetsintherestrictedconeofsizec=0:5radiansforthedijetmassbinwithQ=19GeVbythePythiaTuneA(top).ThecorrelationindataiscomparedtothehadronmomentumcorrelationsbythePythiaTuneAandHerwig6.5eventgenerators.Centraldiagonalproles1=2(middle)and1=2(bottom)ofthedistributionsareshown. ....................................... 104 5-10SameasinFig. 5-9 forQ=27GeV. ........................ 105 5-11SameasinFig. 5-9 forQ=50GeV. ........................ 106 5-12SameasinFig. 5-9 forQ=90GeV. ........................ 107 5-13SameasinFig. 5-9 forQ=119GeV. ........................ 108 5-14dN=dln(kT)distributionsofparticlesinintherestrictedconeofsizec=0:5aroundjetaxisineightdijetmassbins.CDFdatacomparedtotheanalyticalMLLA(dashedline)andNMLLA(solidline)predictions. ............. 109 5-15dN=dln(kT)distributionsofparticlesintherestrictedconeofsizec=0:5aroundjetaxisineightdijetmassbins.CDFIIdatacomparedtothepredictionsbyPythiaTuneAandHerwig6.5MonteCarlogenerators. ............. 110 A-1Trackingeciencycorrectionfactorsasfunctionsofforthreedijetmassbins. 115 A-2Inclusivemomentumdistributionsofparticlesinjets.DistributionsindataarettotheoreticalfucntionascalculatedbyC.P.FongandB.R.Webber. ..... 116 12

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1 ]ofparticlephysicsisatheorywhichdescribesthreeofthefourknownfundamentalinteractionsbetweentheelementaryparticlesthatmakeupallmatter.Itisaquantumeldtheory[ 2 ]developedbetween1970and1973whichisconsistentwithbothquantummechanicsandspecialrelativity.TheStandardModelisbasedontheprincipleofthelocalgaugeinvarianceofthegroupSU(3)cSU(2)LU(1)Y.SU(3)crepresentsthesymmetrygroupofthestronginteractionwhileSU(2)LU(1)Yrepresentsthesymmetrygroupoftheuniedelectroweakinteraction.GravityisnotincludedintheStandardModelbutthestrengthofgravitationalinteractionsissosmallthatitbecomesimportantonlyonmacroscopicscales.ThedetaileddescriptionoftheStandardModelisbeyondthescopeofthisdissertation.HerewediscussonlytheparticlecontentoftheStandardModelanditsaspectsrelevanttothejetfragmentationphysics.Moredetaileddiscussionscanbefoundin[ 3 ]. 15

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1-1 and 1-2 .Theforce-mediatingparticlesdescribedbytheStandardModelallhaveanintrinsicspinwhosevalueis1,makingthembosons.Asaresult,theydonotfollowthePauliExclusionPrinciple.Photonsmediatetheelectromagneticforcebetweenelectricallychargedparticles.Thephotonismasslessandiswell-describedbythetheoryofquantumelectrodynamics(QED).Allknownfermionsinteractviatheweakinteraction.Itismediatedbytheexchangeofthethreegaugebosons:W+,WandZ.Theyaremassive,withtheZbeingmoremassivethanW.Furthermore,theWcarryanelectricchargeandcoupletotheelectromagneticinteractions.Thesethreegaugebosonsalongwiththephotonsaregroupedtogetherwhichcollectivelymediatetheelectroweakinteractions,asdescribedbytheGlashow-Salam-Weinberg(GSW)theory[ 4 5 ].Eachquarkcarriesanyoneofthreecolorcharges-red,greenorblue,enablingthemtoparticipateinstronginteractionsmediatedbytheeightgluons.Gluonsaremassless.Theeight-foldmultiplicityofgluonsislabeledbyacombinationsofcolorandananticolorcharge.Becausethegluonhasaneectivecolorcharge,theycaninteractamongthemselves.Thegluonsandtheirinteractionsaredescribedbythetheoryofquantum 16

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6 7 ].ThepropertiesofgaugebosonsaresummarizedinTable 1-3 .TheonlyparticlepredictedbyStandardModelyettobediscoveredistheHiggsboson(H).Thisbosonplaysakeyroleinexplainingtheoriginsofthemassofotherelementaryparticles,inparticularthedierencebetweenthemasslessphotonandtheveryheavyWandZbosons.Itisalsoneededtogivefermionstheirmasses.Massesariseinagaugeinvariantway,duetoaprocessknownastheHiggsmechanism[ 8 ].Inthismechanism,thelocalSU(2)LU(1)Ysymmetryoftheelectroweakinteractionsisspontaneouslybroken.Thisaspectofthetheorycorrectlypredictstheexistenceoftheweakgaugebosonsaswellastheratiooftheirmasses.Italsopredictstheexistenceofaspin0particle:theHiggsboson.ThesearchfortheStandardModelHiggsbosonremainsoneofthetopprioritiesattheTevatronandthefutureLHCexperiments.Todate,almostallexperimentaltestsofthethreeforcesdescribedbytheStandardModelhaveagreedwithitspredictions.ThemostimpressiveistheagreementbetweenthepredictedandmeasuredvaluesoftheWandZgaugebosonsmasses.TheStandardModelpredictionshavealsoleadtothediscoveryoftopquarkattheTevatron.Still,theStandardModelfallsshortofbeingacompletetheoryoffundamentalinteractions,primarilybecauseofitslackofinclusionofgravity,butalsobecauseofthelargenumberofnumericalparameters(suchasmassesandcouplingconstants)thatmustbeput\byhand"intothetheoryratherthanbeingderivedfromrstprinciples. 17

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9 ].Atthisstage,oneparticle,the++remainedmysterious;inthequarkmodel,itiscomposedofthreeupquarkswithparallelspins.However,sincequarksarefermions,thiscombinationisforbiddenbythePauliexclusionprinciple.In1965thisproblemwasresolvedbyproposingthatquarkspossessanadditionalSU(3)gaugedegreeoffreedom,latercalledcolorcharge[ 10 ]andthatquarksinteractviaanoctetofvectorgaugebosons:thegluons.Acouplingconstantg,isanumberthatdeterminesthestrengthofaninteraction.Inquantumeldtheory,abeta-function(g)encodestherunningofacouplingconstant.Itisdenedbytherelation: : whereistheenergyscaleofagivenphysicalprocess.Innon-Abeliangaugetheories,thebetafunctioncanbenegative,asrstfoundbyF.Wilczek,D.PolitzerandD.Gross[ 11 12 ].AsaresulttheQCDcouplingdecreaseslogarithmicallyathighenergies: 0ln(Q2=2QCD); whereQCDistheenergyscaleatwhichthecouplinginQCDdiverges.ThisbehaviorofthecouplingconstantimpliestwoveryimportantpropertiesofQCD.ItiseasytoseethatathighvaluesofQ2thecouplingconstantbecomessmall,thisleadstothepropertycalledasymptoticfreedom.Basicallyitimpliesthatinhigh-energyscatteringthequarksmovewithinnucleonsareessentiallyfree,non-interactingparticles.AtlowQ2thecouplingdiverges.ThispropertyofQCDisknownasthecolorconnementandisthereasonwhy 18

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4[1+(1k p)2]dk kdk2? where 0ln(k?=); 13 ],i.e.wsln2p1whenkp.Theemissionofapartonatlargeangleisalsopossible,howeveritissuppressed[ 13 ]:ws=1whenkp.Thepartonshowerstateofaneventcannotbeobservedphysically,butisoftenreferredaspartonlevel.DuetothecolorconnementpropertyofQCD,partonsintheshowerhavetohadronizeintothecolorsinglethadrons.Ajetisanarrowconeofhadronsandotherparticlesproducedbythehadronizationofaquarkorgluon.Theparticlecontentofaneventafterthehadronizationisoftenreferredashadronlevel.Thedetectionofhadronsinanexperimentisdoneusingtheirinteractionwiththematerialofthedetector.Physicallymeasuredcollectionofobjectsisusuallytracksandcalorimetertowersreferredtoasthedetectorlevel.Theprimaryhardscatteringcansometimesbeaccompaniedbyanotherparton-partoninteractionwithinthesameproton-antiprotoncollision,thisprocessiscalledMultiplePartonInteraction(MPI).TheMPItogetherwiththebeam-beamremnantscontributetotheunderlyingevent.Thepresenceoftheunderlyingeventcomplicatesmeasurementsinthehadroncolliderenvironmentsinceonehastodisentanglecontributionsofparticlescomingfromthehardscatteringandfromtheunderlyingevent.Itisnotpossibleto 20

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Summaryofquarkproperties. ParticleSpinChargeMass 1stGenerationu1/22/31.5-4MeV/c2d1/2-1/34-8MeV/c2 Summaryofleptonproperties. ParticleSpinChargeMass 1stGeneratione1/2-10.511MeV/c2e1/20<3106 3rdGeneration1/2-11777MeV/c21/20<18.2 Table1-3. SummaryofgaugebosonpropertiesoftheStandardModel. BosonSpinElectricchargeMass Photon()100 W1180:3980:025GeV/c2 22

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2-1 .QCDprovidesthemeanstoapplyperturbativetechniquestohadronicprocesseswithlargetransferredmomenta.Therststage,partonshowering,whichisdrivenbytheemissionofgluonsatrelativelylargemomenta,canbedescribedusingpQCDmethods.ThepQCDcalculationtechniquesusedtodescribethepartonshowerdevelopmentarecommonlyreferredassoftgluonresummations.However,thesecond,colorconnementstageofthejetformation,happensatsmallmomentumtransfers(<1GeV),andthestrongcouplingbecomeslarge,makingitimpossibletoutilizetheperturbativeapproach.AcommonassumptionabouthadronizationisLocalParton-HadronDuality(LPHD)[ 14 ],whichstatesthatpartondistributionsaresimplyrenormalizedintheprocessofhadronization,withoutchangingtheirshape.LPHDoriginatedfromtheideaofsoftpreconnement,wherebypartonsgroupincolorlessclusterswithoutdisturbingtheinitialspectra.PhenomenologicalmodelsofhadronizationhavebeenincorporatedintoMonteCarlosimulationsofinelasticprocessesandinmostcasessupporttheapproximatepropertyofLPHD.TheframeworkofpQCDandLPHDformstheso-calledanalyticalperturbativeapproachtoQCDjetphysics. 23

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15 ]allowsonetoperformaresummedperturbativecalculationofthepartonshowerbykeepingalltermsofordernslnn(Q)andatallordersnofperturbationtheory.Inthisequation,sisthestrongcouplingconstantandQistheenergyscale.Thelogarithmicexpansiontermsnslnn(Q)stemfromthefactthatintheregionofnitemomentumfractionsthequarkcanemitacollineargluonwithprobabilitywq!q+gRsdk2?=k2?,wherek?isthegluonstransversemomentum.TheideaoftheLLAaroseasanattempttodescribethelogarithmicdeviationsfromthetrueBjorkenscalingbehavior.However,despiteitssuccessindeepinelasticscattering,theLLAfailstogiveasatisfyingdescriptionofjetfragmentation,whichisdominatedbythesoftgluonemissions. 24

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16 ],inwhichallthetermsoftheorderofnsln2n(Q)areresummed,whilecontributionofthehigherorderlogarithmictermsisneglected.TheDLAgetsitsnamefromthedoublelogarithmicinfraredandcollinearsingularitiesofgluonemissions.InanyQCDprocess,theenergiesofcascadingpartonsdegradeduringtheirevolution,andaproperaccountingforsoftpartons,theirrecoilduetointeraction,andenergy-momentumconservationlawsshouldbeincluded.AlltheseconsiderationsareneglectedintheDLA,forwhichonlyprocesseswithratherlargegradientofenergiesandemissionanglesateachstageofevolutionareconsidered.Inordertoincludeleadinginfraredsingularitiesonemustaccountfortheeectsofsoftgluoninterference.Ithasbeenshownthattheeectofthisinterferenceiscompletelydestructivetoleadingorderoutsideofanangle-orderedregionforeachpartondecay.Thatis,onecanpreservetheprobabilisticinterpretationofthecascadesimplybyrestrictingthephasespaceallowedforeachpartonbranchingsothattheopeninganglesalwaysdecrease.Thisiscalledangularordering[ 17 ]andleadstoasuppressionofthenumberofsoftpartons.Accountistakenofsoftpartonsandstricttransversemomentumorderinginsubsequenttermsoftheperturbativeseries,suchastheNext-to-LeadingLogApproximation(NLLA)[ 18 ].NLLAallowsonetoperformaresummedperturbativecalculationofthepartonshowerbykeepingalltermsofordernsln2n(Q)andnsln2n1(Q)atallordersnofperturbationtheory.MostoftheparticlesinjetshavekT<1GeV/c,wherekTisthetransversemomentumwithrespecttothejetaxis.Therefore,inordertosuccessfullydescribejetfragmentation,atheoreticalmodelmustbeabletohandleparticleemissionsatverylowtransversemomentascales.InNLLA,asucientlyhighcut-oscaleQcutoisselectedtoensurethatallpartonshavekT>Qcutosothattheperturbativecalculationscanbeapplied.Aftertheresummation,thevalueoftheparameterQcutocanoftenbelowereddowntothevalueofQCD.Thephenomenologicalscalereplacingthetwoinitial 25

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14 ]isahadronizationconjecturethatsuggeststhattheconversionofpartonsintohadronsoccursatalowvirtualityscale,independentofthescaleoftheprimaryhardprocess,andthepropertiesofhadronsandpartonsarecloselyrelated.Therefore,predictionsmadeforpartonswithkT>Qeffshouldbealsovalidforhadrons.Withincreasingenergysensitivitytothecuto,Qeff,decreases,thusLPHDisexpectedtobecorrectasymptotically.InthesimplestinterpretationofLPHD,eachpartonattheendofthepQCDshowerdevelopmentpicksupacolor-matchingpartnerfromthevacuumseaandformsahadron.WithinLPHD,onerelatesparticlemultiplicityofhadronstothemultiplicityofpartonsviaanenergy-independentconstantKLPHD: Thisstatementshouldalsobevalidfortheinclusivemomentumdistributionsofpartonsandhadrons.TheinclusivemomentumdistributionfunctionofparticlesinjetsD()=dN dinNLLA(MLLA)isdenedintermsofvariable=ln(1 Ejetandpisthepartonmomentum.WithintheLPHDframework: 26

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Paststudiesofinclusiveparticledistributionsate+eexperimentsandCDFgavestrongsupporttotheLPHDhypothesis.Inthisdissertation,weextendtheLPHDtestbyexaminingwhetherthetwo-particlemomentumcorrelationspredictedinthepQCDframeworkalsosurvivethehadronization.WealsoaddressthequestionofwhetherMLLAandNMLLApredictionsforthetransversemomentaofparticlesinjetsagreewiththecorrespondingdistributionsforhadrons. 2.4.1MeanParticleMultiplicitiesTheanalyticalperturbativeapproachtoQCDjetphysicsallowsonetomakepredictionsformanydierentobservables.Inthissectionwebrieydiscusstheoreticalpredictionsforthemeanparticlemultiplicityandmomentumdistributionsandprovidemoredetaileddescriptionofthetwo-particlemomentumcorrelationsandthekTdistributionsofparticlesinjets.TheoreticalpredictionsfortheseobservablesarebasedoncalculationscarriedoutintheframeworkofNLLAsupplementedwiththeLPHDhypothesis.Wealsopresentareviewoftheresultsofpastmeasurements.Oneparticularlysimpleobservable,whichcontainsinformationaboutthedynamicsofhadronproduction,isthechargedparticlemultiplicitydistribution.AnumberofQCDmodelsmakepredictionsfortheevolutionoftheshapeandtheleadingmomentsofthemultiplicitydistributionasafunctionofthecenter-of-massenergy.Inaddition,inQCD,quarksandgluonshavedierentprobabilities(proportionaltotheircolorfactors)toemitgluons,thereforejetsproducedbyquarksandgluonsareexpectedtoexhibitadierenceintheirfragmentationproperties.Pastexperimentalstudiesofmeanparticlemultiplicityinjetsine+eenvironmentindicatedqualitativeagreementwiththeoreticalpredictions.However,thereportedresults 27

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20 ],mostofwhichweresignicantlybelowthetheoreticalpredictions,r1:41:8[ 21 ].Inppenvironment,itwasfoundbytheCDFcollaboration[ 23 ],thatdataagreeswithperturbativeQCDcalculationscarriedoutintheframeworkofMLLA,if:a)theratioofpartonmultiplicitiesinquarkandgluonjetsrequals1:70:3,andb)theratioofthenumberofchargedhadronstothenumberofpartonsKchargedLPHDis0:550:10.TheresultsofthemeasurementareshowninFig. 2-2 .Anothermeasurement[ 25 ]basedonthecomparisonofCDFdijetandphoton-jetdata,withdierentcontentsofquarkandgluonjetsinthenalstate,yieldsr=1:80:2whichagreeswellwithre-summedperturbativeQCDcalculations. dinNLLAisdenedintermsofthevariable=ln(1 Ejetandpisthepartonmomentum.ThisdistributionispredictedtohaveadistortedGaussianshape[ 22 ]: p 8k1 2s1 4(2+k)2+1 6s3+1 24k4); with= and = 28

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5(r Hereandareconstantswhichdependonthenumberofavorsandthenumberofeectivelymasslessquarks.Thepositionofthemaximum0anditswidthdependonthejethardnessQ.ThepredicteddependenceoftheinclusivemomentumdistributiononjethardnessisshowninFig. 2-3 .Thepredictionscontainthreefreeparameters:normalizationN(Q),Qe,andanunknownhigherordercorrectiontermO(1)[ 28 ]tothe0.PredictionfortheinclusivemomentumdistributionwerealsoobtainedintheMLLAframework[ 26 27 ],theresultsweresimilartothoseofNLLA[ 28 ].ComparisonsofmomentumdistributionsobservedindatatotheNLLAandMLLApredictionshavebeenperformedinseverale+eandepexperimentsandshowgoodqualitativeagreement.ThedistributionswerettedforthevalueoftheQeffparameterandthenormalizationfactorKchargedLPHD.Qeffwasfoundtohaveavaluearound250MeV.Ontheotherhand,themeasurementsofKchargedLPHDweretoohigh(1:3)tobeconsistentwithone-to-oneparton-hadroncorrespondence.InppenvironmenttheonlymeasurementwasperformedbytheCDFcollaboration.TheresultsofthemeasurementwereQeff=24020MeVandKchargedLPHD=0:560:10.ThetoftheCDFdatatotheMLLAfunctionisshowninFig. 2-4 .Theinclusivemomentumdistributionsarecloselyrelatedtooneofthemaintopicsofthisdissertation-thetwo-particlemomentumcorrelationsinjets,whichwillbediscussedinthenextsection. 28 ]andrecentlyrecalculatedintheModiedLeadingLogApproximation(MLLA)frameworkin[ 29 ].ThesepQCD-drivencorrelationsextendoveralargerange 29

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30 ].Thetwo-particlemomentumcorrelationfunctionR(1;2)isdenedtobetheratioofthetwo-andone-particlemomentumdistributionfunctions: whereD(1;2)=d2N d1d2.Themomentumdistributionsarenormalizedasfollows:RD()d=hni,wherehniistheaveragemultiplicityofpartonsinajet,andRD(1;2)d1d2=hn(n1)iforallpairsofpartonsinajet.TheaveragemultiplicityofparticleshniisafunctionofthedijetmassMjjandthesizeoftheopeninganglec.Forc=0:5,hnivariesfrom6to12forMjjintherange80{600GeV/c2[ 23 ].TheNLLAapproximationofEq.( 2{8 )forthetwo-particlemomentumcorrelationfunction[ 28 ]canbewrittenasfollows: where=0,0isthepositionofthemaximumofD()andparametersr0,r1,andr2denethestrengthofthecorrelationanddependonthevariable=ln(Q=Qe).Eq. 2{9 isvalidonlyforparticleswitharoundthepeak(0)oftheinclusiveparticlemomentumdistribution,intherange1.Theparametersr0,r1,andr2arecalculatedseparatelyforquarkandgluonjets[ 28 ],andaretheresultsdeterminedfromanexpansioninpowersof1=p 30

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Thetheoreticalpredictionoftheshapeofthetwo-particlemomentumcorrelationdistributionfunctionisshowninFig. 2-5 .Thedistributionhasaridge-likeshape.Itscentraldiagonalproles1=2and1=2havelinearandparabolicshapes,respectively.Theobviousfeaturesofthepredictionare(1)thecorrelationshouldbestrongerforparticleswithequalmomenta1=2,and(2)thestrengthofthiseectshouldincreasetowardlargervaluesof(i.e.forsofterparticles).Notethatinthetwo-particlemomentumcorrelationgivenbyEq.( 2{8 ),KLPHDsimplycancels,suggestingthatthecorrelationdistributionsforhadronsandpartonsareexpectedtobethesame.Untilnow,thetwo-particlemomentumcorrelationswerestudiedonlybytheOPALcollaborationinane+eenvironmentatacenterofmassenergyof91GeV[ 31 ].ChargedparticlesinthefullexperimentallyaccessiblesolidanglewereusedinOPAL'sanalysis.ThismadeitpossibleforOPALtoignoresomeeectsofjetreconstruction,butitclearlywentbeyondtherangewherethetheorywasvalid.Strictlyspeaking,thetheorycontrolspartonshowerdevelopmentonlywithinasmallopeninganglecaroundthejetaxis,sothattancsincc.OPAL'smeasureddistributionsshowedapatterninqualitativeagreementwiththeorypredictions,butthettedvaluesofthepartonshowercutoQe(322,2+51,and60+3827MeV)wereinconsistentwiththeQeextractedfromtsoftheinclusivemomentumdistributions(250MeV)[ 32 ].Fig. 2-6 showsthe3-dimentionalmomentumcorrelationdistributionasmeasuredbytheOPALcollaboration.ThesamegurealsoshowssixnarrowbandsforwhichcorrelationindataiscomparedtotheanalyticalpQCDpredictions.TheresultsofthecomparisoninallsixbandsareshowninFig. 2-7 .TheNLLAcorrelationfunctionfromEq.( 2{8 )entanglestwoeects:(1)multiplicityuctuationsofparticlesinajetand(2)actualmomentumcorrelations.Inthisanalysis, 31

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Then,thecorrelationfunctioncanbedenedas: whereF()=hn(n1)i hni2isthesecondbinomialmoment.Theexplicitdependenceofthebinomialmomentsontheenergyscaleforquarkandgluonjetswastakenfromtheory[ 33 ]: 34 ]andNMLLA[ 35 ]wereobtainedfairlyrecently,allowingtomaketherstdirectcomparisonoftheCDFdatatotheresultsoftheanalyticalQCDcalculations.Inaddition,onemayexpectkTdistributionstobemoresensitivetothehadronizationeectthanotherobservablesdescribedearlierinthischapter.Iftheradiatedpartonwith4-momentum(k0;~k)isemittedwithananglewithrespecttothedirectionofthejet,onehaskT=j~kjsink0sin.TheinclusivekTdistributionisthendenedasdN dlnkT.Intheoryitisderivedfromthesocalled\doubledierentialinclusivedistribution",d2N dln(1=x)dln,wherex=k0=Ejet.Thevalidityrangeofthepredictionsisdeterminedbytwofeaturesofthecalculation:a)theassumptionthatmomentumofemittedpartonismuchlessthanjetenergy(softapproximation),andb) 32

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2-8 .TheresultsoftheMLLAcalculationpredictdistributionstohavefewveryinterestingfeatures,namelyveryweeksensitivitytotheoriginofthejet,beingquarkorgluon,andpracticallynodependenceonthepartonshowercutoQeff.ThedependenceofthekTdistributionsonjetoriginandonthevalueofQeffisshowninFig. 2-9 .AttheNMLLAlevelthedependenceonjetoriginbecomesmoreprominent. 33

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wherecicoecients(i=0;1;2)are: wherer=hngi hnqiistheratioofaveragemultiplicitiesofpartonsingluonandquarkjets.ThevalueofrentersinderivationofEqs.( 2{10 ),( 2{11 )[ 28 ],Eq.( 2{15 )[ 33 ]andEq.( 2{19 ).InNLLA,thisratio,rtheoryisequalto9/4.Experimentally,themeasuredvalueofrexpis1:80:2[ 25 ].ThedierencebetweenthesetwovaluesisusedtoevaluatetheassociatedsystematicuncertaintyinourmeasurementofQe.FortheinclusivekTdistributionstheprescriptionformixingismorestraightforward.Thedistributionforamixtureis: dln(kT)=fg(dN dln(kT))g+(1fg)(dN dln(kT))q 34

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Acartoondescriptionofthedierentlevelsofajetevent.Thepartonlevelisthestatebeforepartonshadronize,intheorythisstageofaneventcanbedescribedbythepQCDcalculations.Thehadronlevelisthestateafterhadronization.Thetransition(hadronization)isusuallydescribedusingphenomenologicalmodels,andismostlyunexplored.Thedetectorlevelisaresultoftheeventasreportedbythedetector. 35

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Inclusivemultiplicityofchargedparticleswithincones0.168,0.280and0.466indijetevents.Dataerrorsarecompletelydominatedbycorrelatedsystematicerrors.FitforpossibleoverallnormalizationtoHerwigv5.6predictions,yieldsN=0:890:05.Theleveloftheerrorsdoesnotallowtoclaimthedierencesignicant.Herwigpredictionswerescaledbyafactor0.89andareshownontheplot(lines). Figure2-3. NLLAinclusivepartonmomentumdistributionsforQ=19;50;120GeVandQe=230MeVascalculatedbyC.P.FongandB.R.Webber. 36

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Inclusivemomentumdistributionofchargedparticleswithinrestrictedcones0.466indijeteventsttedwithMLLAlimitingspectrum.DijetmassMjj=378GeV. 37

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TheNLLApatronmomentumcorrelationfunctioncalculatedforagluonjet,Q=50GeVandQe=230MeVascalculatedbyC.P.FongandB.R.Webber. 38

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The3-dimentionalmomentumcorrelationdistributionasmeasuredbytheOPALcollaboration(top).Alsoshownaresixnarrowbands(bottom)forwhichcorrelationindataiscomparedtotheanalyticalpQCDpredictions. 39

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ComparisonoftheOPALdatatoanalyticalQCDcalculations.Thethreesolidcurvesrepresentthenext-to-leadingQCDcalculationsforthreevaluesofQeff,1000MeV(highest),255MeV(middle),and50MeV(lowest).ThedashedlinesindicatetheleadingorderQCDcalculationsforQeff=250MeV. 40

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InclusivekTdistributionofchargedparticlesaspredictedbytheresultsoftheMLLAcalculations.Thedependenceofthepredictionsonjetenergyscaleisshown. 41

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InclusivekTdistributionofchargedparticlesaspredictedbytheresultsoftheMLLAandNMLLAcalculations.A)Thedependenceofthepredictionsonjetorigin,quarkorgluon,(top),andB)valueofpartonshowercutoQeff(bottom)isshown. 42

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36 ].TheTevatronisasuperconductingsynchrotronthatisfourmilesincircumference.AtTevatronbunchesofprotonsandanti-protonscollideatthecenter-of-massenergyofp 43

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3-1 44

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45

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46

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3-2 .Theantiprotonsareusuallyinjectedaftertheprotonsandtheirbunchensembleisthemirrorimageoftheprotonspacing.Thenumberofeventsforaparticularprocessatagivencenter-of-massenergydependsuponthecrosssectionofthisprocessandtheinstantaneousluminosity(i.e.theintensityofcollidingprotonandantiprotonbeams)integratedoverthetotaldatatakingperiod.Theinstantaneousluminosityisdened: 47

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whereNBisthenumberofbunches;NpandNparenumberofprotonsandantiprotonsperbunch,respectively;fisthebunchrevolutionfrequency;andpandparetheaveragecross-sectionalareasofthebunches.Makingp,psmallerandNp,Nplargerincreasestherateofcollisions.Theeortismadetomaximizetheprobabilityofproton-antiprotoncollisionsattwopreciselocations:CDFandD0detectors.Itisachievedbyfocusingthebeamsdirectlybeforeimpact,usingthesocalledlow-betaquadrupolemagnets.TheinstantaneousluminosityishighestatthebeginningofTevatronstoresandgraduallydecreaseswithtime.Aftersometime(20hoursonaverage)theluminositybecomesverylow,thestoreisbeingterminatedandanewcyclestarts.Today,thelongeststoreattheTevatronlastedforalmost54hours.SummaryofthecurrentTevatronperformancecharacteristicsisgiveninTable 3-1 .ThetotalintegratedluminositymeasuredatCDFisshowninFig. 3-3 fromthebeginningofRunIIwhichstartedinApril2001.Theliveluminosity,whichexcludesintegratedluminosityduringallthedetectordead-timesisalsoshown.Thepeakinstantaneousluminosityrecordedis2851030cm2s1.ThedesigngoalfortheTevatronistocollect8fb1bytheendof2009. 37 ].Thedetectorwasdesignedforprecisionmeasurementsoftheenergy,momentumandpositionofparticlesproducedinproton-antiprotoncollisions.SignicantupgradestothedetectorweremadesinceRunItoadjustittotheincreasedcollisionrateandcenter-of-massenergy.Thedetectorisroughlycylindricallyandbackward-forward 48

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3-4 .ThecoordinatesystemusedatCDFisright-handed:the^zaxispointsalongthedirectionoftheprotonbeam,the^xaxisisintheplaneoftheacceleratorring,pointingradiallyoutward,andthe^yaxispointsverticallyup.Thecenterofthedetectorroughlycoincideswiththecenterofthebeamcrossingregion.Duetothesymmetryofthedetector,itissometimesmoreconvenienttousepolar(r;;)coordinatesystem.Inthiscasethepolarangleiscountedfromthepositivedirectionofthe^zaxis.Theazimuthalanglerunsinthetransverse(xy)plane,with=0beingthepositivedirectionofthe^xaxis.Commonly,isreplacedbythepseudo-rapidity,(): Thechoiceofinsteadofismotivatedbythefactthattheactualcollidingparticlesarepartons,carryingonlysomefractionofprotonsandantiprotonsenergy,oftenwithimbalancedlongitudinalcomponentsofthemomenta.Thisleadstolargeboostsintheobservedphysicsinteractions.Thequantitycalledtherapidity: 2lnE+pz isinvariantunderLorentztransformations.Intheultra-relativistic/masslessparticlelimit,therapiditycanbereplacedbythepseudo-rapidity.CDFtakesamulti-layerapproachtomeasureawidevarietyofparticleinteractions,anditconsistsofthefewmajordetectorcomponents.Fromtheinsideoutthereare:trackingsystem,magnet,electromagneticandhadroniccalorimetryandmuondetectors.ThereisalsotheTime-of-Flight(TOF)system,expandingCDF'sparticleidentication 49

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3-5 .Thecomponentsaredescribedindetailsbelow. 50

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38 ]isananchorofCDFstrackingsystem.Itisacylindricalopen-celldriftchamberwithalargetrackingvolume,designedtomeasurethethree-dimensionaltrajectoriesofchargedparticlesinthecentralregion,jj<1:0.TheCOToccupiestheradialregion40to138cm,andmeasures310cmalongthe^zaxis.Itislledwithwithfastgas(50%argon,50%ethane)tomakedrifttimessmallenoughsothatthehitscanbereadoutbetweeneachTevatronbunchcrossing.ThebasicelementoftheCOTisthecell,whichspansthelengthoftheCOT.Withineachcellarehigh-voltageeldpanels,potentialwiresandshaperwireswhichservetosupportaregularelectrostaticeld.Chargedparticlestravelingthroughthegasmixtureleaveatrailofionizationelectrons.Theseelectronsdrifttowardthesensewiresbyvirtueoftheelectriceldcreatedbytheeldpanelsandpotentialwires.Becauseofthemagneticeldalongthe^zaxis,thedriftisnotinthedirectionoftheelectriceld.Insuchcrossedeldselectronsmoveintheplaneperpendiculartothemagneticeldandatananglewithrespecttotheelectriceld.Thevaluesofdependsonthemagnitudeofbotheldsandthegasproperties,intheCOTitis35.Sincetheelectrondriftvelocityisknown,thepositionofthetrackcanbeaccuratelymeasuredbysimplyrecordingthetimeoftheresultingcurrentonthesensewires.AtransverseviewofatypicalcellwiththepositionsofindividualwiresisshowninFig. 3-6 .ThecellsoftheCOTarearrangedintoeightradiallyspacedsuperlayers.Fourofthemhavetheirwiresarrangedparalleltothe^zaxis,allowingtrackmeasurementsintherplane.Otherfoursuperlayershavetheirwirestiltedby2allowingtorecordstereoinformation,trackmeasurementsintherzplane.ThesuperlayergeometryisshowninFig. 3-7 .ThehitpositionresolutionofCOTisapproximately140m,whichtranslatesintothetransversemomentumresolutionpT 51

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38 ].Theprimarypurposeofthesilicondetectorsistoprovideexcellentspatialresolutionforthecharged-particletracks.Thisiscrucialforreconstructionofthedisplacedsecondaryvertexes,and,therefore,identicationofbjets.Theprincipleonwhichthesilicontrackingisbasedissomewhatsimilartothatofthedriftchamber.Whenachargedparticlegoesthroughthesilicon,itionizestheatoms,producingelectronsandholes-theremainingsiliconatomsmissinganelectron.Intheelectriceldelectronstraveltoonesideandtheholesintheother,leavinganelectricsignalthatcanberecorded.Duetothenarrowwidthofthestrips,thesilicondetectorshavemuchbetterresolutionthanCOT.Toprovideexcellentspacialresolutionsilicondetectorshavetobepositionedasclosetothebeamaspossible,imposinganadditionalrequirement,thatthedetectorshouldbeabletowithstandlargedosesofradiationintheregionclosetothebeam-pipe.Layer00isasingle-sidedradiationhardsiliconmicrostripdetector.Itismounteddirectlyonthebeampipe,attheinnerradiusof1.15cmandanouterradiusof2.1cm,soastobeascloseaspossibletotheinteractionpoint.L00isdesignedtoenhancethetrackimpactparameterresolution(theimpactparameterd0isdenedastheshortestdistanceintherplanebetweentheinteractionpointandthetrajectoryoftheparticleobtainedbythetrackingalgorithmt).Therearesixreadoutmoduleswithtwosensorsbondedtogetherineachmodule.TheSiliconVertexDetectoriscomposedofvelayersofdouble-sidedsiliconmicrostripdetectors,itcoversradialcoveragefrom2.5to10.7cm.SVXisbuiltinthreecylindricalbarrelseach29cmlong.Onesideofeachmicrostripdetectorprovidestrackinginformationintherplane,theothersideprovidestrackinginformationintherzplane,thereforeSVXcanreconstructthree-dimensionaltracks.ThreeoftheveSVX 52

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3-8 .TheprimarygoaloftheSVXistodetectsecondaryverticesfromheavyavordecays.ThesecondarygoalistomaximizetrackingperformancebycombiningtheCOTandSVXhitinformation.ThealignmentoftheSVXdetectorisveryimportantforthetrackreconstruction,everyeortismadetopositiontheSVXbarrelsinacoaxialmanner.TheprocessofcombinedCOTandSVXtrackreconstruction[ 39 ]startsinCOT.AfterCOT-onlytrackisreconstructed,itisextrapolatedthroughtheSVX.Becausethetrackparametersaremeasuredwithuncertainties,thetrackismorelikeatubeofcertainradius,determinedbytheerrorsontracksparameters.AteachSVXlayer,hitsthatarewithinacertainradiusareappendedtothetrackandthere-ttingisperformedtoobtainthenewsetofparametersforthetrack.InthisprocesstheremaybeseveraltrackcandidatesassociatedtotheoriginalCOT-onlytrack.Thebestoneintermsofthenumberofhitsandtqualityisselectedattheend.TheimpactparameterresolutionoftheSVXisabout40m.Theresolutioninzisabout70m.Inthecentralregion,asingleISLlayerisplacedataradiusof22cm.Intheplugregion,1:0
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3-9 ).ThecalorimetrydetectorsatCDF[ 38 ]aremechanicallysubdividedintothreeregions:central,wallandplug.Theyarelocatedjustoutsidethesolenoidmagnetinthecentralregion,andjustoutsidethetrackingvolumeintheplugregion.TheelectromagneticandhadroniccomponentsarecalledtheCentralElectro-Magnetic(CEM),CentralHadronic(CHA),WallHadronic(WHA),PlugElectromagnetic(PEM)andPlugHadronic(PHA)calorimeters.TheCEMisdividedinto15wedgesisazimuthalangleandintotentowerssubtending0.1unitsofpseudorapidity.Inconsistsofalternating1=8inchabsorberlayers,madeofaluminum-cledlead,and5mmlayersofpolystyrenescintillator,foratotaldepthof18radiationlengthsofmaterial.EmbeddedintheCEMattheapproximatedepthofmaximumshowerdevelopmentareproportionalwirechambers,CentralElectromagneticStrip(CES).Withthepositionresolutionof2mm,theycontributetoe=identication,usingthepositionmeasurementtomatchwithtracks.Asecondsetofproportionalchambers,theCentralPreshower(CPR),islocatedbetweentheCEMandthemagnetcoil,andprovidegreatlyenhancedphotonandsoftelectronidentication.TheCHAconsistofalternatinglayersofironabsorberandnaphthalenescintillator.TheyaresegmentedtomatchtheCEMtowers,0.1unitsofpseudorapiditypertowerand15ofazimuthperwedge,withatotalthicknessof4.7nuclearinteractionlengths.TheWHAisdesignedtocompensatethelimitedforwardcoverageoftheCHA,andcoversthe 54

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3-2 38 ]:CentralMuonDetector(CMU),CentralMuonUpgrade(CMP),CentralMuonExtension(CMX)andIntermediateMuonDetector 55

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40 ]atCDFinRunIIistomeasuretheluminosity.CLCsuccessfullyprovidesprecisemeasurementsatcurrentpeakinstantaneousluminositiesof31032cm2s1.TheCLCutilizestheeectknownasCherenkovradiation.Whenachargedparticletravelsinamediumfasterthespeedoflightinthismedium(i.e.when=v=c>1=n,wherenistherefractionindexofthemedium),itstartsemittinglightintoaconearounditsdirection.Cone'sopeningangledependsontheratioofthetwospeedsandtherefractionindex. 56

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3-10 .Theyarearrangedaroundthebeam-pipeinthreeconcentriclayers,16countersineach.Thisarrangementallowstomakethedetectormuchmoresensitivetotheparticlescomingdirectlyfromtheinteractionpointbecausetheytransversethefulllengthofacounterandgeneratealargeamountoflight,whichisreadoutbyaphotomultiplyingtube.Particlescomingfromsecondaryinteractionswithmaterialandfrombeam-halointeractionspassthroughthecountersatlargeangles,producingsignicantlysmallersignalthanthatofprimaryparticles.TheluminosityismeasuredusingthefollowingrelationbetweentheinstantaneousluminosityLandthenumberofprimaryinteractionsperbunchcrossing: whereppisthetotalppcross-sectionatp Theprobabilityofhavinganemptybunchcrossingisthen: 57

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cr whereListhepathlengthandpisthemomentummeasuredbythetrackingsystem.TOFhascylindricalgeometrywith2coverageinandroughlyjj<1inpseudorapidity.Itconsistsof216scintillatorbarsinstalledataradiusofabout138cminthe4.7cmspacebetweentheoutershelloftheCOTandthecryostatofthesuperconductingsolenoid.ThecompletedescriptionoftheTOFdetectorcanbefoundin[ 41 ]. 3-11 .Theelaboratedescriptionoftheentiresystemisgivenin[ 38 ]. 58

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42 ]usesinformationfromtheCOTtoreconstructtracks,eventsareacceptedorrejectedbasedonthetrackmultiplicityandtransversemomenta.ThemuonstreamusesinformationfromtheXFTtomatchtrackstohitsinthemuonchamberstoproducemuoncandidates.ThemaximumacceptrateforL1triggeris20kHz,afactoroffewhundredsmallerthantheinputrateof2.5MHz.EventswhichmeettherequirementsoftheL1triggerarepassedtotheLevel-2(L2).AtL2,aneventiswrittenintooneoffourbuerswithintheDAQelectronicsforeachdetectorcomponent.ThesebuersaredierentfromthedatapipelineusedinL1,thedatahereremainsinthebueruntilthedecisionismade.Whileeventdataarebeingprocessed,theycannotbeoverwrittenbyanothereventfromL1.IfanL1acceptoccurswhileallfourL2buersareoccupied,thedeadtimeisincurred.Inordertominimizedeadtime,thelatencyoftheL2decisionmustlessthanapproximately80%oftheaveragetimebetweenL1accepts.Therefore,theL2latencyisdesignedtobe20s.Tomakeadecision,L2usesinformationfromL1aswellasadditionaldatafromtheshowermaximumstripchambers(CES)inthecentralcalorimeterandtherstripsofSVX.L2extendsXFTtracksinsidetheSVXvolumeandaddsthemeasurementofthetrackimpactparameterd0.Signicantimpactparameterindicatesadisplacedvertex,whichisanextremelypowerfulsignature.ThemaximumacceptratefortheL2triggeris300Hz. 59

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60

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43 ],aconealgorithmcombiningobjectsbasedonrelativeseparationinspace;MidPoint,analgorithmsimilartoJetClubuthavingsomemodications;andKT[ 44 ],analgorithmcombiningobjectsbasedontheirrelativetransversemomentumaswellastheirrelativeseparationinspace.TheJetClualgorithmwasusedinthemeasurementspresentedinthisdissertation. Thetowercentroid(i;i)isobtainedby: 61

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whereETiEMandETiHAaretransverseenergiesdepositedintheelectromagnetic(EM)andhadronic(HA)partsofthei-thcalorimetertower,respectively.Inthenextstep,alltowerswithET>0:1GeVwithinR=p where(i;i)istheangularpositionofthei-thcalorimetertower. 62

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45 ].Therststepistocorrectforthe-dependenceofthecalorimeterresponse.Thiscorrectionisespeciallyimportantintheregionswithsignicantnon-uniformitiesanduninstrumentedregions,suchasbetweentwohalvesofthecentralcalorimeter,orbetweencentral,wallandplugcalorimeters.Thecorrectionisbasedonagoodunderstandingofthecentralregionofthecalorimeter.Theideasisthatinaneventwithonlytwojets,theirtransverseenergiesshouldbebalanced.ThepTofa\probe"jet,anywhereinthecalorimeteriscomparedtothepTofa\trigger"jetinthecentralregion,awayfromuninstrumentedregions,0:2
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46 47 ]andHerwig6.5[ 48 ]areusedforstudiesdiscussedinthisdissertation.Jetfragmentationinbothgeneratorstwosteps:theperturbativeinitial-andnal-statepartonshoweringandhadronizationusingphenomenologicalmodels.ThepartonshowermodelsofPythiaandHerwigareverysimilar.ThecascadeevolutionistreatedasabranchingprocessbasedontheLeadingLogApproximation(LLA).Theprobabilityforthedecayofapartonintotwopartonsisevaluatedusing\DGLAP"evolutionequation[ 49 ].TheQCDcoherenceeectsareincludedinbothgenerators,however,withsomedierences.ThetreatmentofhardgluonemissioninHerwigisimprovedbymatchingoftherstgluonbranchingtothethree-jetmatrixelement.InbothgeneratorsthepartonshoweristerminatedwhenthepartonvirtualitiesdropbelowQeff.TheimplementationofhadronizationisdierentinPythiaandHerwig.TheconversionofpartonstohadtonsinPythiaisaccomplishedbytheLundStringModel[ 50 ].Theconceptofthismodelcanbeeasilyunderstoodusinganexampleoftheqqproductionine+eannihilation.Theproducedquarkandantiquarkmoveoutinopposite 64

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51 ],theimplementationofwhichisfollowing.Attheendofpartonshower,allgluonsareforcedtosplitintoqqpairs.Neighboringqqpairsformcolor-neutralclusterswhichdecayintheirrestframeintotwohadrons.Specialtreatmentisgiventoverylightclusters,whichareallowedtodecayintoasinglehadron,andtoveryheavyclusterswhichcandecayintosmallerclusters.Baryonsareproducedfromclusterdecaysintobaryon-antibaryonpairs,i.e.clustersthemselvesalwayshavezerobaryonnumber.BothMCgeneratorshavetheiradvantagesanddisadvantages.ThestringhadronizationmodelusedinPythiawastestedextensivelyine+ecollisionsansshowedandexcellentagreementwithdata.However,alargenumberofphenomenologicalparameterssomewhatshadowstheperturbativeinformation.TheadvantageoftheclustermodelusedinPythiaisitssimplicityandthattheglobaleventshapeisdeterminedbytheparametersdescribingthepartonshower(QCDandQcutoff),andtoalesserextentbythethresholdsofclustermass. 65

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52 ],withsomemodicationsdirectedatmakingthesimulationworkfaster.OncethedetectorisbuiltinthelanguageofGEANT,almostanykindofparticlecanbetrackedthroughitwithallappropriatephysicsprocessestakingplacetomimicthephysicaldetectorresponse.Someinteractionarehandledwithspecicparametrizedmodels,suchasGFLASHshowersimulationpackage[ 53 ],tunedtosingleparticleresponseandshowershapebasedonthetestbeamandcollisiondata.The\raw"data(digitizedphysicaldetectorresponse)afterdetectorsimulationisfedtothealgorithmthatimplementstheactualtriggerlogictodecideiftheeventshouldbeaccepted.Theeventspassingthetriggersimulationgothroughproductionstage,inwhichthecollectionofphysicsobjects(tracks,jets,muons,etc.)arecreatedfromtherawdata. 66

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TheschematicpictureoftheacceleratorchainatFermilab.Thechainconsistsofseveralindividualcomponents:ProtonSource(Cockcroft-Walton,LinacandBooster),MainInjector,AntiprotonSource(Debuncher,AccumulatorandRecycler)andtheTevatron.Thedetectors,CDFandD0,arealsoshown. Table3-1. SummaryofthecurrentTevatronperformancecharacteristics. center-of-massenergy1.96TeVbunchcrossingseparation396nsnumberofprotonsperbunch240109numberofantiprotonsperbunch25109peakluminosity2901030cm2s1 SummaryofquantitiescharacterizingCDFcalorimetry. NameThicknessMaterialResolution(EinGeV) CEM19X03mmPb,5mmScint.13:5%=p CHA4.7025mmFe,10mmScint.75%=p 67

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TheprotonandantiprotonbeamstructureattheTevatron.Eachbeamisdividedintothree\trains"separatedbytheabortgap.Eachtraincontains12bunchesofprotonsorantiprotons.Thetimeseparationbetweenconsequentbunchesis396ns. Figure3-3. ThetotalintegratedluminositydeliveredbytheTevatronfromthebeginningofRunIIwhichstartedinApril2001.Theliveluminosity,whichexcludesintegratedluminosityduringallthedetectordead-timesisalsoshown. 68

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Theschematiccross-sectionviewoftheCDFdetector. 69

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Theschematicr{zviewofonequadrantoftheCDFtrackingsystem.Itscomponents:CentralOuterTracker(COT)andthesilicondetectors:Layer00(L00),SiliconVertexDetector(SVX),andIntermediateSiliconLayers(ISL)areshown. 70

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TransverseviewofthenominalcelllayoutforCOTsuperlayer2.Thearrowshowstheradialdirection.Theelectriceldisroughlyperpendiculartotheeldpanels.Themagneticeldisperpendiculartotheplane.Theanglebetweenwire-planeofthecentralcellandtheradialdirectionis35 1=6thoftheCOTeastendplate.Shownarethewire-planeslotsgroupedintoeightsuperlayers. 71

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SVXbulkheaddesign.Placementofladdersisshownintwoadjacentwedges. 72

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Schematicpictureofonequadrantoftheplugcalorimeterincludingtheelectromagneticandhadronicparts.Theplugcalorimeterhasfull2coverageandextendsto1:1
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TheCherenkovLuminosityCounteratCDF.Thedetectormodulesarelocatedwithinthe\3-degreeholes"insidetheforwardandbackwardcalorimeters. 74

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FunctionalblockdiagramoftheCDFdataow.ThecrossingrateattheTevatronisactuallyonly2.5MHz,butthetriggersystemwasdesignedfortheoriginallyenvisioned7.5MHzcrossing. Figure3-12. Theratio=pprobeT=ptriggerToftransversemomentaofthe\probe"andthe\trigger"jetsusingthe70GeVjettrigger,obtainedusingtwodierentmethods(missingETprojectionfractionanddijetbalancing.The\probe"triggerjethastobeinacentralregion0:2
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4.1.1DataSamplesWereportameasurementofthetwo-particlemomentumcorrelationsforchargedparticlesineventswithdijetinvariantmassesintherange66{563GeV/c2.EventswereproducedattheTevatroncolliderinppcollisionsatacenterofmassenergyof1.96TeVandwererecordedbytheCDFRunIIdetector.TheresultsarebasedondatacollectedduringtherunningperiodfromFebruary2002toAugust2004.Thetotalintegratedluminositywas385pb1.ThedataarettoNLLAanalyticalfunctionsandthevalueofthepartonshowercutoQeisextracted.ThecorrelationsobservedindataarecomparedtoMonteCarlopredictionsbythePythiaTuneAandHerwig6.5eventgenerators.Eventswerecollectedusingasinglecalorimetertowertriggerwithatransverseenergy(ET)thresholdof5GeVandwithsinglejettriggerswithETthresholdsof20,50,70,and100GeV.Eachofthejettriggershadadierentsamplingratesoastonotsaturatetheavailabletriggerbandwidth. 76

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54 ],denedasET==p where~kisavectorsumofmomentaofthetwoleadingjets,istheanglebetweentwoleadingjets,andk?istheresolutionofk?.Thedenitionsof~k,~k?,and~kjjareillustratedinFig. 4-1 .Thecomponentk?isknowntobesensitivetotheenergymismeasurementofjets,whilekjjismoresensitivetothehardgluonradiation.Ineventswithhighenergyjets,asingleparticleemergingfromajetatasucientlylargeanglewithrespecttothejetaxiscanbeidentiedasaseparatejet.Ajetcanalsobeproducedfromtheunderlyingevent.Therefore,rejectionofalleventswithmorethantwojetscanintroducepossiblebiases.Weallowuptotwoextrajets,buttheirenergyis 77

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whereEand~Paretheenergiesandmomentaofthejets,respectively.Themassbinboundaries,averageinvariantmasshMjjiandnumberofeventsineachbinaregiveninTable 4-1 .Thebinwidthisselectedtobe3Mjj,whereMjjisthecalorimeterresolutionforthedijetmassdetermination,Mjj 38 55 ].Poorlyreconstructed 78

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4-2 .ThemeasuredvaluesofzaresummarizedinTable 4-2 .Tracksproducedfrom-conversionsareremovedusingacombinationofcutsonimpactparameterd0andthedistanceRconv(Fig. 4-4 ).Theimpactparameterd0isdenedastheshortestdistanceintherplanebetweentheinteractionpointandthetrajectoryoftheparticleobtainedbythetrackingalgorithmt.Itcanbeshownthatforelectronsandpositronsoriginatingfrom-conversion: wherepTisthetransversemomentumofthechargedparticleinGeV/c,BisthemagneticeldinTeslaandRconvismeasuredinmeters.MonteCarlostudiesindicatethatthed0cutaloneislessecientatremoving-conversiontracksthanitistorequiretrackstohavejd0j<5d0orRconv<13cm.ThevalueRconv=13cmismotivatedbythelocationofSVXportcards.Indeed,conversionsoccurringatthisradiusareclearlyseeninthedata.Theresolutionoftheimpactparameter,d0,isevaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits.TheimpactparameterdistribtuionsfortracksreconstructedwithdierenttrackreconstructionalgorithmsareshowninFig. 4-3 .Themeasuredvaluesofd0aresummarizedinTable 4-3 .Toverifytheeectivenessofthetrackqualitycuts,wecomparedistributionsoftheinclusiveparticlemultiplicityandmomentuminthePythiaTuneAatthegenerator 79

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4-5 andFig. 4-6 .CDFSimpropagatesparticlesthroughthedetectorincludingbothconversionsandin-ightdecaystosimulatetheCDFdetectorresponse.Theagreement,afterselectioncutsareapplied,conrmsthatthecutsdoremovemostofthebackgroundtracks. 4-7 .Thiscanbedonewhenthedijetaxisiswithin45<<135,andthisconditionisautomaticallysatisedbyoureventselection.Weassumethatconesformedinsuchafashioncollectstatisticallythesameamountofbackground(whichisuncorrelatedwithjets)astheconesaroundthejetaxis[ 24 ].InordertoobtainthecorrectedexpressionforC(1;2),oneneedstosubtractthebackgroundfromtheone-andtwo-particlemomentumdistributions.Thiscanbeachievedbyconsideringparticlesinjetconestogetherwithparticlesincomplementarycones.Itcanbeshownthatthemomentumdistributionsafterbackgroundsubtraction~Dare: ~D()=Djet()Dcompl(); ~D(1;2)2Djet(1;2)Djet+compl(1;2)+2Dcompl(1;2); 80

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Thedierencebetweencorrelationdistributionsindata,withandwithoutthisbin-by-binscalefactorapplied,istakenasameasureofthesystematicuncertainty: C(1;2)Data=j(1)C(1;2)Dataj: Furtherinthissectionwediscussdierentsourcesofsystematicuncertaintiesattheleveloftheeventselection.Theircontributionstothevaluesofc0,c1,andc2aregiveninTable 4-4 .Ineachtriggersampleonlyeventswithtriggereciencyhigherthan99%wereused.Tocheckthattriggereectsdonotbiasthemeasurement,weverifythecontinuityofthedistributionsofparticlemultiplicityinajetinthetransitionbetweenadjacentdijettriggersamples.Nodetectableosetsareobserved. 81

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82

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84

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4-5 wherethesubtractionisdonebin-by-bin. 56 ]tomeasurethetrackreconstructionineciencyinsidejetsasafunctionofrandthejetandtracktransversemomenta,usingtrackembeddingtechniques.TheeectofonthekTdistributionsisfoundtobesmallandisabsorbedintothesystematicuncertainty. 85

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Denitionofvariablesinthejetbalancecut.Vector~krepresentsavectorsumofthetwoleadingjets'momenta.The~kjjand~k?componentsof~kareparallelandperpendiculartothebisectoroftwojets. Table4-1. Measurementofmomentumcorrelations:dijetmassbinsboundaries,averageinvariantdijetmasshMjjiandnumberofeventsineachbinaftertheeventselectioncuts. BinLowedge(GeV/c2)Highedge(GeV/c2)hMjji(GeV/c2)Numberofevents 16695761522929513210877246313218014917682418024320280608524332327218528632342836112000742856347519150 Table4-2. Thez,evaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. Algorithmz,cm COT-only1.20Inside-Out(IO)0.60Outside-Inr1.80KalmanOutside-Inr1.80Outside-Instereo0.40KalmanOutside-Instereo0.40Outside-In3D0.21KalmanOutside-In3D0.21SVXOnly0.78 86

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Thezdistribtuionsfortracksreconstructedwithdierenttrackreconstructionalgorithms.Thedataarettoasumoftwo\Gaussians"todeterminethewidth,z,ofthedistributions,usedintheeventselection. Table4-3. Theresolutionoftheimpactparameter,d0,evaluatedfordierentcategoriesoftracksbasedonthenumberofSVXandCOThits. Algorithmd0,mm COT-only0.110Inside-Out(IO)0.013Outside-Inr0.020KalmanOutside-Inr0.020Outside-Instereo0.014KalmanOutside-Instereo0.014Outside-In3D0.0095KalmanOutside-In3D0.0095SVXOnly0.020 87

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Theimpactparameterdistribtuionsfortracksreconstructedwithdierenttrackreconstructionalgorithms.Thedataarettoasumoftwo\Gaussians"todeterminethewidth,d0,ofthedistributions,usedintheeventselection. Figure4-4. IllustrationofthedistanceRconvfromthebeamlinetothepointwheretheconversionoccurred.Here,d0istheimpactparameter. 88

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MonteCarlotrackmultiplicityinjetsbeforeandafterapplyingtrackqualitycuts.ThedistributionsareforthedijetmassbinwithQ=50GeV.Particlesarecountedwithinaconeofopeninganglec=0:5radians.CDFSimreferstothefullCDFdatasimulation. Figure4-6. InclusivemomentumdistributionsofMonteCarlotracksinjetsbeforeandafterapplyingtrackqualitycuts.ThedistributionsareforthedijetmassbinwithQ=50GeV.Particlesarecountedwithinaconeofopeninganglec=0:5radians.CDFSimreferstothefullCDFdatasimulation. 89

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Illustrationofthedenitionofcomplementarycones.Theunlabeledarrowsaretheaxesoftheconescomplementarytojets1and2 Table4-4. Summaryofthesystematicuncertaintiesofthecorrelationparametersc0,c1andc2forthedijetmassbinwithQ=50GeV. Originofsystematicuncertaintyc0c1c2 Table4-5. MeasurementofthekTdistributions:dijetmassbinsboundaries,averageinvariantdijetmasshMjjiandnumberofeventsineachbinaftertheeventselectioncuts. BinLowedge(GeV/c2)Highedge(GeV/c2)hMjji(GeV/c2)Numberofevents 166957617834295132108101619313218014923639418024320211443752433232722647063234283612374274285634753830685637376206638 90

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5.1.1NLLAFitstoDataThetwo-particlemomentumcorrelationdistributionsC(1;2)areproducedforsevenbinsofdijetmassanddoshowtheridge-likeshapeaspredictedbytheory.Inthisdissertationweplotthecentraldiagonalproles1=2and1=2(showninFig. 2-5 )ofdistributions.Figures 5-1 5-7 showthedistributionscorrespondingtothedijetmassbinswithQ=19,27,37,50,68,90,and119GeV,respectively.Thebinsize=0:2ischosentobemuchwiderthanthemomentumresolutioninthettedrange.Smallererrorbarscorrespondtothestatisticaluncertaintyonly,whilethelargererrorbarscorrespondtoboththestatisticalandsystematicuncertaintiesaddedinquadrature.The2-dimensionalmomentumcorrelationdistributionistaccordingtoEq. 2{18 withthreefreeparametersc0,c1,andc2.Thesolidlineshowstheproleofthetfunction.TheextractedvaluesoftparametersaregiveninTable 5-1 .Thetrange1<<1ismotivatedbytheregionofvalidityoftheNLLAcalculations.Thedash-dottedlinescorrespondtothetheoreticalcurvesgivenbyEq. 2{18 forQe=18040MeV,extractedfromtsoftheinclusivemomentumdistributions(see A ).ThedashedlinescorrespondtotheresultsofthePerez-RamoscalculationforthevalueofQe=23040MeVextractedfromtsoftheinclusivemomentumdistributionstotheMLLAfunction[ 24 ].Thefractionofgluonjetsinthesample,usedtomodelthe 91

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57 ].ThesystematicuncertaintyduetothepartondistributionfunctionsisevaluatedbycomparingresultsforthefractionofgluonjetsfgobtainedusingtheCTEQ5LandtheCTEQ6.1[ 58 ]PDFsets.Thesystematicuncertaintyduetothevalueofrwasevaluatedbytakingadierencebetweenthetheoretical(rtheory=9=4)andexperimentallymeasured(rexp=1:8)[ 25 ]valuesandpropagatingittothevalueofQe.Bothsystematicuncertaintieswerefoundtobenegligible.TheoverallqualitativeagreementbetweenthedataandtheNLLAcalculation[ 28 ]isverygood.Thedatafollowtheoreticaltrends,indicatinganenhancedprobabilityofndingtwoparticleswiththesamevalueofmomenta(indicatedbytheparabolicshapeofthe1=2diagonalprolewithitsmaximumat1=2).Thiseectbecomeslargerforparticleswithlowermomenta(thepositiveslopeofthe1=2diagonalprole).Anosetintheoveralllevelofcorrelationisobservedinallsevendijetmassbins,indicatingthattheFong-Webberpredictionoverestimatestheparameterc0ofthecorrelation.TheMLLAcurves[ 29 ]qualitativelyshowthesametrends;however,thequantitativedisagreementisobviouslylargerfortheMLLApredictionscomparedtotheNLLApredictions[ 28 ].Fig. 5-8 showstheevolutionofparametersc0,c1andc2withjethardnessQ.Eachdatapointcorrespondstothevalueofoneparametermeasuredinaparticulardijetmassbin.ThedistributionsarettotheNLLAfunctionwithQetreatedastheonlyfreeparameter.Thetsarerepresentedbysolidlines.Theoreticalcurvesforpurequarkandgluonjetsinthenalstatearealsoshown.WeusedtheresultsoftheFong-Webbercalculation[ 28 ]tottheevolutionoftheseparameterswithjethardnessandtoextracttheparameterQe.ThevalueofQeobtainedfromthetofc1is14510(stat)+7965(syst)MeV.ThevalueofQeobtainedfromthetofc2is12912(stat)+8671(syst)MeV.TheaveragevalueofQe

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2{4 )aswellastheparameterO(1)=0:6.Thereforeonlyitsevolutionwithenergyandnottheabsolutevalueiscontrolledintheory.Forthesereasonsweexcludec0fromthemeasurementofQe.AformalttothetheoreticalfunctiongivesthevalueQe=0:1MeV.Thisvalue,however,doesnothavephysicalmeaningasthedistributionsofc0vs.Qindataandtheoryarenotinagreement.Otherthantheoset,c0showsveryweak,ifany,Qdependence,consistentwiththetheory. 5-9 5-13 showthecorrelationdistributionsindatacomparedtoPythiaTuneAandHerwig6.5predictionsatthelevelofnalstablechargedhadrons. 5.2.1ComparisontoMLLAandNMLLApredictionsThedN=dln(kT)distributionsareproducedforeightbinsofdijetmassandareshowninFig. 5-14 .Theerrorbarscorrespondtostatisticaluncertaintyonly,whiletheshadedareacorrespondstostatisticalandsystematicuncertaintiesaddedinquadrature.ThedashedlinecorrespondstotheMLLAcurvecalculatedaccordingto[ 34 ]forthevalueofQeff=230MeV,extractedfromtsofinclusivemomentumdistributions.ThesolidlinecorrespondstotheNMLLAcurveforthesamevalueofQeff.Thefractionofgluonjetsinthesample,usedtomixthetheoreticalpredictionforquarkandgluonjets,isobtainedusingPythiaTuneAwithCTEQ5Lpartondistributionfunctions[ 57 ]. 93

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58 ]PDFsets.Thissystematicuncertaintywasfoundtobenegligible.TheoverallqualitativeagreementbetweenthedataandtheMLLAcalculationresults[ 34 ]isverygoodwithintherangeofsoftapproximation.Beyondtherange(athighkT),however,theMLLApredictionsfailtoreproducedata,predictingmoreparticleswithhighvaluesofkT.Thevalidityrangeofthesoftapproximationbecomeslargerwithincreasingenergyand,asexpected,thediscrepancybetweendataandMLLApredictionsdecreases.TheNMLLApredictions[ 35 ]providegooddescriptionoftheCDFdataovertheentirerangeofjetenergies.Thefactthatthehadronleveldistributionscanbesuccessfullydescribedbytheperturbativepredictionsmadeforpartonssuggeststhatthepropertiesofjetsareprimarilydeterminedatthepartonicstageofaneventandthesepropertiesarenotalteredsignicantlyintheprocessofhadronization. 5-15 showsdistributionsindatacomparedtoPythiaTuneAandHerwig6.5predictionsatthelevelofnalstableparticles.BothMonteCarlogeneratorsuseLeadingLogApproximationprecisiontodescribetheprocessofpartonshowering.DespitethefactthatMLLApredictions(whichareobtainedwithNext-to-LeadingLogprecision)showsignicantdeviationfromthedataatlargevaluesofln(kT),theagreementbetweentheCDFdataandtheMonteCarlopredictionsisverygood.ThissuggeststhathadronizationparametersinPythiaandHerwigwereheavilytunedtoreproducethedataintheentirerangeofparticlekT. 94

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Summaryofthecorrelationparametersc0,c1andc2measuredinsevendijetmassbins.Therstuncertaintyisstatistical,thesecondoneissystematic. Q(GeV)c0c1c2 95

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Two-particlemomentumcorrelationsinjetsintherestrictedconeofsizec=0:5radiansfordijetmassbinwithQ=19GeV(top).Centraldiagonalproles1=2(middle)and1=2(bottom)ofthedistributionsareshown.ThecorrelationindataiscomparedtothatoftheoryascalculatedbyC.P.FongandB.R.WebberforQe=180MeVandascalculatedbyR.Perez-RamosforQe=230MeV. 96

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SameasinFig. 5-1 forQ=27GeV. 97

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SameasinFig. 5-1 forQ=37GeV. 98

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SameasinFig. 5-1 forQ=50GeV. 99

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SameasinFig. 5-1 forQ=68GeV. 100

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SameasinFig. 5-1 forQ=90GeV. 101

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SameasinFig. 5-1 forQ=119GeV. 102

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Theevolutionofcorrelationparametersc2,c1,andc0withjetenergy.CDFdatapointsarettotheNLLAfunctionascalculatedbyC.P.FongandB.R.Webber.AvalueofQeisextractedfromeachofthesetsseparately.TheNLLApredictionsforpurequarkandpuregluonjetsamplesarealsoshown. 103

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Hadron-leveltwo-particlemomentumcorrelationsinjetsintherestrictedconeofsizec=0:5radiansforthedijetmassbinwithQ=19GeVbythePythiaTuneA(top).ThecorrelationindataiscomparedtothehadronmomentumcorrelationsbythePythiaTuneAandHerwig6.5eventgenerators.Centraldiagonalproles1=2(middle)and1=2(bottom)ofthedistributionsareshown. 104

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SameasinFig. 5-9 forQ=27GeV. 105

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SameasinFig. 5-9 forQ=50GeV. 106

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SameasinFig. 5-9 forQ=90GeV. 107

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SameasinFig. 5-9 forQ=119GeV. 108

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24 ].InthisnotewetthedatatotheFong-WebberNLLAfunctionEq.( 2{4 ).DuetonaturaldierencesinthetwotheoreticalapproachestheextractedvaluesofQeffdonothavetomatch,howevertheyareexpectedtobeofthesameorder.TheprincipaldierencebetweentheFong-WebberandtheMLLApredictionsisthatFong-WebberfunctioncontainsoneextraparameterO(1)-anuncertaintyinthepeakpositionofthedistribution.Thisuncertaintyisnotcontrolledbytheory.ThereforewhileinMLLAparametrizationQeffcontrolsbothpeakpositionandwidthofthedistribution,inFong-Webber'sitcontrolsonlythewidthwhiletheO(1)parametereectivelycontrolsthepeakposition.Eventandtrackselection,aswellastheevaluationofsystematicuncertaintiesisdoneinthesamefashionasforthemeasurementofthetwo-particlemomentumcorrelationdistributions.Theonlyeectaccounteddierentlyistrackingineciency.Thisisduetothefactthatmomentumdistributionsareexpectedtobemoresensitivetoineciencyeectsthanthecorrelations.Higheciencyoftrackreconstructionisensuredbyselectingeventswithcentraljetsandeliminatingpoorlyreconstructedandspurioustracks.However,therestillmaybesomenon-reconstructedtracksinsidejets.Thetrackingineciencyvariesasafunctionofthedistancebetweentrackandjetaxisinthespaceandtransversemomentaofbothjetandtrack.Thedetailedstudieshavebeenperformed[ 56 ]tomeasurethetrackreconstructionineciencyinsidejetsasafunctionofrandthejetandtracktransversemomenta,usingtrackembeddingtechniques.WeusedPythiaTuneAandtheresultsofthesestudiestosimulateineciencyeectsbyloosingMonteCarlotracksaccordingtotheparametrizationobtainedin[ 56 ].Acorrectionfactor 113

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A-1 .Thecorrespondingcorrectionfactorsarethenappliedtothedistributionsindata.Thedierencebetweendistributionsindata,withandwithoutthisscalefactorapplied,isassignedasthesystematicuncertainty.TheinclusivemomentumdistributionsD()=dN dinallsevenexperimentaldijetmassbinsaresimultaneouslyttothetheoreticalFong-Webberfunction.InthettheQeandO(1)parametersarerequiredtohavesamevalueinalldijetmassbinswhilenormalizationparameterN(Q)isallowedtovaryfromonebintoanother.Figure A-2 showsthedistributionsindatacorrespondingtothedijetmassbinswithQ=27,50,and90GeV,respectively.Theerrorbarscorrespondtoboththestatisticalandsystematicuncertaintiesaddedinquadrature.ThesolidcurvescorrespondtothetofCDFdatatothetheoreticalFong-Webberfunction.TheextractedvaluesofthetparametersareQe=18040MeVandO(1)=0:60:1. 114

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Trackingeciencycorrectionfactorsasfunctionsofforthreedijetmassbins. 115

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Inclusivemomentumdistributionsofparticlesinjets.DistributionsindataarettotheoreticalfucntionascalculatedbyC.P.FongandB.R.Webber. 116

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SergoR.JindarianiwasborninTbilisi,(Republicof)GeorgiaonAugust18,1980.Hereceivedprimaryeducationatthe37thmiddleschool.In1994hesuccessfullypassedtheexaminationandwasadmittedtotheVekuaHighSchool,theschoolorientedonprovidingexceptionallevelofeducationinphysicsandmathematics.DuringhisyearsathighschoolSergoparticipatedinInternationalYoungPhysicistTournaments(thirdteamawardin1996and1997,rstindividualawardin1996),aswellasinthenationalphysicsandmathematicsolympiads(multipleawards1995-1997).Healsoplayedbasketballatthepointguardposition.In1997hereceivedathankyouletterfromthePresidentofGeorgia,E.Shevardnadze,foracademicexcellenceandleadership.In1997SergograduatedwithhonorsfromhighschoolandappliedtotheDepartmentofPhysicsatTbilisiStateUniversity(TSU).Forhisachievementsduringtheyearsofhighschoolhewasadmittedwithoutqualifyingexaminations.HewasalsoaselectedtobearecipientofGeorgeSorosStipend(1997-2000).Thisstipendwasestablishedtoprovidenancialsupporttooutstandingstudentsduringtheircollegeyearsincountrieswithverypooreconomy.InhisearlyyearsincollegeSergogotintroducedtothebasicsofparticlephysics,andhisinteresttothehighenergyphysicsgrewquickly.AtthesametimeheworkedassystemadministratorattheInternetserviceprovider\Geonet"andwasoneoftherstfewtoimplementtheconceptofIP-telephonyinGeorgia.In2001SergograduatedfromTSUwithB.S.inPhysics,SummaCumLaude.InlateninetiestheeconomyinGeorgiawasstrugglingandthelevelofeducationhasalsogonedown.This,togetherwithSergosinterestinparticlephysics,inuencedhisdecisiontotakearesearchassistantpositionattheJointInstituteofNuclearResearchinDubna,Russia.There,attheUniversityCenter,healsocontinuedhiseducationtowardMastersandPhDdegrees.Hisresearchwasmainlyfocusedondevelopingnumericalmethodstosolveequationsdescribingveryhighmultiplicityhadronprocesses. 121

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