Charmonium correlation and spectral functions in quenched lattice QCD at finite temperature [Elektronische Ressource] / vorgelegt von Heng-Tong Ding

De
Publié par

Charmonium Correlation and Spectral Functionsin Quenched Lattice QCD at Finite TemperatureDissertationzur Erlangung des Doktorgradesder Fakult¨at fu¨r Physikder Universita¨t Bielefeldvorgelegt vonHeng-Tong DingSeptember 2010Charmonium Correlation and Spectral Functionsin Quenched Lattice QCD at Finite TemperatureHeng-Tong DingVollst¨andiger Abdruck der von der Fakult¨at fu¨r Physik der Universit¨at Bielefeldzur Erlangung des akademischen Grades einesDoktors der Naturwissenschaften (Dr. rer. nat.)genehmigten Dissertation.Pru¨fer der Dissertation (Gutachter):Prof. Dr. Edwin LaermannProf. Dr. Helmut SatzWeitere Mitglieder des Pru¨fungsausschusses:Prof. Dr. Mikko LaineTag der mu¨ndlichen Pru¨fung (Disputation): 12. Oktober 2010Table of ContentsIntroduction 11 Lattice QCD - A brief introduction 51.1 Gluon fields on the lattice . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Matter fields on the lattice . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.1 Na¨ıve action and fermion doublers . . . . . . . . . . . . . . . . . 81.2.2 Wilson fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 The continuum limit of lattice QCD . . . . . . . . . . . . . . . . . . . . 121.4 Simulation technique and error estimation . . . . . . . . . . . . . . . . . 141.5 Simulation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.5.1 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . 181.5.
Publié le : vendredi 1 janvier 2010
Lecture(s) : 10
Tags :
Source : NBN-RESOLVING.DE/URN:NBN:DE:HBZ:361-17732
Nombre de pages : 152
Voir plus Voir moins

CharmoniumCorrelationandSpectralFunctions
inQuenchedLatticeQCDatFiniteTemperature

Dissertation
zurErlangungdesDoktorgrades
derFakulta¨tfu¨rPhysik
derUniversita¨tBielefeld

vorgelegtvon
Heng-TongDing

September2010

CharmoniumCorrelationandSpectralFunctions
inQuenchedLatticeQCDatFiniteTemperature

Heng-TongDing

Vollsta¨ndigerAbdruckdervonderFakulta¨tfu¨rPhysikderUniversita¨tBielefeld
zurErlangungdesakademischenGradeseines
DoktorsderNaturwissenschaften(Dr.rer.nat.)
genehmigtenDissertation.

Pru¨ferderDissertation(Gutachter):
Prof.Dr.EdwinLaermann
Prof.Dr.HelmutSatz
WeitereMitgliederdesPru¨fungsausschusses:
Prof.Dr.MikkoLaine

Tagdermu¨ndlichenPru¨fung(Disputation):12.Oktober2010

Introduction

TableofContents

1LatticeQCD-Abriefintroduction
1.1Gluoneldsonthelattice..........................
1.2Mattereldsonthelattice.........................
1.2.1Na¨veactionandfermiondoublers.................
1.2.2Wilsonfermions...........................
1.3ThecontinuumlimitoflatticeQCD....................
1.4Simulationtechniqueanderrorestimation.................
1.5Simulationdetails..............................
1.5.1Simulationparameters........................
1.5.2Scaledetermination.........................
1.5.3J/ masstuning...........................
1.6Renormalizationconstants..........................

2Mesoniccorrelationandspectralfunctions
2.1Mesoniccorrelationandspectralfunctions.................
2.1.1Acloselookattheintegrandkernel................
2.1.2Thereconstructedcorrelator....................
2.1.3Sumrules...............................
2.2MaximumEntropyMethod.........................
2.2.1Likelihoodfunction..........................
2.2.2Entropicpriorinformation......................
2.2.3Posteriorprobability.........................
2.2.4Distributionsandtheirnormalizations...............
2.2.5MEMalgorithm...........................
2.2.6TheextendedMEM.........................
2.2.7MEManalysiswithzeromodecontributionsuppressed......
2.2.8RemarksonMEM..........................
2.3Freetemporalcorrelationandspectralfunction..............

i

1

5788921418181910242

929263738393041424344444747484

2.3.1Freespectralfunctioninthecontinuum..............49
2.3.2FreespectralfunctionforWilsonfermionsonthelattice.....53
2.3.3Comparisonoffreespectralfunctionandcorrelator........55
2.4LinearresponsetheoryandHeavyquarkdiusion.............59
2.5Charmoniumatnitetemperatureonthelattice:abriefreview.....67
3Analysisofcharmoniumpropertiesatvanishingmomentum71
3.1Toymodeltestofspectralfunction.....................71
3.2MockdatatestofMEM...........................75
3.3Eectivemass.................................81
3.4SpectralfunctionsbelowTc.........................84
3.5Reconstructedcorrelator...........................88
3.5.1Thepseudoscalarcorrelators....................88
3.5.2ThePwavecorrelators.......................89
3.5.3Thevectorcorrelators........................90
3.6Estimateofthezeromodecontribution..................94
3.6.1Thermalmomentsofcorrelators..................96
3.7SpectralfunctionsaboveTc.........................100
3.7.1Defaultmodeldependences.....................100
3.7.2Systematicuncertaintiesandstatisticalerrors...........105
4Analysisofcharmoniumpropertiesatnon-zeromomentum115
4.1Screeningmassanddispersionrelation...................115
4.2Longitudinalandtransversecorrelationfunction.............117
4.3Thereconstructedcorrelators........................119
Conclusionandoutlook123
ATheEuclideanDiracmatricesandtheSU(N)generators127
A.1Diracmatrices................................127
A.2SU(N)generators...............................128
BMemoryoptimizationforthecloverterm129
References131
Acknowledgements145
ii

Introduction

In1974,anunusualresonancewasdiscoveredalmostsimultaneouslyattheBrookhaven
NationalLaboratory(BNL)[1]andattheStanfordLinearAcceleratorCenter(SLAC)
[2].Thisnewresonance,whichiscalled“J/ ”,wastherstobservedboundstateof
acharmquarkanditsantiquark(cc¯).Byanalogytopositronium,theboundstateof
cc¯ingeneralisthennamedcharmonium.Thecharmoniumsystem,whichismainly
governedbythestrongforce,shouldbethesimplestobjectforstudyingthestrong
interaction.Itwashopedtoplaythesameroleinunderstandinghadronicsystemas
itsanalog,thehydrogenatom,whichisgovernedbytheelectromagneticforce,had
playedinunderstandingatomicphysics.Indeed,thishasbeenthecase.Theanalyses
ofpropertiesofcharmoniumandofitshighersiblingbottomoniumhaveinducedthe
developmentofmanymethodsinQCD[3,4].
Physicsthrivesonanalogies.Sincecharmoniumhasbeenausefulcandidatetostudy
hadronicsystemsatzerotemperature,T.MatsuiandH.Satzwerewonderingwhether
itcouldalsobeusefultostudysomesortofnew“medium”atnitetemperature.Due
tothesuccessofthepotentialmodelatzerotemperature,in1986theyproposedthe
suppressionofJ/ inthemediumasasignaloftheformationoftheQuarkGluon
Plasma(QGP)assumingthequark-antiquarkpotentialbeingcolorscreened[5].This
ideahasbeentriggeringintenselystudiesonthepropertiesofheavyquarkoniumstates
(charmoniumandbottonium)inahotanddenseQCDmedium,bothexperimentally
andtheoretically[3,6,7].
TheexperimentscarriedoutattheSPSatCERNandtheRHICatBNLhaveindeed
observedJ/ suppression[3,6,7].Theinterpretationofexperimentaldata,however,
isnotasstraightforwardastheoriginalideaproposedsincetheobservedmodication
whencomparingJ/ productioninnuclei-nuclei(AA)collisionstothatinproton-
proton(pp)collisionscouldbecausedbytwodistinctclassesofeects.Ontheone
handtherearecoldnuclearmattereects,whichoriginatefromthepresenceofcold
nuclearmatterintargetandprojectile.ThesecanbestudiedfrompAcollisionswith
respecttoppcollisions[8].Ontheotherhandtherearehotmediumeects,whichare
oftheprimaryinterestandconcernthepropertiesoftheQGPwewanttostudy.In

1

ordertodisentanglethesetwoeects,itiscrucialtohaveagoodunderstandingofthe
dynamicsofthequarkoniumintheQGPandthefateofitspossibleboundstates.
Fromthetheoreticalpointofview,thecharmoniumspectralfunctionatnitetem-
perature[9,10],whichcontainsalltheinformationofthehadronpropertiesinthe
thermalmedium,suchasthepresence,thelocationandthewidthofboundstates
(andthusaboutdissociationtemperatures)aswellastransportproperties,isthekey
quantitytobeinvestigated.Sincethisisadiculttask,severaltheoreticalapproaches
todeterminethequarkoniumpropertiesatnitetemperaturehavebeenfollowed.
Themosttraditionaloneisthenon-relativisticpotentialmodel,whichassumesthe
interactionbetweenaheavyquarkpairinsidethequarkoniumcanbedescribedbya
potential[11].Duetoitssuccessatzerotemperature,thepotentialmodelisappliedto
thisphenomenonatnitetemperature[12–23].Itisbasedeitheronmodelsoron

Soyez le premier à déposer un commentaire !

17/1000 caractères maximum.