We investigate the behaviour of the gluon and ghost propagators, especially their infrared properties, at non-vanishing temperatures. To this end we solve their Dyson-Schwinger equations on a torus and find an infrared enhanced ghost propagator and an infr

QCDPropagatorsatnon-vanishingtemperatures

1B.Gr¨uter1,R.Alkofer1,A.Maas2,J.Wambach2Inst.f.TheoretischePhysik,Universit¨atT¨ubingen,D-72076T¨ubingen,Germany

2Inst.f¨urKernphysik,TUDarmstadt,D-64289Darmstadt,Germany TalkgivenbyB.G.attheEricesummerschoolonNuclearPhysics,Sept.16–24,2003,Erice,ItalyarXiv:hep-ph/0401164v1 22 Jan 2004AbstractWeinvestigatethebehaviourofthegluonandghostpropagators,especiallytheirinfraredprop-erties,atnon-vanishingtemperatures.TothisendwesolvetheirDyson-Schwingerequationsonatorusand ndaninfraredenhancedghostpropagatorandaninfraredvanishinggluonpropagator.Latticesimulationsprovideevidencethatzero- avourQCDundergoesa”decon ning”phasetran-sitionatsomecriticaltemperature.Thepropertiesofthegluonandtheghostpropagatorat nitetemperaturecanprovideinsightsintothemechanismsofthisphasetransitionandtheyarerelatedtotheissueofcon nementanddecon nement.WestudytheDyson-Schwingerequations(DSEs)ofthesepropagatorsinLandaugaugeforwhichawellunderstoodtruncationschemeatzerotemperatureisavailableTheinfraredbehaviourofthegluonandghostpropagatorscanbedeterminedanalyticallyandweobtainpower-laws.ThisisconsistentwiththeKugo-Ojimacon nementpictureforLandaugauge,whichrequirestheghostpropagatortodivergestrongerthanafreepropagatoratzeromomentum.Ontheotherhandthegluonpropagatorisinfraredsuppressed(Dµν(k→0)=0).ThusitviolatespositivityandthegluonsareremovedfromthephysicalspectrumSincethisinfraredsingularstructureisexpectedtopersistfornon-vanishingtemperaturesacontinuumbasedmethodforstudyingthedecon nementphasetransitionisdesirable.Atnon-vanishingtemperaturestheanalyticaldeterminationoftheinfraredbehaviourhasnotbeenachievedyet,thusweneedaninfraredregulator.Apossibleoneistocompactifyspace-timetoafourdimensionaltorusbyimposingperiodicboundaryconditionsonthe elds.Thishasbeendonealreadyatzerotemperature[3].

Thetruncationschemeatzerotemperaturedescribedinisextendedto nitetemperaturesintheMatsubara-Formalism(imaginarytimeformalism)forthermodynamicalequilibrium.TheDSEsinpureYang-Mills-Theoryforthegluonandtheghostpropagatorareconsidered.Sincetheheatbathde nesapreferedreferenceframe,thefullgluon-propagatorinLandaugaugenowdependsontwoindependenttransversetensorstructures,aheat-bathtransverseandlongitudinalpart,leadingtothefollowingdecompositionabDµν(k):=δab

PLµν(k)=Pµν(k) PTµν(k),Pµν=δµν k2kµkν,(1)PT00=PTi0=PT0i=0,

k2G(k0,| k|).Note,thatthedressingfunctionsofthegluon(ZTandZL)andtheghost