Scalar susceptibility in QCD and the multiflavor Schwinger model

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1、SUNY-NTG-95/50ScalarsusceptibilityinQCDandthemulti avorSchwingermodelA.SmilgaITEP,B.Cheremushkinskaya25,Moscow117259,RussiaandJ.J.M.VerbaarschotDepartmentofPhysicsSUNY,StonyBrook,NewYork11794AbstractWeevaluatetheleadinginfraredbehaviorofthescalarsusceptibilityinQCDandinthem

2、ulti avorSchwingermodelforsmallnon-zeroquarkmassmand/orsmallnonzerotemperatureaswellasthescalarsusceptibilityforthenitevolumeQCDpartitionfunc-tion.InQCD,itisdeterminedbyone-loopchiralperturbationtheory,withtheresultthatptheleadinginfraredsingularitybehavesaslogmatzerotemp

3、eratureandasT=matnitetemperature.IntheSchwingermodelwithseveral avorsweuseexactresultsforthescalarcorrelationfunction.WendthattheSchwingermodelhasaphasetransitionatT=0withcriticalexponentsthatsatisfythestandardscalingrelations.Thesingularbehaviorofthismodeldependsonthenu

4、mberof avorswithascalarsusceptibilitythat?2=(N+1)fbehavesasm.AtnitevolumeVweshowthatthescalarsusceptibilityispro-2portionalto1=mV.RecentlatticecalculationsofthisquantitybyKarschandLaermannarediscussed.November19951Introduction.ThescalarsusceptibilityinQCDisdenedasNNNZfff

5、XXX1422=dxhqq(x)qq(0)i?Vhqqi=@logZ;(1.1)iiiiiimm=0Vi=1i=1i=1whereVisthefourdimensionalEuclideanvolumeandtheaveragingisperformedeitheroverthevacuumstateoroverthethermalensemble.(IntheEuclideanapproachthelattercorrespondstoanasymmetricboxwithimaginarytimeextensionof=1=TL

6、,3i.e.V=L).Thedenition(1.1)isforadiagonalmassmatrixwithequalquarkmasses.Itisespeciallyinterestingtostudythisquantityintheneighborhoodofthethermalphasetransitionpoint.ItisexpectedthatforQCDwithtwomassless avorsasecondorderphasetransitionoccursleadingtorestorationofchiralsym

7、metry[1](see[2,3]forrecentreviews)withadivergingsusceptibility.ThiscanbeunderstoodsimplyintermsofLandaumeaneldtheory.ForasystemwithorderparametercoupledtoexternaleldhwithasecondorderphasetransitionatT=T,the uctuationsofthecorderparameteraredescribedbytheeectivepotential

8、e24V()=A(T?T)+B+Ch:(1.2)cInQCDisthechiralcondensateandhisthequarkmass.AtT=T,