Analysis of full-QCD and quenched-QCD lattice propagators

Recent lattice-QCD results for the dressed-gluon propagator are used within the quark Dyson-Schwinger equation to determine the gluon-quark vertex dressing necessary to reproduce the lattice-QCD results for the dressed-quark propagator. Both quenched and f

Analysisoffull-QCDandquenched-QCDlatticepropagators

M.S.BhagwatandP.C.Tandy

CenterforNuclearResearch,DepartmentofPhysics,KentStateUniversity,Kent,Ohio44242

U.S.A.

Abstract.Recentlattice-QCDresultsforthedressed-gluonpropagatorareusedwithinthequarkDyson-Schwingerequationtodeterminethegluon-quarkvertexdressingnecessarytoreproducethelattice-QCDresultsforthedressed-quarkpropagator.BothquenchedandfullQCDlatticesimulations,forarangeoflowquarkcurrentmasses,areanalyzed.ThechiralextrapolationismadethroughthiscontinuumDSEform.Resultingchiralandphysicalpionobservablesareinvestigated.Keywords:Dyson-Schwingerequation,chiralsymmetry,dressedquark-gluonvertex,lattice-QCD.PACS:12.38.Lg,12.38.Gc,12.38.Aw,24.85.+p

arXiv:nucl-th/0601020v1 7 Jan 2006INTRODUCTIONLattice-QCDsimulationsaddresshadronicobservablesviamatrixelementsofcurrentsandsources;necessaryapproximationsandtruncationsintroducesystematicerrorsfrom:a nitevolumeofdiscretizedspace-time,unphysicallylargecurrentquarkmasses,andthequenchedapproximation.Whilesteadyprogressisbeingmadeinthereductionofsucherrors,itisusefultogaininsightintodominant eldtheorymechanismsbycomparingtohadronicresultsfromcovariantmodelingofcontinuumQCD.TheDyson-Schwingerequations(DSEs),theequationsofmotionofthetheory,providesuchanopportunity.Heresystematicerrorscanarisefromtruncationsthatreplacehigh-ordercorrelationsbyinfraredphenomenologyoflow-ordern-pointfunctions.Symmetriescanprovidesigni cantqualitycontrol.Thedressedquarkandgluonpropagatorsandlow-orderverticesofthetheoryareimportantelementsofthekernelsneededforthebound

stateequations:Bethe-Salpeterequation(BSE)formesonsandFaddeevequationforbaryons.Priortothelastfewyears,onehadonlytheknownultra-violetbehaviorofthen-pointfunctionsasaguide.

Recently,full-QCDlatticeresultsforgluon[1]andquark[2]propagatorshavebeenmadeavailable;thesearetwoofthethreenonperturbativequantitieslinkedbythequarkpropagatorDSE.Phenomenologicalinformationonthethirdquantity,thedresseda(k,p),canthereforebeinferred.Wehavepreviouslycarriedquark-gluonvertexΓνoutsuchananalysisofquenched-QCDlatticepropagators[3]andthequark-gluonvertex[4];theproceduresandtechnicaldetailsemployedherearedescribedinRef.[3].Here,andinthelatticesimulations,LandaugaugeandtheEuclideanmetricisused.Brie y,theapproachisthefollowing.FromtherenormalizedquarkDSE,wehave

Recent lattice-QCD results for the dressed-gluon propagator are used within the quark Dyson-Schwinger equation to determine the gluon-quark vertex dressing necessary to reproduce the lattice-QCD results for the dressed-quark propagator. Both quenched and f

FIGURE1.LeftPanel:Full-QCDlatticeresults[2]reproducedfromthefull-QCDlatticegluonprop-agator[1]viathecontinuumDSE.Noteverticallogscale.Valuesoflatticemandmaareshown;RightPanel:FouriertransformoftheDiracscalarpartofthechiralS(p).Cuspsindicatecon nement.S 1(p)=Z2iγ·p+Z4m(µ)+Σ′(p,Λ)andtheregulatedself-energyis

Σ(p,Λ)=Z1′ Λ

qgDµν(p q)2λa

γνΓ1(k2).HereDlatµν(k)isa ttothelattice

gluonpropagatorandthequantityΓ1(k2)isaphenomenologicalvertexamplitudede-terminedsothattheDSEsolutionforS(p) tsthelatticedata.Ingeneralthetransversevertexhaseightamplitudesandadependenceupontwomomenta;howeverthedatabeing ttedheredonotwarrantmore.Wenotethatonemayidentifythekernelas0th4παeff(k2)D0µν(k)whereDµνisthe0ordergluonpropagator.Weensurethattheleadinglogbehaviorofallquantitiesconformtothe1-looprenormalizationgroupbehaviorofQCD.2

RESULTS

TABLE1.Chiralcondensateandpiondecayconstant(chiral0,physicalf)fromthelattice-guidedDSEkernel.fππ

qq¯

fπµ=1GeV-(0.24GeV)30.092GeV-(0.23GeV)30.075GeV-(0.19GeV)30.066GeV

Recent lattice-QCD results for the dressed-gluon propagator are used within the quark Dyson-Schwinger equation to determine the gluon-quark vertex dressing necessary to reproduce the lattice-QCD results for the dressed-quark propagator. Both quenched and f

Our ttothefull-QCDDlatµν(k)usesthe“modelA”formpreviouslyemployedforquencheddata[5]butnowwithNf=3andthenewparametervalues:A=3.25,Λg=0.54,α=1.15andZg=1.22.Our tgaveprioritytoM(p)forthefouravailablevaluesoflatticemashown,alongwiththeresults,intheleftpanelofFig.1.TheparameterizedformusedforΓ1(k2)isthesameaswehavepreviouslyused[3]forthequenchedlatticecase.The(dimensionless)parametersofΓ1(k2)foundhereforthefull-QCDcaseare:a1=4.5,a2=2.1,a3=18.1,b=0.31.TheresultofthechiralextrapolationprovidedbytheDSEkernelisalsoshown.Thelatticecurrentmassesareequallyspacedand,intheregionp 3GeV,thelatticeresultsareonlyapproximatelyso;thema=0.01casedeviatesmostfromthepattern.TheDSE thasbeenmadewiththeconstraintthattheM(p,m)approachthecorrectratio.

Ifapropagatorofa eldtheoryinEuclideanmetricviolatestheOsterwalder-Schraderaxiomofrelectionpositivity[6],thenthisisasuf cientconditionforcon nementofthecorrespondingexcitation[7].IntherightpanelofFig.1wedisplaythemagnitudeof

p=0),theDiracscalaramplitudeofthechirallimittheFouriertransformofσs(p4,

quarkpropagator.Forafreeparticlewithmassm, S(T)∝exp( mT).Thecuspsindicatechangesofsignandthuscon nementinbothquenchedandfull-QCD.Thedottedlinecorrespondstoapropagatorthathasasinglepairofcomplexconjugatepolesatp2= 0.3092±i0.1922GeV2.Thedashedcurvecorrespondstotheladder-rainbowmodelthatdescribesalargevarietyoflightquarkobservables[8].

TheformofthededucedDSEkernelallowsachiralsymmetry-preservingBethe-Salpeterkerneltobeobtainedasintheladder-rainbowcase[9].ThisproducesthechiralphysicsobservablesshowninTable1.Full-QCDevidentlyproducesanacceptablecondensate,whilethequenchedapproximationunderestimatesbyafactoroftwo[3].Thevaluesoffπ,bothchiralandphysical,aremarginallyimprovedbyfull-QCDbuttheyremainabout15%toolow.

ACKNOWLEDGMENTS

ConversationswithCraigRobertsandPieterMarishavebeenvaluable.ThisworkhasbeenpartiallysupportedbyNSFgrantno.PHY-0301190.

REFERENCES

1.P.O.Bowman,U.M.Heller,D.B.Leinweber,M.B.Parappilly,andA.G.Williams,Phys.Rev.D70,034509(2004),hep-lat/0402032.

2.P.O.Bowman,etal.,Phys.Rev.D71,054507(2005),hep-lat/0501019.

3.M.S.Bhagwat,M.A.Pichowsky,C.D.Roberts,andP.C.Tandy,Phys.Rev.C68,015203(2003),nucl-th/0304003.

4.M.S.Bhagwat,andP.C.Tandy,Phys.Rev.D70,094039(2004),hep-ph/0407163.

5.D.B.Leinweber,J.I.Skullerud,A.G.Williams,andC.Parrinello,Phys.Rev.D60,094507(1999),hep-lat/9811027.

6.K.Osterwalder,andR.Schrader,Commun.Math.Phys.42,281(1975).

7.G.Krein,C.D.Roberts,andA.G.Williams,Int.J.Mod.Phys.A7,5607–5624(1992).

8.P.Maris,andP.C.Tandy,Phys.Rev.C60,055214(1999),nucl-th/9905056.

9.A.Bender,C.D.Roberts,andL.VonSmekal,Phys.Lett.B380,7–12(1996),nucl-th/9602012.

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