Bulk first-order phase transition in three-flavor lattice QC

Three-flavor QCD simulation with the $O(a)$-improved Wilson fermion action is made employing an exact fermion algorithm developed for odd number of quark flavors. For the plaquette gauge action, an unexpected first-order phase transition is found in the st

KEK-CP-151,UTCCS-P-3,UTHEP-489,HUPD-0401

Bulk rst-orderphasetransitioninthree- avorlatticeQCDwithO(a)-improved

Wilsonfermionactionatzerotemperature

S.Aoki,1M.Fukugita,2S.Hashimoto,3K-I.Ishikawa,4N.Ishizuka,1,5Y.Iwasaki,1K.Kanaya,1,5T.Kaneko,3Y.Kuramashi,1,5M.Okawa,4N.Tsutsui,3A.Ukawa,1,5N.Yamada,6andT.Yoshi´e1,5

(JLQCDCollaboration)

1

GraduateSchoolofPureandAppliedSciences,UniversityofTsukuba,Tsukuba,Ibaraki305-8571,Japan

2

InstituteforCosmicRayResearch,UniversityofTokyo,Kashiwa,Chiba277-8582,Japan3

HighEnergyAcceleratorResearchOrganization(KEK),Tsukuba,Ibaraki305-0801,Japan4

DepartmentofPhysics,HiroshimaUniversity,Higashi-Hiroshima,Hiroshima739-8526,Japan5

CenterforComputationalScience,UniversityofTsukuba,Tsukuba,Ibaraki305-8577,Japan6

RIKENBNLResearchCenter,BrookhavenNationalLaboratory,Upton,NY11973,USA

(Dated:February1,2008)Three- avorQCDsimulationwiththeO(a)-improvedWilsonfermionactionismadeemployinganexactfermionalgorithmdevelopedforoddnumberofquark avors.Fortheplaquettegaugeaction,anunexpected rst-orderphasetransitionisfoundinthestrongcouplingregime(β<～5.0)atrelativelyheavyquarkmasses(mPS/mV～0.74–0.87).Strongmetastabilitypersistsonalargelatticeofsize123×32,whichindicatesthatthetransitionhasabulknature.Thephasegapbecomessmallertowardweakercouplingsandvanishesatβ 5.0,whichcorrespondstoalatticespacinga 0.1fm.Thephasetransitionisnotfoundiftheimprovedgaugeactionsareemployed.OurresultsimplythatrealisticsimulationsofQCDwiththree avorsofdynamicalWilson-typefermionsatlatticespacingsintherangea=0.1–0.2fmrequireuseofimprovedgaugeactions.Possibleoriginsofthephasetransitionisdiscussed.

PACSnumbers:11.15.Ha,12.38.Gc,05.70.Fh

arXiv:hep-lat/0409016v1 4 Sep 2004

I.INTRODUCTION

RealisticsimulationsofthestronginteractionthroughlatticeQCDrequiredynamicaltreatmentofup,downandstrangequarksincorporatingtheirpaircreationandannihilatione ectsinthevacuum.Whilesimulationswiththedynamicalupanddownquarkshavenowbe-comeroutine(forrecentstudies,seeRefs.2,addingadynamicalstrangequarkisstillinthedevelop-mentstage.Thisisprimarilybecausenoexactalgorithmtotreatoddnumberof avorswasknownuntilrecently.InfactwiththeconventionalHybridMonteCarlo(HMC)algorithmthenumberof avorsislimitedtoeven.TheRalgorithm[6]canbeusedforanynumberof a-vors,asappliedinrecentthree- avorsimulationswiththestaggeredquarkactionHowever,theresultsaresubjecttosystematicerrorsduetoa nitestepsizeinthemoleculardynamicsevolution,andthishastobecontrolledbytakingthelimitofzerostepsizewhichisquitecomputertimeconsuming.

Recently,however,severalexactalgorithmsforanar-bitrarynumberof avorshavebeenproposedbothfortheWilson-type10]andthestaggered-typefermionactions.TheyhavebeenshowntoworkwithrealisticlatticevolumeswithoutmuchincreaseofcomputationalcostcomparedtoHMC[10,Thus,apracticalbar-riertoperformrealisticthree- avorQCDsimulationshasbeeneliminated.

Thenextsteptowardrealisticsimulationsistoexploretheparameterspaceofthethree- avorlatticeQCDtoensurethatthesystemisfreefromlatticeartifactsoverarangeoflatticespacingaandquarkmassmqadequateforTypesetbyREVTEX

phenomenology.Inpracticethismeans ndingaregioncorrespondingtoa 0.1–0.2fmandmq=(1/3～1)×ms,withmsthephysicalstrangequarkmass.

FortheWilson-typefermionaction,thereisarelatedimportanttheoreticalissuetosettle.Forevennumberof avors,evidencehasbeenaccumulatedovertheyearsthatvanishingofpionmassatacriticalhoppingparame-terκc(β)(β=6/g2withgthegaugecoupling)isduetospontaneousbreakingof avor-parityrotationalsymme-try[12,Whetherthisunderstandingholdsforoddnumberof avorsstillneedscon rmation.Itisthere-foremandatorytocovertheentireparameterspaceofthelatticeactionforthree- avorQCD.

Inthisworkwenumericallyexploretheparameterspace(β,κ)ofthree- avorlatticeQCDwiththeO(a)-improvedWilsonfermionaction[14].Thethreequark avorsareassumedtobedegenerateinmass.Forthegaugeaction,wetestboththeplaquetteandrenormal-izationgroup(RG)improvedgaugeactions.TheO(a)-improvementcoe cientcSWis xedtotheone-loopper-turbativevalueasfullynon-perturbativevaluesfortherelevantgaugeactionswerenotavailableuntilafterthepresentworkwaswellinprogress[15,16,Forthestandardplaquettegaugeaction,weunexpect-edly nd[18]aclearevidenceoftheexistenceofanor-deredphaseforlargeκseparatedbya rst-orderphasetransitionfromthedisorderedphaseatsmallerκ.Thetransitionpersistsforlargevolumes,andhenceitisabulkphasetransition.Contrarytothedisorderedphase,theorderedphasedoesnotexhibitsthestandardfeaturesofthecon ningphase.Forexample,thepseudo-scalar-to-vectormesonmassratioissimilarinthedisordered

Three-flavor QCD simulation with the $O(a)$-improved Wilson fermion action is made employing an exact fermion algorithm developed for odd number of quark flavors. For the plaquette gauge action, an unexpected first-order phase transition is found in the st

andorderedphasesataround0.8,butthelatticespac-ingisunnaturallylargeintheorderedphase.The rst-orderphasetransitionisobservedinthestrongcouplingregime.Thegapofphysicalquantitiesacrossthetransi-tiondiminishestowardweakercouplings,andappearstovanishatβ 5.0,whichcorrespondstoalatticespacinga 0.1fm.

Theseresultsindicatethatthereisaparameterregionwhichisnotsmoothlyconnectedtocontinuumthree- avorQCD.Inotherwords,thecontinuumthree- avorQCDcanbeapproachedonlyifoneuseslatticesmuch nerthana 0.1fm,ifoneemploystheplaquettegaugeaction.

We ndthatthemetastabilitysignalsdisappearifoneemploysimprovedgaugeactionssuchastherenormaliza-tiongroup(RG)improvedaction[19]orO(

a

2

)-improvedL¨uscher-Weiszaction[20].Withtheseactions,thecon-tinuumextrapolationshouldbepossiblefromaconven-tional …… 此处隐藏：28709字，全部文档内容请下载后查看。喜欢就下载吧 ……