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Non-perturbative renormalization for a renormalization group improved gauge action

Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schr\"odinger functional

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002 tcO 61 1v8210110/tal-ep:hviXraUTHEP-452UTCCP-P-117

Non-perturbativerenormalizationforarenormalizationgroupimprovedgaugeaction

CP-PACSCollaboration:

S.Aoki,aR.Burkhalter,a,bM.Fukugita,cS.Hashimoto,dK.Ide,aN.Ishizuka,a,bY.Iwasaki,a,bK.Kanaya,

a

T.Kaneko,dY.Kuramashi,dV.Lesk,bM.Okawa,dY.Taniguchi,a

A.Ukawaa,bandT.Yoshi´ea,b

aInstituteofPhysics,UniversityofTsukuba,Tsukuba,Ibaraki305-8571,Japan

bCenterforComputationalPhysics,UniversityofTsukuba,Tsukuba,Ibaraki305-8577,Japan

c

InstituteforCosmicRayResearch,UniversityofTokyo,Kashiwa,Chiba277-8582,Japand

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

Renormalizationconstantsofvector(ZV)andaxial-vector(ZA)currentsaredeterminednon-perturbativelyinquenchedQCDforarenormalizationgroupimprovedgaugeactionandatadpoleimprovedcloverquarkactionusingtheSchr¨odingerfunctionalmethod.Non-perturbativevaluesofZVandZAturnouttobesmallerthantheone-loopperturbativevaluesbyO(10%)ata 1≈1GeV.Asizablescalingviolationofmesondecayconstantsfπandfρobservedwiththeone-looprenormalizationfactorsremainsevenwithnon-perturbativerenormalization.

1.Introduction

Reliablelatticecalculationsofhadronicma-trixelementsandquarkmassesrequirebothhighprecisionnumericalsimulationsandnon-perturbativedeterminationsofrenormalizationconstants(Z-factors).TheCP-PACScollabo-rationrecentlycarriedoutasophisticatedspec-trumcalculationinNf=2fullQCD[1]usingarenormalizationgroup(RG)improvedgaugeactionandatadpoleimprovedcloverquarkac-tion.However,non-perturbativeZ-factorswerenotavailableforthisactioncombination.Henceanalyseshadtorelyonone-loopperturbativeval-ues.

Asa rststeptowardasystematicstudyofnon-perturbativerenormalizationforthisaction,weapplytheSchr¨odingerfunctionalmethod[2]tocalculationsofZfactorsforvector(ZV)andaxial-vector(ZA)currentsinquenchedQCDwiththesameimprovedaction.Weexamineinpartic-ularwhetheralargescalingviolationofmesondecayconstantsobservedforthisaction[1]isim-provedwithnon-perturbativeZ-factors.Were-portpreliminaryresultsintheseproceedings.

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