Mixing and Decay Constants of Pseudoscalar Mesons

We propose a new eta-eta' mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents - which embody the

MixingandDecayConstantsofPseudoscalarMesons

Th.Feldmann ,P.Kroll

FachbereichPhysik,Universit¨atWuppertal,D-42097Wuppertal,Germany

B.Stech

Institutf¨urTheoretischePhysik,Universit¨atHeidelberg,D-69120Heidelberg,Germany

(Copyright1998byTheAmericanPhysicalSociety.)

Weproposeanewη–η′mixingschemewherewestartfromthequark avorbasisandassume

thatthedecayconstantsinthatbasisfollowthepatternofparticlestatemixing.Onexploiting

thedivergencesoftheaxialvectorcurrents–whichembodytheaxialvectoranomaly–allbasic

parametersare xedto rstorderof avorsymmetrybreaking.Thatapproachnaturallyleadsto

amassmatrix,quadraticinthemasses,withspeci edelements.Wealsotestourmixingscheme

againstexperimentanddeterminecorrectionstothe rstordervaluesofthebasicparametersfrom

phenomenology.Finally,wegeneralizethemixingschemetoincludetheηc.Againthedivergences

oftheaxialvectorcurrents xthemassmatrixand,hence,mixinganglesandthecharmcontentof

theηandη′.

PACS:14.40.Aq,11.40.Ha,11.30.Hv

arXiv:hep-ph/9802409v2 20 Jul 1998I.INTRODUCTIONη–η′mixingisasubjectofconsiderableinterestthathasbeenexaminedinmanyinvestigations,seee.g.[1–4]andreferencestherein.Asitiswell-known[5],theU(1)Aanomalyplaysadecisiverole.Fortheoctet-singletmixingangleθofthesepseudoscalarmesonsvaluesintherangeof 10 to 23 havebeenobtaineddependingondetailsoftheanalysis,seee.g.[3].Thephenomenologicalanalysisofteninvolvesdecayprocesseswhere,besidesstatemixing,alsoweakdecayconstantsappear.Thedecayconstantsarede nedbyii 0|Jµ5|P(p) = fPpµ(i=8,1;P=η,η′),(1.1)81whereJµ5denotestheSU(3)FoctetandJµ5theSU(3)Fsingletaxial-vectorcurrent,respectively.Frequently,itisassumedthatthedecayconstantsfollowthepatternofstatemixing:8=f8cosθ,fη8fη′=f8sinθ,1= f1sinθ,fη1fηf1cosθ.′=(1.2)However,recenttheoretical[6]aswellasphenomenological[7]investigationshaveshownthatEq.(1.2)cannotbecorrect.Adoptingthenewandgeneralparametrization[6]

8=f8cosθ8,fη8fη′=f8sinθ8,1= f1sinθ1,fη1fηf1cosθ1.′=(1.3)

θ1andθ8turnedouttodi erconsiderably.Thephenomenologicalanalysis[7],whichinvolvedthecombinedanalysisofthetwo-photondecaywidthsoftheηandη′,theηγandη′γtransitionformfactorsandtheadditionalconstraintfromtheradiativeJ/ψdecays,allowedtodeterminethefourquantitiesoccuringinEq.(1.3).Mostimportantly,thevaluesobtainedsatisfytheconstraints[6]fromchiralperturbationtheory(ChPT).

Theappearanceofthefourparametersf8,f1,θ8,θ1raisesanewtheproblemoftheirmutualrelationsandtheirconnectionwiththemixingangleoftheparticlestates.Thisangleisnecessarilyasingleonesincemixingwithhigherstates–theηcforinstance–canbeneglectedatthisstage.TherelationofthisanglewiththefourparametersinEq.(1.3)doesnotneedtobesimple:inapartonlanguage[8]thedecayconstantsarecontrolledbyspeci cFock