Mixing and Decay Constants of Pseudoscalar Mesons(8)

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

Thesevaluesforthebasicdecayconstantsdi erfromthetheoreticalvalues(2.19)onlymildly.Since,withintheerrors,boththevaluesoffsdeterminedhereagreewitheachother,theexperimentalvaluesof

the

two-photondecaywidthsarewellreproducedbytheparameterset(3.11),(3.15).

Asanimmediatetestoftheparameters(3.11)and(3.15)wecomputethePγtransitionformfactorsalongthelinesdescribedindetailin[7].We ndexcellentagreementbetweentheoryandexperiment[14].Thenewresultsarepracticallyindistinguishablefromthe tperformedin[7](χ2/d.o.f.is28/34ascomparedto26/33in[7]).TheformfactoranalysisisbasedonapartonFockstatedecompositionofthephysicalmesons.ThewavefunctionsofthevalenceFockstates,providingtheleadingcontributiontotheformfactoraboveQ2=1GeV2,areassumedtohavetheasymptoticform.Thevaluesofthesewavefunctionsattheoriginofcon gurationspacearerelatedtothedecayconstants[7].

AcomparisonbetweenthetheoreticalandphenomenologicalvaluesofthemixingparametersismadeinTableI.Ascanbenoticedthereisnosubstantialdeviationbetweenbothsetofvalues,i.e.higherorder1/Nccorrections,absorbedinthephenomenologicalvalues,seemtobereasonablysmall.InTableIIwelistthevaluesoftheparametersde nedinEq.(1.3),i.e.intheparametrizationintroducedbyLeutwyler[6],asobtainedfromvarioussources.Thetheoreticalvaluesoff8,f1,θ8arecomputedfromthedecayconstantsgiveninEq.(2.19)andthetheoreticalmixinganglelistedinTableIwhilethephenomenologicalvaluesfollowfromEqs.(3.11)and(3.15).Ascanbeseentheresultsobtainedfromtheanalysesperformedinthisworkandin[6,7]agreeratherwellwitheachother.Theconventionalanalyses,e.g.[3,15],arenotincludedinthetablebecausethedi erencebetweenθ8andθ1isnotconsidered.

IV.GENERALIZINGTOη–η′–ηcMIXING

Fromtheprevioussectionswelearnedthatourcentralassumption(1.4)combinedwiththedivergencesoftheaxialvectorcurrentsleadstoavarietyofinterestingpredictionswhichcomparewellwithexperiment.Thereasonforthissuccessislikelytheratherlargedi erencebetweenthecurrentmassesofthestrangeandtheup/downquarks.Sincethecharmquarkmassisevenheavierthanthestrangeone,itistemptingtogeneralizetotheqs–c

q–scbasisreads(i,j=q,s,c),

222M2qsc=U(φ,θy,θc)diag(Mη,Mη′,Mηc)U(φ,θy,θc).(4.3)

Ontheotherhand,generalizingEq.(2.11)andusingtheabbreviations(2.12),(2.13)and(2.14)introducedinSect.II,wemaywritethemassmatrixasfollows

√ 2 222ay2amqq00√2 .+M2=0m0(4.4)yqscss200mcc2a2yza2z2a2

OnexploitingagainthedivergencesoftheaxialvectorcurrentsandthepropertiesofthemassmatrixanumberofconsequencesfollowsfromwhichallnewparametersappearinginEq.(4.4)canbe xed

z=fq/fc,θy=θ8,

222=m2Mηcc+zac(4.5)