Mixing and Decay Constants of Pseudoscalar Mesons(7)

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

Fromthemeasuredvalue

[17]RJ/ψ=5

.

±

.6themixingangleφbecomes39.0 ±1.6 .Obviously,Eq.(3.10)isnotequivalenttothenaivesingletdominancepredictionforwhichthefactorcotθ8wouldhavetobereplacedbycotθ.AswelearnedinSect.II,θ8markedlydi ersfromtheoctet-singletmixingangle.

FIG.1.a)ElectromagneticcontributiontoJ/ψ→ρη,η′.b)PoleansatzfortheDs→P νsemi-leptonicdecay.

Aweightedaverageoftheabovesevenhigh-lightedvaluesyields

2,Cs=1/9)

Γ[η→γγ]=9α2

fq

16π3

andsolvingforfqandfs,wearriveat

fq=3Cqα

sinφΓ[η→3γγ]/Mη3Mη′ Cssinφ 2 Cqsinφfs,(3.13)+sinφ Γ[η′→3γγ]/Mη′4π3/2 1.(3.14)

WeevaluateEq.(3.14)withthemixingangleaccordingtoEq.(3.11)andthefollowingexperimentalvaluesforthedecaywidthsΓ[η→γγ]=(0.51±0.026)keVandΓ[η′→γγ]=(4.26±0.19)keV[17].Thevalueof0.324±0.046keV,obtainedfromthePrimako productionmeasurementofη→γγ,isnotincluded.Itturnsoutthatfsisnotwelldeterminedthisway,itacquiresaratherlargeerrorfs=(1.42±0.16)fπ.Wethereforeevaluatefsalsofromfqandthephenomenologicalvalueoftheratioyandformtheweightedaverageofbothvaluesto ndamoreprecisevalueforfs.Bythismeansweobtain

fq=(1.07±0.02)fπ,

fs=(1.34±0.06)fπ.(3.15)