Mixing and Decay Constants of Pseudoscalar Mesons(6)

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

where

kf=Mi[1 Mf2/Mi2]/2,(3.6)

beingthe3-momentaofthe nalstatemesonf.

M

i

denotes

the

mass

of

the

decaying

meson.

αisthe nestructureconstant.

Using

state

mixing(2.1),one nds

gρη′γ

Γ[a2→ηπ]=tan2φ kη′π

σ(π p→ηn)2=tan2φ(s MP)(3.9)

Thetwoexperimentsleadtoφ=36.5 ±1.4 [21]and39.3 ±1.2 [22].Sincethetworesultsarenotfully¯.consistentwitheachotherwewilldoubletheerrorsintheevaluationoftheaveragedvalueφ

Annihilationprocessespp¯→PM(M=π0,η,ω):TheCrystalBarrelCollaboration[23]measuredtheratiosforannihilationintoηMandη′Mandquotedavalueofφ=37.4 ±1.8 forthemixingangle.However,sincetheexperimentwascarriedthroughatlowenergies,theresultforφisrathersensitivetophasespacefactorsandtothemomentumdependenceoftheannihilationamplitudes.Wethereforediscardthatvalueofφinthedeterminationoftheaveragedmixinganglealthoughitwillturnouttobeconsistentwithit.

ThedecayJ/ψ→Pγ:Accordingto[24,15]thephotonisemittedbythecquarkswhichthenannihilateintolighterquarkpairsthroughthee ectoftheanomaly.Thus,thecreationofthecorrespondinglightmesonsiscontrolledbythematrixelement 0|αs

Γ[J/ψ→ηγ]=tan2φ4Mη′

kη 3=cot2θ8 kη′

Onemayextendthisanalysistotheωandφcases.Ignoringthesmalle ectduetotheω φmixing,onederivesgωη′γ/gωηγ tanφandgφη′γ/gφηγ cotφ,respectively.Fromthemeasuredvalues/bounds[17]weobtainφ 37 ±8 andφ>21 ,respectively.2