Mixing and Decay Constants of Pseudoscalar Mesons(4)

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

Forlateruseitisalsoconvenienttointroducetheabbreviation

a2=αs1 0|2fq

2

y=22(Mη′ Mη)sin2φ,.(2.15)(2.16)2a2

ThecombinationofEqs.(2.13)and(2.16)providesaninterestingrelationbetweenfq/fsandthemixingangleφ.Alsoworthnotingistherelationbetweenφandθ8thatisobtainedbycombiningEq.(2.5)withEqs.(2.13)and(2.16)

cotθ8= 2Mη′

2 f2.2fKπ(2.19)

NotethatV-spinconsiderationsprovidealinearrelationbetweenthedecayconstantsfs,fπandfKwhich,totheconsideredorderof avorsymmetrybreaking,canbereplacedbytheabovequadraticrelation.AscanbeseenfromEq.(2.6),thesetheoreticalresultsforfqandfsleadtoasubstantialdi erencebetweenθ1andθ8.OnlyinthestrictSU(3)Flimitwherefq=fs(or,equivalently,fK=fπorf8=f1)onewouldhaveθ1=θ8=θ,withθbeingtheoctet-singletmixingangle.AccordingtoLeutwyler[6],ChPTprovidestworelations(upto1/Nccorrections)amongthedecayconstants

22 1fKf8=3