Study of \eta-\eta' mixing from radiative decay processes

Abstract

We perform a thorough analysis of the VP\gamma(\gamma*) and P\gamma\gamma(\gamma*) decays in the resonance chiral theory, where V stand for the vector resonances \rho, K*, \omega, \phi, P stand for \pi, K, \eta, \eta' and \gamma* subsequently decays into lepton pairs. Upon imposing QCD short-distance constraints on resonance couplings, the \omega -> \pi \gamma(\gamma*), \rho -> \pi \gamma(\gamma*), K^{*0} -> K^0\gamma processes only depend on one free parameter and \pi -> \gamma \gamma(\gamma*) can be completely predicted. The four mixing parameters of the \eta-\eta' system, i.e. two mixing angles \theta8, \theta0 and two decay constants F8, F0, are determined from radiative decays involving \eta or \eta'. The higher order low energy constants of the pseudo-Goldstone Lagrangian in the chiral anomaly sector are predicted by integrating out heavy resonances. We also predict the decay widths of \rho -> \pi e^+ e^-, \eta' -> \gamma e^+ e^- and \phi -> \eta \mu^+ \mu^-, which can be compared with the future measurement in these channels.