$\pi^0$-$\eta$-$\eta^{\prime}$ mixing from $V\!\rightarrow\!P\gamma$ and $P\!\rightarrow\!V\gamma$ decays

Abstract

An enhanced phenomenological model that includes isospin-symmetry breaking is presented in this letter. The model is then used in a number of statistical fits to the most recent experimental data for the radiative transitions $V\!P\gamma$ ($V=\rho$, $K^*$, $\omega$, $\phi$ and $P=\pi$, $K$, $\eta$, $\eta^{\prime}$) and estimations for the mixing angles amongst the three pseudoscalar states with vanishing third-component of isospin are obtained. The quality of the performed fits is good, e.g. $\chi^2_{\textrm{min}}/\textrm{d.o.f} = 1.9$. The current experimental uncertainties allow for isospin symmetry violations with a confidence level of approximately $2.5\sigma$.