${\pi }^0$-$\eta$-${\eta }^{\prime }$ mixing from $V\to P\gamma$ and $P\to V\gamma$ 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 $VP\gamma$ ($V=\rho$, $K^{\ast }$, $\omega$, $\varphi$ 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. ${\chi }_{\text{min}}^2/\text{d.o.f}=1.9$. The current experimental uncertainties allow for isospin symmetry violations with a confidence level of approximately $2.5\sigma$.

Comments: 10 pages, 3 tables