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$π^0$-$η$-$η^{\prime}$ mixing from $V\!\rightarrow\!Pγ$ and $P\!\rightarrow\!Vγ$ decays

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 $V\!Pγ$ ($V=ρ$, $K^*$, $ω$, $ϕ$ and $P=π$, $K$, $η$, $η^{\prime}$) 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. $χ^2_{\textrm{min}}/\textrm{d.o.f} = 1.9$. The current experimental uncertainties allow for isospin symmetry violations with a confidence level of approximately $2.5σ$.