Contact interaction treatment of $\mathcal{V}\to\mathcal{P}\gamma$ for light-quark mesons

Abstract

The $\mathcal{V}\to\mathcal{P}\gamma$ and $\eta(\eta^\prime) \to \gamma\gamma$ decays are evaluated within a Dyson-Schwinger and Bethe-Salpeter equations framework (here $\mathcal{V}=\{\rho^{\pm},K^{\star\pm},\phi\}$ and $\mathcal{P}=\{\pi^{\pm},K^{\pm},\eta,\eta^{\prime}\}$). The so-called impulse approximation (IA) is employed in the computation of the decay constants involved and decay widths, and so in the estimation of the associated charge and interaction radii. For their part, the required propagators and vertices stem from a contact interaction model, embedded within a beyond rainbow-ladder (RL) truncation that accounts for the typical ladder exchanges, quark anomalous magnetic moment, as well as the non-Abelian anomaly. While the examined transitions produce decay widths plainly compatible with the available experimental data, those processes involving the $\eta-\eta'$ mesons highlight the incompleteness of the IA when considering beyond RL effects in the interaction kernels.