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

TL;DR

This paper calculates light-quark meson decay processes using Dyson-Schwinger and Bethe-Salpeter equations with a contact interaction model, highlighting the model's successes and limitations in describing experimental data.

Contribution

It introduces a beyond rainbow-ladder truncation within a contact interaction framework to study meson decays, incorporating non-Abelian anomaly effects.

Findings

Decay widths agree with experimental data

Charge and interaction radii estimated from decay constants

IA limitations evident in η-η' transition analysis

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.