$\eta^{(')}\to\pi^+\pi^-\gamma^{(\ast)}$ in large-$N_c$ chiral perturbation theory

Abstract

We present a calculation of the decays $\eta^{(')}\to\pi^+\pi^-\gamma^{(\ast)}$ at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-$N_c$ chiral perturbation theory. The numerical evaluation of the results is performed successively at LO, NLO, and NNLO, fitting the relevant low-energy constants to the available experimental data. We discuss the widths and decay spectra of $\eta^{(')}\to\pi^+\pi^-\gamma$ as well as $\eta^{(')}\to\pi^+\pi^-l^+l^-$, with $l=e,\ \mu$.