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

Abstract

We present a calculation of the decays ${\eta }^{{(}^{\prime })}\to {\pi }^{+}{\pi }^{-}{\gamma }^{(\ast )}$ 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 ${\eta }^{{(}^{\prime })}\to {\pi }^{+}{\pi }^{-}\gamma$ as well as ${\eta }^{{(}^{\prime })}\to {\pi }^{+}{\pi }^{-}{l}^{+}{l}^{-}$, with $l=e,\mu$.