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

TL;DR

This paper calculates the decay processes of eta and eta prime mesons into pions and photons or lepton pairs using large-Nc chiral perturbation theory up to NNLO, fitting constants to experimental data.

Contribution

It provides a detailed NNLO calculation of eta and eta prime decays into pions and photons or leptons within large-Nc chiral perturbation theory, including numerical evaluations and data fitting.

Findings

Decay widths and spectra are computed at various orders.

Theoretical results are fitted to experimental data.

Predictions for decay channels involving electrons and muons.

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 $l=e,\ \mu$.