Two-photon decays and transition form factors of ${\pi }^0$, $\eta$, and ${\eta }^{\prime }$ in large-$N_c$ chiral perturbation theory

Abstract

We present a calculation of $P\to {\gamma }^{(\ast )}{\gamma }^{(\ast )}$ processes, where $P={\pi }^0,\eta ,{\eta }^{\prime }$, at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-$N_c$ chiral perturbation theory. The results are numerically evaluated successively at LO, NLO, and NNLO. The appearing low-energy constants are determined through fits to the available experimental data. We investigate the decay widths to real photons, the single-virtual transition form factors, and the widths of $P\to \gamma l^{+}{l}^{-}$, where $l=e,\mu$. Furthermore, we provide results for the slopes and curvatures of the transition form factors.