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

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