$\pi^0,\eta,\eta'\to\gamma\gamma$ Decays and the explicit chiral symmetry breaking

Corrections to the Wess–Zumino–Witten anomaly caused by the explicit breaking of the $SU(3) \times SU(3)$ chiral symmetry are studied using the effective meson Lagrangian based on the Nambu–Jona-Lasinio model with the simultaneous expansion in derivatives, current quark masses, and $1/N_c$ powers. The leading contribution and the first correction for the amplitudes of the $\pi^0,\eta,\eta'\to\gamma\gamma$ decays and the contact term in the $\eta,\eta'\to\pi^+\pi^-\gamma$ amplitudes have been calculated. The results are compared with similar $1/N_c$ chiral perturbation calculations and existing experimental data.