The $\gamma\gamma\to\pi^0\pi^0$ and $\eta\to\pi^0\gamma\gamma$ Transitions in the Extended NJL Model

Abstract

We calculate within the Extended Nambu--Jona-Lasinio model the leading in $1/N_c$ contribution to $\gamma\gamma\to\pi^0\pi^0$ to all orders in the external momenta and quark masses. This result is then combined with the known two-loop Chiral Perturbation Theory and compared with the data and other calculations. A technical difficulty in the same calculation beyond order $p^6$ for $\eta\to\pi^0\gamma\gamma$ is identified and for this decay results up to order $p^6$ are presented.