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.

Comments: 13 pages, LaTeX, uses epsf.sty, 3 postscript figures included, complete postscript file available at http://www.nordita.dk/locinfo/preprints/95084.ps.gz