A note on the GG-->PI 0 PI 0 reaction in the 1/N expansion of ChPT

Abstract

In this work we present the results of a complete calculation of the $\gamma \gamma \to {\pi }^0{\pi }^0$ amplitude to leading order in the large $N$ approximation ($N$ being the number of Goldstone bosons) up to order $m_{\pi }^2/F^2$. The amplitude turns to be proportional to that of ${\pi }^{+}{\pi }^{-}\to {\pi }^0{\pi }^0$. In spite of the fact that this factorization property cannot hold in general (as it was recently pointed out by Morgan and Penington), it appears here since in the large $N$ limit only the $I=J=0$ channel contributes to the $\gamma \gamma \to {\pi }^0{\pi }^0$ reaction. Moreover it seems to be a reasonable approximation in this case since it is possible to reproduce, as a prediction, the experimental data starting from a one-parameter fit of the $\pi \pi$ scattering data.

Comments: 16 pages, LaTeX