A note on the γγ → π0π0 reaction in the 1N expansion of χPT

In this work we present the results of a complete calculation of the γγ → π0π0 amplitude to leading order in the large N approximation (N being the number of Goldstone bosons) up to order mπ2F2. The amplitude turns to be proportional to that of π+π− → π0π0. 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 γγ → π0π0 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 ππ scattering data.