LOW-ENERGY DYNAMICS OF THE GAMMA-GAMMA -] PI-PI REACTION IN THE NJL MODEL

We calculate the one-quark-loop amplitude for the low-energy pi pi --> pi pi collision in the context of the Nambu and Jona-Lasinio model wi th scalar and pseudoscalar four-quark couplings to all orders in the e xternal momenta. We show that the NJL predictions for the gamma gamma --> pi(+) pi(-) reaction are not far from the Born amplitude, which is close to the data and is compatible with the chiral perturbation theo ry estimations, We determine the corrections given by the NJL model in leading order of 1/N-c to the chiral loop amplitude for pi pi --> pi( 0) pi(0). Numerical results for the gamma gamma --> pi pi cross sectio ns and for pion polarizabilities are given.