Bethe-Salpeter approach for meson-meson scattering in chiral perturbation theory

The Bethe-Salpeter equation restores exact elastic unitarity in the s-chann el by summing up an infinite set of chiral loops. We use this equation to s how how a chiral expansion can be undertaken by successive approximations t o the potential which should be iterated. Renormalizability of the amplitud es in a broad sense can be achieved by allowing for an infinite set of coun ter-terms as it is the case in ordinary Chiral Perturbation Theory. Within this framework we calculate the pi pi scattering amplitudes both for s- and p-waves at lowest order in the proposed expansion where a successful descr iption of the low-lying resonances (sigma- and rho) and threshold parameter s is obtained. We also extract the SU(2) low energy parameters (l) over bar ,(1,2,3,4) from our amplitudes. (C) 1999 Published by Elsevier Science B.V. All rights reserved.