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

The Bethe-Salpeter equation restores exact elastic unitarity in the s-channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken by successive approximations to the potential which should be iterated. Renormalizability of the amplitudes in a broad sense can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Within this framework we calculate the ππ scattering amplitudes both for s- and p-waves at lowest order in the proposed expansion where a successful description of the low-lying resonances (σ and ρ) and threshold parameters is obtained. We also extract the SU(2) low energy parameters l̄1,2,3,4 from our amplitudes.