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. PACS: 11.10.St;11.30.Rd; 11.80.Et; 13.75.Lb; 14.40.Cs; 14.40.Aq