Chiral Symmetry Amplitudes in the S-wave Isoscalar and Isovector Channels

We use a nonpertubative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f0 and a0 resonances. The ππ → ππ , ππ → KK̄ phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π0η and KK̄ mass distributions in the T = 1 channel. Furthermore, the total and partial decay widths of the f0 and a0 resonances are properly reproduced including also the decay into the γγ channel. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below √ s ≃ 1.2 GeV .