Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma, f_0(980), a_0 (980)$ scalar mesons

Abstract

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 $\sigma$, f_0 and a_0 resonances. The $\pi \pi \to \pi \pi, \pi \pi \to K \bar{K}$ phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the $\pi^0 \eta$ and $K \bar{K}$ mass distributions in the T = 1 channel. Furthermore, the total and partial decay widths of the f_0 and a_0 resonances are properly reproduced including also the decay into the $\gamma \gamma$ 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 $\sqrt{s} \simeq 1.2 GeV$.