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 nonperturbative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangians. 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-->\pi\pi, \pi\pi-->K\bar{K} phase shifts and inelasticities in the T=0 scalar channel are well reproduced as well as the \pi^-\eta and K^-K^0 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)=1.2 GeV.