The $S_{11}- N$(1535) and $-N$(1650) Resonances in Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory

Abstract

The $s-$wave meson-baryon scattering is analyzed for the strangeness S=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $πN$, $ηN$, $K Λ$, $K Σ$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism and low energy constants are fitted to the elastic $πN $ phase-shifts and the $π^- p \to ηn$ and $π^- p \to K^0 Λ$ cross section data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of the $S_{11}-$ $N$(1535) and $-N$(1650) resonances, in reasonable agreement with experiment. A good overall description of data, from $πN$ threshold up to 2 GeV, is achieved keeping in mind that the two pion production channel has not been included.