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: $\pi N$, $\eta N$, $K\Lambda$, $K\Sigma$. 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 $\pi N$ phase-shifts and the ${\pi }^{-}p\to \eta n$ and ${\pi }^{-}p\to K^0\Lambda$ 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 $\pi N$ threshold up to 2 GeV, is achieved keeping in mind that the two pion production channel has not been included.

Comments: 35 pages, LaTeX + 7 ps-figure files. Some minor mistakes have been corrected for and a new appendix discussing the matching to HBChPT has been also added