Chiral Symmetry and s-wave Low-Lying Meson-Baryon Resonances

Abstract

The $s-$wave meson-baryon scattering is analyzed for the isospin-strangeness $I=1/2, S=0$ and $I=0,S=-1$ sectors, in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. For both sectors, four channels have been considered: $\pi N$, $\eta N$, $K \Lambda$, $K \Sigma$ and $\pi \Sigma$, $\bar K N$, $\eta \Lambda$, $K \Xi$, respectively. The needed two particle irreducible matrix amplitudes are taken from lowest order Chiral Perturbation Theory in a relativistic formalism. There appear undetermined low energy constants, as a consequence of the renormalization of the amplitudes, which are obtained from fits to the available data: elastic $\pi N $ phase-shifts, $\pi^- p \to \eta n$ and $\pi^- p \to K^0 \Lambda$ cross sections and to $\pi\Sigma\to\pi\Sigma$ mass-spectrum, the elastic $\bar K N \to \bar K N$ and $ \bar K N\to \pi \Sigma$ $t$--matrices and to the $ K^- p \to \eta \Lambda$ cross section data. The position and residues of the complex poles in the second Riemann sheet of the scattering amplitude determine masses, widths and branching ratios of the $S_{11}-$ $N$(1535) and $-N$(1650) and $S_{01}-$ $\Lambda$(1405) and $-\Lambda$(1670) resonances, in reasonable agreement with experiment. A good overall description of data, from threshold up to around 2 GeV is achieved despite the fact that three-body channels have not been explicitly included.