S=--1 Meson-Baryon Scattering in Coupled Channel Unitarized Chiral Perturbation Theory

Abstract

The $s-$wave meson-baryon scattering amplitude is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four two-body channels have been considered: $\bar K N$, $πΣ$, $ηΛ$, $ K Ξ$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behaviour is parameterized in terms of low energy constants, which outnumber those assumed in previous works and provide a better fit to the data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of the $Λ(1405)$ and $Λ(1670)$ resonances which compare well with accepted numbers.