$S=-1$ Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory and the $S_{01}-$ $\Lambda$(1405) and $-\Lambda$(1670) Resonances

Abstract

The $s-$wave meson-baryon scattering is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $\pi \Sigma$, $\bar{K}N$, $\eta \Lambda$ and $K\Xi$. The required input to solve the Bethe-Salpeter equation is 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 $\pi \Sigma \to \pi \Sigma$ mass-spectrum, to 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 $S_{01}-$ $\Lambda$(1405) and $-\Lambda$(1670) resonances, in reasonable agreement with experiment. A good overall description of data, from $\pi \Sigma$ threshold up to 1.75 GeV, is achieved despite the fact that three-body channels have not been explicitly included.

23 pages, Latex, 10 Figures. In this revised version a new subsection 3.6 on Heavy Baryon Expansion and new references have been added

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