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

Garcia-Recio, C.; Nieves, J.; Arriola, E. Ruiz; Vacas, M. J. Vicente

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

Authors

Description

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: $πΣ$, $\bar K N$, $ηΛ$ and $K Ξ$. 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 $πΣ\toπΣ$ mass-spectrum, to the elastic $\bar K N \to \bar K N$ and $ \bar K N\to πΣ$ $t$--matrices and to the $ K^- p \to ηΛ$ 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 $S_{01}-$ $Λ$(1405) and $-Λ$(1670) resonances, in reasonable agreement with experiment. A good overall description of data, from $πΣ$ 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