S-waveΛπphase shift is not large

Abstract

We study the strong interaction S-wave $\ensuremath{\Lambda}\ensuremath{\pi}$ phase shift in the region of the $\ensuremath{\Xi}$ mass in the framework of a relativistic chiral unitary approach based on coupled channels. All parameters have been previously determined in a fit to strangeness $S=\ensuremath{-}1$ S-wave kaon-nucleon data. We find $0\ifmmode^\circ\else\textdegree\fi{}<~{\ensuremath{\delta}}_{0}<~1.1\ifmmode^\circ\else\textdegree\fi{}$ in agreement with previous chiral perturbation theory calculations (or extensions thereof). We also discuss why a recent coupled channel K-matrix calculation gives a result for ${\ensuremath{\delta}}_{0}$ that is negative and much bigger in magnitude. We argue why that value should not be trusted.