$Λ-π$ phase shift in Chiral Perturbation Theory

Abstract

We calculate the S and P wave phase shifts in $Λ- π$ scattering at the $Ξ$ mass using the full relativistic $SU(3)_L \times SU(3)_R$ chiral perturbation theory. We get small phase shifts similar to previous calculations using $ SU(2)_L \times SU(2)_R$ chiral perturbation theory in the heavy baryon limit. We also consider possible off--shell effects in the coupling of the Rarita-Schwinger particle $Σ^*(1385)$. Using SU(3) we estimate the off--shell coupling of the $Σ^*$ to $Λπ$ from the off--shell coupling of the $Δ$ to $N π$ which is obtained from a fit to the pion--nucleon data. We find that the contributions from the off--shell coupling can be of the same size as the other terms in the $Λπ$ scattering amplitude.