$\Lambda-\pi$ phase shift in Chiral Perturbation Theory

We calculate the S and P wave phase shifts in $\Lambda - \pi$ scattering at the $\Xi$ 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 $\Sigma^*(1385)$. Using SU(3) we estimate the off--shell coupling of the $\Sigma^*$ to $\Lambda \pi$ from the off--shell coupling of the $\Delta$ to $N \pi$ 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 $\Lambda \pi$ scattering amplitude.