Solution of the Bethe-Salpeter equation for pion-nucleon scattering

Abstract

A relativistic description of pion-nucleon scattering based on the four-dimensional Bethe-Salpeter equation is presented. The kernel of the equation consists of s- and u-channel nucleon and $\ensuremath{\Delta}(1232)$ pole diagrams, as well as $\ensuremath{\rho}$ and $\ensuremath{\sigma}$ exchange in the t channel. The Bethe-Salpeter equation is solved by means of a Wick rotation, and good fits are obtained to the s- and p-wave $\ensuremath{\pi}N$ phase shifts up to 360 MeV pion laboratory energy. The coupling constants determined by the fits are consistent with the commonly accepted values in the literature.