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 delta pole diagrams, as well as rho and 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 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.

Comments: 34 pages, RevTeX; 7 figures. Several references added, a few typos corrected. Accepted for publication in Physical Review C