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

A relativistic description of pian-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(1232) 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 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. [S0556-2813(99)05008-6].