A relativistic meson-exchange model of pion-nucleon scattering

Abstract

Pion-nucleon scattering is investigated using the Kadyshevsky three-dimensional reduction of the Bethe-Salpeter equation. The resulting potential includes the direct and crossed N, Delta terms, and the t-channel sigma and rho -exchange terms. The nucleon pole condition is imposed to define the renormalization of the nucleon mass and the pi NN coupling constant. A mixture of the scalar and vector sigma pi pi couplings is introduced to simulate the effect of the broad width of the s-wave correlated two-pion exchange mechanism. Good descriptions of the pi N phase shifts up to 400 MeV have been obtained in all S- and P-waves. The off-shell behaviours for our model differ significantly from those obtained using different reduction schemes.