N, Δ and ϱ-exchange in pion-nucleon scattering

Abstract

The N, Δ and ϱ-exchange contributions to the πN charge exchange amplitude as derived from fixed- t and fixed angle θ = 180° dispersion relations are compared with the corresponding terms in a chiral Lagrangian. A new evaluation of the backward dispersion relation combined with the forward dispersion relation gives information on the physical origin and the magnitude of the corrections to the simple ϱ-dominance and N, Δ, ϱ-exchange models. The result for the πNΔ-coupling constant g ∗2/4π = 0.26 differs from that of other authors and the determination of the ϱNN coupling constants leads to difficulties which were ignored in earlier work. The equality between the forward and backward amplitudes at threshold gives a relation between coupling constants similar to a result which was recently derived from chiral Lagrangians.