Contour Distortions in Relativistic Three-Particle Scattering Equations

Abstract

It is shown how to relate the physical three-baryon scattering amplitude as given by a generalized Bethe-Salpeter equation to the soltuion of an integral equation with an $L^2$ kernel. This is done by demonstrating that the contours for the integration variables in a perturbation contribution to the amplitude may be distorted so that no propagator vanishes. The method is an extension of techniques used earlier by Tiktopoulos for the two-particle Bethe-Salpeter equation. The results hold for center-of-mass energies less than half way to the threshold for production of a meson.