Pion-nucleon scattering in the Mandelstam representation

Abstract

Using the analytic properties of partial wave scattering amplitudes, as derived from Mandelstam's representation, we have studied the J=3/2, P state of the pion-nucleon system. The method used is covariant, it incorporates unitarity, and the effect of a possible pion-pion resonance has been investigated. Using the "single nucleon term" and the low-energy scattering properties of the "crossed states," we obtain a resonance in the J=3/2, T=3/2 pion-nucleon state without the aid of a cutoff. We have also investigated the scattering in the T=1/2 state. The pion-pion resonance appears to have only a very small effect in the T=3/2 state whereas in the T=1/2 state it increases the phase shift by a factor of 2. The resonance obtained in the T=3/2 state occurs at too low an energy. There are several factors which may account for this: We have not been able to include fully the contributions from crossed states, and we have not systematically included inelastic scattering.