Partial-Wave Dispersion Relations for the Processπ+π→N+N¯

Abstract

The problems of pion-nucleon and nucleon-nucleon scattering and nucleon electromagnetic structure involve the matrix element for two pions producing a nucleon-antinucleon pair. By use of the Mandelstam representation we are able to write dispersion relations for the partial-wave scattering amplitudes of this process. In the low-energy range these dispersion relations can be transformed into integral equations whose kernels are simply related to pion-nucleon and pion-pion scattering amplitudes.