Application of General Unitarity to Pion-Nucleon Scattering

Abstract

The pi - pi -N intermediate state is included in the unitarity condition of pion-nucleon scattering. The general unitarity relations then couple the amplitudes for pi -N and pi - pi -N scattering, and one-pion production or absorption. The kinematical structure of these amplitudes is discussed and a formal decomposition into partial waves is outlined. The dynamical approach is based on a system of coupled partial wave dispersion relations. The dynamical singularities of pi -N scattering can be taken from the Mandelstam representation, whereas perturbation-theoretic approximations must be made for the other amplitudes. The dispersion relations can be solved by the generalized N/D method. As an example, a one-pion exchange approximation for the production and absorption amplitudes is considered. It is shown that amplitudes can be chosen which do not have any kinematical singularities. The N/D method here takes a more simple form by setting up integral equations for the N functions rather than for the D functions. Integrations over contours in the complex plane are then avoided. (auth)