Scattering and Production Amplitudes with Unstable Particles

Abstract

An $S$-matrix theory is developed for a system of strongly interacting particles in which unstable particles are included. The particular system considered is $\pi +N\leftrightarrow \pi +N$, $\pi +N\leftrightarrow \rho +N$, and $\rho +N\leftrightarrow \rho +N$. Only the one-pion-exchange interaction is included. The relationship to the strip approximation and the application to the higher resonances in pion-nucleon scattering are discussed. Complex singularities are evaluated, and their relationship to the generalized unitarity condition for the pion-pion system is stressed. An extended $N{D}^{-1\mathrm{}}$ method is used to develop a system of nonsingular, uncoupled, Fredholm integral equations, from which the transition amplitudes can be evaluated.