Dynamical isobar models andπ−Nscattering data

Abstract

Isobar amplitudes for pion-nucleon elastic and production reactions are constructed from a dynamical theory. The framework of point form relativistic quantum mechanics is used to derive a relativistic Lippmann-Schwinger equation linking elastic and production channels. The dynamics is contained in a mass operator which is the sum of a free and interacting mass operator. For a separable interacting mass operator, the Lippmann-Schwinger equations can be solved analytically; the resulting matrix equations have determinants whose zeros give the positions of multiple resonances in the same angular momentum channels. Though varying parameters to fit data is highly nonlinear, procedures are developed for fitting elastic and inelastic data. Fits to data are presented for the $P_{33}$ partial wave channel in pion-nucleon scattering.