Self-Consistent Relativistic Model for Pion-Nucleon Scattering.

We introduce a relativistic model for pion-nucleon scattering which includes an elementary delta dressed by its decay. Crossing-symmetric single-particle exchange is augmented by parametrized multiple-scattering interactions, with covariant side-ways form factors in both 3- and 4 -field vertices. Causality is enforced by dispersion relations. Unitary fits to observed on-shell amplitudes are obtained; a modest number of parameters precisely reproduce all 6 S- and P -wave pi-N amplitudes up to 1.36 GeV invariant mass.