Crossing symmetric potential model of pion-nucleon scattering

TL;DR

This paper develops a crossing symmetric potential model for pion-nucleon scattering that ensures unitarity and gauge invariance, and also provides consistent amplitudes for related pion photoproduction and Compton scattering processes.

Contribution

It introduces a crossing symmetric and gauge invariant framework for pion-nucleon scattering based on a dressed nucleon propagator and potential model, unifying multiple scattering processes.

Findings

Amplitudes are unitary when on-shell with the potential model.

Provides expressions for pion photoproduction and Compton scattering.

Ensures crossing symmetry and gauge invariance in the model.

Abstract

A crossing symmetric $\pi N$ scattering amplitude is constructed through a complete attachment of two external pions to the dressed nucleon propagator of an underlying $\pi N$ potential model. Our formulation automatically provides expressions also for the crossing symmetric and gauge invariant pion photoproduction and Compton scattering amplitudes. We show that our amplitudes are unitary if they coincide on-shell with the amplitudes obtained by attaching one pion to the dressed $\pi NN$ vertex of the same potential model.