Electromagnetic currents of the pion-nucleon system

TL;DR

This paper develops a gauge-invariant, covariant framework for calculating pion photoproduction amplitudes by coupling photons to dressed pion-nucleon and nucleon vertices, ensuring consistency with fundamental symmetries.

Contribution

It introduces a comprehensive method for calculating electromagnetic currents in the pion-nucleon system that maintains gauge invariance and unitarity, with explicit derivation of the photon-nucleon vertex.

Findings

Calculated pion photoproduction amplitudes consistent with gauge invariance

Derived nucleon electromagnetic form factors from the dressed vertex

Ensured unitarity and covariance in the amplitude calculations

Abstract

Pion photoproduction amplitudes are calculated from a set of equations that have been derived by coupling an external photon to all places in a dressed pion-nucleon vertex. The calculation is consistent with gauge invariance, charge conservation, unitarity and covariance. To provide input to the photoproduction amplitude, a photon-nucleon vertex is calculated from a set of equations derived by complete attachment of photons to a dressed nucleon propagator. We check the accuracy of this vertex by extracting its nucleon electromagnetic form factors.