Dressing the electromagnetic nucleon current

TL;DR

This paper develops a gauge-invariant, microscopically consistent framework for the electromagnetic nucleon current within pion photoproduction, enabling more accurate modeling of various photon- and electron-induced processes on nucleons.

Contribution

It introduces a novel, gauge-invariant formulation of the fully dressed electromagnetic nucleon current using an effective Lagrangian approach, improving upon previous models.

Findings

Derived a gauge-invariant expression for the dressed nucleon current.

Ensured the Ward-Takahashi identity is satisfied for the dressed propagator.

Proposed a practical truncation scheme for reaction dynamics.

Abstract

A field-theory-based approach to pion photoproduction off the nucleon is used to derive a microscopically consistent formulation of the fully dressed electromagnetic nucleon current in an effective Lagrangian formalism. It is shown how the rigorous implementation of local gauge invariance at all levels of the reaction dynamics provides equations that lend themselves to practically manageable truncations of the underlying nonlinearities of the problem. The requirement of consistency also suggests a novel way of treating the pion photoproduction problem. Guided by a phenomenological implementation of gauge invariance for the truncated equations that has proved successful for pion photoproduction, an expression for the fully dressed nucleon current is given that satisfies the Ward-Takahashi identity for a fully dressed nucleon propagator as a matter of course. Possible applications include meson photo- and electroproduction processes, bremsstrahlung, Compton scattering, and $ee'$ processes off nucleons.