Gauge invariance of meson photo- and electroproduction currents revisited

TL;DR

This paper derives an exact, gauge-invariant expression for meson production currents off nucleons, facilitating approximation schemes that preserve local gauge invariance in theoretical models of photon-induced meson production.

Contribution

It provides a model-independent, exact formulation that separates gauge-invariant tree-level terms from transverse FSI contributions, aiding accurate and consistent theoretical modeling.

Findings

Exact gauge-invariant expression derived

Separation of tree-level and FSI terms achieved

Facilitates approximation schemes preserving gauge invariance

Abstract

An exact expression is derived for the meson production current off the nucleon for real and virtual photons which cleanly separates, in a model-independent manner, a tree-level expression that manifestly preserves local gauge invariance in terms of a generalized Ward-Takahashi identity from transverse final-state-interaction (FSI) terms. As discussed in some detail, this exact formulation is particularly well suited for implementing approximation schemes of exchange-current and FSI contributions (which in practice generally will be necessary) at any level of sophistication without violating local gauge invariance.