Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach

TL;DR

This paper calculates the transition electromagnetic form factor for a two-body system's electrodisintegration using the Bethe-Salpeter approach in Minkowski space, emphasizing gauge invariance and current conservation.

Contribution

It demonstrates that consistent solutions of the Bethe-Salpeter equation for initial and final states are essential for accurate form factor calculations and current conservation.

Findings

Gauge invariance is numerically verified in the Bethe-Salpeter framework.

Current conservation results from a cancellation between different contributions.

Consistent dynamical solutions are crucial for reliable form factor results.

Abstract

The transition form factor for electrodisintegration of a two-body bound system is calculated in the Bethe-Salpeter framework. For the initial (bound) and the final (scattering) states, we use our solutions of the Bethe-Salpeter equation in Minkowski space which were first obtained recently. The gauge invariance, which manifests itself in the conservation of the transition electromagnetic current Jq = 0, is studied numerically. It results from a cancellation between the plane wave and the final state interaction contributions. This cancellation takes place only if the initial bound state BS amplitude, the final scattering state and the operator of electromagnetic current are strictly consistent with each other, that is if they are found in the same dynamical framework. A reliable result for the transition form factor can be obtained in this case only.