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

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 J · q = 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.

Bound state structure and electromagnetic form factor beyond the ladder approximation

“…This cancellation found numerically would be indeed a powerful test, as in Ref. [27], where this cancellation was demonstrated numerically for the transition form factor associated with the EM breakup process: bound → scattering state. In the present work we restrict ourselves by the elastic case only.…”

Direct Bethe-Salpeter solutions in Minkowski space

“…Using our Minkowski space solutions for the initial (bound) and final (scattering) states, we calculate the elastic form factor [3] and the transition one for electrodisintegration of a two-body system [11]. We show in Fig.…”

Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

“…However, though certain quantities such as binding energies and transverse amplitudes exactly coincide with those determined by the Minkowski BS equation, the Euclidean BS amplitude is not the physical one and does not give direct access to most of the dynamical observables. For example, the electromagnetic transition form factor, associated with the breakup of a two-body bound state, can be computed in Minkowski space in the whole kinematical region including the final state interaction [3], while this task has not yet been accomplished with Euclidean space calculations. For general purposes one needs the Minkowski BS amplitude.…”