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 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.

23 pages, 9 figures, to be published in Phys. Rev. D

References in corpus (17)

• Solving Bethe-Salpeter equation in Minkowski space
• Solving the Bethe-Salpeter Equation for Scalar Theories in Minkowski Space
• Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space
• Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
• Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane
• Cross-ladder effects in Bethe-Salpeter and Light-Front equations
• Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space
• Solutions of the Bethe-Salpeter equation in Minkowski space and applications to electromagnetic form factors
• Solving Bethe-Salpeter scattering state equation in Minkowski space
• Solving the Bethe-Salpeter equation for a pseudoscalar meson in Minkowski space
• Covariant relativistic separable kernel approach for electrodisintegration of the deuteron at high momentum transfer
• Electromagnetic interactions for the two-body spectator equations
• Bethe-Salpeter scattering amplitude in Minkowski space
• Final state interaction effects in electrodisintegration of the deuteron within the Bethe-Salpeter approach
• Present status of the Bethe-Salpeter approach in Minkowski space
• Transition electromagnetic form factor in the Minkowski space Bethe-Salpeter approach
• Solutions of the Bethe-Salpeter Equation in Minkowski space: a comparative study

Cited by in corpus (10)

• Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach
• Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space
• Bound state structure and electromagnetic form factor beyond the ladder approximation
• Zero energy scattering calculation in Euclidean space
• Three-boson bound states in Minkowski space with contact interactions
• Radiative decays of heavy-light quarkonia through $M1$, and $E1$ transitions in the framework of Bethe-Salpeter equation
• $E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation
• Hybrid nature of the abnormal solutions of the Bethe-Salpeter equation in the Wick-Cutkosky model
• Scattering solutions of Bethe-Salpeter equation in Minkowski and Euclidean spaces
• Direct Bethe-Salpeter solutions in Minkowski space