Form factors in relativistic quantum mechanics: constraints from space-time translations

TL;DR

This paper investigates how space-time translation constraints affect form factor calculations in relativistic quantum mechanics, proposing a method to incorporate two-body currents that reconcile discrepancies across different approaches.

Contribution

It introduces a way to implement translation invariance constraints via two-body currents, improving consistency among relativistic quantum mechanics methods for form factors.

Findings

Discrepancies between approaches can be reduced with these constraints.

Standard front-form approach ($q^+=0$) already satisfies the constraints.

Relation established between this approach and dispersion-relation results.

Abstract

The comparison of form factors calculated from a single-particle current in different relativistic quantum mechanic approaches evidences tremendous discrepancies. The role of constraints coming from space-time translations is considered here with this respect. It is known that invariance under these translations implies the energy-momentum conservation relation that is usually assumed to hold globally. Transformations of the current under these translations, which lead to this result, also imply constraints that have been ignored so far in relativistic quantum mechanic approaches. An implementation of these constraints is discussed in the case of a model with two scalar constituents. It amounts to incorporate selected two-body currents to all orders in the interaction. Discrepancies for form factors in different approaches can thus be removed, contributing to restore the equivalence of different approaches. Results for the standard front-form approach ($q^+=0$) are found to fulfill the constraints and are therefore unchanged. The relation with results from a dispersion-relation approach is also made.