PS-meson form factors in relativistic quantum mechanics and constraints from covariant space-time translations

TL;DR

This paper explores the importance of Poincaré covariant space-time translation constraints in calculating pseudoscalar-meson charge form factors within relativistic quantum mechanics, highlighting their impact on the validity of single-particle current assumptions.

Contribution

It identifies and discusses previously overlooked constraints from Poincaré covariance that affect form factor calculations and proposes methods to incorporate these constraints for consistent results.

Findings

Constraints are crucial for Poincaré covariance in form factors.

Violations depend on the relativistic quantum mechanics form used.

Restoring constraints aligns different approaches and relates to dispersion relations.

Abstract

The role of Poincar\'e covariant space-time translations is investigated in the case of the pseudoscalar-meson charge form factors calculated within a relativistic quantum mechanics framework. It is shown that this role extends beyond the standard energy-momentum conservation, which is accounted for in all works based on this general approach. It implies constraints that have been largely ignored until now but should be nevertheless fulfilled to ensure the full Poincar\'e covariance. The violation of these constraints, which is more or less important depending on the form of relativistic quantum mechanics that is employed, points to the validity of using a single-particle current, which is generally assumed in calculations of form factors. In short, these constraints concern the relation of the momentum transferred to the constituents to the one transferred to the system, which most often differ in relativistic quantum mechanics while they are equal in field theory. How to account for the constraints, as well as restoring the equivalence of different relativistic quantum mechanics approaches in estimating form factors, is discussed. It is mentioned that the result so obtained can be identified to a dispersion-relation one. A short conclusion relative to the underlying dynamics is given in the pion case.