RQM description of PS meson form factors, constraints from space-time translations, and underlying dynamics

TL;DR

This paper explores how Poincaré covariant space-time translations impose important constraints on pseudoscalar meson form factors, revealing limitations of single-particle current assumptions and emphasizing the need for full covariance in relativistic quantum mechanics calculations.

Contribution

It introduces the importance of space-time translation constraints in form factor calculations and discusses their implications for the validity of single-particle current approximations.

Findings

Constraints are essential for full Poincaré covariance in form factors.

Violations of these constraints vary with the relativistic quantum mechanics form used.

Implications for the underlying dynamics of pseudoscalar mesons, especially pions.

Abstract

The role of Poincar\'e covariant space-time translations is investigated in the case of the pseudoscalar-meson charge form factors. It is shown that this role extends beyond the standard energy-momentum conservation, which is accounted for in all relativistic quantum mechanics calculations. It implies constraints that have been largely ignored until now but should be 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. How to account for the related constraints, as well as restoring the equivalence of different relativistic quantum mechanics approaches in estimating form factors, is discussed. Some conclusions relative to the underlying dynamics are given in the pion case.