Form factors in RQM approaches: constraints from space-time translations, extension to constituents with spin-1/2 and unequal masses

TL;DR

This paper investigates how space-time translation constraints affect form factor calculations in relativistic quantum mechanics, extending previous work to systems with spin-1/2 constituents and unequal masses, ensuring consistency with field-theoretic results.

Contribution

It extends the analysis of space-time translation constraints to systems with spin-1/2 constituents and unequal masses, improving the consistency of RQM form factor calculations.

Findings

Discrepancies between approaches are reduced when constraints are applied.

Extension to spin-1/2 constituents with unequal masses is achieved.

Results may be useful for calculating pion and kaon form factors.

Abstract

Constraints related to transformations of currents under space-time translations have been considered for the relativistic quantum mechanics calculation of form factors of J=0 systems composed of scalar constituents with equal masses. Accounting for these constraints amounts to take into account many-body currents that restore the equality of the momentum transferred separately to the system and to the constituents, which holds in field-theory approaches but is not generally fulfilled in relativistic quantum mechanics ones. When this was done, discrepancies between results from different approaches could be found to vanish. The results are extended here to systems composed of spin-1/2 constituents with unequal masses. Moreover, as far as the equivalence of different approaches is concerned, some intermediate step could be skipped and the presentation of these results therefore slightly differs from the previous one. Due to the technical aspect of present results, this work is not aimed to be published but it could be useful for some applications like the form factors of the pion or kaon particles.