Form factors in the “point form” of relativistic quantum mechanics: Single- and two-particle currents

Abstract

Electromagnetic and Lorentz-scalar form factors are calculated for a bound system of two spinless particles exchanging a zero-mass scalar particle. Different approaches are considered including solutions of a Bethe-Salpeter equation, a "point form" approach to relativistic quantum mechanics and a non-relativistic one. The comparison of the Bethe-Salpeter results, which play the role of an "experiment" here, with the ones obtained in "point form" in single-particle approximation, evidences sizable discrepancies, pointing to large contributions from two-body currents in the latter approach. These ones are constructed using two constraints: ensuring current conservation and reproducing the Born amplitude. The two-body currents so obtained are qualitatively very different from standard ones. Quantitatively, they turn out not to be sufficient to remedy all the shortcomings of the "point form" form factors evidenced in impulse approximation.

Form factors in RQM approaches: Constraints from space-time translations

“…At low Q 2 , it is noticed that the fast drop off of the form factor appearing in some cases has disappeared. This result supports the suggestion made elsewhere [20] that this strange behavior of the form factor was in relation with some symmetry breaking. At high Q 2 , the right power-law behavior of the charge form factor is obtained after restoring properties related to space-time translations, though it was not always so before ("P.F.").…”

“…Getting a small total mass can be achieved by increasing the attraction between constituents. While it is then expected that the system shrinks, some approaches have instead show that the charge radius was increasing and could go to ∞ while M → 0 [20]. This strange result could be the sign that some important symmetries, like those considered in this paper, are missed.…”

“…Such a case is better to check that the incorporation of relativistic effects considered here is correctly done. Systems with a small binding considered elsewhere [3,4,20] would not be so probing. Moreover, in these cases, discrepancies due to an incomplete account of relativistic effects could have a size comparable to discrepancies with an "exact" calculation, due to uncertainties in determining the mass operator.…”

Nucleon electromagnetic form factors

“…Within the context of a toy model calculation in Refs. [Des04,Des06], it has e.g. been shown that the neglect of two-body currents in the point form does affect the FFs in a more drastic way than their neglect in the instant or light-front forms.…”

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

“…(12). Calculating the contribution of many-particle terms is quite tedious and this has been done for a limited number of cases with the aim of accounting for current conservation [50] or getting the expected asymptotic behavior of the charge form factors for the pion [45] or for a system of scalar constituents in the point form-approach [50]. Moreover, if these extra terms restore the equivalence of predictions of different approaches, we expect that they should occur at all orders in the interaction.…”