RQM description of the charge form factor of the pion and its asymptotic behavior

TL;DR

This paper calculates the pion's charge and scalar form factors using relativistic quantum mechanics with a confining and one-gluon-exchange mass operator, comparing different forms and configurations to experimental data and QCD predictions.

Contribution

It provides a comparative analysis of form factor calculations in various relativistic frameworks and discusses the role of two-body currents and constituent spin in matching experimental and QCD asymptotic behaviors.

Findings

Perpendicular momentum configurations yield better experimental agreement.

Two-body currents are crucial for the correct QCD power-law behavior.

Scalar form factor exhibits correct power-law behavior regardless of configuration.

Abstract

The pion charge and scalar form factors, $F_1(Q^2)$ and $F_0(Q^2)$, are first calculated in different forms of relativistic quantum mechanics. This is done using the solution of a mass operator that contains both confinement and one-gluon-exchange interactions. Results of calculations, based on a one-body current, are compared to experiment for the first one. As it could be expected, those point-form, and instant and front-form ones in a parallel momentum configuration fail to reproduce experiment. The other results corresponding to a perpendicular momentum configuration (instant form in the Breit frame and front form with $q^+=0$) do much better. The comparison of charge and scalar form factors shows that the spin-1/2 nature of the constituents plays an important role. Taking into account that only the last set of results represents a reasonable basis for improving the description of the charge form factor, this one is then discussed with regard to the asymptotic QCD-power-law behavior $Q^{-2}$. The contribution of two-body currents in achieving the right power law is considered while the scalar form factor, $F_0(Q^2)$, is shown to have the right power-law behavior in any case. The low-$Q^2$ behavior of the charge form factor and the pion-decay constant are also discussed.}