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

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.}