Eur. Phys. J. A (2009) 42: 219-236
https://doi.org/10.1140/epja/i2009-10864-8

Regular Article - Theoretical Physics

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

Laboratoire de Physique Subatomique et de Cosmologie, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, INPG, F-38026, Grenoble Cedex, France

^* e-mail: desplanq@lpsc.in2p3.fr

Received: 18 June 2009
Revised: 13 August 2009
Accepted: 27 August 2009
Published online: 9 October 2009

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 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-Q² behavior of the charge form factor and the pion decay constant are also discussed.