Transition from a relativistic constituent-quark model to the quantum-chromodynamical asymptotics: a quantitative description of the pion electromagnetic form factor at intermediate values of the momentum transfer

Abstract

We adopt a non-perturbative relativistic constituent-quark model for the pi-meson electromagnetic form factor, which have successfully predicted experimental results, and supplement it with the effective momentum-dependent quark mass to study quantitatively the transition to the perturbative QCD asymptotics. The required asymptotical behaviour (including both the Q^{-2} fall-off and the correct coefficient) settles down automatically when the quark mass is switched off; however, the present experimental data on the form factor suggest that this cannot happen at the values of the momentum transfer below ~10 GeV^2. The effective constituent-quark mass below this scale acquires substantial non-perturbative contributions.

Comments: 7 pages, RevTex 4.1, 5 figures. V2: a reference added, minor textual changes, version accepted by Phys. Rev. D