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

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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