Constraining scenarios of the soft/hard transition for the pion electromagnetic form factor with expected data of 12 GeV Jefferson Lab experiments and of the electron-ion collider

Abstract

It has been shown previously [S. V. Troitsky and V. E. Troitsky, Phys. Rev. D 88, 093005 (2013)] that a nonperturbative relativistic constituent-quark model for the $\ensuremath{\pi}$-meson electromagnetic form factor allows for a quantitative description of the soft/hard transition, resulting in the correct quantum-chromodynamical asymptotics, including normalization, from the low-energy data without further parameter tuning. This happens universally whenever the constituent-quark mass is switched off. The energy range where the transition happens is therefore determined by the quark-mass running at intermediate energies and is not tightly constrained theoretically. Here we consider possible ways to pin down this energy range with coming experimental data. We demonstrate that expected experimental uncertainties of the 12 GeV Jefferson Lab data are larger than the span of predictions of the model, so these data might be used for testing the model but not for determination of the soft/hard transition scale. Contrarily, the projected electron-ion collider will be capable of pinning down the scale.