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 π-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.PACS numbers: 13.

Poincaré-invariant constituent quark model for light mesons: capabilities and constraints

“…Let us note that our RQM describes well the experimental data for the pion form factor including the recent points [3]. The upper of our curves corresponds to the model (18), the lower -to the models (19) with n = 3.…”

“…We can demonstrate that wave functions in the momentum representation without poles in the momentum complex plane do not yield the resonance behavior of the pion form factor for timelike transferred momenta. In particular, this is the case for a wave function of the Gaussian type (18) widely used in composite models, and this result holds independently of the model parameter 2016) values. We therefore encounter the problem of finding a wave function that produces resonances and establishing the relation between the locus of the resonance in the pion form factor and the locus of the wave function poles.…”

“…Values of all parameters used in these expressions are taken from the π-meson calculation, see, e.g., Ref. [18].…”

“…So, the following parameters enter our calculations: 1) the parameters that describe the constituent quarks per se (the quark mass M, the anomalous magnetic moments of the quarks κ q , that enter our formulae through the sum s q = κ u + κd, and the quark mean square radius (MSR) r 2 q ); 2) the parameters b π,ρ that enter the quark wave functions (18), (19) and is determined by the quark interaction potential.…”

Electroweak properties ofρ-meson in the instant form of relativistic quantum mechanics

“…The choice of form factor of the constituent quark as (15), (16) due to the fact that the asymptotic of the electromagnetic pion form factor at Q 2 → ∞ obtained in our nonperturbative approach with (16) does coincide with that predicted by QCD including the pre-asymptotic factor (see, e.g., [21] for details).…”