On high $Q^{2}$ behavior of the pion form factor for transitions $γ^{\ast}γ\to π^{0}$ and $γ^{\ast} γ^{\ast}\toπ^{0}$ within the nonperturbative approach

The behavior of the pion form factor for the transitions $\gamma ^{\star}\gamma \to \pi ^{0}$ and $\gamma ^{\star}\gamma ^{\star}\to \pi ^{0}$ at large values of space-like photon momenta is estimated within the nonlocal covariant quark-pion model. It is shown that in general the asymptotic coefficient depends dynamically on the ratio of the constituent quark mass and the average virtuality of quarks in the vacuum; and kinematically on the ratio of photon virtualities. This result does not confirm the statement made by D. Kekez and D. Klabu\v{c}ar [Phys. Lett. B 457 (1999) 359] about universality of the asymptotic coefficient within the nonperturbative approach.