On high $Q^{2}$ behavior of the pion form factor for transitions $\gamma^{\ast} \gamma \to \pi^{0}$ and $\gamma ^{\ast} \gamma^{\ast} \to \pi^{0}$ within the nonlocal quark-pion model

TL;DR

This paper investigates the high $Q^2$ behavior of the pion transition form factor within a nonlocal quark-pion model, revealing its dependence on quark virtuality and nonperturbative QCD vacuum effects.

Contribution

It introduces a dynamic and kinematic analysis of the pion form factor at large momentum transfers, linking the form factor to the quark-pion vertex and QCD vacuum nonlocality.

Findings

The leading asymptotic coefficient depends on quark mass and virtuality ratio.

The form factor's kinematic dependence relates to the pion light-cone distribution amplitude.

High momentum transfer form factor is sensitive to nonlocality size of QCD vacuum fluctuations.

Abstract

The behavior of the transition pion form factor for processes \gamma^*\gamma -> \pi^0 and \gamma^* \gamma^* -> \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 coefficient of the leading asymptotic term 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. The kinematic dependence of the transition form factor allows us to obtain the relation between the pion light-cone distribution amplitude and the quark-pion vertex function. The dynamic dependence indicates that the transition form factor \gamma^* \gamma -> \pi^0 at high momentum transfers is very sensitive to the nonlocality size of nonperturbative fluctuations in the QCD vacuum.