Influence of confining gluon configurations on the $P\to\gamma^*\gamma $ transition form factors

Abstract

Transition form factors $F_{P\gamma^*\gamma^{(*)}}$ of pseudoscalar mesons are studied within the framework of the domain model of confinement, chiral symmetry breaking and hadronization. In this model, the QCD vacuum is described by the statistical ensemble of domain wall networks which represents the almost everywhere homogeneous Abelian (anti-)self-dual gluon field configurations. Calculations of the form factors are performed consistently with mass spectra of light, heavy-light and double-heavy mesons, their weak and strong decay constants. Influence of the nonperturbative intermediate range gluon fields on asymptotic behaviour of pion transition form factor is of particular interest, as it can potentially lead to the growth of $Q^2F_{\pi\gamma^*\gamma}(Q^2)$. It is found that $Q^2F_{\pi\gamma^*\gamma}(Q^2)$ approaches a constant value at asymptotically large $Q^2$. However, this limit differs from the standard factorization bound, though for pion form factor complies with Belle data more likely than with BaBar ones. At the same time the generally accepted factorization bound is shown to be satisfied for the case of the symmetric kinematics, $Q^2F_{P\gamma^*\gamma^*}(Q^2)$. Peculiarities of description of $\eta$, $\eta'$ and $\eta_c$ form factors within the model are discussed in detail.