Photon-pion transition form factor at high photon virtualities within the nonlocal chiral quark model

Recently, the BABAR collaboration reported the measurments of the photon-pion transition form factor $F_{\pi\gamma\gamma^{\ast}}(Q^2) $, which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exists two asymptotic regimes for the pion transition form factor. One regime with asymptotics $F_{\pi\gamma^{\ast}\gamma}(Q^2)\sim1/Q^2$ corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as $F_{\pi\gamma^{\ast}\gamma}(Q^2)\sim\ln(Q^2)/Q^2$. Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.