(Anti-)self-dual homogeneous gluon field and axial anomaly in QCD

The transition form factor, decay width and charge form factor of pion are calculated within the model of induced nonlocal quark currents based on the assumption that the nonperturbative QCD vacuum can be characterized by a homogeneous (anti-)self-dual gluon field. It is shown that the interaction of the quark spin with the vacuum gluon field, being responsible in the model for the chiral symmetry breaking and the spectrum of light mesons, can also play the decisive role in forming the transition form factor and two-photon decay width. Asymptotic behavior of quark loops in the presence of the background gluon field for large momentum transfer is discussed.