Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball

We generalize the dispersive approach to axial anomaly by A.D. Dolgov and V.I. Zakharov to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the $\pi^0,\eta,\eta'\rightarrow\gamma\gamma^*$ transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element $\langle 0 |G\tilde{G} |\gamma\gamma^*(q^2) \rangle$ in both spacelike and timelike regions. We found a significant contribution of the non-Abelian axial anomaly to the processes with one virtual photon, comparable to that of the electromagnetic anomaly. The duality between the axial and the vector channels was observed: the values of duality intervals and mixing parameters in the axial channel were related to vector resonances' masses and residues. The possibility of a light pseudoscalar glueball-like state is conjectured.