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 [Nucl. Phys. B27, 525 (1971).] 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' -> gamma gamma* transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element < 0 vertical bar G (G) over tilde vertical bar gamma gamma* (q(2))) 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.