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).] a non-Abelian case with arbitrary photon virtualites. derive sum rule for singlet current obtain ${\ensuremath{\pi}}^{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}$ transition form factors. Using them, we established behavior of nonperturbative gluon matrix element $⟨0|G\stackrel{\texttildelow{}}{G}|\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}({q}^{2})⟩$ in both spacelike timelike regions. found significant contribution processes one virtual photon, comparable that electromagnetic anomaly. The duality between vector channels was observed: values intervals mixing parameters channel were related resonances' masses residues. possibility light pseudoscalar glueball-like state is conjectured.