Abstract
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.
Highlights
One of the fundamental features of QCD, the axial anomaly, has many theoretical and phenomenological applications
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
Substituting the transition form factors (TFFs) (25) directly into the anomaly sum rule (ASR) for the singlet current (19), we evaluate the s0 as a function of Q2
Summary
One of the fundamental features of QCD, the axial anomaly, has many theoretical and phenomenological applications. It can be derived considering the imaginary part of the VVA diagram [3], where the anomaly arises as a sum rule for a structure function in the dispersion representation of the three point VVA correlation function [4,5,6] (for a review, see [7,8]) Such sum rules, combined with the global quark-hadron duality, can be employed to study the γγ decays of the pseudoscalar mesons as well as their transition form factors γγà → π0; η; η0. Was related to the pion TFF [9], while the anomaly sum rule for the octet axial current was developed and used to study the η; η0 TFFs, including the cases of spacelike [10,11,12,13] and timelike [14] photon virtualities.
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