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

TL;DR

This paper extends the dispersive approach to the non-Abelian axial anomaly, deriving transition form factors, analyzing gluon matrix elements, and exploring duality and the potential existence of a light pseudoscalar glueball.

Contribution

It generalizes the dispersive approach to non-Abelian axial anomalies and establishes duality relations between axial and vector channels, also proposing a pseudoscalar glueball candidate.

Findings

Significant non-Abelian axial anomaly contribution to processes with virtual photons.

Established duality between axial and vector channels with related parameters.

Proposed the existence of a light pseudoscalar glueball-like state.

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.