Dispersive approach to non-Abelian axial anomaly

TL;DR

This paper applies a dispersive approach to axial anomalies to analyze two-photon decays of eta and eta' mesons, deriving an anomaly sum rule and estimating gluon and electromagnetic anomaly contributions.

Contribution

It introduces a dispersive method to evaluate axial anomalies in meson decays, generalizes low energy theorems for mixed states, and estimates anomaly contributions.

Findings

Gluon anomaly contribution is significantly suppressed.

Derived an anomaly sum rule incorporating strong and electromagnetic anomalies.

Numerically estimated anomaly contributions to meson decays.

Abstract

Manifestations of strong and electromagnetic axial anomalies in two-photon decays of $\eta$ and $\eta'$ mesons are studied. Applying dispersive approach to axial anomaly in the singlet current, we obtain an anomaly sum rule containing strong and electromagnetic anomaly contributions. The relevant low energy theorem was generalized to the case of mixed states and used to evaluate the subtraction constant of the strong anomaly-related form factor $\langle 0 |G\tilde{G} |\gamma\gamma \rangle$. We made a numerical estimation of the contributions of gluon and electromagnetic anomalies to the two-photon decays of $\eta$ and $\eta'$ mesons and found significant suppression of the gluon anomaly contribution.