$\eta'\to\gamma\gamma$ and the topological susceptibility

TL;DR

This paper investigates the radiative decays of eta and eta prime mesons, incorporating gluonic effects into axial anomaly formulas, and proposes a method to extract topological susceptibility from decay measurements.

Contribution

It introduces modified PCAC and Dashen formulas accounting for gluonic contributions and links decay data to topological susceptibility in QCD with dynamical quarks.

Findings

Modified PCAC formulas including gluonic effects.

Generalized Witten--Veneziano formula for eta' mass.

Method to extract topological susceptibility from decay measurements.

Abstract

The radiative decays $\eta'(\eta)\rta\gamma\gamma$ are discussed. The modifications of the conventional PCAC formulae due to the gluonic contribution to the flavour singlet axial anomaly are given. The decay constants satisfy a modified Dashen formula which generalises the Witten--Veneziano formula for the mass of the $\eta'$. It is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of $\eta'(\eta)\rta\gamma\gamma$.