$η'\toγγ$ and the topological susceptibility

Abstract

The radiative decays $η'(η)\rtaγγ$ 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 $η'$. It is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of $η'(η)\rtaγγ$.