${\eta }^{\prime }\to \gamma \gamma$ and the topological susceptibility

Abstract

The radiative decays ${\eta }^{\prime }(\eta )\text{rta}\gamma \gamma$ 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 ${\eta }^{\prime }$. It is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of ${\eta }^{\prime }(\eta )\text{rta}\gamma \gamma$.

Comments: 4 pages, LaTeX, uses espcrc2.sty. To appear in Proceedings, QCD99 Montpellier