Quark-Glue Structure of the $\eta$ and ${\eta }^{\prime }$ Mesons, with Application to $\psi \to \eta \left({\eta }^{\prime }\right)\gamma$ and ${\psi }^{\prime }\to \psi \eta$

A careful analysis of the Ward identities involving the axial divergences ${\partial }^{\mu }{A}_{\mu }$, combined with a fit to the $2\gamma$ decays of the ${\pi }^0$, $\eta$, and ${\eta }^{\prime }$ via the quantum electrodynamic anomaly, allows a consistent description of the pseudoscalar nonet with zero (or small) quantum chromodynamic surface term. The gluonic matrix elements $〈0\left|F\tilde{F}\right|P〉$ of the $\eta$ and ${\eta }^{\prime }$ obtained from the Ward identities lead to a good quantitative understanding of the relative rates $\frac{(\psi \to {\eta }^{\prime }\gamma )}{(\psi \to \eta \gamma )}$, and a qualitative understanding of the nonsuppression of ${\psi }^{\prime }\to \psi \eta$.