Anomalous $\eta/\eta^\prime$ Decays: The Triangle and Box Anomalies

We examine the decay modes $\eta/\etp\ra \pi^+ \pi^- \gamma$ within the context of the Hidden Local Symmetry (HLS) Model. Using numerical information derived in previous fits to $VP\gamma$ and $Ve^+e^-$ decay modes in isolation and the $\rho$ lineshape determined in a previous fit to the pion form factor, we show that all aspects of these decays can be predicted with fair accuracy. Freeing some parameters does not improve the picture. This is interpreted as a strong evidence in favor of the box anomaly in the $\eta/\etp$ decays, which occurs at precisely the level expected. We also construct the set of equations defining the amplitudes for $\eta/\etp\ra \pi^+ \pi^- \gamma$ and $ \eta/\etp \ra \ggam $ at the chiral limit, as predicted from the anomalous HLS Lagrangian appropriately broken. This provides a set of four equations depending on only one parameter, instead of three for the traditional set. This is also shown to match the (two--angle, two--decay--constant) $\eta-\etp$ mixing scheme recently proposed and is also fairly well fulfilled by the data. The information returned from fits also matches expectations from previously published fits to the $VP\gamma$ decay modes in isolation.