Anomalies, $\eta$ , $\eta$' as keys to glueballs

Abstract

Glueballs are the most straightforward prediction of QCD, yet while they have likely been produced, none has been unequivocally identified. We pursue a backdoor approach through anomalies, and singularly the $\eta$ and $\eta$' which brings light to this irritating situation. In particular, we advocate to consider the full decay chain $J/\psi \rightarrow X \gamma , X \rightarrow \eta \eta'$ (into glue-rich states followed by glue-rich decays). We also suggest new BES III searches, namely for the $\pi_1$ into $\eta(') \pi^0$, (this would be the partner of their recently observed $\eta_1(1855)$). Another useful investigation would be for other channels (or semi-inclusive) $f_0 (1500)$ decays (see last section)