Anomalous interactions between mesons with nonzero spin and glueballs

Topologically nontrivial fluctuations control the anomalous interactions for the $\eta$ and and $\eta \mathrm{\prime }$ pseudoscalar mesons. We consider the anomalous interactions for mesons with higher spin, the heterochiral nonets with $J^{PC}=1^{+-}$ and $2^{-+}$. Under the approximation of a dilute gas of instantons, the mixing angle between non-strange and strange mesons decreases strongly as $J$ increases, and oscillates in sign. Anomalous interactions also open up new, rare decay channels. For glueballs, anomalous interactions indicate that the $X(2600)$ state is primarily gluonic.