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

Anomalous interactions between mesons with nonzero spin and glueballs