Influence of the axial anomaly on the decay $N(1535) \rightarrow Nη$
The decay width of $N(1535)\rightarrow Nη$ is as large as that of $N(1535)\rightarrow Nπ$. This is in evident conflict with simple expectations based on flavor symmetry and phase space. Similarly, the decay width of $Λ(1670) \rightarrow Λ(1116) η$ is larger than predicted by flavor symmetry. In this work, we propose that the axial $U(1)_{A}$ anomaly is responsible for an enhanced coupling of (some) excited baryons to the $η$ meson. We test this idea by including a new, chirally symmetric but $U(1)_{A}$ anomalous, term in an effective hadronic model decribing baryons and their chiral partners in the mirror assignment. This term enhances the decay of the chiral partners into baryons and an $η$ meson, such as $N(1535)\rightarrow Nη$. Moreover, a strong coupling of $N(1535)$ to $N η^\prime $ emerges (this is important for studies of $η^\prime$ production processes). Our approach shows that $N(1535)$ is predominantly the chiral partner of $N(939)$, and $Λ(1670)$ the chiral partner of $Λ(1116)$. Finally, our formalism can be used to couple the pseudoscalar glueball $\tilde{G}$ to baryons. We expect a large cross section for the reaction $\bar{p}p \rightarrow \tilde{G} \rightarrow \bar{p}p(1535)$, which can be experimentally tested in the future PANDA experiment.