Influence of the axial anomaly on the decay $N(1535)\to N\eta$

Abstract

The decay width of $N(1535)\to N\eta$ is as large as that of $N(1535)\to N\pi$. This is in evident conflict with simple expectations based on flavor symmetry and phase space. Similarly, the decay width of $\Lambda (1670)\to \Lambda (1116)\eta$ 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 $\eta$ 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 $\eta$ meson, such as $N(1535)\to N\eta$. Moreover, a strong coupling of $N(1535)$ to $N{\eta }^{\prime }$ emerges (this is important for studies of ${\eta }^{\prime }$ production processes). Our approach shows that $N(1535)$ is predominantly the chiral partner of $N(939)$, and $\Lambda (1670)$ the chiral partner of $\Lambda (1116)$. Finally, our formalism can be used to couple the pseudoscalar glueball $\tilde{G}$ to baryons. We expect a large cross section for the reaction $\bar{p}p\to \tilde{G}\to \bar{p}p(1535)$, which can be experimentally tested in the future PANDA experiment.

Comments: 14 pages, 4 figures, to appear in Phys. Rev. D