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

TL;DR

This paper investigates how the axial $U(1)_A$ anomaly influences the decay processes of excited baryons, proposing an effective model that explains enhanced decay widths and predicts new couplings relevant for future experiments.

Contribution

It introduces a new $U(1)_A$ anomalous term in an effective hadronic model, explaining enhanced baryon decays and chiral partner assignments, with implications for $ar{p}p$ reactions and $ ilde{G}$ coupling.

Findings

The $U(1)_A$ anomaly explains the large decay width of $N(1535) ightarrow N exteta$.

$N(1535)$ is identified as the chiral partner of $N(939)$.

Predicted large cross section for $ar{p}p ightarrow ilde{G} ightarrow ar{p}p(1535)$.

Abstract

The decay width of $N(1535)\rightarrow N\eta$ is as large as that of $N(1535)\rightarrow N\pi$. This is in evident conflict with simple expectations based on flavor symmetry and phase space. Similarly, the decay width of $\Lambda(1670) \rightarrow \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 $N(1535)\rightarrow N\eta$. 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 $\bar{p}p \rightarrow \tilde{G} \rightarrow \bar{p}p(1535)$, which can be experimentally tested in the future PANDA experiment.