Roles of the $N(1535)$ and $a_0(980)$ in the process $\Lambda_c^+ \to \pi^+\eta n$

TL;DR

This paper investigates the roles of the $N(1535)$ resonance and $a_0(980)$ meson in the decay process $oldsymbol{ ext{Lambda}_c^+ o ext{pi}^+ ext{eta} n}$, revealing near-threshold enhancements and cusp structures that can be tested experimentally.

Contribution

It introduces a model considering the dynamical generation of $N(1535)$ and $a_0(980)$, providing predictions for invariant mass distributions in $ ext{Lambda}_c^+$ decay.

Findings

Significant near-threshold enhancement in $ ext{eta} n$ invariant mass distribution.

Clear cusp structure of $a_0(980)$ in $ ext{pi}^+ ext{eta}$ invariant mass.

Estimated ratio $R oughly 0.313$ for specific decay channels.

Abstract

We have investigated the process $\Lambda_c^+ \to \pi^+\eta n$ by taking into account the contributions from the nucleon resonance $N(1535)$ and the scalar meson $a_0(980)$, which could be dynamically generated by the interaction of the $S$-wave pseudosalar meson-octet baryon and the $S$-wave pseudosalar meson-pseudosalar meson, respectively. Our results show that, in $\eta n$ invariant mass distribution, there is a significant near-threshold enhancement structure, which could be associated with $N(1535)$. On the other hand, one can find a clear cusp structure of $a_0(980)$ in $\pi^+\eta$ invariant mass distribution. We further estimate the ratio $R$ = $\mathcal{B}(\Lambda_c^+ \to a_0(980)^+ n)/\mathcal{B}(\Lambda_c^+ \to \pi^+\eta n)\approx 0.313$. Our results can be tested by BESIII, Belle~II, and the proposed Super Tau-Charm Facility experiments in the future.