Roles of the $N(1535)$ and $a_0(980)$ in the process ${\mathrm{\Lambda }}_c^{+}\to {\pi }^{+}\eta n$

We have investigated the process ${\mathrm{\Lambda }}_c^{+}\to {\pi }^{+}\eta n$ 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 $R$ = $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to a_0(980{)}^{+}n)\mathrm{/}\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to {\pi }^{+}\eta n)\approx 0.313$. Our results can be tested by BESIII, Belle~II, and the proposed Super Tau-Charm Facility experiments in the future.