Studying the heavy quark spin symmetry multiplet of hadronic molecules ${\bar{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{(\ast )}$ in the three-body decays of ${\bar{D}}^{(\ast )}{\mathrm{\Lambda }}_c\pi$

The decay behavior of an exotic state can be used to probe its internal structure. We note that the hidden-charm pentaquark states, $P_{\psi }^N(4312)$, $P_{\psi }^N(4440)$, and $P_{\psi }^N(4457)$, have only been observed in the $J\mathrm{/}\psi p$ channel. In this work, we employ the effective Lagrangian approach to systematically investigate the two-body and three-body decays of the heavy quark spin symmetry multiplet of hadronic molecules ${\bar{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{(\ast )}$. Our results show that the partial decay widths of the hidden-charm pentaquark molecules into ${\bar{D}}^{(\ast )}{\mathrm{\Lambda }}_c\pi$ are sizable so that ${\bar{D}}^{(\ast )}{\mathrm{\Lambda }}_c\pi$ are promising channels to search for them, which can help clarify their molecular nature.