Strong decay patterns of the hidden-charm pentaquark states $P_c(4380)$ and $P_c(4450)$

Abstract: With the heavy quark symmetry and spin rearrangement scheme, we study the strong decay behavior of the hidden-charm pentaquark states with $J^P={\frac{3}{2}}^{\pm}, {\frac{5}{2}}^{\pm}$ assuming they are molecular candidates composed of ${\bar D}^{(\ast)}$ and ${\Sigma}_c^{(\ast)}$. We obtain several typical ratios of the partial decay widths of the hidden-charm pentaquarks. For the three S-wave $(\bar{D}\Sigma_c^*)$, $(\bar{D}^*\Sigma_c)$ and $(\bar{D}^\Sigma_c^)$ molecular pentaquarks with $J^P={{3}/{2}}^{-}$, we have obtained the ratio of their $J/\psi N$ decay widths: $\Gamma\left[(\bar D{\Sigma^{\ast}_c})\right]:\Gamma\left[({\bar D}^{\ast}{\Sigma}_c)\right]:\Gamma\left[({\bar D}^{\ast}{\Sigma^{\ast}_c})\right]=2.7:1.0:5.4$, which may be useful to further test the possible molecular assignment of the $P_c$ states.