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

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 $Σ_c^{(\ast)}$. We obtain several typical ratios of the partial decay widths of the hidden-charm pentaquarks. For the three S-wave $(\bar{D}Σ_c^*)$, $(\bar{D}^*Σ_c)$ and $(\bar{D}^*Σ_c^*)$ molecular pentaquarks with $J^P={{3}/{2}}^{-}$, we have obtained the ratio of their $J/ψN$ decay widths: $Γ\left[(\bar D{Σ^{\ast}_c})\right]:Γ\left[({\bar D}^{\ast}Σ_c)\right]:Γ\left[({\bar D}^{\ast}{Σ^{\ast}_c})\right]=2.7:1.0:5.4$, which may be useful to further test the possible molecular assignment of the $P_c$ states.