Strong decay mode $J/\psi p$ of hidden charm pentaquark states $P_c^+(4380)$ and $P_c^+(4450)$ in $\Sigma_c \bar{D}^*$ molecular scenario

We study the strong decay channels $P_c^+(4380) \to J/\psi p$ and $P_c^+(4450) \to J/\psi p$ under $\Sigma_c \bar{D}^*$ molecular state ansatz. With various spin-parity assignments, the partial decay widths of $J/\psi p$ final state are calculated. Our results show that all the $P$ wave $\Sigma_c {\bar D}^*$ assignments are excluded, while $S$ wave $\Sigma_c {\bar D}^*$ pictures for $P_c(4380)$ and $P_c(4450)$ are both allowed by present experimental data. The $J^P=3/2^-$ $\Sigma_c^* \bar{D}$ and $\Sigma_c^* \bar{D}^*$ molecules are also discussed in the heavy quark limit, and find that the $\Sigma_c^* \bar{D}$ system for $P_c(4380)$ is possible. More experimental information on spin-parities and partial decay widths and theoretical investigations on other decay modes are needed to clarify the nature of the two $P_c$ states.