$P_c$ Resonances in Molecular Picture.

We study hidden-charm pentaquarks in the baryon-meson molecule picture within the framework of the constituent quark model, considering all the possible quark configurations for the ground state. The strong decays of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ resonances are investigated. It is found that pentaquark states of all quark configurations in the model can decay through the $N J/\psi$ channel, but only five pentaquark states may decay dominantly in open-charm modes. The partial decay widths in the $p\eta_c$ channel are in the same order as in the $p J/\psi$ channel for $J^P=1/2^-$ baryon-meson pentaquark states, but the $p\eta_c$ channel is forbidden for $J^P=3/2^-$ states. For $P_c(4440)$ and $P_c(4457)$, the $p \eta_c$, $\Sigma_c\bar{D}$ and $\Lambda_c^+\bar{D}$ channels are open only for $J^P=1/2^-$ and the $\Sigma_c^*\bar{D}$ channel is open only for $J^P=3/2^-$ while for $P_c(4312)$, due to the mass threshold of $\Sigma_c\bar{D}$ and $\Sigma_c^*\bar{D}$ higher than 4312 MeV, the $p \eta_c$ and $\Lambda_c^+\bar{D}$ channels are open for $J^P=1/2^-$ but no open-charm cannel open for $J^P=3/2^-$. We strongly suggest that the spin of the $P_c$ resonances may be determined in experiments by investigating the $p \eta_c$ and open-charm channels.