$P_c$ states in the mixture of molecular and pentaquark pictures

We systematically study hidden charm pentaquark states in the constituent quark model with a general Hamiltonian for multiquark systems, considering the coupling between the ${\mathrm{\Sigma }}_c^{(\ast )}{\bar{D}}^{(\ast )}$ molecular states and the $q^{3}c\bar{c}$ compact pentaquark states by the one-gluon exchange hyperfine interaction. The ground state hidden-charm pentaquark mass spectra and the strong decay widths are calculated. This work suggests that $P_c(4312)$, $P_c(4457)$ and $P_c(4380)$ resonances might be mainly ${\mathrm{\Sigma }}_c\bar{D}$, ${\mathrm{\Sigma }}_c{\bar{D}}^{\ast }$ and ${\mathrm{\Sigma }}_c^{\ast }\bar{D}$ hadronic molecules respectively, and $P_c(4440)$ might include sizable pentaquark components.