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The $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ observed by the LHCbCollaboration are very likely to be $S$-wave $\Sigma_c\bar{D}^{(*)}$ molecularcandidates due to their near-threshold character. In this work, we study thehidden-charm decay modes of these $P_c$ states, $P_c\to J/\psi p(\eta_cp)$,using a quark interchange model. The decay mechanism for the $P_c\to J/\psip(\eta_cp)$ processes arises from the quark-quark interactions, where allparameters are determined by the mass spectra of mesons. We present our resultsin two scenarios. In scenario I, we perform the dynamical calculations andtreat the $P_c$ states as pure $\Sigma_c \bar D^{(*)}$ molecules. In scenarioII, after considering the coupled channel effect between different flavorconfigurations $\Sigma^{(*)}_c\bar D^{(*)}$, we calculate these partial decaywidths again. The decay patterns in these two scenarios can help us to explorethe molecular assignment and the inner flavor configurations for the $P_c$states. In particular, the decay widths of $\Gamma(P_c(4312)\to\eta_cp)$ arecomparable to the $J/\psi p$ decay widths in both of these two scenarios.Future experiments like LHCb may confirm the existence of the $P_c(4312)$ inthe $\eta_cp$ channel.

Probing hidden-charm decay properties of $P_c$ states in a molecular scenario