arXiv2020
Within the chiral unitary approach and with the constraints of heavy quark spin symmetry, we study the coupled channel interactions of ${\bar D}^{(*)}Σ_c^{(*)}$ channels, close to whose thresholds three pentaquark-like $P_c$ states have been reported by the LHCb Collaboration. In the present work, we take into account the contributions of pion exchanges via box diagrams to the interaction potentials, and therefore lift the degeneracy in the masses of ${\bar D}^*Σ_c^{(*)}$ spin multiplets. Fitting the $J/ψp$ invariant mass distributions in the $Λ_b^0 \to J/ψK^- p$ decay, we find that the LHCb pentaquark states can not be reproduced in the direct $J/ψp$ production in the $Λ_b^0$ decay, and can only be indirectly produced in the final state interactions of the $Λ_b^0$ decay products, ${\bar D}^*Σ_c^{(*)}$, which further supports the nature of these states as $\bar{D}Σ_c$ molecules. Based on the fit results obtained, we study the partial decay widths/branching ratios to other decay channels, $\bar{D}^* Λ_c$, $\bar{D} Λ_c$, and $η_c N$, and the corresponding invariant mass distributions. The resonances with $J^P=\frac{1}{2}^-$, $P_c(4312)$, $P_c(4440)$ and the one of $\bar{D}^* Σ_c^*$ around 4500 MeV, have large partial decay width into $η_c N$, and thus, can be easily seen in the $η_c N$ invariant mass distributions. By contrast, the states with $J^P=\frac{3}{2}^-$, $P_c(4457)$, the (predicted) narrow $P_c(4380)$ and the bound state of $\bar{D}^* Σ_c^*$ with a mass of about 4520 MeV, do not decay into $η_c N$. Therefore, the $η_c N$ channel should be studied in future to provide further insights into the nature of these states, especially that of the $P_c(4440)$ and $P_c(4457)$.