Decay behaviors of Pc hadronic molecules
The $P_c(4380)$ and $P_c(4450)$ states observed recently by LHCb experiment were proposed to be either $\bar{D} Σ_c^*$ or $\bar{D}^* Σ_c$ S-wave bound states of spin parity $J^P={\frac32}^-$. We analyze the decay behaviors of such two types of hadronic molecules within the effective Lagrangian framework. With branching ratios of ten possible decay channels calculated, it is found that the two types of hadronic molecules have distinguishable decay patterns. While the $\bar{D} Σ_c^*$ molecule decays dominantly to $\bar{D}^* Λ_c$ channel with a branching ratio by 2 orders of magnitude larger than to $\bar{D}Λ_c$, the $\bar{D}^* Σ_c$ molecule decays to these two channels with a difference of less than a factor of 2. Our results show that the total decay width of $P_c(4380)$ as the spin-parity-${\frac32}^-$ $\bar{D} Σ_c^*$ molecule is about a factor of 2 larger than the corresponding value for the $\bar{D}^* Σ_c$ molecule. It suggests that the assignment of $\bar{D} Σ_c^*$ molecule for $P_c(4380)$ is more favorable than the $\bar{D}^* Σ_c$ molecule. In addition, $P_c(4450)$ seems to be a $\bar{D}^* Σ_c$ molecule with $J^P={\frac52}^+$ in our scheme. Based on these partial decay widths of $P_c(4380)$, we estimate the cross sections for the reactions $γp \to J/ψp $ and $ πp\to J/ψp $ through the s-channel $P_c(4380)$ state. The forthcoming $γp$ experiment at JLAB and $πp$ experiment at JPARC should be able to pin down the nature of these $P_c$ states.