Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$

Abstract

We study the newly reported hidden-charm pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the LHCb Collaboration, in the framework of the effective-range expansion and resonance compositeness relations. The scattering lengths and effective ranges from the $S$-wave ${\Sigma }_c\bar{D}$ and ${\Sigma }_c{\bar{D}}^{\ast }$ scattering are calculated by using the experimental results of the masses and widths of the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$. Then we calculate the couplings between the $J/\psi p,{\Sigma }_c\bar{D}$ channels and the pentaquark candidate $P_c(4312)$, with which we further estimate the probabilities of finding the $J/\psi p$ and ${\Sigma }_c\bar{D}$ components inside $P_c(4312)$. The partial decay widths and compositeness coefficients are calculated for the $P_c(4440)$ and $P_c(4457)$ states by including the $J/\psi p$ and ${\Sigma }_c{\bar{D}}^{\ast }$ channels. Similar studies are also carried out for the three $P_c$ states by including the ${\Lambda }_c{\bar{D}}^{\ast }$ and ${\Sigma }_c{\bar{D}}^{(\ast )}$ channels.

Comments: 11 pages, 4 tables. To match the published version in Phys.Lett.B