Molecular interpretation of the LHCb pentaquarks from an analysis of $J/\psi p$ spectrum

Abstract

A coupled-channel approach including the ${\Lambda }_c{\bar{D}}^{(\ast )}$ and ${\eta }_{c}p$ channels in addition to the ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$ and $J/\psi p$ channels, as required by unitarity and heavy quark spin symmetry (HQSS), is applied to the hidden-charm pentaquark $P_c$ states, i.e., $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by LHCb Collaboration. It is demonstrated that to obtain cutoff independent results, the one-pion exchange potential in the multichannel systems is to be supplemented with next-leading order counter terms responsible for the $S$-wave-to-$D$-wave transitions. We show that the experimental data for the $J/\psi p$ mass distributions are fully in line with the ${\Sigma }_c\bar{D}$ and ${\Sigma }_c{\bar{D}}^{\ast }$ hadronic molecular interpretation of the $P_c(4312)$ and $P_c(4440)/P_c(4457)$, respectively. A narrow ${\Sigma }_c^{\ast }\bar{D}$ molecule around 4.38 GeV is required by the HQSS with the evidence for its existence seen in the $J/\psi p$ spectrum. Moreover, we predict the line shapes for the elastic and inelastic channels.

Comments: Contribution to the proceedings of A Virtual Tribute to Quark Confinement and the Hadron Spectrum (vConf21), August 2nd-6th 2021, to be published in EPJ Web of Conferences