Revisiting the nature of the $P_c$ pentaquarks

Abstract

The nature of the three narrow $P_c$ states, i.e., $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, is under intense discussion since their discovery from the updated analysis by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. \bf{124}, 072001 (2020)] by including the ${\Lambda }_c{\bar{D}}^{(\ast )}$ and ${\eta }_{c}p$ as explicitly in addition to the $J/\psi p$, as required by unitarity and heavy quark spin symmetry (HQSS). Since inelastic parameters are very badly constrained by the current data, three schemes are considered: (a) scheme I with pure contact interactions and without the ${\Lambda }_c{\bar{D}}^{(\ast )}$ interactions, (b) scheme II, where the one-pion exchange is added to scheme I, and (c) scheme III, where the ${\Lambda }_c{\bar{D}}^{(\ast )}$ are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with $S$-$D$ mixing contact terms. We demonstrate that the experimental data for the $J/\psi p$ invariant mass distribution are consistent with the interpretation of the $P_c(4312)$ and $P_c(4440)/P_c(4457)$ as ${\Sigma }_c\bar{D}$ and ${\Sigma }_c{\bar{D}}^{\ast }$ hadronic molecules, respectively, and that the data show clear evidence for a new narrow $P_c(4380)$, as a ${\Sigma }_c^{\ast }\bar{D}$ molecule, which should exist as a consequence of HQSS. While two equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the $P_c(4440)$ and $P_c(4457)$ being $J^P=3/2^{-}$ and $1/2^{-}$, respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the $P_c(4440)$ and the $P_c(4457)$ in the corresponding ${\Sigma }_c^{(\ast )}\bar{D}$ and ${\eta }_{c}p$ mass distributions allow one to confirm the quantum numbers given above, once the data are available.

Comments: 57 pages, 14 figures, and 13 tables