Decays of $P_c$ into $J/\psi N$ and ${\eta }_{c}N$ with heavy quark spin symmetry

Abstract

We investigate the consequences of heavy quark spin symmetry (HQSS) on hidden-charm pentaquark $P_c$ states. As has been proposed before, assuming the $P_c(4440)$ and the $P_c(4457)$ as $S$-wave ${\bar{D}}^{\ast }{\Sigma }_c$ molecules, seven hadronic molecular states composed of $\bar{D}{\Sigma }_c$, $\bar{D}{\Sigma }_c^{\ast }$, ${\bar{D}}^{\ast }{\Sigma }_c$, and ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ can be obtained, with the $\bar{D}{\Sigma }_c$ molecule corresponding to the $P_c(4312)$. These seven states can decay into $J/\psi N$ and ${\eta }_{c}N$, and we use HQSS to predict ratios of partial widths of the $S$-wave decays. For the decays into $J/\psi N$, it is found that among all six $P_c$ molecules with spin $1/2$ or $3/2$, at least four states decay much more easily into the $J/\psi N$ than the $P_c(4312)$, and two of them couple dominantly to the ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$. While no significant peak around the ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ threshold is found in the $J/\psi p$ distribution, these higher $P_c$ states either are produced with lower rates or some special production mechanism for the observed $P_c$ states might play an important role, such as an intricate interplay between the production of pentaquarks and triangle singularities.

Comments: 24 pages, 2 figures