Search for hidden-charm pentaquark states in three-body final states

Abstract

The three pentaquark states, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by the LHCb Collaboration in 2019, are widely recognized as ${\bar{D}}^{(\ast )}{\Sigma }_c$ hadronic molecules. Together with their four ${\bar{D}}^{(\ast )}{\Sigma }_c^{\ast }$ partners dictated by heavy quark spin symmetry they present a complete multiplet of hadronic molecules of ${\bar{D}}^{(\ast )}{\Sigma }_c^{(\ast )}$. It is widely recognized that to understand their nature, other discovery channels play an important role. In this work, we investigate two three-body decay modes of the ${\bar{D}}^{(\ast )}{\Sigma }_c^{(\ast )}$ molecules. The tree-level modes proceed via off-shell ${\Sigma }_c^{(\ast )}$ baryons, ${\bar{D}}^{(\ast )}{\Sigma }_c^{(\ast )}\to {\bar{D}}^{(\ast )}\left({\Sigma }_c^{(\ast )}\to {\Lambda }_c\pi \right)\to {\bar{D}}^{(\ast )}{\Lambda }_c\pi$, while the triangle-loop modes proceed through ${\bar{D}}^{\ast }{\Sigma }_c^{(\ast )}\to J/\psi N\pi$, ${\eta }_{c}N\pi$ via $\bar{D}{\Sigma }_c^{(\ast )}$ rescattering to $J/\psi N$ and ${\eta }_{c}N$. Our results indicate that the decay widths of the $P_c(4457)$ and ${\bar{D}}^{(\ast )}{\Sigma }_c^{\ast }$ states into ${\bar{D}}^{(\ast )}{\Lambda }_c\pi$ are several MeV, as a result can be observed in the upcoming Run 3 and Run 4 of LHC. The partial decay widths into ${\bar{D}}^{(\ast )}{\Lambda }_c\pi$ of the $P_c(4312)$ and $P_c(4440)$ states range from tens to hundreds of keV. In addition, the partial decay widths of ${\bar{D}}^{\ast }{\Sigma }_c$ molecules into $J/\psi N\pi$ and ${\eta }_{c}N\pi$ are several keV and tens of keV, respectively, and the partial decay widths of ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ molecules into $J/\psi N\pi$ vary from several keV to tens of keV. These three-body decay modes of the pentaquark states are of great value to further observations of the pentaquark states and to a better understanding of their nature.

Comments: version accpeted for publication in EPJC