Eur. Phys. J. C (2022) 82: 1061
https://doi.org/10.1140/epjc/s10052-022-11026-0

Regular Article - Theoretical Physics

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

¹ School of Physics, Beihang University, 100191, Beijing, China
² Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing, China
³ School of Space and Environment, Beihang University, 100191, Beijing, China
⁴ Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, 100191, Beijing, China
⁵ School of Physics and Microelectronics, Zhengzhou University, 450001, Zhengzhou, Henan, China

^c zhengmz11@buaa.edu.cn

Received: 1 May 2022
Accepted: 12 November 2022
Published online: 24 November 2022

Abstract

The three pentaquark states, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by the LHCb Collaboration in 2019, are often interpreted as ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c$ molecules. Together with their four ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{\ast }$ partners dictated by heavy quark spin symmetry they represent a complete multiplet of hadronic molecules of ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{(\ast )}$. The pentaquark states were observed in the $J/\psi p$ invariant mass distributions of the ${\mathrm{\Lambda }}_b\to J/\psi pK$ decay. 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 ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{(\ast )}$ molecules. The tree-level modes proceed via off-shell ${\mathrm{\Sigma }}_c^{(\ast )}$ baryons, ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{(\ast )}\to {\overline{D}}^{(\ast )}({\mathrm{\Sigma }}_c^{(\ast )}\to {\mathrm{\Lambda }}_c\pi )\to {\overline{D}}^{(\ast )}{\mathrm{\Lambda }}_c\pi$, while the triangle-loop modes proceed through ${\overline{D}}^{\ast }{\mathrm{\Sigma }}_c^{(\ast )}\to J/\psi N\pi$, ${\eta }_{c}N\pi$ via $\overline{D}{\mathrm{\Sigma }}_c^{(\ast )}$ rescattering to $J/\psi N$ and ${\eta }_{c}N$. Our results indicate that the decay widths of the $P_c(4457)$ and ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{\ast }$ states into ${\overline{D}}^{(\ast )}{\mathrm{\Lambda }}_c\pi$ are several MeV, as a result can be observed in the upcoming Run 3 and Run 4 of LHC. The partial decay widths into ${\overline{D}}^{(\ast )}{\mathrm{\Lambda }}_c\pi$ of the $P_c(4312)$ and $P_c(4440)$ states range from tens to hundreds of keV. In addition, the partial decay widths of ${\overline{D}}^{\ast }{\mathrm{\Sigma }}_c$ 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 ${\overline{D}}^{\ast }{\mathrm{\Sigma }}_c^{\ast }$ molecules into $J/\psi N\pi$ vary from several keV to tens of keV. In particular, we show that the spin-5/2 ${\overline{D}}^{\ast }{\mathrm{\Sigma }}_c^{\ast }$ state can be searched for in the $J/\psi N\pi$ and ${\overline{D}}^{\ast }{\mathrm{\Lambda }}_c\pi$ invariant mass distributions, while the latter one is more favorable. 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.