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 often interpreted as {bar{D}}^{(*)}Sigma _c molecules. Together with their four {bar{D}}^{(*)}Sigma _{c}^{*} partners dictated by heavy quark spin symmetry they represent a complete multiplet of hadronic molecules of {bar{D}}^{(*)}Sigma _{c}^{(*)}. The pentaquark states were observed in the J/psi p invariant mass distributions of the Lambda _brightarrow J/psi p K 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 {bar{D}}^{(*)}Sigma _{c}^{(*)} molecules. The tree-level modes proceed via off-shell Sigma _{c}^{(*)} baryons, {bar{D}}^{(*)}Sigma _{c}^{(*)} rightarrow {bar{D}}^{(*)}left( Sigma _{c}^{(*)}rightarrow Lambda _{c}pi right) rightarrow {bar{D}}^{(*)}Lambda _{c}pi , while the triangle-loop modes proceed through {bar{D}}^{*}Sigma _{c}^{(*)}rightarrow J/psi Npi , eta _{c}Npi via {bar{D}}Sigma _{c}^{(*)} rescattering to J/psi N and eta _{c}N. Our results indicate that the decay widths of the P_{c}(4457) and {bar{D}}^{(*)}Sigma _{c}^{*} states into {bar{D}}^{(*)}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}}^{(*)}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}}^{*}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}}^{*}Sigma _{c}^{*} molecules into J/psi N pi vary from several keV to tens of keV. In particular, we show that the spin-5/2 {bar{D}}^{*}Sigma _{c}^{*} state can be searched for in the J/psi N pi and {bar{D}}^{*}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.