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

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 D¯ ^(∗)Σ _c molecules. Together with their four D¯(∗)Σc∗ partners dictated by heavy quark spin symmetry they represent a complete multiplet of hadronic molecules of D¯(∗)Σc(∗). The pentaquark states were observed in the J/ ψp invariant mass distributions of the Λ _b→ J/ ψpK 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 D¯(∗)Σc(∗) molecules. The tree-level modes proceed via off-shell Σc(∗) baryons, D¯(∗)Σc(∗)→D¯(∗)(Σc(∗)→Λcπ)→D¯(∗)Λcπ, while the triangle-loop modes proceed through D¯∗Σc(∗)→J/ψNπ, η_cNπ via D¯Σc(∗) rescattering to J/ ψN and η_cN. Our results indicate that the decay widths of the P_c(4457) and D¯(∗)Σc∗ states into D¯ ^(∗)Λ _cπ are several MeV, as a result can be observed in the upcoming Run 3 and Run 4 of LHC. The partial decay widths into D¯ ^(∗)Λ _cπ of the P_c(4312) and P_c(4440) states range from tens to hundreds of keV. In addition, the partial decay widths of D¯ ^∗Σ _c molecules into J/ ψNπ and η_cNπ are several keV and tens of keV, respectively, and the partial decay widths of D¯∗Σc∗ molecules into J/ ψNπ vary from several keV to tens of keV. In particular, we show that the spin-5/2 D¯∗Σc∗ state can be searched for in the J/ ψNπ and D¯ ^∗Λ _cπ 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.