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

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