Production rates of hidden-charm pentaquark molecules in $Λ_b$ decays

Abstract

The partial decay widths and production mechanism of the three pentaquark states, $P_ψ^{N}(4312)$, $P_ψ^{N}(4440)$, and $P_ψ^{N}(4457)$, discovered by the LHCb Collaboration in 2019, are still under debate. In this work, we employ the contact-range effective field theory approach to construct the $\bar{D}^{(*)}Σ_{c}^{(*)}$, $\bar{D}^{*}Λ_c$, $\bar{D}Λ_c$, $J/ψp$, and $η_c p$ coupled-channel interactions to dynamically generate the multiplet of hidde-charm pentaquark molecules by reproducing the masses and widths of $P_ψ^{N}(4312)$, $P_ψ^{N}(4440)$, and $P_ψ^{N}(4457)$. Assuming that the pentaquark molecules are produced in the $Λ_b$ decay via the triangle diagrams, where $Λ_{b}$ firstly decays into $D_{s}^{(\ast)}Λ_{c}$, then $D_{s}^{(\ast)}$ scatters into $\bar{D}^{(\ast)}K$, and finally the molecules are dynamically generated by the $\bar{D}^{(\ast)}Λ_{c}$ interactions, we calculate the branching fractions of the decays $Λ_b \to {P_ψ^{N}}K$ using the effective Lagrangian approach. With the partial decay widths of these pentaquark molecules, we further estimate the branching fraction of the decays $ Λ_b \to ( P_ψ^{N} \to J/ψp )K $ and $ Λ_b \to ( P_ψ^{N}\to \bar{D}^* Λ_c )K $. Our results show that the pentaquark states $P_ψ^{N}(4312)$, $P_ψ^{N}(4440)$, and $P_ψ^{N}(4457)$ as hadronic molecules can be produced in the $Λ_b$ decay, and on the other hand their heavy quark spin symmetry partners are invisible in the $J/ψp$ invariant mass distribution because of the small production rates. Our studies show that is possible to observe some of the pentaquark states in the $Λ_b\to \bar{D}^*Λ_c K$ decays.