Production rates of hidden-charm pentaquark molecules in $\Lambda_b$ decays

TL;DR

This paper models the production of hidden-charm pentaquark molecules in Lambda_b decays using effective field theory and coupled-channel interactions, predicting observable decay rates and providing insights into their production mechanisms.

Contribution

It introduces a dynamical generation model for pentaquark molecules in Lambda_b decays, employing contact-range effective field theory and triangle diagram mechanisms.

Findings

Pentaquark states can be produced in Lambda_b decays.

Heavy quark spin symmetry partners are hard to observe.

Some pentaquark states are likely observable in specific decay channels.

Abstract

The partial decay widths and production mechanism of the three pentaquark states, $P_{\psi}^{N}(4312)$, $P_{\psi}^{N}(4440)$, and $P_{\psi}^{N}(4457)$, 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 $\bar{D}^{(*)}\Sigma_{c}^{(*)}$, $\bar{D}^{*}\Lambda_c$, $\bar{D}\Lambda_c$, $J/\psi p$, and $\eta_c p$ coupled-channel interactions to dynamically generate the multiplet of hidde-charm pentaquark molecules by reproducing the masses and widths of $P_{\psi}^{N}(4312)$, $P_{\psi}^{N}(4440)$, and $P_{\psi}^{N}(4457)$. Assuming that the pentaquark molecules are produced in the $\Lambda_b$ decay via the triangle diagrams, where $\Lambda_{b}$ firstly decays into $D_{s}^{(\ast)}\Lambda_{c}$, then $D_{s}^{(\ast)}$ scatters into $\bar{D}^{(\ast)}K$, and finally the molecules are dynamically generated by the $\bar{D}^{(\ast)}\Lambda_{c}$ interactions, we calculate the branching fractions of the decays $\Lambda_b \to {P_{\psi}^{N}}K$ using the effective Lagrangian approach. With the partial decay widths of these pentaquark molecules, we further estimate the branching fraction of the decays $ \Lambda_b \to ( P_{\psi}^{N} \to J/\psi p )K $ and $ \Lambda_b \to ( P_{\psi}^{N}\to \bar{D}^* \Lambda_c )K $. Our results show that the pentaquark states $P_{\psi}^{N}(4312)$, $P_{\psi}^{N}(4440)$, and $P_{\psi}^{N}(4457)$ as hadronic molecules can be produced in the $\Lambda_b$ decay, and on the other hand their heavy quark spin symmetry partners are invisible in the $J/\psi p$ invariant mass distribution because of the small production rates. Our studies show that is possible to observe some of the pentaquark states in the $\Lambda_b\to \bar{D}^*\Lambda_c K$ decays.