# Theoretical description of the decays $\Lambda_b \to \Lambda^{(\ast)}(\frac12^\pm,\frac32^\pm) + J/\psi$

## TL;DR

This paper provides a theoretical analysis of the decay amplitudes for $ ext{Lambda}_b$ baryon decays into various $ ext{Lambda}^*$ states plus $J/ ext{psi}$, aiding in the identification of hidden charm pentaquark states.

## Contribution

It offers a covariant quark model calculation of decay amplitudes for multiple $ ext{Lambda}^*$ states, including excited states with different spins and parities.

## Key findings

- Helicity amplitudes for certain excited states are suppressed compared to ground states.
- The analysis helps distinguish between different $ ext{Lambda}^*$ contributions in decay chains.
- Supports identification of pentaquark states in $ ext{Lambda}_b$ decays.

## Abstract

We calculate the invariant and helicity amplitudes for the transitions $\Lambda_b~\to~\Lambda^{(\ast)}(J^P)~+~J/\psi$ where the $\Lambda^{(\ast)}(J^P)$ are $\Lambda(sud)$-type ground and excited states with $J^P$ quantum numbers $J^P=\frac12^{\pm},\frac32^{\pm}$. The calculations are performed in the framework of a covariant confined quark model previously developed by us. We find that the values of the helicity amplitudes for the $\Lambda^\ast(1520,\,\frac32^-)$ and the $\Lambda^\ast(1890,\,\frac32^+)$ are suppressed compared with those for the ground state $\Lambda(1116,\,\frac12^+)$ and the excited state $\Lambda^\ast(1405,\,\frac12^-)$. This analysis is important for the identification of the hidden charm pentaquark states $P_c^+(4380)$ and $P_c^+(4450)$ which were discovered in the decay chain $\Lambda_b^0~\to~P_c^+(~\to~p~J/\psi)~+~K^- $ because the cascade decay chain $\Lambda_b~\to~\Lambda^\ast(\frac32^\pm)(~\to~pK^-)~+~J/\psi$ involves the same final state.