Hidden charm pentaquark and $\Lambda(1405)$ in the $\Lambda^0_b \to \eta_c K^- p (\pi \Sigma)$ reaction

TL;DR

This paper investigates the production of the $ar{K}N$, $ar{K}N$, and $ar{K}N$ channels in $ar{K}N$ interactions, revealing the nature of the $ar{K}N$ interaction and the existence of a hidden charm pentaquark resonance, with implications for ongoing experiments.

Contribution

It introduces a novel analysis of $ar{K}N$ interactions and predicts a hidden charm pentaquark resonance observable in specific invariant mass distributions.

Findings

The $ar{K}N$ interaction produces a clear $ar{K}N$ resonance.

A hidden charm pentaquark resonance is predicted near the $ar{K}N$ threshold.

Experimental signals for the resonance are expected in LHCb data.

Abstract

We have performed a study of the $\Lambda^0_b \to \eta_c K^- p$ and $\Lambda^0_b \to \eta_c \pi \Sigma$ reactions based on the dominant Cabibbo favored weak decay mechanism. We show that the $K^- p$ produced only couples to $\Lambda^*$ states, not $\Sigma^*$ and that the $\pi \Sigma$ state is only generated from final state interaction of $\bar{K}N$ and $\eta \Lambda$ channels which are produced in a primary stage. This guarantees that the $\pi \Sigma$ state is generated in isospin $I=0$ and we see that the invariant mass produces a clean signal for the $\Lambda(1405)$ of higher mass at $1420$ MeV. We also study the $\eta_c p$ final state interaction, which is driven by the excitation of a hidden charm resonance predicted before. We relate the strength of the different invariant mass distributions and find similar strengths that should be clearly visible in an ongoing LHCb experiment. In particular we predict that a clean peak should be seen for a hidden charm resonance that couples to the $\eta_c p$ channel in the invariant $\eta_c p$ mass distribution.