$\Lambda\Lambda N$-$\Xi NN$ $S$ wave resonance

TL;DR

This paper investigates a three-body resonance in the $\Lambda\Lambda N - \Xi ext{NN}$ system using separable interactions based on recent HAL QCD results, revealing a resonance near the $\Xi d$ threshold sensitive to the $\Lambda\Lambda - \Xi N$ interaction.

Contribution

It introduces a three-body resonance model in the $\Lambda\Lambda N - \Xi ext{NN}$ system that depends on the $\Lambda\Lambda - \Xi N$ interaction, highlighting the role of the $H$-dibaryon channel.

Findings

A three-body resonance appears 2.3 MeV above the $\Xi d$ threshold.

The resonance disappears if the $\Lambda\Lambda - \Xi N$ $H$-dibaryon channel is excluded.

The existence of the resonance is sensitive to the $\Lambda\Lambda - \Xi N$ interaction.

Abstract

We use an existing model of the $\Lambda\Lambda N - \Xi NN$ three-body system based in two-body separable interactions to study the $(I,J^P)=(1/2,1/2^+)$ three-body channel. For the $\Lambda\Lambda$, $\Xi N$, and $\Lambda\Lambda - \Xi N$ amplitudes we have constructed separable potentials based on the most recent results of the HAL QCD Collaboration. They are characterized by the existence of a resonance just below or above the $\Xi N$ threshold in the so-called $H$-dibaryon channel, $(i,j^p)=(0,0^+)$. A three-body resonance appears {2.3} MeV above the $\Xi d$ threshold. We show that if the $\Lambda\Lambda - \Xi N$ $H$-dibaryon channel is not considered, the $\Lambda\Lambda N - \Xi NN$ $S$ wave resonance disappears. Thus, the possible existence of a $\Lambda\Lambda N - \Xi NN$ resonance would be sensitive to the $\Lambda\Lambda - \Xi N$ interaction. The existence or nonexistence of this resonance could be evidenced by measuring, for example, the $\Xi d$ cross section.