Effect of thresholds on the width of three-body resonances

TL;DR

This paper investigates how threshold effects influence the width of three-body resonances, explaining a narrow resonance near the $ ext{N} ext{Λ} ext{Λ}- ext{Ξ} ext{N} ext{N}$ system using perturbation theory and applying it to realistic interactions.

Contribution

It introduces a perturbation theory-based explanation for narrow three-body resonances near thresholds, applicable to various systems with multiple thresholds.

Findings

Narrow resonance observed near the $ ext{N} ext{Λ} ext{Λ}- ext{Ξ} ext{N} ext{N}$ threshold.

Perturbation theory explains the small width despite open channels.

Applicable to other multi-threshold systems.

Abstract

It has been recently reported an intriguing theoretical result of a narrow three-body resonance with a large available phase space. The resonance was reported in the $N\Lambda\Lambda-\Xi NN$ system near the $\Xi d$ threshold, having a very small width in spite of the open $N\Lambda\Lambda$ channel lying around 23 MeV below the $\Xi NN$ channel. We use first-order perturbation theory as a plausible argument to explain this behavior. We apply our result to realistic local interactions. Other systems involving several thresholds are likely to follow the same behavior.