$D^*$ $\Xi N$ bound state in strange three-body systems

TL;DR

This paper investigates the potential existence of stable three-body strange systems involving a predicted $\Xi N$ bound state, using updated Nijmegen potentials, and finds stable states in specific configurations.

Contribution

It demonstrates that certain three-body systems containing a $\Xi N$ bound state are stable, providing new insights into strange matter interactions.

Findings

Stable $\Xi NN$ and $\Xi \Xi N$ states identified.

$\Xi \Lambda N$ and $\Xi \Sigma N$ systems are unbound.

Updated potentials support the existence of these states.

Abstract

The recent update of the strangeness $-2$ ESC08c Nijmegen potential incorporating the NAGARA and KISO events predicts a $\Xi N$ bound state, $D^*$, in the $^3S_1 (I=1)$ channel. We study if the existence of this two-body bound state could give rise to stable three-body systems. For this purpose we solve the bound state problem of three-body systems where the $\Xi N$ state is merged with $N$'s, $\Lambda$'s, $\Sigma's$ or $\Xi$'s, making use of the most recent updates of the two-body ESC08c Nijmegen potentials. We found that there appear stable states in the $\Xi NN$ and $\Xi \Xi N$ systems, the $\Xi \Lambda N$ and $\Xi \Sigma N$ systems being unbound.