Possible lightest $\Xi$ Hypernucleus with Modern $\Xi N$ Interactions

TL;DR

This paper investigates the possibility of the lightest $ ext{Xi}$ hypernucleus by analyzing three- and four-body systems with modern $ ext{Xi}N$ interactions, predicting a bound $NNN ext{Xi}$ state with potential experimental relevance.

Contribution

It introduces a combined analysis using phenomenological and first-principles $ ext{Xi}N$ potentials to predict bound hypernuclear states with modern interaction models.

Findings

The $NNN ext{Xi}$ system with $(T=0, J^{ ext{pi}}=1^+)$ is predicted to be bound.

Different $ ext{Xi}N$ potentials yield a bound state below the $ ext{^3H}/ ext{^3He}+ ext{Xi}$ threshold.

The study suggests experimental searches for this hypernucleus are promising.

Abstract

Experimental evidence exists that the $\Xi$-nucleus interaction is attractive. We search for $NN\Xi$ and $NNN\Xi$ bound systems on the basis of the AV8 $NN$ potential combined with either a phenomenological Nijmegen $\Xi N$ potential or a first principles HAL QCD $\Xi N$ potential. The binding energies of the three-body and four-body systems (below the $d+\Xi$ and $^3{\rm H}$/$^3{\rm He}+\Xi$ thresholds, respectively) are calculated by a high precision variational approach, the Gaussian Expansion Method. Although the two $\Xi N$ potentials have significantly different isospin ($T$) and spin ($S$) dependence, the $NNN\Xi$ system with quantum numbers $(T=0, J^{\pi}=1^+$) appears to be bound (one deep for Nijmegen and one shallow for HAL QCD) below the $^3{\rm H}$/$^3{\rm He}+\Xi$ threshold. Experimental implications for such a state are discussed.