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

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 ${}^3\mathrm{H}$/${}^3\mathrm{He}+\Xi$ 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 ${}^3\mathrm{H}$/${}^3\mathrm{He}+\Xi$ threshold. Experimental implications for such a state are discussed.

Comments: 5 pages, 5 figures, preprint