Possible lightest $Ξ$ Hypernucleus with Modern $ΞN$ Interactions

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

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