Possible Lightest <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Ξ</mml:mi></mml:math> Hypernucleus with Modern <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Ξ</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:math> Interactions
Emiko Hiyama, Kenji Sasaki, Takaya Miyamoto, Takumi Doi, Tetsuo Hatsuda, Yasuo Yamamoto, Th. A. Rijken
Abstract
Experimental evidence exists that the $\mathrm{\ensuremath{\Xi}}$-nucleus interaction is attractive. We search for $NN\mathrm{\ensuremath{\Xi}}$ and $NNN\mathrm{\ensuremath{\Xi}}$ bound systems on the basis of the AV8 $NN$ potential combined with either a phenomenological Nijmegen $\mathrm{\ensuremath{\Xi}}N$ potential or a first principles HAL QCD $\mathrm{\ensuremath{\Xi}}N$ potential. The binding energies of the three-body and four-body systems (below the $d+\mathrm{\ensuremath{\Xi}}$ and $^{3}\mathrm{H}/^{3}\mathrm{He}+\mathrm{\ensuremath{\Xi}}$ thresholds, respectively) are calculated by a high precision variational approach, the Gaussian expansion method. Although the two $\mathrm{\ensuremath{\Xi}}N$ potentials have significantly different isospin ($T$) and spin ($S$) dependence, the $NNN\mathrm{\ensuremath{\Xi}}$ system with quantum numbers ($T=0$, ${J}^{\ensuremath{\pi}}={1}^{+}$) appears to be bound (one deep for Nijmegen and one shallow for HAL QCD) below the $^{3}\mathrm{H}/^{3}\mathrm{He}+\mathrm{\ensuremath{\Xi}}$ threshold. Experimental implications for such a state are discussed.