Possible Lightest $\mathrm{\ensuremath{\Xi}}$ Hypernucleus with Modern $\mathrm{\ensuremath{\Xi}}N$ Interactions

Possible Lightest $Ξ$ Hypernucleus with Modern $Ξ N$ Interactions

E. Hiyama, K. Sasaki, T. Miyamoto, T. Doi, T. Hatsuda, Y. Yamamoto, and Th. A. Rijken

Phys. Rev. Lett. 124, 092501 – Published 4 March 2020

Abstract

Experimental evidence exists that the $Ξ$ -nucleus interaction is attractive. We search for $N N Ξ$ and $N N N Ξ$ bound systems on the basis of the AV8 $N N$ potential combined with either a phenomenological Nijmegen $Ξ N$ potential or a first principles HAL QCD $Ξ N$ potential. The binding energies of the three-body and four-body systems (below the $d + Ξ$ and ${}^{3}H / {}^{3}{He} + Ξ$ thresholds, respectively) are calculated by a high precision variational approach, the Gaussian expansion method. Although the two $Ξ N$ potentials have significantly different isospin ( $T$ ) and spin ( $S$ ) dependence, the $N N N Ξ$ 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 ${}^{3}H / {}^{3}{He} + Ξ$ threshold. Experimental implications for such a state are discussed.

Received 19 October 2019
Revised 18 January 2020
Accepted 22 January 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.092501

Physics Subject Headings (PhySH)

Hypernuclei & mesic nuclei

Nuclear Physics

Authors & Affiliations

E. Hiyama

Department of Physics, Kyushu University, Fukuoka, Japan, 819-0395 and Strangeness Nuclear Physics Laboratory, RIKEN Nishina Center, Wako 351-0198, Japan

K. Sasaki

Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

T. Miyamoto

Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan and Quantum Hadron Physics Laboratory, RIKEN Nishina Center, Wako 351-0198, Japan

T. Doi

Quantum Hadron Physics Laboratory, RIKEN Nishina Center, Wako 351-0198, Japan and Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako 351-0198, Japan

T. Hatsuda

Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako 351-0198, Japan and Quantum Hadron Physics Laboratory, RIKEN Nishina Center, Wako 351-0198, Japan

Y. Yamamoto

Physics Section, Tsuru University, Tsuru, Yamanashi 402-8555, Japan and Strangeness Nuclear Physics Laboratory, RIKEN Nishina Center, Wako 351-0198, Japan

Th. A. Rijken