Possible Lightest Ξ Hypernucleus with Modern ΞN Interactions

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 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 H/ 3 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 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.

Strangeness in nuclei and neutron stars

“…In Ref. [300], on the other hand, the authors have searched for ΞN N and ΞN N N bound systems using phenomenological potentials and the ΞN potential extracted from LQCD [232]. The ΞN N N system with isospin 0 and J π = 1 + appears to be bound, being deeply bound for the Nijmegen potential and shallow for the HAL QCD one, below the 3 H/ 3 He + Ξ threshold.…”

Nuclear Structure at the Crossroads

“…If the NN force could be calculated, this would help to understand what happens in neutron stars at higher densities. Moreover, hyperon-nucleon interactions from lattice QCD can also be used in few-body calculations of hypernuclei [44]. Another opportunity is LECs for three-body forces in the T = 3/2 sector and three-neutron observables.…”

$$A=4-7$$ $$\varXi $$ hypernuclei based on interactions from chiral effective field theory

“…In this work we explore the possible existence of light Ξ hypernuclei up to A = 7. For the lightest system, 3 Ξ H, several calculations can be found in the literature [16][17][18][19]. Not surprisingly, the predictions strongly depend on the interaction models used.…”

“…Not surprisingly, the predictions strongly depend on the interaction models used. For example, Garcilazo et al [16] and Hiyama et al [18] both obtained a deeply bound 3 Ξ H (J π = 3/2 + , T = 1/2) state employing an effective Ξ N potential that mimics the phase shifts of the Nijmegen ESC08c potential [20]. On the other hand, for interactions derived within chiral effective field theory (EFT) [21] or for Ξ N potentials deduced from lattice QCD simulations by the HAL QCD Collaboration [22], the system is found to be unbound [18,19].…”

“…For example, Garcilazo et al [16] and Hiyama et al [18] both obtained a deeply bound 3 Ξ H (J π = 3/2 + , T = 1/2) state employing an effective Ξ N potential that mimics the phase shifts of the Nijmegen ESC08c potential [20]. On the other hand, for interactions derived within chiral effective field theory (EFT) [21] or for Ξ N potentials deduced from lattice QCD simulations by the HAL QCD Collaboration [22], the system is found to be unbound [18,19]. It has to be said that a strongly attractive Ξ N force as suggested by that ESC08c potential, which even yields a Ξ N two-body bound state [20], is not supported by the currently available empirical constraints [23] including the aforementioned femtoscopic measurements, and also not by lattice simulations at almost physical masses [22].…”