The Ξ-nuclear potential constrained by recent Ξ⁻ hypernuclei experiments

Abstract

The $\Xi$-nuclear potential is investigated in the quark mean-field (QMF) model based on recent results of the $\Xi^-+^{14}\rm{N}$ ($_{\Xi^-}^{15}\rm{C}$) system. The experimental data on the binding energy of $1p$-state $\Xi^-$ hyperon in $_{\Xi^-}^{15}\rm{C}$ hypernuclei in KISO, IBUKI, E07-T011, E176-14-03-35 events are merged as $B_{\Xi^-}(1p)=1.14\pm0.11$ MeV. With this constraint, the coupling strengths between the $\omega$ vector meson and $\Xi$ hyperon are fixed in three QMF parameter sets. At the same time, the $\Xi^-$ binding energy of $1s$ state in $_{\Xi^-}^{15}\rm{C}$ is predicted as $B_{\Xi^-}(1s)=5.66\pm0.38$ MeV with the same interactions, completely consistent with the data from the KINKA and IRRAWADDY events. Finally, the $\Xi$-nuclear potential is calculated in the symmetric nuclear matter in the framework of QMF models. It is $U_{\Xi }=-11.96\pm 0.85$ MeV at nuclear saturation density, which will be essential to determine the onset density of $\Xi$ hyperon in neutron star.

The hyperonic star in relativistic mean-field model

“…R σY and R ωY are defined as R σY = Γ σY /Γ σN and R ωY = Γ ωY /Γ ωN . We choose the hyperon-nucleon potentials of Λ, Σ and Ξ as U N Λ = −30 MeV, U N Σ = +30 MeV and U N Ξ = −14 MeV, respectively from the recent hypernuclei experimental observables [72,80,134].…”

“…A few double-Λ hypernuclei were discovered in the light nuclei [66,67] and the first deep bound state of single-Ξ hypernuclei was confirmed in the Ξ − + 14 N ( 15 Ξ − C) system [68][69][70]. The observations of these hypernuclei imply that the Λ-nucleon and Ξ-nucleon potentials in nuclear medium should be attractive around nuclear saturation density [71,72].…”