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

The Ξ-nuclear potential is investigated in the quark mean-field (QMF) model based on recent results on the Ξ^- + ¹⁴N ( ${}_{{{\Xi}}^{-}}{}^{15}\mathrm{C}$ ) system. The experimental data on the binding energy of 1p-state Ξ^- hyperon in ${}_{{{\Xi}}^{-}}{}^{15}\mathrm{C}$ hypernuclei in KISO, IBUKI, E07-T011, E176-14-03-35 events are merged as ${B}_{{{\Xi}}^{-}}(1p)=1.14\pm 0.11$ MeV. With this constraint, the coupling strengths between the ω vector meson and Ξ hyperon are fixed in three QMF parameter sets. At the same time, the Ξ^- binding energy of 1s state in ${}_{{{\Xi}}^{-}}{}^{15}\mathrm{C}$ is predicted as ${B}_{{{\Xi}}^{-}}(1s)=5.66\pm 0.38$ MeV with the same interactions, completely consistent with the data from the KINKA and IRRAWADDY events. Finally, the Ξ-nuclear potential is calculated in the symmetric nuclear matter in the same framework. It is found to be U _Ξ = -11.96 ± 0.85 MeV at nuclear saturation density, which is important for the discussions of the role of strangeness in a neutron star.