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.
Measuring the neutron star compactness and binding energy with supernova neutrinos
