Single-$\Xi^-$ hypernuclei with quark mean field model

The single-$\Xi^-$ hypernuclei are studied using a quark mean field model. At the quark level, the $\Xi^-$ hyperon is composed of one $d$ quark and two $s$ quarks, which are confined by the harmonic oscillator potentials. In the case of hadrons, the baryons interact with each other by exchanging $\sigma, ~\omega$, and $\rho$ mesons between quarks in different baryons. The single-$\Xi^-$ binding energies of $\Xi$ hypernuclei are investigated from $\ce{_{\Xi^{-}}^{12}Be}$ to $\ce{^{208}_{\Xi^-}Tl}$ using different parameter sets, which are determined by the ground-state properties of several stable nuclei and the empirical values of the single-$\Lambda$ and $\Xi$ potentials at the nuclear saturation density. For the bound states of $\ce{\Xi^{-}{+}^{14}N}$ (i.e., $\ce{^{15}_{\Xi^-}C}$) system named as KISO event in KEK-E373 experiment, it is found that the $\Xi^-$ binding energies are around $5.61-5.89$ MeV for $1s$ state and $0.94-1.21$ MeV for $1p$ state with QMF-NK1S, QMF-NK2S, and QMF-NK3S parameter sets, whose single $\Xi$ potentials are $-12$ MeV. These results and those from cluster models with the Gaussian expansion method concerning on the $\ce{\Xi^{-}{+}^{12}Be}$ show that in the KISO event, the $\Xi^-$ hyperon may occupy the $1p$ state. Furthermore, the $\Xi^-$ binding energies are achieved around $27$ MeV for the $\ce{\Xi^{-}{+}^{207}Pb}$ (i.e., $\ce{^{208}_{\Xi^-}Tl}$) system. The energies were nearly comparable to the single-$\Lambda$ binding energy of $\ce{^{208}_{\Lambda}Pb}$ observed by experiments. It demonstrates that the $\Lambda$ and $\Xi^-$ hyperons seem to appear simultaneously in a neutron star.