Single- Ξ− hypernuclei within a quark mean-field model

Abstract

The single-${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hypernuclei are studied using a quark mean-field model. At the quark level, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ 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 $\ensuremath{\sigma},\ensuremath{\omega}$, and $\ensuremath{\rho}$ mesons between quarks in different baryons. The single-${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ binding energies of $\mathrm{\ensuremath{\Xi}}$ hypernuclei are investigated from $\mathrm{Be}$ to $\mathrm{Tl}$ using different parameter sets, which are determined by the ground-state properties of several stable nuclei and the empirical values of the single-$\mathrm{\ensuremath{\Lambda}}$ and single-$\mathrm{\ensuremath{\Xi}}$ potentials at the nuclear saturation density. For the bound states of ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}+\phantom{\rule{0.16em}{0ex}}^{14}\mathrm{N}$ (i.e., $\mathrm{C}$) system named as KISO event in the KEK-E373 experiment, it is found that the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ 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-$\mathrm{\ensuremath{\Xi}}$ potentials are $\ensuremath{-}12$ MeV. These results and those from cluster models with the Gaussian expansion method concerning on the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}+\phantom{\rule{0.16em}{0ex}}^{12}\mathrm{Be}$ show that in the KISO event, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hyperon may occupy the $1p$ state. Furthermore, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ binding energies are achieved around $27\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}+\phantom{\rule{0.16em}{0ex}}^{207}\mathrm{Pb}$ (i.e., $\mathrm{Tl}$) system. The energies were nearly comparable to the single-$\mathrm{\ensuremath{\Lambda}}$ binding energy of $\mathrm{Pb}$ observed by experiments. It demonstrates that the $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ hyperons seem to appear simultaneously in a neutron star.