Single-$Ξ^-$ hypernuclei with quark mean field model

Abstract

The single-$Ξ^-$ hypernuclei are studied using a quark mean field model. At the quark level, the $Ξ^-$ 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 $σ, ~ω$, and $ρ$ mesons between quarks in different baryons. The single-$Ξ^-$ binding energies of $Ξ$ hypernuclei are investigated from $\ce{_{Ξ^{-}}^{12}Be}$ to $\ce{^{208}_{Ξ^-}Tl}$ using different parameter sets, which are determined by the ground-state properties of several stable nuclei and the empirical values of the single-$Λ$ and $Ξ$ potentials at the nuclear saturation density. For the bound states of $\ce{Ξ^{-}{+}^{14}N}$ (i.e., $\ce{^{15}_{Ξ^-}C}$) system named as KISO event in KEK-E373 experiment, it is found that the $Ξ^-$ 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 $Ξ$ potentials are $-12$ MeV. These results and those from cluster models with the Gaussian expansion method concerning on the $\ce{Ξ^{-}{+}^{12}Be}$ show that in the KISO event, the $Ξ^-$ hyperon may occupy the $1p$ state. Furthermore, the $Ξ^-$ binding energies are achieved around $27$ MeV for the $\ce{Ξ^{-}{+}^{207}Pb}$ (i.e., $\ce{^{208}_{Ξ^-}Tl}$) system. The energies were nearly comparable to the single-$Λ$ binding energy of $\ce{^{208}_ΛPb}$ observed by experiments. It demonstrates that the $Λ$ and $Ξ^-$ hyperons seem to appear simultaneously in a neutron star.