Description of the recently observed hypernucleus $^{15}{\!\!\!_{\Xi^-}}$C within a quark-meson coupling model

Abstract

We investigate within a quark-meson coupling (QMC) model, the structure of the bound $\Xi^-$ hypernucleus $^{15}{\!\!\!_{\Xi^-}}$C ($^{14}$N + $\Xi^-$), which has been observed in a recent analysis of the KEK-E373 experiment. In the QMC model, light quarks in nonoverlapping nucleon and $\Xi^-$ bags interact self-consistently with isoscalar-scalar ($\sigma$), isoscalar-vector ($\omega$), and isovector-vector ($\rho$) mesons in the mean field approximation. The parameters of the model (quark-meson coupling constants and masses) are mostly fixed from the nuclear matter saturation properties. The QMC model closely reproduces the separation energies of the two $\Xi^-$ hyperon states in $^{15}{\!\!\!_{\Xi^-}}$C reported in the KEK-E373 analysis, and identifies their quantum numbers. We also make predictions for the cross sections for the production of the $^{15}{\!\!\!_{\Xi^-}}$C hypernuclear specta in the ($K^-, K^+$) reaction on a $^{15}$O target within a covariant effective Lagrangian model using the $\Xi^-$ bound state spinors obtained within the same QMC model.