Probing high-density nuclear symmetry energy with $\Xi^{-}/\Xi^{0}$ ratio in heavy-ion collisions at $\sqrt{s_{NN}} \sim 3$ GeV

Recent beam energy scan (BES) experiments at RHIC by the STAR Collaboration (PLB {\bf 827},137003 (2022) and PRL {\bf 128}, 202303 (2022)) found that hadronic interactions dominate the collective flow and the proton cumulant ratios are driven by baryon number conservation in a region of high baryon density in $\sqrt{s_{NN}}$ = 3 GeV Au+Au reactions, indicating the dense medium formed in such collisions is likely hadronic matter. Within an updated ART (A Relativistic Transport) model with momentum dependent isoscalar and isovector single-nucleon mean-field potentials corresponding to different symmetry energies at suprasaturation densities, the $n/p$, $\pi^{-}/\pi^{+}$, $K_{s}^{0}/K^{+}$, $\Sigma^{-}/\Sigma^{+}$ and $\Xi^{-}/\Xi^{0}$ ratios are studied for central Au+Au collisions at $\sqrt{s_{NN}}$ = 3 GeV where the maximum central density reaches about $(3.6\sim 4.0)\rho_0$. The doubly strange $\Xi^{-}/\Xi^{0}$ ratio is found to have the strongest sensitivity to the variation of high-density nuclear symmetry energy. Thus, the $\Xi^{-}/\Xi^{0}$ ratio in relativistic heavy-ion reactions at $\sqrt{s_{NN}} \sim 3$ GeV may help probe sensitively the poorly known symmetry energy of dense neutron-rich matter critically important for understanding various properties of neutron stars.