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Recent beam energy scan (BES) experiments at RHIC by the STAR Collaboration(PLB {\bf 827},137003 (2022) and PRL {\bf 128}, 202303 (2022)) found thathadronic interactions dominate the collective flow and the proton cumulantratios are driven by baryon number conservation in a region of high baryondensity in $\sqrt{s_{NN}}$ = 3 GeV Au+Au reactions, indicating the dense mediumformed in such collisions is likely hadronic matter. Within an updated ART (ARelativistic Transport) model with momentum dependent isoscalar and isovectorsingle-nucleon mean-field potentials corresponding to different symmetryenergies at suprasaturation densities, the $n/p$, $\pi^{-}/\pi^{+}$,$K_{s}^{0}/K^{+}$, $\Sigma^{-}/\Sigma^{+}$ and $\Xi^{-}/\Xi^{0}$ ratios arestudied for central Au+Au collisions at $\sqrt{s_{NN}}$ = 3 GeV where themaximum 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 thevariation of high-density nuclear symmetry energy. Thus, the $\Xi^{-}/\Xi^{0}$ratio in relativistic heavy-ion reactions at $\sqrt{s_{NN}} \sim 3$ GeV mayhelp probe sensitively the poorly known symmetry energy of dense neutron-richmatter critically important for understanding various properties of neutronstars.

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