${\mathrm{\Omega }}^{-}$ production as a probe of equation of state of dense matter near the QCD phase transition in relativistic heavy-ion collisions

The production of doubly strange hyperon ${\mathrm{\Xi }}^{-}$ and trebly strange hyperon ${\mathrm{\Omega }}^{-}$ in relativistic Au+Au collisions at $\sqrt{s_{NN}}$ = 4.2 GeV is explored based on a relativistic transport model that is interweaved with hadronic mean-field potentials for heavy-ion collisions. Upon comparison, it appears that relative to the double strangeness observable ${\mathrm{\Xi }}^{-}$, the yield and collective flows of the triple strange ${\mathrm{\Omega }}^{-}$ exhibit a higher sensitivity to the equation of state (EoS) of dense matter. This characteristic makes the ${\mathrm{\Omega }}^{-}$ an essential observable for studying the properties of densely formed matter in relativistic heavy-ion collisions.