Sensitivity of Au+Au collisions to the symmetric nuclear matter equation of state at 2 -- 5 nuclear saturation densities

We demonstrate that proton and pion flow measurements in heavy-ion collisions at incident energies ranging from 1 to 20 GeV per nucleon in the fixed target frame can be used for an accurate determination of the symmetric nuclear matter equation of state at baryon densities equal 2--4 times nuclear saturation density $n_0$. We simulate Au+Au collisions at these energies using a hadronic transport model with an adjustable vector mean-field potential dependent on baryon density $n_B$. We show that the mean field can be parametrized to reproduce a given density-dependence of the speed of sound at zero temperature $c_s^2(n_B, T = 0)$, which we vary independently in multiple density intervals to probe the differential sensitivity of heavy-ion observables to the equation of state at these specific densities. Recent flow data from the STAR experiment at the center-of-mass energies $\sqrt{s_{NN}} = \{3.0, 4.5 \}\ $ GeV can be described by our model, and a Bayesian analysis of these data indicates a hard equation of state at $n_B \in (2,3) n_0$ and a possible phase transition at $n_B \in (3,4) n_0$. More data at $\sqrt{s_{NN}} = 2-5$ GeV, as well as a more thorough analysis of the model systematic uncertainties will be necessary for a more precise conclusion.