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 $\mathrm{Au}+\mathrm{Au}$ 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 $\sqrt{{s}_{NN}}={3.0,4.5}\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$ can be described by our model, and a Bayesian analysis of these data indicates a hard equation of state at ${n}_{B}\ensuremath{\in}(2,3){n}_{0}$ and a possible phase transition at ${n}_{B}\ensuremath{\in}(3,4){n}_{0}$. More data at $\sqrt{{s}_{NN}}=2--5\phantom{\rule{4pt}{0ex}}\text{GeV}$, as well as a more thorough analysis of the model systematic uncertainties will be necessary for a more precise conclusion.