Sensitivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Au</mml:mi><mml:mo>+</mml:mo><mml:mi>Au</mml:mi></mml:mrow></mml:math> collisions to the symmetric nuclear matter equation of state at 2–5 nuclear saturation densities
Dmytro Oliinychenko, Agnieszka Sorensen, Volker Koch, Larry McLerran
Abstract
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.