Beam energy dependence of the expansion dynamics in relativistic heavy ion collisions: Indications for the critical end point?

Abstract

The flow harmonic $v_{n}$ and the emission source radii $R_{\text{out}}$, $R_{\text{side}}$ and $R_{\text{long}}$ are studied for a broad range of centrality selections and beam collision energies in Au+Au ($\sqrt{s_{NN}}= 7.7 - 200$ GeV) and Pb+Pb ($\sqrt{s_{NN}}= 2.76$ TeV) collisions at RHIC and the LHC respectively. They validate the acoustic scaling patterns expected for hydrodynamic-like expansion over the entire range of beam energies studied. The combined data sets allow estimates for the \sqsn\ dependence of the mean expansion speed $\left<c_s\right>$, emission duration $\left<\Delta\tau\right>$ and the viscous coefficients $\left<\beta''\right>$ that encode the magnitude of the specific shear viscosity $\left<\eta/s\right>$. The estimates indicate initial-state model independent values of $\left<\eta/s\right>$ which are larger for the plasma produced at 2.76 TeV (LHC) compared to that produced at 200 GeV (RHIC) ($\left<4\pi\eta/s\right>_{\text{LHC}}=2.2\pm 0.2$ and $\left<4\pi\eta/s\right>_{\text{RHIC}}=1.3\pm 0.2$). They also show a non-monotonic \sqsn\ dependence for $\left<\beta''\right>$, $\left<c_s\right>$ and $\left<\Delta\tau\right>$, with minima for $\left<\beta''\right>$ and $\left<c_s\right>$, and a complimentary maximum for $\left<\Delta\tau\right>$. These dependencies signal a significant change in reaction dynamics in a narrow span of $\sqrt{s_{NN}}$, which may be linked to reaction trajectories close to the critical end point (CEP) in the phase diagram for nuclear matter.