Moving Forward to Constrain the Shear Viscosity of QCD Matter

We demonstrate that measurements of rapidity differential anisotropic flow in heavy-ion collisions can constrain the temperature dependence of the shear viscosity to entropy density ratio $\eta /s$ of QCD matter. Comparing results from hydrodynamic calculations with experimental data from the RHIC, we find evidence for a small $\eta /s\approx 0.04$ in the QCD crossover region and a strong temperature dependence in the hadronic phase. A temperature independent $\eta /s$ is disfavored by the data. We further show that measurements of the event-by-event flow as a function of rapidity can be used to independently constrain the initial state fluctuations in three dimensions and the temperature dependent transport properties of QCD matter.

Figure 1

The four scenarios of temperature dependent $\eta T/(ϵ+P)$ at ${\mu }_B=0$.

Figure 2

$dN/d{\eta }_p$ of charged hadrons in two different centrality classes for the four scenarios compared to experimental data from the PHOBOS Collaboration [47].

Figure 3

$v_2$ of charged hadrons as a function of pseudorapidity for the four different shear viscosity scenarios compared to experimental data from the PHOBOS Collaboration [48, 49]. (Top panel) 0%–40% centrality. (Bottom panel) 3%–15% and 15%–25% centralities.

Figure 4

Predictions for $v_3$ of charged hadrons as a function of pseudorapidity for the four scenarios.

Figure 5

Variance of the $v_2$ event-by-event distribution for different temperature dependent $\eta T/(ϵ+P)$’s. Dash-dotted lines are the scaled variances of the eccentricity distributions in the initial state. The data points represent PHOBOS data [55] for $N_{\text{part}}=214$ ($\approx 20\%–25\%$) and 296 ($\approx 0\%–5\%$).