Strongly Interacting Low-Viscosity Matter Created in Relativistic Nuclear Collisions

Substantial collective flow is observed in collisions between large nuclei at BNL RHIC (Relativistic Heavy Ion Collider) as evidenced by single-particle transverse momentum distributions and by azimuthal correlations among the produced particles. The data are well reproduced by perfect fluid dynamics. A calculation of the dimensionless ratio of shear viscosity $\eta$ to entropy density $s$ by Kovtun, Son, and Starinets within anti-de Sitter space/conformal field theory yields $\eta /s=\hslash /4\pi k_B$, which has been conjectured to be a lower bound for any physical system. Motivated by these results, we show that the transition from hadrons to quarks and gluons has behavior similar to helium, nitrogen, and water at and near their phase transitions in the ratio $\eta /s$. We suggest that experimental measurements can pinpoint the location of this transition or rapid crossover in QCD.

Figure 1

The ratio $\eta /s$ as a function of $T$ for helium with $s$ normalized such that $s(T=0)=0$. The curves correspond to fixed pressures, one of them being the critical pressure, and the others being greater (1 MPa) and the other smaller (0.1 MPa). Below the critical pressure there is a jump in the ratio, and above the critical pressure there is only a broad minimum. They were constructed using data from NIST and CODATA.

Figure 2

The ratio $\eta /s$ as a function of $T$ for nitrogen with $s$ normalized such that $s(T=0)=0$. The curves correspond to fixed pressures, one of them being the critical pressure, and the others being greater (10 MPa) and the other smaller (0.1 MPa). Below the critical pressure there is a jump in the ratio, and above the critical pressure there is only a broad minimum. They were constructed using data from NIST and CODATA. The curves are plotted on logarithmic scale to make the behavior around the critical point more visible.

Figure 3

The ratio $\eta /s$ as a function of $T$ for water with $s$ normalized such that $s(T=0)=0$. The curves correspond to fixed pressures, one of them being the critical pressure, and the others being greater (100 MPa) and the other smaller (10 MPa). Below the critical pressure there is a jump in the ratio, and above the critical pressure there is only a broad minimum. They were constructed using data from NIST and CODATA.

Figure 4

The ratio $\eta /s$ for the low temperature hadronic phase and for the high temperature quark-gluon phase. Neither calculation is very reliable in the vicinity of the critical or rapid crossover temperature.