Viscous Hydrodynamics and the Quark Gluon Plasma

TL;DR

The paper analyzes the large elliptic flow observed in RHIC collisions to constrain the shear viscosity of QCD near the deconfinement transition. By comparing viscous hydrodynamics and kinetic theory with data, it argues that the quark-gluon plasma has a small $η/s$, near the AdS/CFT bound, with a preferred range around $η/s ≈ (1\leftrightarrow 3) × 1/(4π)$. It provides a comprehensive treatment of ideal and second-order viscous hydrodynamics, Bjorken evolution, and kinetic theory, highlighting how viscosity shapes flow observables and the conditions for hydrodynamic applicability. The findings support the view that RHIC probes a strongly coupled, nearly perfect fluid and emphasize ongoing uncertainties related to initial conditions and freezeout in precisely determining $η/s$.

Abstract

One of the most striking results from the Relativistic Heavy Ion Collider is the strong elliptic flow. This review summarizes what is observed and how these results are combined with reasonable theoretical assumptions to estimate the shear viscosity of QCD near the phase transition. A data comparison with viscous hydrodynamics and kinetic theory calculations indicates that the shear viscosity to entropy ratio is surprisingly small, $η/s < 0.4$. The preferred range is $η/s \simeq (1\leftrightarrow 3) \times 1/4π$.

Figures (23)

• Figure 1: Overview of a heavy ion event. In the left figure the two nuclei collide along the beam axis usually labeled as $Z$. At RHIC the nuclei are length contracted by a factor of $\gamma\simeq 100$. The right figure shows the collision vertex of a typical event as viewed in a schematic particle detector and shows a few of the thousands of charged particle tracks recorded per event. The angle $\theta$ is usually reported in pseudo-rapidity variables as discussed in the text.
• Figure 2: A schematic of the transverse plane in a heavy ion event. Both the magnitude and direction of the impact parameter ${\bf b}$ can be determined on an event by event basis. $X$ and $Y$ label the reaction plane axes and the dotted lines indicate the lab axis. $\Psi_{RP}$ is known as the reaction plane angle.
• Figure 3: The conventional explanation for the observed elliptic flow. The spectators continue down the beam pipe leaving behind an excited oval shape which expands preferentially along the short axis of the ellipse. The finally momentum asymmetry in the particle distribution $v_2$ reflects the response of the excited medium to this geometry. The dot with transverse coordinate ${\bf x} = (x,y)$ is illustrated to explain a technical point in Section \ref{['elliptic']}.
• Figure 4: The standard Glauber eccentricity $\epsilon_{\rm s,part}$ as a function of the number of participants. $N_p^{\rm max}\simeq 340$ is the maximum number of participants in a central AuAu event and $R_A\simeq6.3\,{\rm fm}$ is the gold radius. The top axis shows the translation between impact parameter and participants. The root mean square radius $R_{\rm rms}$ and the standard Glauber eccentricity are given in Eq. (\ref{['epsilonpart']}) and Eq. (\ref{['Rrms']}).
• Figure 5: Elliptic flow $v_2(p_T)$ as measured by the STAR collaboration STARV2STAR:2008ed for different centralities. The measured elliptic flow has been divided by the eccentricity -- $\epsilon_{\rm hydro}\equiv \epsilon_{s,\rm part}$ in this work. The curves are ideal hydrodynamic calculations based on Refs.Huovinen:2006jpHuovinen:2001cy rather than the viscous hydrodynamics discussed in much of this review.