Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV

TL;DR

This work develops and applies conformal relativistic viscous hydrodynamics to RHIC bulk observables, implementing second-order gradient terms to bridge weak- and strong-coupling physics. It analyzes Glauber and CGC initial conditions in 2+1D, showing that key observables like multiplicity, radial flow, and elliptic flow are robust against variations in the five second-order coefficients, while $\eta/s$ strongly shapes $v_2$. The results indicate that a realistic quark-gluon plasma viscosity lies near the conjectured lower bound, though uncertainties in initial conditions and non-flow effects prevent a precise first-principles determination. The study highlights that early thermalization is not strictly required for hydrodynamics to describe $v_2$, given plausible pre-equilibrium evolution, and calls for further work on fluctuations and pre-hydro dynamics to reduce systematic uncertainties. Overall, the conformal viscous framework provides controlled evolution with quantified sensitivities, improving our understanding of QCD matter under extreme conditions.

Abstract

A new set of equations for relativistic viscous hydrodynamics that captures both weak-coupling and strong-coupling physics to second order in gradients has been developed recently. We apply this framework to bulk physics at RHIC, both for standard (Glauber-type) as well as for Color-Glass-Condensate initial conditions and show that the results do not depend strongly on the values for the second-order transport coefficients. Results for multiplicity, radial flow and elliptic flow are presented and we quote the ratio of viscosity over entropy density for which our hydrodynamic model is consistent with experimental data. For Color-Glass-Condensate initial conditions, early thermalization does not seem to be required in order for hydrodynamics to describe charged hadron elliptic flow.

Figures (10)

• Figure 1: The speed of sound squared from Ref. Laine:2006cp, used in the hydrodynamic simulations. See text for details.
• Figure 2: (Color online) Space-time cut through the three-dimensional hypersurface for a central collision within the Glauber model. Simulation parameters used were $a=1$ GeV$^{-1}$, $\tau_0=1$ fm/c, $T_i=0.36$ GeV, $T_f=0.15$ GeV, $\tau_\Pi=6 \frac{\eta}{s}$ and $\lambda_1=0$ (see next sections for definitions). As can be seen from the figure, inclusion of viscosity only slightly changes the form of the surface.
• Figure 3: (Color online) The correlation function $f(\tau,{\bf k})$ as a function of momentum $k=|{\bf k}|$ for a lattice with $a=1$ GeV$^{-1}$, $64^2$ sites and averaged over 30 initial configurations (symbols), compared to the result from the linearized hydrodynamic equations (lines).
• Figure 4: (Color online) Left: The initial spatial anisotropy for the Glauber and CGC model. Right: The time evolution of the spatial and momentum anisotropy for a collision with $b=7$ fm in ideal hydrodynamics.
• Figure 5: (Color online) Spatial and momentum anisotropy for the Glauber model at $b=7$ fm with $T_i=0.353$ GeV, $\tau_0=1$ fm/c and various values for the viscosity (grid spacing $a=2\ {\rm GeV}^{-1}$). (a): The dependence on the initialization value of the shear tensor: shown are results for vanishing initial value ($\Pi^{\mu\nu}_{\rm init}=0$) and Navier-Stokes initial value ($\Pi^{\mu\nu}_{\rm init}\neq 0$), given in Eq. (\ref{['FOvalue']}). (b): The dependence on the choice of value for $\tau_\Pi,\lambda_1$: shown are results for $\tau_\Pi=\frac{6}{T}\frac{\eta}{s}$, $\lambda_1=0$ (labelled "IS") and $\tau_\Pi=\frac{2(2-\ln2)}{T}\frac{\eta}{s}$, $\lambda_1=\frac{\eta}{2 \pi T}$ (labelled "AdS"). For $\tau_\Pi=\frac{2(2-\ln2)}{T}\frac{\eta}{s}$, the results for $\lambda_1=0$ (not shown) would be indistinguishable by bare eye from those for $\lambda_1=\frac{\eta}{2 \pi T}$.