Perfect Fluidity of the Quark Gluon Plasma Core as Seen through its Dissipative Hadronic Corona

TL;DR

This paper argues that the apparent near-perfect fluidity of the sQGP seen at RHIC arises not from an anomalously low viscosity per se, but from a large entropy-density jump at the QCD deconfinement transition, which lowers the viscosity-to-entropy ratio in the sQGP core relative to the hadronic corona. It systematically analyzes how different hadronic-phase treatments—chemical equilibrium, chemical freezeout, and hadronic cascades—affect key observables like pT spectra, radial flow, and differential elliptic flow v2(pT). The main finding is that while the sQGP core can behave as a nearly perfect fluid, the hadronic corona is strongly dissipative and cannot be described by inviscid hydrodynamics; reproducing all RHIC data requires a hybrid hydro+cascade approach. The work highlights deconfinement signatures via entropy-driven fluidity and emphasizes the need for unified dynamical frameworks to validate the interpretation across energies and rapidities.

Abstract

The agreement of hydrodynamic predictions of differential elliptic flow and radial flow patterns with Au+Au data is one of the main lines of evidence suggesting the nearly perfect fluid properties of the strongly coupled Quark Gluon Plasma, sQGP, produced at RHIC. We study the sensitivity of this conclusion to different hydrodynamic assumptions on chemical and thermal freezeout after the sQGP hadronizes. We show that if chemical freezeout occurs at the hadronization time, the differential elliptic flow for pions increase with proper time in the late hadronic phase until thermal freezeout and leads to a discrepancy with the data. In contrast, if both chemical and thermal equilibrium are maintained past the hadronization, then the mean pT per pion increases in a way that accidentally preserves v2(pT) from the sQGP phase in agreement with the data, but at the cost of the agreement with the hadronic yields. In order that all the data on hadronic ratios, radial flow, and differential elliptic flow be reproduced, the sQGP must expand with a minimal viscosity, η_Q, that is however even greater than the viscosity, η_H, of its hadronic corona. However, because of the large entropy density difference of the two phases of QCD matter, the larger viscosity in the sQGP phase leads to nearly perfect fluid flow while the smaller entropy density of the hadronic corona strongly hinders the applicability of Euler hydrodynamics. The ``perfect fluid'' property of the sQGP is thus not due to a sudden reduction of the viscosity at the critical temperature Tc, but to a sudden increase of the entropy density of QCD matter and is therefore an important signature of deconfinement.

Figures (8)

• Figure 1: Illustration of the approximately monotonic increase of absolute value of the shear viscosity with temperature. The kink shown at $T_c$ is expected to be smeared out by the $\Delta T_c/T_c\sim 0.1$ width of the QCD cross-over transition. The solid blue curve shows $\eta(T<T_c)=T/\sigma_H$ for a HRG followed by the more rapid increase of the viscosity in the sQGP phase with $\eta_{\mathrm{sQGP}}\approx \eta_{\mathrm{SYM}} \equiv K_{\mathrm{SB}}T^3/4\pi \approx T^3$. The horizontal line shows that near $T_c$, $\eta\approx\eta_c\equiv T_c^3$. At high $T\gg T_c$ asymptotic freedom leads to an even more rapid growth of viscosity as the sQGP evolves gradually into the weakly coupled wQGP. In this figure, $w=1$ in Eq. (\ref{['final']}) is taken to emphasize the possibility that the highly viscous but nearly"perfect fluid" sQGP may become an ordinary "viscous fluid" already for $T\mathrel{\hbox{$\stackrel{ >}{\sim}$}} 2 T_c$.
• Figure 2: Illustration of the rapid variation of the dimensionless ratio of the shear viscosity, $\eta(T)$, to the entropy density, $s(T)$. The sharp discontinuity illustrated is not due to a rapid change of the transport coefficient (see Fig. \ref{['fig1a']}) but to the rapid increase of the entropy density in QCD near $T_c$. As in Fig. \ref{['fig1a']}, we expect the discontinuity to be smeared into a rapid drop within $\Delta T_c/T_c\sim 0.1$. Solid (dashed) blue curve illustrates the change of $\eta/s$ of a HRG with $c_H^2=1/3$ (1/6), $s_Q/s_H=10$ (3) into an approximate "perfect fluid" sQGP at $T_c$. The red long dashed curve is $(\eta/s)_{\mathrm{SYM}}=1/4\pi$. At $T\gg T_c$ asymptotic freedom gradually transforms the sQGP into an ordinary viscous fluid wQGP (green), here shown for $w={ \frac{1}{2} }, 1$.
• Figure 3: The ratio of number density and entropy density for massive pions. Solid (Dashed) line represents the ratio for chemical equilibrium (chemical freezeout). Chemical freezeout temperature is assumed to be $T^{\mathrm{ch}}=170$ MeV.
• Figure 4: Average transverse momentum for pions as a function of thermal freezeout temperature for the models CE (solid) and PCE (dashed).
• Figure 5: $v_2$ for pions as a function of $T^{\mathrm{th}}$ for the models CE (solid) and PCE (dashed).