[Paper Review] Is the quark gluon plasma produced in RHIC collisions strongly coupled?

R. Lacey, Arkadij Taranenko+1 more|ArXiv.org|May 27, 2009

High-Energy Particle Collisions Research3 citations

TL;DR

This paper uses double-differential measurements of elliptic ($v_2$) and hexadecapole ($v_4$) flow in Au+Au collisions at $√s_{NN} = 200$ GeV to constrain the degree of local equilibrium, mean free path ($\lambda$), and viscosity-to-entropy density ratio ($\eta/s$) of the quark-gluon plasma (QGP). It finds that the QGP achieves near-perfect local equilibrium—within 5–10% of the conjectured lower bound of $1/4\pi$—and exhibits $4\pi(\eta/s) = 1.3 \pm 0.3$ and $\lambda = 0.25{-}0.3$ fm, indicating strong coupling and low viscosity.

ABSTRACT

Recent hexadecapole (v4) and elliptic (v2) flow measurements are used to constrain estimates for the degree of local equilibrium, mean free path $λ$, and the viscosity to entropy density ratio (eta/s) of the plasma produced in Au+Au collisions at RootS = 200 GeV. The eccentricity-scaled flow coefficients v2/e2 and v4/e4 indicate that the plasma achieves a degree of local equilibrium within 5 - 10% of the value expected for a fluid with eta/s equal to the conjectured lower bound of 1/4pi. Estimates for $λ$ and eta/s as a function of collision centrality and particle transverse momentum pT, points to transverse expansion dynamics compatible with a strongly coupled low viscosity plasma.

Motivation & Objective

• To determine the degree of local equilibrium and transport properties of the quark-gluon plasma (QGP) produced in central and mid-central Au+Au collisions at RHIC.
• To assess whether the QGP is strongly or weakly coupled by estimating the viscosity-to-entropy density ratio ($\eta/s$) and mean free path ($\lambda$) from flow data.
• To test hydrodynamic scaling violations in $v_2/\varepsilon_2$ and $v_4/\varepsilon_4$ as probes of non-ideal fluid behavior and local equilibrium.
• To constrain $\eta/s$ and $\lambda$ as functions of collision centrality and transverse momentum ($p_T$) using a modified Knudsen number formalism.
• To evaluate whether the observed flow dynamics are consistent with a strongly coupled, low-viscosity QGP near the $1/4\pi$ lower bound.

Proposed method

• Uses double-differential $v_2$ and $v_4$ measurements from charged hadrons in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV.
• Applies a modified hydrodynamic scaling ansatz: $\frac{v_{2k}}{\varepsilon_{2k}} = \frac{v_{2k}^{\rm{h}}}{\varepsilon_{2k}} \left[ \frac{K^{-1}}{K^{-1} + K_0^{-1}} \right]^k$, where $K = \lambda / \bar{R}$ and $K_0 = 0.7 \pm 0.03$.
• Fits the eccentricity-scaled flow coefficients ($v_2/\varepsilon_2$, $v_4/\varepsilon_4$) to extract $K$ as a function of $N_{\rm part}$ and $p_T$.
• Estimates $\lambda = \bar{R} K$ using centrality-dependent transverse size $\bar{R}$ and $T = 220 \pm 20$ MeV from lattice QCD equations of state.
• Calculates $\eta/s$ using the relation $4\pi(\eta/s) = \left( \frac{v_{2k}^{\rm{h}}}{v_{2k}} \right)^{1/k} \cdot \text{const}$, with $K$-dependent viscous corrections.
• Validates results using both fKLN and Glauber model eccentricities, showing consistent trends despite magnitude differences.

Experimental results

Research questions

• RQ1 To what extent does the QGP produced in RHIC Au+Au collisions achieve local equilibrium, as probed by $v_2/\varepsilon_2$ and $v_4/\varepsilon_4$ scaling violations?
• RQ2 What is the viscosity-to-entropy density ratio ($\eta/s$) of the QGP, and does it approach the conjectured lower bound of $1/4\pi$?
• RQ3 How does the mean free path ($\lambda$) of partons in the QGP vary with collision centrality and transverse momentum ($p_T$)?
• RQ4 Is the observed $p_T$ dependence of $\eta/s$ consistent with viscous corrections in hydrodynamics, or does it indicate intrinsic medium properties?
• RQ5 Can the combined $v_2$ and $v_4$ data constrain the coupling strength of the QGP, supporting a strongly coupled, nearly perfect fluid behavior?

Key findings

• The QGP achieves a degree of local equilibrium within 5–10% of the value expected for a fluid with $\eta/s = 1/4\pi$, indicating near-perfect thermalization.
• The extracted $4\pi(\eta/s) = 1.3 \pm 0.3$ is consistent with the conjectured lower bound of $1/4\pi$, supporting a strongly coupled, low-viscosity plasma.
• The mean free path is estimated at $\lambda = 0.25{-}0.3$ fm, indicating strong scattering and short-range momentum transport, consistent with strong coupling.
• The $p_T$ dependence of $4\pi(\eta/s)$ increases quadratically, reflecting viscous corrections proportional to $(p_T/T)^2 K$, not intrinsic medium properties.
• The $N_{\rm part}$-independent $4\pi(\eta/s)$ band suggests that transverse size and initial geometry dominate the scaling, not centrality-dependent $\lambda$.
• The results are robust across different eccentricity models (fKLN and Glauber), with only magnitude differences, confirming the validity of the hydrodynamic scaling approach.