[Paper Review] Energy-momentum tensor correlators and viscosity

Harvey B. Meyer|arXiv (Cornell University)|Sep 30, 2008

High-Energy Particle Collisions Research28 references7 citations

TL;DR

This paper presents a lattice quantum chromodynamics (QCD) computation of energy-momentum tensor correlators in the Euclidean SU(3) pure gauge theory to extract shear and bulk viscosities via Kubo formulas. It introduces advanced techniques to combine data from multiple channels and spatial momenta, enabling improved constraints on viscosity at temperatures up to 4T_c, with the key result being a rigorous upper bound of η/s < 1.0 at T < 2T_c under weak assumptions.

ABSTRACT

Collective flow has been observed in heavy ion collisions, with a large anisotropic component, and ideal hydrodynamic calculations had significant successful in describing the distribution of produced particles at the RHIC experiments. In order to account for this near ideal fluid behavior, the shear and bulk viscosity of the quark gluon plasma (QGP) must be computed from first principles in a regime where the QGP is not weakly coupled. In this talk I describe recent progress in computing energy-momentum tensor correlators on the lattice from which the viscosities can be extracted via Kubo formulas. I also show how to cumulate information from several channels, including at non-vanishing spatial momentum, in order to best constrain the viscosities. These methods should soon yield predictions at the higher temperatures that will be explored at the LHC experiments.

Motivation & Objective

• To compute the shear and bulk viscosities of the quark-gluon plasma (QGP) from first principles in a non-perturbative regime.
• To address the challenge of computing viscosity in strongly coupled QCD where perturbation theory fails.
• To extend hydrodynamic phenomenology to higher temperatures expected at the LHC by predicting viscosities at ≈3T_c.
• To improve viscosity extraction by combining correlator data across multiple channels and spatial momenta.
• To test the liquid-like behavior of the QGP by comparing spatial energy density correlations with those in strongly coupled SYM theory.

Proposed method

• Compute Euclidean energy-momentum tensor correlators on the lattice in SU(3) pure gauge theory at finite temperature.
• Use Kubo formulas to relate the spectral functions of the energy-momentum tensor to transport coefficients like shear and bulk viscosity.
• Incorporate analytic constraints from perturbation theory (ultraviolet) and hydrodynamics (infrared) to improve spectral function reconstruction.
• Utilize spatial momentum dependence in correlators to extract additional information on transport properties.
• Apply Ward identities and Källén-Lehmann representations to constrain vacuum and thermal contributions to the correlators.
• Combine data from different channels (e.g., T_00, T_33, T_12) to cumulate information and reduce uncertainties in viscosity extraction.

Experimental results

Research questions

• RQ1 What is the value of the shear viscosity to entropy density ratio η/s in the quark-gluon plasma at temperatures near 2T_c?
• RQ2 How can lattice QCD correlators of the energy-momentum tensor be used to extract transport coefficients like viscosity?
• RQ3 What role does spatial momentum dependence in the correlators play in constraining viscosity?
• RQ4 How do thermal energy density correlations reflect liquid-like behavior in the QGP?
• RQ5 To what extent do results from pure gauge theory approximate full QCD for viscosity at fixed T/T_c?

Key findings

• An upper bound of η/s < 1.0 was derived at T < 2T_c using only weak assumptions, based on the first accurate lattice data in the shear channel.
• The thermal contribution to the energy density correlator exhibits non-monotonic behavior on scales of order 1/T, suggesting spatial ordering akin to short-range order in classical fluids.
• Spatial correlators provide complementary information that may help explain the QGP’s ability to flow like a nearly perfect fluid.
• The matrix element for the lightest glueball state was related to the trace anomaly via a_{0} = s/(3M_{0}^{3}), with s calculated in prior work.
• The tensor glueball matrix element was related to the trace anomaly via a_{2} = 2√3 t/(3M_{2}^{3}), with t defined in earlier studies.
• The methods developed are expected to yield predictions at higher temperatures, such as ≈3T_c, relevant for LHC experiments.