[Paper Review] The errant life of a heavy quark in the quark-gluon plasma

Harvey B. Meyer|arXiv (Cornell University)|Dec 1, 2010

High-Energy Particle Collisions Research550 citations

TL;DR

This lattice QCD study computes the momentum diffusion coefficient of a heavy quark in the quark-gluon plasma using heavy-quark effective field theory (HQET) and a Kubo formula. It finds a 20% increase in the Euclidean correlator from 6T_c to 2T_c, indicating stronger interactions at lower temperatures, with perturbative NLO calculations agreeing at the few-percent level but requiring additional low-frequency spectral weight to match lattice data at 3.1T_c.

ABSTRACT

In the high-temperature phase of QCD, the heavy quark momentum diffusion constant determines, via a fluctuation-dissipation relation, how fast a heavy quark kinetically equilibrates. This transport coefficient can be extracted from thermal correlators via a Kubo formula. We present a lattice calculation of the relevant Euclidean correlators in the gluon plasma, based on a recent formulation of the problem in heavy-quark effective field theory (HQET). We find a $\approx20%$ enhancement of the Euclidean correlator at maximal time separation as the temperature is lowered from $6T_c$ to $2T_c$, pointing to stronger interactions at lower temperatures. At the same time, the correlator becomes flatter from $6T_c$ down to $2T_c$, indicating a relative shift of the spectral weight to lower frequencies. A recent next-to-leading order perturbative calculation of the correlator agrees with the time dependence of the lattice data at the few-percent level. We estimate how much additional contribution from the $ω\lesssim T$ region of the perturbative spectral function would be required to bring it in agreement with the lattice data at $3.1T_c$.

Motivation & Objective

• To compute the momentum diffusion coefficient of a heavy quark in the quark-gluon plasma from first principles using lattice QCD.
• To investigate the temperature dependence of the Euclidean correlator relevant to the momentum diffusion coefficient via the Kubo formula.
• To compare lattice results with next-to-leading-order perturbative calculations and assess their agreement.
• To estimate the required spectral weight in the ω ≲ T region to reconcile perturbative predictions with lattice data at 3.1T_c.

Proposed method

• Formulates the momentum diffusion problem within heavy-quark effective field theory (HQET) to define the relevant thermal correlators.
• Computes Euclidean correlators of the spatial heavy-quark current using Monte-Carlo lattice simulations at temperatures from 2T_c to 6T_c.
• Applies the Kubo formula to extract the momentum diffusion coefficient from the long-time behavior of the Euclidean correlator.
• Uses the spectral representation and analytic continuation to relate Euclidean correlators to the retarded correlator and spectral function.
• Compares lattice results with next-to-leading-order perturbative calculations of the correlator at finite temperature.
• Estimates the missing spectral weight in the low-frequency region (ω ≲ T) needed to bring perturbative results into agreement with lattice data at 3.1T_c.

Experimental results

Research questions

• RQ1 How does the momentum diffusion coefficient of a heavy quark evolve with temperature in the quark-gluon plasma?
• RQ2 To what extent do next-to-leading-order perturbative calculations reproduce lattice QCD results for the Euclidean correlator of the heavy-quark current?
• RQ3 What is the required spectral weight in the ω ≲ T region to reconcile perturbative predictions with lattice data at 3.1T_c?
• RQ4 How does the shape of the Euclidean correlator change with temperature, and what does this imply about the spectral function?
• RQ5 What is the role of strong interactions at lower temperatures, as indicated by the temperature dependence of the correlator?

Key findings

• The Euclidean correlator increases by approximately 20% at maximal time separation when temperature is lowered from 6T_c to 2T_c, indicating stronger interactions at lower temperatures.
• The correlator becomes flatter from 6T_c down to 2T_c, suggesting a shift of spectral weight to lower frequencies.
• Next-to-leading-order perturbative calculations agree with the lattice data's time dependence at the few-percent level.
• At 3.1T_c, the perturbative spectral function requires additional contribution from the ω ≲ T region to match the lattice data.
• The results suggest that non-perturbative effects are significant at temperatures near 2T_c, where the perturbative expansion may not fully capture the dynamics.
• The study provides a first-principles lattice determination of the momentum diffusion coefficient, crucial for understanding heavy quark equilibration in heavy-ion collisions.