Colour-electric spectral function at next-to-leading order

TL;DR

This paper calculates the colour-electric spectral function at next-to-leading order in weak coupling, providing results useful for lattice QCD calibration and non-perturbative estimates of heavy quark diffusion.

Contribution

It presents the first next-to-leading order computation of the spectral function, including high- and low-frequency regimes, and connects perturbative results with lattice simulations.

Findings

High-frequency spectral function is temperature-independent.

Low-frequency part agrees with previous results after resummation.

Euclidean correlator can be defined in the confined phase via a limiting procedure.

Abstract

The spectral function related to the correlator of two colour-electric fields along a Polyakov loop determines the momentum diffusion coefficient of a heavy quark near rest with respect to a heat bath. We compute this spectral function at next-to-leading order, O(alpha_s^2), in the weak-coupling expansion. The high-frequency part of our result (omega >> T), which is shown to be temperature-independent, is accurately determined thanks to asymptotic freedom; the low-frequency part of our result (omega << T), in which Hard Thermal Loop resummation is needed in order to cure infrared divergences, agrees with a previously determined expression. Our result may help to calibrate the overall normalization of a lattice-extracted spectral function in a perturbative frequency domain T << omega << 1/a, paving the way for a non-perturbative estimate of the momentum diffusion coefficient at omega -> 0. We also evaluate the colour-electric Euclidean correlator, which could be directly compared with lattice simulations. As an aside we determine the Euclidean correlator in the lattice strong-coupling expansion, showing that through a limiting procedure it can in principle be defined also in the confined phase of pure Yang-Mills theory, even if a practical measurement could be very noisy there.