A hard thermal loop benchmark for the extraction of the nonperturbative $Q\bar{Q}$ potential

TL;DR

This paper benchmarks the extraction of the heavy quark potential at finite temperature using leading order HTL calculations, confirming the lowest spectral peak suffices and analyzing spectral features affecting numerical extraction methods.

Contribution

It provides an analytical HTL benchmark for the spectral extraction of the Qar{Q} potential, evaluating the effectiveness of peak fitting and the Maximum Entropy method.

Findings

Lowest spectral peak accurately yields the potential.

Full spectrum reveals features complicating analytic continuation.

Maximum Entropy method's performance in reproducing spectral functions.

Abstract

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the Wilson loop. General arguments tell us that the lowest lying spectral peak encodes, through its position and shape, the real and imaginary part of this complex potential. Here we benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. I.e. we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real- and imaginary part and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. Access to the full spectrum allows an investigation of spectral features that do not contribute to the potential but can pose a challenge to numerical attempts of an analytic continuation from imaginary time data. Differences in these contributions between the Wilson loop and gauge fixed Wilson line correlators are discussed. To better understand the difficulties in a numerical extraction we deploy the Maximum Entropy method with extended search space to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary part are reproduced. Possible venues for improvement of the extraction strategy are discussed.