A gauge invariant Debye mass for the complex heavy-quark potential

TL;DR

This paper introduces a gauge invariant Debye mass for the complex heavy-quark potential in QCD, derived from lattice QCD data, revealing deviations from traditional approaches especially near the phase transition.

Contribution

It proposes a novel gauge invariant definition of the Debye mass using lattice QCD and a generalized Gauss-Law, connecting non-perturbative and perturbative aspects of quark binding.

Findings

The Debye mass behavior differs from perturbative predictions.

Near the phase transition, the Debye mass approaches zero faster.

The approach successfully describes lattice potential data with a single temperature-dependent parameter.

Abstract

The concept of a screening mass is a powerful tool to simplify the intricate physics of in-medium test charges surrounded by light charge carriers. While it has been successfully used to describe electromagnetic properties, its definition and computation in QCD is plagued by questions of gauge invariance and the presence of non-perturbative contributions from the magnetic sector. Here we present a recent alternative definition of a gauge invariant Debye mass parameter following closely the original idea of Debye and Hueckel. Our test charges are a static heavy quark-antiquark pair whose complex potential and its in-medium modification can be extracted using lattice QCD. By combining in a generalized Gauss-Law the non-perturbative aspects of quark binding with a perturbative ansatz for the medium effects, we succeed to describe the lattice values of the potential with a single temperature dependent parameter, in turn identified with a Debye mass. We find that its behavior, as evaluated in a recent quenched lattice QCD study, deviates from that in other approaches, such as hard-thermal-loop perturbation theory or from electric field correlators on the lattice. In particular around the phase transition its values tend to zero significantly faster than at weak-coupling.