An in-Medium Heavy-Quark Potential from the $Q\bar{Q}$ Free Energy

TL;DR

This paper develops a method to extract the static heavy-quark potential in a quark-gluon plasma from lattice QCD free energy data, incorporating imaginary parts and confining effects, with implications for heavy-quark transport.

Contribution

It introduces a thermodynamic T-matrix approach that includes imaginary parts and confining remnants to better extract the in-medium heavy-quark potential from lattice data.

Findings

Imaginary parts significantly affect the potential extraction.

The potential shows long-range confining remnants.

Implications for heavy-quark transport coefficients.

Abstract

We investigate the problem of extracting a static potential between a quark and its antiquark in a quark-gluon plasma (QGP) from lattice-QCD computations of the singlet free energy, $F_{Q\bar{Q}}(r)$. We utilize the thermodynamic $T$-matrix formalism to calculate the free energy from an underlying potential ansatz resummed in ladder approximation. Imaginary parts of both $Q\bar Q$ potential-type and single-quark selfenergies are included as estimated from earlier results of the $T$-matrix approach. We find that the imaginary parts, and in particular their (low-) energy dependence, induce marked deviations of the (real part of the) potential from the calculated free energy. When fitting lattice results of the latter, the extracted potential is characterized by significant long-range contributions from remnants of the confining force. We briefly discuss consequences of this feature for the heavy-quark transport coefficient in the QGP.