Static potentials for quarkonia at finite temperatures

TL;DR

This paper reviews static potentials used in quarkonium models at finite temperature, highlighting issues with commonly used potentials and proposing a gauge-invariant real-time potential derived from pNRQCD for more accurate descriptions.

Contribution

It introduces a gauge-invariant static real-time potential at finite T, generalizing pNRQCD, and discusses its perturbative and non-perturbative aspects.

Findings

Polyakov loop correlator potentials are inappropriate for quarkonia.

The qar{q} free energy has incorrect spatial decay.

A gauge-dependent singlet free energy is unphysical.

Abstract

We review non-perturbative static potentials commonly used in potential models for quarkonia at finite T. Potentials derived from Polyakov loop correlators are shown to be inappropriate for this purpose. The q\bar{q} free energy is physical but has the wrong spatial decay and perturbative limit. The so-called singlet free energy is gauge dependent and unphysical. An appropriate static real time potential can be defined through a generalisation of pNRQCD to finite T. In perturbation theory, its real part reproduces the Debye-screened potential, its imaginary part accounts for Landau damping. Possibilities for its non-perturbative evaluation are discussed.