Li\'enard-Wiechert potential of a heavy quark moving in QGP medium

TL;DR

This paper extends the concept of retarded potentials to heavy quarkonium in a quark-gluon plasma, incorporating Lorentz transformations and medium screening effects, and analyzes the resulting potential and quarkonium thermal width.

Contribution

It introduces a Lorentz-transformed retarded potential for moving heavy quarkonium in QGP, including thermal screening effects, and provides analytical and numerical results for the potential and thermal width.

Findings

Real and imaginary parts of the potential are computed for various velocities and temperatures.

The thermal width of quarkonia increases with velocity and temperature.

Analytical expressions approximate the potential in the small velocity limit.

Abstract

We investigate the nature of the complex retarded potential of a heavy quarkonium moving in a hot and dense static deconfined nuclear medium. The well-known concept of the retarded potential in electrodynamics is extended to the context of the heavy-quark by modifying the static vacuum Cornell potential through Lorentz transformation to the static frame of the medium. The resulting potential in the vacuum is further corrected to incorporate the screening effect offered by the thermal medium. To do so, the retarded Cornell potential is modified by the dielectric function of the static quark-gluon plasma (QGP) medium. We present the numerical results for the real and imaginary parts of the potential along with the analytical expression of the potential approximated by a small velocity limit. Finally, we present the thermal width of quarkonia in the QGP medium derived using the imaginary part of the potential and study its dependence on velocity and temperature.