The complex heavy-quark potential in an anisotropic quark-gluon plasma -- Statics and dynamics

TL;DR

This paper extends a complex heavy-quark potential model to anisotropic quark-gluon plasmas, enabling simplified calculations of quarkonium properties and dynamics with high accuracy by using angle-averaged screening masses.

Contribution

It introduces an anisotropic potential model with angle-dependent screening masses and demonstrates its effectiveness in reproducing three-dimensional results and describing quarkonium dynamics.

Findings

The anisotropic potential accurately reproduces 3D binding energies and decay widths.

The effective 1D potential describes the time evolution of quarkonium states.

The model captures polarization splitting in anisotropic plasmas.

Abstract

We generalize a complex heavy-quark potential model from an isotropic QCD plasma to an anisotropic one by replacing the Debye mass $m_D$ with an anisotropic screening mass depending on the quark pair alignment with respect to the direction of anisotropy. Such an angle-dependent mass is determined by matching the perturbative contributions in the potential model to the exact result obtained in the Hard-Thermal-Loop resummed perturbation theory. An advantage of the resulting potential model is that its angular dependence can be effectively described by using a set of angle-averaged screening masses as proposed in our previous work. Consequently, one could solve a one-dimensional Schr\"odinger equation with a potential model built by changing the anisotropic screening masses into the corresponding angle-averaged ones, and reproduce the full three-dimensional results for the binding energies and decay widths of low-lying quarkonium bound states to very high accuracy. Finally, turning to dynamics, we demonstrate that the one-dimensional effective potential can accurately describe the time evolution of the vacuum overlaps obtained using the full three-dimensional anisotropic potential. This includes the splitting of different p-wave polarizations.