The effective complex heavy-quark potential in an anisotropic quark-gluon plasma

TL;DR

This paper presents a method to simplify the complex anisotropic heavy-quark potential in a quark-gluon plasma into an effective isotropic potential, enabling easier computation of quarkonium states while capturing anisotropic effects.

Contribution

The authors introduce an effective screening mass dependent on quantum numbers to reduce anisotropic potentials to isotropic form, facilitating accurate 1D Schrödinger equation solutions for heavy-quarkonium energies.

Findings

The 1D effective potential reproduces 3D results with high accuracy.

The method captures polarization splitting of p-wave states.

It enables inclusion of anisotropy effects in quantum system simulations.

Abstract

We introduce a method for reducing anisotropic heavy-quark potentials to isotropic potentials by using an effective screening mass that depends on the quantum numbers $l$ and $m$ of a given state. We demonstrate that, using the resulting 1D effective potential model, one can solve a 1D Schr\"odinger equation and reproduce the full 3D results for the energies and binding energies of low-lying heavy-quarkonium bound states to relatively high accuracy. This includes the splitting of different p-wave polarizations. The resulting 1D effective model provides a way to include momentum anisotropy effects in open quantum system simulations of heavy-quarkonium dynamics in the quark-gluon plasma.