# Quarkonium Phenomenology from a Generalised Gauss Law

## TL;DR

This paper introduces a new analytic model for the in-medium heavy quark potential based on a generalized Gauss law, combining non-perturbative and perturbative QCD elements, fitting lattice data with a single temperature-dependent parameter, and applying it to heavy-ion collision predictions.

## Contribution

It provides a novel, self-consistent parametrization of the heavy quark potential that accurately reproduces lattice QCD results using only the Debye mass as a parameter.

## Key findings

- Successfully reproduces lattice QCD data
- Models potential at finite baryo-chemical potential
- Estimates quarkonium ratios in heavy-ion collisions

## Abstract

We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum potential with a weak-coupling description of the QCD medium. The resulting Gauss-law parametrisation is able to reproduce full lattice QCD data by using only a single temperature dependent parameter, the Debye mass $m_D$. Using this parametrisation we model the in-medium potential at finite baryo-chemical potential, which allows us to estimate the $\Psi^\prime$/$J/\Psi$ ratio in heavy-ion collisions at different beam energies.