Improved Gauss law model and in-medium heavy quarkonium at finite density and velocity

TL;DR

This paper develops an improved complex-valued potential model based on a generalized Gauss law to study heavy-quarkonium properties in medium at finite density and velocity, aligning well with lattice QCD data.

Contribution

It introduces a novel derivation of the generalized Gauss law for in-medium quarkonium, connecting non-perturbative vacuum physics with medium effects, and extends the model to finite density and velocity regimes.

Findings

Reproduces lattice QCD heavy quark potential with a single parameter

Extends potential model to finite baryon density and velocity

Predicts $ ext{ψ'}/J/ ext{ψ}$ ratio consistent with experimental data

Abstract

We explore the in-medium properties of heavy-quarkonium states at finite baryo-chemical potential and finite transverse momentum based on a modern complex-valued potential model. Our starting point is a novel, rigorous derivation of the generalized Gauss law for in-medium quarkonium, combining the non-perturbative physics of the vacuum bound state with a weak coupling description of the medium degrees of freedom. Its relation to previous models in the literature is discussed. We show that our approach is able to reproduce the complex lattice QCD heavy quark potential even in the non-perturbative regime, using a single temperature dependent parameter, the Debye mass $m_D$. After vetting the Gauss-law potential with state-of-the-art lattice QCD data, we extend it to the regime of finite baryon density and finite velocity, currently inaccessible to first principles simulations. In-medium spectral functions computed from the Gauss-law potential are subsequently used to estimate the $\psi'/J/\psi$ ratio in heavy-ion collisions at different beam energies and transverse momenta. We find qualitative agreement with the predictions from the statistical model of hadronization for the $\sqrt{s_{NN}}$ dependence and a mild dependence on the transverse momentum.