Heavy Quarkonium at finite temperature and chemical potential

TL;DR

This paper extends the understanding of heavy quarkonium behavior in thermal and dense environments, deriving formulas for energy shifts and decay widths at weak coupling, and highlighting the different dissociation mechanisms at zero and finite temperatures.

Contribution

It provides a generalized framework for heavy quarkonium in finite density conditions, including formulas for energy shifts and decay widths, and analyzes the role of magnetic modes and screening effects.

Findings

Decay width requires temperature above binding energy, regardless of chemical potential.

At zero temperature, dissociation is due solely to screening, not thermal effects.

Results are applicable to experimental conditions like SIS and NICA, with comparison to lattice data.

Abstract

We generalize known results for heavy quarkonium in a thermal bath to the case of a finite baryonic density, and provide a number of formulas for the energy shift and decay width that hold at weak coupling for sufficiently large temperature and/or chemical potential. We find that a non-vanishing decay width requires a temperature larger than the typical binding energy, no matter how large the chemical potential is. This implies that at zero temperature the dissociation mechanism of heavy quarkonium is due entirely to screening, unlike in the finite temperature case. We use several effective theories in order to sort out the contributions of the relevant energy and momentum scales. In particular, we consider contributions of the so called quasi-static magnetic modes. The generalization to the case of a finite isospin/strangeness chemical potential is trivial. We discuss possible applications to the SIS and NICA conditions, and compare with available lattice results.