One-dimensional complex potentials for quarkonia in a quark-gluon plasma

TL;DR

This paper develops a one-dimensional complex potential model for quarkonium in quark-gluon plasma, capturing key properties from three-dimensional lattice QCD to simplify and improve the description of quarkonium dynamics.

Contribution

It introduces a parameterized one-dimensional complex potential that accurately reproduces spectral properties of three-dimensional lattice QCD inspired potentials for quarkonium.

Findings

The potential reproduces temperature-dependent masses of eigenstates.

The potential matches decay widths from lattice QCD.

Spectral decompositions confirm compatibility with master equations.

Abstract

Master equations of the Lindblad type have recently been derived to describe the dynamics of quarkonium states in the quark-gluon plasma. Because their full resolution in three dimensions is very challenging, the equations are often reduced to one dimension. The main ingredient of these equations is the complex potential that describes the binding of the heavy quark-antiquark pairs and their interactions with the medium. In this work, we propose a one-dimensional complex potential parameterized to reproduce at best two key properties -- the temperature-dependent masses of the eigenstates and their decay widths -- of a three-dimensional lattice QCD inspired potential. Their spectral decompositions are calculated to check their compatibility with the positivity of the master equations.