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

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.