Effective Debye Screening Mass in an Anisotropic Quark Gluon Plasma

TL;DR

This paper introduces an effective isotropic Debye screening mass to simplify modeling of heavy-quarkonium states in an anisotropic quark-gluon plasma, enabling efficient 1D Schrödinger equation solutions that approximate full 3D results.

Contribution

The authors develop a method to reduce anisotropic heavy-quark potentials to isotropic forms using quantum number-dependent screening masses, simplifying complex calculations.

Findings

Effective screening masses reproduce 3D results with high accuracy.

Simplified 1D Schrödinger equation solutions are feasible for anisotropic potentials.

Method facilitates inclusion of momentum-anisotropy effects in quarkonium simulations.

Abstract

Due to the rapid longitudinal expansion of the quark-gluon plasma created in heavy-ion collisions, large local-rest-frame momentum-space anisotropies are generated during the system's evolution. These momentum-space anisotropies complicate the modeling of heavy-quarkonium dynamics in the quark-gluon plasma due to the fact that the resulting inter-quark potentials are spatially anisotropic, requiring real-time solution of the 3D Schr\"odinger equation. Herein, we introduce a method for reducing anisotropic heavy-quark potentials to isotropic ones by introducing an effective screening mass that depends on the quantum numbers $l$ and $m$ of a given state. We demonstrate that, using the resulting effective Debye screening masses, one can solve a 1D Schr\"odinger equation and reproduce the full 3D results for the energies and binding energies of low-lying heavy-quarkonium bound states to relatively high accuracy. The resulting effective isotropic potential models could provide an efficient method for including momentum-anisotropy effects in open quantum system simulations of heavy-quarkonium dynamics in the quark-gluon plasma.