Effective Debye Screening Mass in an Anisotropic Quark Gluon Plasma

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.