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 Schrödinger 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 Schrödinger 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.

The complex heavy-quark potential in an anisotropic quark-gluon plasma -- Statics and dynamics

“…Thus, besides the results given in ref. [44], with the inclusion of an imaginary part in the potential, our work further confirms that the 1D effective potential model could provide an efficient method for including momentum-anisotropy effects.…”

“…With the concept of the "most similar state" introduced in ref. [44], M lm (λ, ξ) is not universal for all the quarkonium states.…”

“…This is indeed the main obstacle to developing phenomenological applications which include momentum-anisotropy effects. As proposed in our previous work, one possible solution to this difficulty is to employ an angle-averaged effective screening mass M lm (λ, ξ) which by definition reads [44]…”

“…In ref. [44], a comprehensive analysis of the validity of using such an effective screening mass is provided where only the real part of the HQ potential is discussed. In this work, we apply the same idea to the imaginary part and the corresponding M re lm (λ, ξ) (which replaces mD (λ, ξ, θ) in eq.…”

“…Whether it is possible to have an effectively isotropic potential model that reproduces the full 3D results on the binding energies and decay widths of different bound states turns out to be very crucial when one attempts to include the effect of momentum anisotropies on quarkonium evolution using real-time solution of the Schrödinger equation. Previous work has assessed this conjecture for a real-valued potential model [44]. However, to do it properly one must demonstrate that the same logic can be applied to the imaginary part as well.…”