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 interquark 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.
Highlights
The ongoing heavy-ion collision experiments at the Relativistic Heavy Ion Collider and the Large Hadron Collider aim to create and study a primordial state of matter called a quark gluon plasma (QGP)
IV, we demonstrate that highly accurate results of the eigen/binding energies of quarkonium states can be obtained by solving the Schrödinger equation with only the leading-order contribution in the above Taylor expansion of the HQ potential
We introduced a prescription for an isotropic effective Debye mass that depends on the quantum numbers l and m of heavy-quarkonium state
Summary
The ongoing heavy-ion collision experiments at the Relativistic Heavy Ion Collider and the Large Hadron Collider aim to create and study a primordial state of matter called a quark gluon plasma (QGP). As will be discussed in this work, information on the physical properties of quarkonium states in an anisotropic QCD plasma can be obtained at a quantitative level by analyzing the corresponding problem in an “isotropic” medium characterized by the angle-averaged screening mass Mlmðλ; ξÞ. For several low-lying heavy-quarkonium bound states, the exact 3D results of the eigen/binding energies based on the potential model in Eq (4), together with the corresponding discrepancies from using the one-dimensional potential model based on the effective screening masses are listed in Appendix, which provides a direct numerical check of our method.
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