Thermalization of Bottomonium in the Quark-Gluon Plasma

TL;DR

This paper investigates how bottomonium particles thermalize in the quark-gluon plasma using large-scale quantum simulations, revealing how temperature and medium coupling influence the thermalization process and steady states.

Contribution

It introduces a detailed simulation framework for bottomonium thermalization in the quark-gluon plasma and analyzes the effects of medium interactions on steady states.

Findings

Thermalization times increase with decreasing temperature and coupling.

Steady states show small corrections to Gibbs states, diminishing with weaker coupling.

At 450 MeV, bottomonium approaches a nearly thermal state with minor deviations.

Abstract

We study the approach to equilibrium of bottomonium in the quark-gluon plasma within the open quantum system framework. We perform large-scale simulations of the long-time behavior in three dimensions using the quantum trajectory method to observe the emergence of steady states and determine the timescale of thermalization in position-, angular-momentum-, and color-space. We find that the thermalization timescale increases with decreasing temperature and decreasing coupling to the medium, which is given by transport coefficients of the medium. Additionally, we observe that the steady states exhibit small corrections to the Gibbs state due to medium interactions and show that these corrections diminish for weaker medium coupling and higher temperature. At a temperature of $450\,$MeV, quarkonium relaxes to a state that is approximately thermal, with the most significant correction being a smaller overlap of the $1S$ state with respect to the Gibbs state. We compare these findings with the master equation obtained at leading order in the expansion of the binding energy over the temperature, which we find to have a trivial steady state.