Approach to equilibrium of quarkonium in quark-gluon plasma

TL;DR

This paper investigates how bottomonium states, specifically $(1S)$, reach equilibrium in quark-gluon plasma by calculating dissociation and recombination rates, and studying their evolution through Boltzmann dynamics.

Contribution

It introduces a detailed dynamical model of bottomonium evolution in quark-gluon plasma using potential non-relativistic QCD and Boltzmann equations, highlighting the importance of medium interactions.

Findings

Interactions are essential for equilibrium achievement.

Angular distribution reveals recombination stages.

Different initial conditions lead to distinct final flavor ratios.

Abstract

We calculate the dissociation and recombination rates of $\Upsilon(1S)$ in quark-gluon plasma by using potential non-relativistic QCD. We then study the dynamical in-medium evolution of the $b\bar{b}-\Upsilon$ system in a periodic box via the Boltzmann equation and explore how the system reaches equilibrium. We find that interactions between the free heavy quarks and the medium are necessary for the system to reach equilibrium. We find that the angular distribution of $\Upsilon(1S)$ probes the stages at which recombination occurs. Finally, we study the system under a longitudinal expansion and show that different initial conditions evolve to distinct final ratios of hidden and open $b$ flavors. We argue that experimental measurements of the ratio could address open questions in the quarkonium production in heavy ion collisions.