Energy hierarchies governing quarkonium dynamics in Heavy Ion Collisions

TL;DR

This paper analyzes the energy scale hierarchies affecting quarkonium behavior in the quark-gluon plasma, emphasizing the importance of the full gluonic spectral function when traditional scale limits do not apply.

Contribution

It demonstrates that most of the quarkonium evolution occurs outside the simple scale hierarchy limits, requiring a full spectral function approach for accurate quantum dynamics modeling.

Findings

Scale hierarchies often do not fall into known limits, necessitating full spectral analysis.

Quantum evolution becomes non-local in time when binding energy is comparable to temperature.

Full spectral functions are essential for accurate quarkonium dynamics in the medium.

Abstract

In this paper, we critically examine hierarchies between energy scales that determine quarkonium dynamics in the quark gluon plasma. A particularly important role is played by the ratio of the binding energy of species ($E_b$) and the medium scales; temperature ($T$) and Debye mass ($m_D$). It is well known that if these ratios are much larger than one then the dominant process governing quarkonium evolution is dissociation by thermal gluons (gluo-dissociation). On the other hand, if this ratio is much smaller than one then quarkonium dynamics is dominated by screening and Landau damping of the exchanged gluons. Here we show that over most of the evolution, the scale hierarchies do not fall in either limit and one needs to use the full structure of the gluonic spectral function to follow the dynamics of the $Q\bar{Q}$ pair. This has a significant bearing when we follow the quantum dynamics of quarkonia in the medium. The inverse medium relaxation time is also $\sim T$ and if $E_b$ is comparable (or larger) in magnitude to $T$, the quantum evolution of $Q\bar{Q}$ is non-local in time within the Brownian approximation.