Energy hierarchies governing quarkonium dynamics in heavy ion collisions

In this paper, we critically examine hierarchies between the 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 (Eb) and the medium scales; temperature (T) and Debye mass (mD). It is well known that if these ratios are much larger than 1 then the dominant process governing quarkonium evolution is dissociation by thermal gluons (gluodissociation). On the other hand, if the ratio Eb/T 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 QQ¯ pair. This has a significant bearing when we follow the quantum dynamics of quarkonia in the medium. The inverse medium relaxation time is also ≈T and if Eb is comparable (or larger) in magnitude to T, the quantum evolution of QQ¯ is nonlocal in time within the Brownian approximation. Published by the American Physical Society 2024