Static quark-antiquark pairs at finite temperature

TL;DR

This paper investigates the real-time evolution and potential of static quark-antiquark pairs in a finite temperature medium, revealing mechanisms for thermal decay and new potential contributions relevant to quarkonium dissociation.

Contribution

It derives the finite-temperature potential and decay width of static quark-antiquark pairs, including the first quantification of the color singlet to octet breakup mechanism.

Findings

The potential includes real and imaginary parts relevant at different temperature regimes.

The dominant decay mechanism varies with the relation between Debye mass and binding energy.

New contributions to the potential are identified for temperatures below 1/r.

Abstract

In a framework that makes close contact with modern effective field theories for non-relativistic bound states at zero temperature, we study the real-time evolution of a static quark-antiquark pair in a medium of gluons and light quarks at finite temperature. For temperatures ranging from values larger to smaller than the inverse distance of the quark and antiquark, 1/r, and at short distances, we derive the potential between the two static sources, and calculate their energy and thermal decay width. Two mechanisms contribute to the thermal decay width: the imaginary part of the gluon self energy induced by the Landau damping phenomenon, and the quark-antiquark color singlet to color octet thermal break up. Parametrically, the first mechanism dominates for temperatures such that the Debye mass is larger than the binding energy, while the latter, which we quantify here for the first time, dominates for temperatures such that the Debye mass is smaller than the binding energy. If the Debye mass is of the same order as 1/r, our results are in agreement with a recent calculation of the static Wilson loop at finite temperature. For temperatures smaller than 1/r, we find new contributions to the potential, both real and imaginary, which may be relevant to understand the onset of heavy quarkonium dissociation in a thermal medium.