  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.
