Non-Abelian electric field correlator for quarkonium transport and thermal dark matter relic abundance

Quantifying the transport properties of heavy particles traveling through thermal non-abelian plasmas is of paramount importance to interpret measurements on those particles conducted after the freezeout. One such example is quarkonium suppression in heavy-ion collisions (HIC). Depending on the nature of dark matter (DM), another example is the thermal DM relic abundance.

In this work, we perform the first complete NLO calculation of the gauge-invariant non-Abelian electric correlator that determines the transition rate between a bound singlet state and an adjoint representation unbound state in potential Non-Relativistic Effective Field Theory (pNREFT) inside a thermal SU(N_c) non-abelian plasma. We show that our result is infrared and collinear safe, as well as explicitly gauge invariant in perturbation theory within R_xi gauges. We find that if the temperature is of the same order as the binding energy the NLO rates are significantly enhanced compared to the LO ones, which can be crucial to correctly interpret the final quarkonium yields in HIC and the present-day DM abundance in terms of an underlying model.