The errant life of a heavy quark in the quark-gluon plasma

In the high-temperature phase of QCD, the heavy quark momentum diffusion constant determines, via a fluctuation-dissipation relation, how fast a heavy quark kinetically equilibrates. This transport coefficient can be extracted from thermal correlators via a Kubo formula. We present a lattice calculation of the relevant Euclidean correlators in the gluon plasma, based on a recent formulation of the problem in heavy-quark effective field theory (HQET). We find a $\approx 20$ enhancement of the Euclidean correlator at maximal time separation as the temperature is lowered from $6T_c$ to $2T_c$, pointing to stronger interactions at lower temperatures. At the same time, the correlator becomes flatter from $6T_c$ down to $2T_c$, indicating a relative shift of the spectral weight to lower frequencies. A recent next-to-leading order perturbative calculation of the correlator agrees with the time dependence of the lattice data at the few-percent level. We estimate how much additional contribution from the $\omega \lesssim T$ region of the perturbative spectral function would be required to bring it in agreement with the lattice data at $3.1T_c$.