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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 ≈20% enhancement of the Euclidean correlator at maximal time separation as the temperature is lowered from 6Tc to 2Tc, pointing to stronger interactions at lower temperatures. At the same time, the correlator becomes flatter from 6Tc down to 2Tc, 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-per cent level. We estimate how much additional contribution from the ωT region of the perturbative spectral function would be required to bring it in agreement with the lattice data at 3.1Tc.

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