Many lattice studies of heavy quark diffusion originate from a colour-electric correlator, obtained as a leading term after an expansion in the inverse of the heavy-quark mass. In view of the fact that the charm quark is not particularly heavy, we consider subleading terms in the expansion. Working out correlators up to $O(1/M^2)$, we argue that the leading corrections are suppressed by $O(T/M)$, and one of them can be extracted from a colour-magnetic correlator. The corresponding transport coefficient is non-perturbative already at leading order in the weak-coupling expansion, and therefore requires a non-perturbative determination.
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