  The bulk viscosity of thermalized QCD matter at temperatures above a few
hundred MeV could be significantly influenced by charm quarks because their
contribution arises four perturbative orders before purely gluonic effects. In
an attempt to clarify the challenges of a lattice study, we determine the
relevant imaginary-time correlator (of massive scalar densities) up to NLO in
perturbation theory, and compare with existing data. We find discrepancies much
larger than in the vector channel; this may hint, apart from the importance of
taking a continuum limit, to larger non-perturbative effects in the scalar
channel. We also recall how a transport peak related to the scalar density
spectral function encodes non-perturbative information concerning the charm
quark chemical equilibration rate close to equilibrium.
