  Motivated by applications in thermal QCD and cosmology, we elaborate on a
general method for computing next-to-leading order spectral functions for
composite operators at vanishing spatial momentum, accounting for real, virtual
as well as thermal corrections. As an example, we compute these functions
(together with the corresponding imaginary-time correlators which can be
compared with lattice simulations) for scalar and pseudoscalar densities in
pure Yang-Mills theory. Our results may turn out to be helpful in
non-perturbative estimates of the corresponding transport coefficients, which
are the bulk viscosity in the scalar channel and the rate of anomalous
chirality violation in the pseudoscalar channel. We also mention links to
cosmology, although the most useful results in that context may come from a
future generalization of our methods to other correlators.
