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

Next-to-leading order thermal spectral functions in the perturbative domain