The analytic structure of the QCD propagators, confinement, and deconfinement

We present the first complete calculation of the analytic structure of the zero-spatial-momentum finite-temperature Landau-gauge gluon propagator carried out at one loop by a massive deformation of QCD perturbation theory -- the screened massive expansion -- at temperatures ranging from $T=0$ to $T\approx 3T_{c}$. We find no signatures of deconfinement in the form of meaningful changes in said structure. We argue that, beyond Euclidean space, massive perturbative methods -- including the Curci-Ferrari model -- might be missing crucial dynamical information as a consequence of the perturbative violation of QCD's Ward identities.