Static correlation lengths in QCD at high temperatures and finite densities

We use a perturbatively derived effective field theory and three-dimensional lattice simulations to determine the longest static correlation lengths in the deconfined QCD plasma phase at high temperatures (T\gsim 2 Tc) and finite densities (\mu\lsim 4 T). For vanishing chemical potential, we refine a previous determination of the Debye screening length, and determine the dependence of different correlation lengths on the number of massless flavours as well as on the number of colours. For non-vanishing but small chemical potential, the existence of Debye screening allows us to carry out simulations corresponding to the full QCD with two (or three) massless dynamical flavours, in spite of a complex action. We investigate how the correlation lengths in the different quantum number channels change as the chemical potential is switched on.