Magnetic screening in the high temperature phase of the standard model

Non-perturbative effects in the high-temperature phase of the electroweak theory are characterized by a magnetic screening length. Its size influences the range of validity of perturbation theory, and it also determines the critical Higgs boson mass where the first-order phase transition changes to a crossover. We propose a gauge-invariant definition of the magnetic screening length and discuss its role in several gauge-dependent and gauge-invariant correlation functions.