Crossover and mass gap of the SU(2)-Higgs model at high temperature

Analytic estimates of screening masses in the symmetric, high-temperature phase of the SU(2)-Higgs model are reviewed. The size of the mass gap in the symmetric phase is closely related to the critical Higgs mass where the first-order electroweak phase transition changes to a smooth crossover. We also discuss some conjectures concerning the connection between the screening masses of propagators in a fixed gauge and screening masses of gauge-invariant operators.