Thermalization of the Higgs Field at the Electroweak Phase Transition

The thermalization rate for long wavelength fluctuations in the Higgs field is calculated from the imaginary part of the finite temperature effective action in the unbroken phase of the Standard Model. We use improved propagators including a resummation of hard thermal loops. The thermalization rate is computed at one loop level, but an estimate of the two--loop contribution appears to give an indication that they are comparable to the one--loop result for small thermal higgs mass. We show also that the Higgs field fluctuations are likely to thermalize very fast compared with the electroweak phase transition time.