Non-perturbative contributions to the hot electroweak potential and the crossover

We discuss non-perturbative contributions to the three-dimensional 1-loop e ffective potential of the electroweak theory at high temperatures in the fr amework of the stochastic vacuum model. It assumes a gauge-field background with Gaussian correlations which leads to confinement. The instability of [F-2] = 0 in Yang-Mills theory appears for small Higgs expectation value [p hi(2)] in an IR regularized form. The gauge-boson propagator obtains a posi tive momentum-dependent "diamagnetic" effective (mass)(2) due to confinemen t effects and a negative one due to ''paramagnetic" spin-spin interactions which are related to the [F-2] = 0 instability. Numerical evaluation of an approximate effective potential containing these masses shows qualitatively the fading away of the first-order phase transition with increasing Higgs mass which was observed in lattice calculations. The crossover point can be roughly determined postulating that the effective phi(4) and phi(2) terms vanish there. (C) 1999 Elsevier Science B.V.