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

We discuss non-perturbative contributions to the three-dimensional 1-loop effective potential of the electroweak theory at high temperatures in the framework of the stochastic vacuum model. It assumes a gauge-field background with Gaussian correlations which leads to confinement. The instability of 〈F2〉 = 0 in Yang-Mills theory appears for small Higgs expectation value 〈φ2〉 in an IR regularized form. The gauge-boson propagator obtains a positive momentum-dependent “diamagnetic” effective (mass)2 due to confinement effects and a negative one due to “paramagnetic” spin-spin interactions which are related to the 〈F2〉 = 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 φ4 and φ2 terms vanish there.