Nonperturbative Contributions to the Hot Electroweak Potential and the Crossover

Abstract

We discuss nonperturbative contributions to the 3-dimensional one-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 <F^2>=0 in Yang-Mills theory appears for small Higgs expectation value <ϕ^2> in an IR regularized form. The gauge boson propagator obtains a positive momentum-dependent ``diamagnetic&#39;&#39; effective (mass)^2 due to confinement effects and a negative one due to ``paramagnetic&#39;&#39; 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 ϕ^4 and ϕ^2 terms vanish there.