Effective Scalar Field Theory for the Electroweak Phase Transition

TL;DR

This paper develops an effective 3D scalar field model for the electroweak phase transition, analyzing its properties using mean field and Monte Carlo methods, and highlighting the importance of non-perturbative gauge effects.

Contribution

It introduces a 3D effective theory for the electroweak transition derived via dimensional reduction, incorporating nonperturbative effects and comparing mean field and Monte Carlo results.

Findings

Identifies a discontinuous phase transition at Higgs mass 37 GeV.

Monte Carlo results show a weaker first order transition than mean field predictions.

Non-perturbative gauge effects significantly influence the transition characteristics.

Abstract

We investigate an effective model for the finite temperature restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the $3+1$ dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a $3$-dimensional $O(4)$ ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, $m_H=37~{\rm GeV}$, considered in the present investigation, we find a discontinuous symmetry restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first order phase transition as compared to the mean field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first order transition could result only from non-perturbative effects related to the gauge degrees of freedom.