A Self Consistent Study of the Phase Transition in the Scalar Electroweak Theory at Finite Temperature

TL;DR

This paper introduces a self-consistent two-step method combining dimensional reduction and renormalization techniques to study the phase transition in the scalar electroweak theory at finite temperature, improving upon traditional approaches.

Contribution

It presents a novel approach that integrates perturbative and non-perturbative methods for analyzing phase transitions in gauge theories at finite temperature.

Findings

Method avoids lack of self-consistency in traditional treatments.

Effective 3D lattice action suitable for computer simulations.

Provides a systematic way to separate infrared and ultraviolet problems.

Abstract

We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two - step method. It combines i) dimensional reduction to a 3-dimensional {\it lattice\/} theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. % This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations.