A Critical Look at the Electroweak Phase Transition

TL;DR

This paper critically examines the electroweak phase transition, addressing issues in perturbative calculations and developing gauge-invariant, robust tools for analyzing phase transitions in particle physics models.

Contribution

It introduces a consistent power-counting scheme to eliminate gauge and infrared problems and computes the two-loop finite temperature effective potential in a general gauge.

Findings

Gauge invariance is maintained in the new perturbative approach

The two-loop effective potential is computed for the Standard Model

The method resolves issues of gauge dependence and infrared divergences

Abstract

The electroweak phase transition broke the electroweak symmetry. Perturbative methods used to calculate observables related to this phase transition suffer from severe problems such as gauge dependence, infrared divergences, and a breakdown of perturbation theory. In this paper we develop robust perturbative tools for dealing with phase transitions. We argue that gauge and infrared problems are absent in a consistent power-counting. We calculate the finite temperature effective potential to two loops for general gauge-fixing parameters in a generic model. We demonstrate gauge invariance, and perform numerical calculations for the Standard Model in Fermi gauge.