Three-dimensional effective theories for the two Higgs doublet model at high temperature

TL;DR

This paper derives three-dimensional effective theories for the two Higgs doublet model at high temperature, enabling non-perturbative lattice studies of the electroweak phase transition.

Contribution

It provides a detailed derivation of the dimensional reduction from 4D to 3D for the 2HDM, facilitating future non-perturbative analyses.

Findings

Derivation of 3D effective theories for 2HDM

Mapping between 4D and 3D theories detailed

Framework for lattice simulations of EWPT in 2HDM

Abstract

Due to the infrared problem of high-temperature field theory, a robust study of the electroweak phase transition (EWPT) requires use of non-perturbative methods. We apply the method of high-temperature dimensional reduction to the two Higgs doublet model (2HDM) to obtain three-dimensional effective theories that can be used for non-perturbative simulations. A detailed derivation of the mapping between the full four-dimensional and the effective three-dimensional theories is presented. The results will be used in future lattice studies of the 2HDM. In the limit of large mass mixing between the doublets, existing lattice results can be recycled. The results of such a study are presented in a companion paper.