The renormalized gauge coupling and non-perturbative tests of dimensional reduction

TL;DR

This paper compares non-perturbative lattice results of the renormalized gauge coupling in the Standard Model to the MSbar scheme, testing the validity of dimensional reduction at finite temperature through electroweak phase transition analysis.

Contribution

It provides a novel non-perturbative comparison between lattice and MSbar scheme gauge couplings to validate dimensional reduction in finite temperature theories.

Findings

Agreement between 4d lattice and 3d effective theory for critical temperatures

Validation of dimensional reduction through non-perturbative gauge coupling comparison

Enhanced understanding of electroweak phase transition dynamics

Abstract

In 4d lattice simulations of Standard Model like theories, the renormalized gauge coupling in the broken phase can be determined from the prefactor of the Yukawa term in the static potential. We compute the same quantity in terms of the conventional MSbar scheme gauge coupling. The result allows for a further non-perturbative test of finite temperature dimensional reduction, by a comparison of the critical temperatures for the electroweak phase transition as obtained with 4d lattice simulations and with 3d effective theory simulations.