Phase Transitions in Dimensional Reduction up to Three Loops

TL;DR

This paper computes phase-transition parameters up to three loops in a scalar model similar to the Higgs sector, revealing the significance of higher-order corrections for strong phase transitions and potential gravitational wave signals.

Contribution

It provides the first three-loop calculation of phase transition parameters in a Higgs-like model using dimensional reduction, including detailed correction quantification.

Findings

1-loop dimension-6 corrections can compete with 2-loop quartic corrections.

3-loop thermal mass corrections are generally smaller than 1- and 2-loop effects.

Higher-order corrections are crucial for accurate predictions of strong phase transitions.

Abstract

We perform the first computation of phase-transition parameters to cubic order in $\lambda\sim m^2/T^2$, where $m$ is the scalar mass and $T$ is the temperature, in a simple model resembling the Higgs sector of the SMEFT. We use dimensional reduction, including 1-loop matching corrections for terms of dimension 6 (in 4-dimensional units), 2-loop contributions for dimension-4 ones and 3-loops for the squared mass. We precisely quantify the size of the different corrections, including renormalisation-group running as well as quantum effects from light fields in the effective theory provided by the Coleman-Weinberg potential, and discuss briefly the implications for gravitational waves. Our results suggest that, for strong phase transitions, 1-loop corrections from dimension-6 operators can compete with 2-loop ones from quartic couplings, but largely surpass those from 3-loop thermal masses.