Singlet-assisted electroweak phase transition at two loops

TL;DR

This paper performs a detailed two-loop analysis of the electroweak phase transition in a singlet-extended Standard Model, revealing significant deviations from one-loop predictions and providing a framework for non-perturbative studies.

Contribution

It advances the understanding of the electroweak phase transition by calculating the two-loop effective potential and deriving a dimensionally-reduced theory for lattice simulations.

Findings

Deviations of 20-50% in transition strength and temperature from one-loop results.

Larger discrepancies for extremely strong transitions due to scalar couplings.

Provision of a dimensionally-reduced effective theory for non-perturbative analysis.

Abstract

We investigate the electroweak phase transition in the real-singlet extension of the Standard Model at two-loop level, building upon existing one-loop studies. We calculate the effective potential in the high-temperature approximation and detail the required resummations at two-loop order. In typical strong-transition scenarios, we find deviations of order $20\% - 50\%$ from one-loop results in transition strength and critical temperature for both one- and two-step phase transitions. For extremely strong transitions, the discrepancy with one-loop predictions is even larger, presumably due to sizable scalar couplings in the tree-level potential. Along the way, we obtain a dimensionally-reduced effective theory applicable for non-perturbative lattice studies of the model.