How arbitrary are perturbative calculations of the electroweak phase transition?

TL;DR

This paper assesses the uncertainties in perturbative calculations of the electroweak phase transition, focusing on gauge, renormalisation, and treatment scheme dependencies, and finds that some aspects cause significant variability in predictions.

Contribution

It systematically analyzes how gauge choices, renormalisation schemes, and diagram treatments affect the reliability of electroweak phase transition calculations in an extended Standard Model.

Findings

Different schemes cause modest changes in critical temperature predictions.

Gauge and scale dependence can significantly alter the existence of the phase transition.

Goldstone and daisy diagram treatments have limited impact on results.

Abstract

We investigate the extent to which perturbative calculations of the electroweak phase transition are arbitrary and uncertain, owing to their gauge, renormalisation scale and scheme dependence, as well as treatments of the Goldstone catastrophe and daisy diagrams. Using the complete parameter space of the Standard Model extended by a real scalar singlet with a $\mathbb{Z}_2$ symmetry as a test, we explore the properties of the electroweak phase transition in general $R_\xi$ and covariant gauges, OS and $\overline{\text{MS}}$ renormalisation schemes, and for common treatments of the Goldstone catastrophe and daisy diagrams. Reassuringly, we find that different renormalisation schemes and different treatments of the Goldstone catastrophe and daisy diagrams typically lead to only modest changes in predictions for the critical temperature and strength of the phase transition. On the other hand, the gauge and renormalisation scale dependence may be significant, and often impact the existence of the phase transition altogether.