Revisiting electroweak phase transition in the standard model with a real singlet scalar

TL;DR

This paper reevaluates the electroweak phase transition in the standard model extended with a real scalar, comparing different calculation schemes and highlighting the effects of Nambu-Goldstone resummation and gauge dependence on the transition's strength.

Contribution

It systematically compares gauge-dependent and gauge-independent methods for analyzing the electroweak phase transition with a real scalar, quantifying scheme effects and uncertainties.

Findings

Nambu-Goldstone resummation impacts the transition strength by about 1%.

Gauge-dependent and -independent methods yield qualitatively similar results.

Scale uncertainties exceed 10%, emphasizing the need for higher-order corrections.

Abstract

We revisit the electroweak phase transition in the standard model with a real scalar, utilizing several calculation methods to investigate scheme dependences. We quantify the numerical impacts of Nambu-Goldstone resummation, required in one of the schemes, on the strength of the first-order electroweak phase transition. We also employ a gauge-independent scheme to make a comparison with the standard gauge-dependent results. It is found that the effect of the Nambu-Goldstone resummation is typically $\sim1\%$. Our analysis shows that both gauge-dependent and -independent methods give qualitatively the same result within theoretical uncertainties. In either methods, the scale uncertainties in the ratio of critical temperature and the corresponding Higgs vacuum expectation value are more than 10%, which signifies the importance of higher-order corrections.