Two-loop electroweak threshold corrections in the Standard Model

TL;DR

This paper calculates two-loop electroweak threshold corrections in the Standard Model, providing precise relations between on-shell and bar schemes, crucial for vacuum stability analyses, while ensuring gauge invariance and comparing approximation methods.

Contribution

It presents the first full two-loop electroweak threshold corrections in the Standard Model, including tadpole contributions and gauge invariance considerations.

Findings

Computed full two-loop electroweak threshold corrections.

Compared gaugeless-limit approximation with full calculation.

Provided gauge-invariant relations between parameters.

Abstract

We study the relationships between the basic parameters of the on-shell renormalization scheme and their counterparts in the $\overline{\mathrm{MS}}$ scheme at full order ${\cal O}(\alpha^2)$ in the Standard Model. These enter as threshold corrections the renormalization group analyses underlying, e.g., the investigation of the vacuum stability. To ensure the gauge invariance of the parameters, in particular of the $\overline{\mathrm{MS}}$ masses, we work in $R_\xi$ gauge and systematically include tadpole contributions. We also consider the gaugeless-limit approximation and compare it with the full two-loop electroweak calculation.