Vacuum expectation value renormalization in the Standard Model and beyond

TL;DR

This paper investigates how the renormalization of the Higgs vacuum expectation value affects gauge dependence in the Standard Model and explores the connections between different tadpole renormalization schemes, including the Fleischer-Jegerlehner approach.

Contribution

It clarifies the role of the Higgs vacuum expectation value renormalization in gauge dependence and relates the FJ scheme to other tadpole renormalization methods, offering new insights.

Findings

Identifies the gauge dependence caused by the Higgs VEV renormalization constant.

Shows the relationship between the FJ scheme and other tadpole renormalization approaches.

Provides a new perspective on the Higgs background field renormalization.

Abstract

We show how the renormalization constant of the Higgs vacuum expectation value, fixed by a tadpole condition, is responsible for gauge dependences in various definitions of parameters in the $R_{\xi}$-gauge. Then we show the relationship of this renormalization constant to the Fleischer-Jegerlehner (FJ) scheme, which is used to avoid these gauge dependences. In this way, we also present a viewpoint on the FJ-scheme complementary to the ones already existing in the literature. Additionally, we compare and discuss different approaches to the renormalization of tadpoles by identifying the similarities and relations between them. The relationship to the Higgs background field renormalization is also discussed.