Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations: 1. Standard Model

TL;DR

This paper introduces a new gauge-invariant scheme for electroweak renormalization in the Standard Model that improves perturbative stability and gauge independence by combining advantages of existing tadpole renormalization methods.

Contribution

The paper proposes the Gauge-Invariant Vacuum expectation value Scheme (GIVS), a hybrid tadpole renormalization scheme based on non-linear Higgs representations, ensuring gauge independence and perturbative stability.

Findings

GIVS is gauge independent and stable under perturbation.

Conversion between on-shell and MSbar masses demonstrates GIVS's stability.

The scheme improves electroweak parameter renormalization in the SM.

Abstract

The renormalization of vacuum expectation value parameters, such as $v$ in the Standard Model (SM), is an important ingredient in electroweak renormalization, where this issue is connected to the treatment of tadpoles. Tadpole counterterms can be generated in two different ways in the Lagrangian: in the course of parameter renormalization, or alternatively via Higgs field redefinitions. The former typically leads to small corrections originating from tadpoles, but in general suffers from gauge dependences if MSbar renormalization conditions are used for mass parameters. The latter is free from gauge dependences, but is prone to very large corrections in MSbar schemes, jeopardizing perturbative stability in predictions. In this paper we propose a new scheme for tadpole renormalization, dubbed Gauge-Invariant Vacuum expectation value Scheme (GIVS), which is a hybrid scheme of the two mentioned types, with the benefits of being gauge independent and perturbatively stable. The GIVS is based on the gauge-invariance property of Higgs fields, and the corresponding parameters like $v$, in non-linear representations of Higgs multiplets. We demonstrate the perturbative stability of the GIVS in the SM by discussing the conversion between on-shell and MSbar renormalized masses.