Removing the gauge parameter dependence of the effective potential by a field redefinition

TL;DR

This paper demonstrates how to eliminate gauge parameter dependence in the effective potential of the Standard Model using a field redefinition, ensuring gauge invariance in calculations.

Contribution

It introduces a method based on solving PDEs with characteristics to remove gauge dependence from the effective potential in the Standard Model.

Findings

Gauge dependence is fully removed through the proposed method.

The approach is applicable up to next-leading logarithmic order.

Ensures gauge invariance in effective potential calculations.

Abstract

The gauge parameter dependence of the effective potential is determined by partial differential equations involving also the Higgs boson field expectation value. Solving these equations by the method of characteristics leads to complete elimination of the gauge parameter dependence of the effective potential. The construction is carried out in the case of the standard model of electroweak unification for the renormalization group improved effective potential up to the next-leading logarithmic order.