Gauge fixing and renormalisation scale independence of tunneling rate in abelian Higgs model and in the Standard Model

TL;DR

This paper demonstrates gauge fixing independence of tunneling rates in the abelian Higgs model and discusses implications for the Standard Model, ensuring gauge invariance in calculations involving nonrenormalisable operators.

Contribution

It provides a method to compute tunneling rates in gauge theories that remains gauge invariant even with higher order operators, applicable to the Standard Model.

Findings

Gauge fixing independence of tunneling rates is explicitly shown.

Nielsen identities are preserved with higher order operators.

Gauge invariant computation of tunneling rates in the Standard Model context.

Abstract

We explicitly show perturbative gauge fixing independence of the tunneling rate to a stable radiatively induced vacuum in the abelian Higgs model. We work with a class of $R_\xi$ gauges in the presence of both dimensionless and dimensionful gauge fixing parameters. We show that Nielsen identities survive the inclusion of higher order oparators and compute the tunnelling rate to the vacua modified by the nonrenormalisable operators in a gauge invariant manner. We also discuss implications of this method for the complete Standard Model.