The One-Loop Effective Potential in Non-Linear Gauges

TL;DR

This paper computes the one-loop effective potential in a non-linear gauge for an Abelian Higgs model, demonstrating gauge parameter independence at extrema and extending renormalization results.

Contribution

It introduces a renormalizable non-linear gauge class for the Abelian Higgs model and analyzes the gauge independence of the effective potential at one-loop level.

Findings

Effective potential at extrema is gauge parameter independent.

Provides explicit one-loop renormalizations in the non-linear gauge.

Extends the Feynman-'t Hooft gauge to a broader class of gauges.

Abstract

We calculate the 1-loop effective potential of an Abelian Higgs model within the R_{\xi/\sigma} class of non-linear gauges that preserves the Higgs-boson low-energy theorem. The R_{\xi/\sigma} gauge involves two gauge-fixing parameters \xi and \sigma, and is a renormalizable extension of the Feynman--'t Hooft R_\xi set of gauges beyond the 1-loop level. By taking consistently into account Goldstone--gauge-boson mixing effects, we show how the 1-loop effective potential evaluated at its extrema is independent of both \xi and \sigma, in agreement with the Nielsen identity. The 1-loop constant and wavefunction renormalizations are presented within this non-linear R_{\xi/\sigma} class of gauges.