Interplay of Infrared Divergences and Gauge-Dependence of the Effective Potential

TL;DR

This paper investigates the infrared divergences and gauge-dependence issues in the effective potential, demonstrating that proper resummation techniques resolve both problems and are applicable to the Standard Model.

Contribution

It shows that resummation of Goldstone propagators addresses IR divergences and gauge-dependence in the effective potential, with explicit analysis in the Abelian Higgs model and generalization to the Standard Model.

Findings

Resummation fixes IR divergences in the effective potential.

Resummation also cures gauge-dependence at the potential minimum.

A specific IR divergence in Fermi gauge is identified and addressed.

Abstract

The perturbative effective potential suffers infrared (IR) divergences in gauges with massless Goldstones in their minima (like Landau or Fermi gauges) but the problem can be fixed by a suitable resummation of the Goldstone propagators. When the potential minimum is generated radiatively, gauge-independence of the potential at the minimum also requires resummation and we demonstrate that the resummation that solves the IR problem also cures the gauge-dependence issue, showing this explicitly in the Abelian Higgs model in Fermi gauge. In the process we find an IR divergence (in the location of the minimum) specific to Fermi gauge and not appreciated in recent literature. We show that physical observables can still be computed in this gauge and we further show how to get rid of this divergence by a field redefinition. All these results generalize to the Standard Model case.