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

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.

29 pages

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Cited by in corpus (11)

• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• Theoretical uncertainties for cosmological first-order phase transitions
• Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
• Two-loop scale-invariant scalar potential and quantum effective operators
• Effective potential at three loops
• Stop comparing resummation methods
• Inflation without gauge redundancy
• Gauge invariance of the vector meson mass in the Coleman-Weinberg model
• Gauge independence of the physical fermion mass in the effective action of theories with radiative symmetry breaking
• Radiative symmetry breaking from the on-shell perspective