Resummation of Goldstone Infrared Divergences: A Proof to All Orders

Abstract

The perturbative effective potential calculated in Landau gauge suffers from infrared problems due to Goldstone boson loops. These divergences are spurious and can be removed by a resummation procedure that amounts to a shift of the mass of soft Goldstones. We prove this to all loops using an effective theory approach, providing a compact recipe for the shift of the Goldstone mass that relies on the use of the method of regions to split soft and hard Goldstone contributions.

30 pages, 3 figures

References in corpus (8)

• Algorithm FIRE -- Feynman Integral REduction
• Taming Infrared Divergences in the Effective Potential
• Taming the Goldstone contributions to the effective potential
• Consistent Use of Effective Potentials
• Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
• Effective potential at three loops
• Interplay of Infrared Divergences and Gauge-Dependence of the Effective Potential

Cited by in corpus (9)

• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• How arbitrary are perturbative calculations of the electroweak phase transition?
• Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors
• Two-loop effective potential for generalized gauge fixing
• A new perspective on the electroweak phase transition in the Standard Model Effective Field Theory
• On the relationship between gauge dependence and IR divergences in the $\hslash$-expansion of the effective potential
• External leg corrections as an origin of large logarithms
• Vacuum stability of Froggatt-Nielsen models
• Real effective potentials for phase transitions in models with extended scalar sectors