Taming Infrared Divergences in the Effective Potential

Abstract

The Higgs effective potential in the Standard Model (SM), calculated perturbatively, generically suffers from infrared (IR) divergences when the (field-dependent) tree-level mass of the Goldstone bosons goes to zero. Such divergences can affect both the potential and its first derivative and become worse with increasing loop order. In this paper we show that these IR divergences are spurious, we perform a simple resummation of all IR-problematic terms known (up to three loops) and explain how to extend the resummation to cure all such divergences to any order. The method is of general applicability and would work in scenarios other than the SM. Our discussion has some bearing on a scenario recently proposed as a mechanism for gauge mediation of scale breaking in the ultraviolet, in which it is claimed that the low-energy Higgs potential is non-standard. We argue that all non-decoupling effects from the heavy sector can be absorbed in the renormalization of low-energy parameters leading to a SM-like effective theory.

26 pages, LaTeX

References in corpus (5)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Introduction to Effective Field Theory
• Taming the Goldstone contributions to the effective potential
• Cosmological Signatures of a UV-Conformal Standard Model

Cited by in corpus (22)

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• Precise Higgs mass calculations in (non-)minimal supersymmetry at both high and low scales
• On the two-loop corrections to the Higgs masses in the NMSSM
• Light Dark Matter, Naturalness, and the Radiative Origin of the Electroweak Scale
• Gauge-Independent Scales Related to the Standard Model Vacuum Instability
• Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
• Two-loop scale-invariant scalar potential and quantum effective operators
• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
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• Interplay of Infrared Divergences and Gauge-Dependence of the Effective Potential
• Pole mass of the W boson at two-loop order in the pure MS-bar scheme
• Strongly First-Order Electroweak Phase Transition and Classical Scale Invariance
• Higgs vacua with potential barriers
• Gravitational Wave Imprints of Left-Right Symmetric Model with Minimal Higgs Sector
• Two-loop Higgs mass calculation from a diagrammatic approach
• Matching relations for decoupling in the Standard Model at two loops and beyond
• External leg corrections as an origin of large logarithms
• Properties of the vacuum expectation values in $R_{\xi }$ and general gauge
• All one-loop scalar vertices in the effective potential approach