Taming the Goldstone contributions to the effective potential

Abstract

The standard perturbative effective potential suffers from two related problems of principle involving the field-dependent Goldstone boson squared mass, G. First, in general G can be negative, and it actually is negative in the Standard Model; this leads to imaginary contributions to the effective potential that are not associated with a physical instability, and therefore spurious. Second, in the limit that G approaches zero, the effective potential minimization condition is logarithmically divergent already at two-loop order, and has increasingly severe power-law singularities at higher loop orders. I resolve both issues by resumming the Goldstone boson contributions to the effective potential. For the resulting resummed effective potential, the minimum value and the minimization condition that gives the vacuum expectation value are obtained in forms that do not involve G at all.

25 pages. v2: typo in 21st line of eq. (4.20) fixed. Reference added

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• 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
• Cosmological implications of the Higgs mass measurement
• The Probable Fate of the Standard Model
• Taming Infrared Divergences in the Effective Potential
• On the gauge dependence of the Standard Model vacuum instability scale
• (No) Eternal Inflation and Precision Higgs Physics
• Removing the gauge parameter dependence of the effective potential by a field redefinition
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