Abstract
In view of the current status of measured Higgs boson properties, we consider a question whether only the Higgs self-interactions can deviate significantly from the Standard-Model (SM) predictions. This may be possible if the Higgs effective potential is irregular at the origin. As an example we investigate an extended Higgs sector with singlet scalar(s) and classical scale invariance. We develop a perturbative formulation necessary to analyze this model in detail. The behavior of a phenomenologically valid potential in the perturbative regime is studied around the electroweak scale. We reproduce known results: the Higgs self-interactions are substantially stronger than the SM predictions, while the Higgs interactions with other SM particles are barely changed. We further predict that the interactions of singlet scalar(s), which is a few to several times heavier than the Higgs boson, tend to be fairly strong. If probed, these features will provide vivid clues to the structure of the vacuum. We also examine Veltman’s condition for the Higgs boson mass.
Highlights
Of the self-interactions of the Higgs boson is still missing, which is indispensable to unveil the structure of the Higgs potential
In various physics of spontaneous symmetry breakdown, there appear effective potentials which cannot be expanded in polynomials in the field variables, namely effective potentials which are irregular at the origin
With a flat direction at LO, with an appropriate choice of the couplings, VLO + VNLO exhibits a minimum on the φ-axis by the CW mechanism, and the Higgs boson becomes massive at next-to-leading order (NLO)
Summary
The scale-invariant limit of the SM has long been excluded experimentally. To impose classical scale invariance, we need to extend the Higgs sector. We consider a scale-invariant extension of the SM with an additional real singlet scalar field with a Higgs-portal coupling. We consider the case where the singlet scalar field is in the. Fundamental representation of a global O(N ) group: S = (S1, · · · , SN )T. Where the real singlet field S interacts with itself and the Higgs doublet field H via the self-interaction and portal interaction with the coupling constants λS and λHS, respectively
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