Abstract
We investigate a model with two real scalar fields that minimally generates exponentially different scales in an analog of the Coleman-Weinberg mechanism. The classical scale invariance — the absence of dimensionful parameters in the tree-level action, required in such a scale generation — can naturally be understood as a special case of the multicritical-point principle. This two-scalar model can couple to the Standard Model Higgs field to realize a maximum multicriticality (with all the dimensionful parameters being tuned to critical values) for field values around the electroweak scale, providing a generalization of the classical scale invariance to a wider class of criticality. As a bonus, one of the two scalars can be identified as Higgs-portal dark matter. We find that this model can be consistent with the constraints from dark matter relic abundance, its direct detection experiments, and the latest LHC data, while keeping the perturbativity up to the reduced Planck scale. We then present successful benchmark points satisfying all these constraints: the mass of dark matter is a few TeV, and its scattering cross section with nuclei is of the order of 10−9 pb, reachable in near future experiments. The mass of extra Higgs boson H is smaller than or of the order of 100 GeV, and the cross section of e+e− → ZH can be of fb level for collision energy 250 GeV, targetted at future lepton colliders.
Highlights
Minimal dimensional transmutationWe briefly review the minimal dimensional transmutation model based on the multicritical-point principle (MPP) that naturally realizes the analog of the CW mechanism [34]
The tremendous success of the standard cosmology requires at least three scales in the SM Lagrangian: the cosmological constant, electroweak, and Planck scales of the order of 10−12 GeV, 102 GeV, and 1018 GeV, respectively
We find that this model can be consistent with the constraints from dark matter relic abundance, its direct detection experiments, and the latest LHC data, while keeping the perturbativity up to the reduced Planck scale
Summary
We briefly review the minimal dimensional transmutation model based on the MPP that naturally realizes the analog of the CW mechanism [34]. The model is composed of additional two real scalar fields φ and S that are singlet under the SM gauge symmetry. The MPP in short is “the more (dimensionful) parameters in the low-energy effective potential are tuned to a set of critical values, the more likely to be realized by nature.”. The CSI scalar potential invariant under the Z2 ×Z2 symmetry consists of the following terms at tree level: V0tree. When we do not assume CSI nor Z2 symmetry, the tree-level potential can have the following additional terms: V tree. We examine possible multipoint criticality by turning on either the m2φ or μφ term separately, for cases without the CSI One should examine each multipoint criticality including these six dimensionful parameters, which will be an interesting research work in itself. Here instead, we examine possible multipoint criticality by turning on either the m2φ or μφ term separately, for cases without the CSI
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