Abstract
We suggest a scalar singlet extension of the standard model, in which the multiple-point principle (MPP) condition of a vanishing Higgs potential at the Planck scale is realized. Although there have been lots of attempts to realize the MPP at the Planck scale, the realization with keeping naturalness is quite difficult. Our model can easily achieve the MPP at the Planck scale without large Higgs mass corrections. It is worth noting that the electroweak symmetry can be radiatively broken in our model. In the naturalness point of view, the singlet scalar mass should be of ${\cal O}(1)\,{\rm TeV}$ or less. We also consider right-handed neutrino extension of the model for neutrino mass generation. The model does not affect the MPP scenario, and might keep the naturalness with the new particle mass scale beyond TeV, thanks to accidental cancellation of Higgs mass corrections.
Highlights
The observed mass of the Higgs boson may imply that Higgs self-coupling vanish at a high energy scale in the framework of the standard model (SM)
One is our vacuum at the electroweak (EW) scale, and the other vacuum lies at the Planck scale, which can be realized by the Planck-scale boundary conditions of vanishing effective Higgs self-coupling, λH(MPl) = 0, and its beta function, βλH (MPl) = 0
We have investigated the scalar singlet extension of the SM with the multiple-point principle (MPP) condition, in which the scalar potential has two degenerate vacua at the EW and a UV scales
Summary
The observed mass of the Higgs boson may imply that Higgs self-coupling vanish at a high energy scale in the framework of the standard model (SM). An asymptotic safety scenario of gravity [2] predicted 125 GeV Higgs boson mass with a few GeV uncertainty This scenario pointed out λH(MPl) ∼ 0 and βλH (MPl) ∼ 0 We will investigate the MPP condition in a scalar singlet extended model, which can be consistent with the 125 GeV Higgs boson mass. It will be pointed out that even if the singlet scalar and the right-handed neutrinos are much heavier than the EW scale, the model might keep the naturalness thanks to an accidental cancellation of Higgs mass corrections coming from them.
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