Abstract
We propose a minimal model that can explain the electroweak scale, neutrino masses, Dark Matter (DM), and successful inflation all at once based on the multicritical-point principle (MPP). The model has two singlet scalar fields that realize an analogue of the Coleman–Weinberg mechanism, in addition to the Standard Model with heavy Majorana right-handed neutrinos. By assuming a Z_2 symmetry, one of the scalars becomes a DM candidate whose property is almost the same as the minimal Higgs-portal scalar DM. In this model, the MPP can naturally realize a saddle point in the Higgs potential at high energy scales. By the renormalization-group analysis, we study the critical Higgs inflation with non-minimal coupling xi |H|^2 R that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for xi =25 and that the heaviest right-handed neutrino is predicted to have a mass around 10^{14}mathrm{GeV} to meet the current cosmological observations. Such a small value of xi can be realized by the Higgs-portal coupling lambda _{SH}simeq 0.32 and the vacuum expectation value of the additional neutral scalar langle phi rangle simeq 2.7 TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section 1.8times 10^{-9} pb, and the mass of additional neutral scalar 190 GeV.
Highlights
171.4 GeV [1] for the theoretical border between stability and instability of the effective Higgs potential for the observed Higgs mass 125 GeV; see Refs. [2,3,4].1 This critical value of the top pole mass is consistent at the 1.4 σ level with the latest combination of the experimental results m pole t
We first note that the effective potential exists independently of the renormalization scale, up to the renormalization of the field, for a given set of bare parameters. (In other words, the renormalization scale dependence should only arise due to truncation at some loop level.) In Fig. 1, we list examples of the possible effective potentials resulting from the multicriticalpoint principle (MPP): In panel A, we show the first kind of tuning Vφ=φours = Vφ=φanother given in the original version of the MPP [6,7,8]
In order to sweep the parameters near the saddle point, we use the results of Sect. 3.2: For each λSH, we find the value of MR that gives the saddle-point criticality, δ = 0, as well as the corresponding parameters hs and λc
Summary
171.4 GeV [1] for the theoretical border between stability and instability (or metastability) of the effective Higgs potential for the observed Higgs mass 125 GeV; see Refs. [2,3,4].1 This critical value of the top pole mass is consistent at the 1.4 σ level with the latest combination of the experimental results m pole t. It is possible to maintain the saddle point of the Higgs potential at high energy scales in the existence of new scalar field(s) when MR ∼ 1014 GeV [22] This is one of the interesting predictions of the MPP. We will focus on a specific model proposed in [61,62] (namely only the CP 2-2 among various multicritical points in the parameter space) in the following, the analysis of Higgs inflation does not much depend on the details of the model because only the scalar coupling λSH and the neutrino Yukawa yν play important roles to determine the behaviours of the Higgs potential at high energy scales. We choose these parameters in such a way that the Higgs potential has a (near) saddle-point at high scale region.
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