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Register a new userStability and symmetry breaking in the general three-Higgs-doublet model
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Stability, electroweak symmetry breaking, and the stationarity equations of the general three-Higgs-doublet model (3HDM) where all doublets carry the same hypercharge are discussed in detail. Employing the bilinear formalism the study of the 3HDM potential turns out to be straightforward. For the case that the potential leads to the physically relevant electroweak symmetry breaking we present explicit formulae for the masses of the physical Higgs bosons.
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For potentials with n-Higgs-boson doublets stability, electroweak symmetry breaking, and the stationarity equations are discussed in detail. This is done within the bilinear formalism which simplifies the investigation, in particular since irrelevant gauge degrees of freedom are systematically avoided. For the case that the potential leads to the physically relevant electroweak symmetry breaking the mass matrices of the physical Higgs bosons are given explicitly.
Motivated by the neutrino data, an extension of the Standard Model with three Higgs-boson doublets has been proposed. Imposing an O(2) x Z2 family symmetry, a neutrino mixing matrix with theta23 = pi/4 and theta13 = 0 appears in a natural way. Even though these values for the mixing matrix do not follow the recent experimental constraints, they are nevertheless a good approximation. We study the Higgs potential of this model in detail. We apply recent methods which allow for the study of any three-Higgs-boson doublet model. It turns out that for a variety of parameters the potential is stable, has the correct electroweak symmetry breaking, and gives the correct vacuum expectation value.
We worked out in detail the three-Higgs-doublet extension of the standard model when the $A_4$ symmetry, which is imposed to solve the flavor problem, is extended to the scalar sector. The three doublets may be related to the fermion mass generation and, in particular, they may be the unique responsible for the generation of the neutrino masses. If this is the case, the respective VEVs have to be quite smaller than the electroweak scale if no fine tuning in the Yukawa couplings is assumed. We consider here the mass spectra in the scalar sector in three different situations. In one of them there are no light scalars at all, but in the other ones a light or two massless scalars, at the tree level, may survive. The later fields are safe, from the phenomenological point of view, since it couples mainly with neutrinos and/or becomes enough massive at the tree level if there exist trilinear interactions. Quantum effects may be important too.
We apply the unitarity bounds and the bounded-from-below (BFB) bounds to the most general scalar potential of the two-Higgs-doublet model (2HDM). We do this in the Higgs basis, i.e. in the basis for the scalar doublets where only one doublet has vacuum expectation value. In this way we obtain bounds on the scalar masses and couplings that are valid for all 2HDMs. We compare those bounds to the analogous bounds that we have obtained for other simple extensions of the Standard Model (SM), namely the 2HDM extended by one scalar singlet and the extension of the SM through two scalar singlets.
A model with three scalar doublets can be conveniently accommodated within an A4 symmetric framework. The A4 symmetry permits only a restricted form for the scalar potential. We show that for the global minima of this potential alignment follows as a natural consequence. We also verify that in every case positivity and unitarity constraints are satisfactorily met.
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