Abstract
Abstract 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.
Highlights
We consider the tree-level Higgs potential of models with three Higgs-boson doublets satisfying SU(2)L × U(1)Y electroweak gauge symmetry
It is convenient to discuss the properties of the Higgs potential such as its stability and its stationary points in terms of gauge invariant bilinears
In our example 3HDM Higgs potential, (3.15), we find stationary points for vanishing fields, corresponding to an unbroken EW symmetry, from the set (6.3) we get no solution with K0 > 0, and from the set (6.1) we get one real solution with
Summary
We consider the tree-level Higgs potential of models with three Higgs-boson doublets satisfying SU(2)L × U(1)Y electroweak gauge symmetry. Any hermitian 3 × 3 matrix with rank equal or smaller than 2 which clearly has vanishing determinant, det(K) = 0, determines the Higgsboson fields φi, i = 1, 2, 3 uniquely, up to a gauge transformation. This was shown in detail in [4] in their theorem 5 for the general case of n-Higgs-boson doublets. Based on the bilinears we shall in the following discuss the potential, basis transformations, stability, minimization, and electroweak symmetry breaking of the general 3HDM
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