Abstract
We consider a 4-Higgs-doublet model in which each Higgs doublet gives mass to one of the fermion sets {mt}, {mb, mτ, mc}, {mμ, ms}, and {md, mu, me}. The sets have the feature that within each of them the masses are similar. Our model explains the mass hierarchies of the sets by hierarchies of the vacuum expectation values of the Higgs doublets associated to them. All Yukawa couplings are therefore of order one. Neutrino masses are generated by a type-I seesaw mechanism with PeV-scale singlet neutrinos. To avoid the appearance of tree-level flavour changing neutral currents, we assume that all Yukawa matrices are singularly aligned in flavour space. We mean by this that the Yukawa matrices are given as linear combinations of the rank 1 matrices that appear in the singular value decomposition of the mass matrix. In general, singular alignment allows to avoid flavour changing neutral currents in models with multiple Higgs doublets.
Highlights
Why is the top quark mass the only fermion mass of the order of the electroweak (EW) scale, mt ≈ vEW with vEW 174 GeV?
Within the Standard Model (SM) the huge hierarchy of Yukawa couplings remains a puzzle. In this regard we used the fact that the observed fermion masses indicate that the following sets have similar Yukawa couplings: {mt}, {mb, mτ, mc}, {mμ, ms} and {md, mu, me}
We have shown that a 4HDM can be constructed that explains this feature
Summary
Having multiple Higgs doublets coupling to fermions with the same electric charge will produce tree-level FCNC, which are experimentally strongly constrained. In this case diagonalization of the l.h.s. means diagonalization of the r.h.s. For N Higgs doublets, the easiest way to achieve this is via a symmetry of the form. Models may lead to Yukawa matrices with ranks less than 3 In this case the singular alignment can still hold and the only new difference would be to have some of the constants ηi, Ωi, Λi appearing in eq (2.12) equal to zero. Singular alignment is the very strong Ansatz of choosing Yukawa matrices to be related to the rank 1 matrices appearing in the SVD. Through this alignment, no treelevel FCNC appear for any number of Higgs doublets.
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