We consider a 4-Higgs-doublet model in which each Higgs doublet gives mass to one of the fermion sets {m t }, {m b , m τ , m c }, {m µ , m s }, and {m d , m u , m e }. 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.

We perform a systematic study of the generic Gatto-Sartori-Tonin relation, tan 2 θ ij = m i /m j . This study of fermion mixing phenomena leads us to the necessary conditions that are needed in order to obtain it without any approximation. We begin by considering two Dirac fermion families. By means of the hierarchy in the masses, it is found that a sufficient and necessary condition is to have a normal matrix with m 11 = 0. This matrix can be decomposed into two different linearly independent contributions. The origin for such two independent contributions can be naturally explained by what we shall call the flavor-blind principle. This principle states that Yukawa couplings shall be either flavor-blind or decomposed into several sets obeying distinct permutation symmetries. In general, it is shown that the symmetry properties of the introduced set of Yukawa matrices follow for n fermion families the unique sequential breakingThe particular case of three fermion families explains why the four mass ratios parametrization that we recently proposed can be used even in the case of no hierarchical masses.

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We explore a common symmetrical origin for two long standing problems in particle physics: the strong CP and the fermion mass hierarchy problems. The Peccei-Quinn mechanism solves the former one with an anomalous global U(1)PQ symmetry. Here we investigate how this U(1)PQ could at the same time explain the fermion mass hierarchy. We work in the context of a four-Higgs-doublet model which explains all quark and charged fermion masses with natural, i.e. order 1, Yukawa couplings. Moreover, the axion of the model constitutes a viable dark matter candidate and neutrino masses are incorporated via the standard type-I seesaw mechanism. A simple extension of the model allows for Dirac neutrinos.

The strong C P problem is one of many puzzles in the theoretical description of elementary particle physics that still lacks an explanation. While top-down solutions to that problem usually comprise new symmetries or fields or both, we want to present a rather bottom-up perspective. The main problem seems to be how to achieve small C P violation 1 jldiaz@fcfm.buap.mx 2 w.hollik@desy.de 3 usaldana@fcfm.buap.mx