When β meets all the mixing angles
Abstract
Models with two-Higgs-doublets and natural flavour conservation contain β = v2 / v1 as a physical parameter. We offer here a generalization of a recently proposed idea where only the Cabibbo angle, θc 0.22, was related to β by virtue of the D4 dihedral symmetry group. The original proposal consisted of a massless first generation of quarks and no mixing with the third generation. In our case, through the addition of a third Higgs doublet with a small vacuum-expectation-value but very large masses, thus later decoupling, all quarks become massive and quark mixing is fully reproduced. In fact, all quark mixing angles are expressed in terms of β and one recovers trivial mixing in the limit β → 0. We also explore the consequences in lepton mixing by adopting a type I seesaw mechanism with three heavy right-handed neutrinos.