When tanβ meets all the mixing angles

Abstract Models with two-Higgs-doublets and natural flavour conservation contain tan ⁡ β = v 2 / v 1 as a physical parameter. We offer here a generalization of a recently proposed idea where only the Cabibbo angle, θ c ≃ 0.22 , was related to tan ⁡ β by virtue of the D 4 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 tan ⁡ 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.