When $\tan \beta$ meets all the mixing angles

Abstract

Models with two-Higgs-doublets and natural flavour conservation contain $\tan \beta =v_2/v_1$ as a physical parameter. We offer here a generalization of a recently proposed idea where only the Cabibbo angle, ${\theta }_{\text{c}}\simeq 0.22$, was related to $\tan \beta$ by virtue of the ${\mathbb{D}}_4$ 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 $\tan \beta$ and one recovers trivial mixing in the limit $\beta \to 0$. We also explore the consequences in lepton mixing by adopting a type I seesaw mechanism with three heavy right-handed neutrinos.

Major improvement to the overall content of the paper; 15 pages, 8 figures, new sections, appendices and references; Matches published version in PLB

References in corpus (4)

• Basis-independent methods for the two-Higgs-doublet model II. The significance of tan(beta)
• An Exclusive Window onto Higgs Yukawa Couplings
• Precision measurements constraints on the number of Higgs doublets
• Relating the Cabibbo angle to $\tan \beta$ in a two Higgs-doublet model

Cited by in corpus (8)

• Universal Inverse seesaw mechanism as a source of the SM fermion mass hierarchy
• Fermion masses and mixings and $g-2$ muon anomaly in a 3-3-1 model with $D_4$ family symmetry
• Fermion mass hierarchy and g-2 anomalies in an extended 3HDM Model
• Higgs sector phenomenology in the 3-3-1 model with an axionlike particle
• Diluting quark flavor hierarchies using dihedral symmetry
• Natural 2HDMs without FCNCs
• Fermion masses and mixings in a $U(1{)}_X$ model based on the $\Sigma (18)$ discrete symmetry
• $\mathbf{B}-\mathbf{L}$ model with ${\mathbf{D}}_4\times {\mathbf{Z}}_4\times {\mathbf{Z}}_2$ symmetry for fermion mass hierarchies and mixings