When \(\tan \beta\) meets all the mixing angles

• Published in: arXiv.org
• Main Authors: Cárcamo Hernández, Antonio E, Dib, Claudio O, Saldaña-Salazar, Ulises J
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 31.08.2020
• Subjects: Decoupling; Flavor (particle physics); Leptons; Neutrinos; Physical properties; Quarks
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2001.07140

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 \(\beta \rightarrow 0\). We also explore the consequences in lepton mixing by adopting a type I seesaw mechanism with three heavy right-handed neutrinos.