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#### When tanß meets all the mixing angles

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##### Citation

Hernández, A. E. C., Dib, C. O., & Saldaña-Salazar, U. J. (2020). When tanß meets
all the mixing angles.* Physics Letters B,* *809*: 135750.
doi:10.1016/j.physletb.2020.135750.

Cite as: https://hdl.handle.net/21.11116/0000-0009-0328-7

##### 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

\rightarrow 0$. We also explore the consequences in lepton mixing by adopting a

type I seesaw mechanism with three heavy right-handed neutrinos.

\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.