Fermion Masses, Neutrino Mixing and Higgs-Mediated Flavor Violation in 3HDM with $S_3$ Permutation Symmetry

TL;DR

This paper explores an $S_3$-symmetric three-Higgs doublet model, fitting fermion masses and mixings, predicting neutrino CP violation, and analyzing constraints from flavor physics and EDM measurements, with heavy Higgs masses around 17 TeV.

Contribution

The study provides the first comprehensive fit of fermion masses and mixings in an $S_3$-symmetric 3HDM, including predictions for neutrino CP violation and detailed constraints from flavor observables.

Findings

Excellent fit to fermion masses and mixings achieved.

Neutrino mass ordering is flexible, with a predicted CP phase of about 120°.

Heavy Higgs bosons are constrained to be above approximately 17 TeV.

Abstract

The Yukawa and scalar sectors of a general $S_3$-symmetric three-Higgs doublet model (3HDM) are investigated. The Yukawa interactions are constructed in an $S_3$-invariant way, while the scalar potential contains $S_3$ soft-breaking terms. Global fits to the quark/lepton masses and CKM/PMNS matrices are performed. Excellent fits to all fermion mass and mixing parameters are obtained. Both normal ordering and inverted ordering of neutrino masses are found to be admissible within the framework, with a prediction for the CP-violation phase, $\delta_{CP} \simeq 120^0$. The fit results in the Yukawa sector are further investigated, together with the scalar sector, imposing constraints from Higgs-mediated neutral meson mixing and neutron electric dipole moment (EDM). We explore the lowest allowed mass of the heavy Higgs bosons, consistent with these constraints, and find it to be about 17 TeV. The corresponding neutron EDM is around $1.7\times10^{-27}$ e-cm, which is within reach of proposed experiments. It is found that the constraints from the $K$-meson system dominate, while those from the $D$ meson system are marginal.