Fermion masses, neutrino mixing and Higgs-mediated flavor violation in 3HDM with S3 permutation symmetry

The Yukawa and scalar sectors of a general S3-symmetric three-Higgs doublet model (3HDM) are investigated. The Yukawa interactions are constructed in an S3-invariant way, while the scalar potential contains S3 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 similar or equal to 120 degrees. 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 x 10-27 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.