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As an extension of the Standard Model (SM), the 3HDM (Three-Higgs-Doublet Model) defines additional relationships among the fermions. In the visible leptonic Yukawa sector of the 3HDM, we investigate the existence of flavor symmetries under discrete non-abelian groups up to order 1032. When the VEVs are not allowed to depart from their alignment imposed by the condition of minimal potential in the Higgs scalar sector, there will be severe mass degeneracies and a lack of lepton flavor mixing for any nontrivial flavor group. Yet we propose to study the Yukawa terms of the lepton sector for in case the VEV alignment would not be protected, hence leaving the VEV ratios as free parameters. Then, as it turns out, mass splitting for the charged leptons and the neutrinos is obtained although it is still impossible to obtain correct fits to the experimentally known lepton mass spectrum and to the PMNS matrix simultaneously. [ABSTRACT FROM AUTHOR]

Abstract: We consider in detail the non-renormalisable scalar potential of three Higgs doublets transforming as an irreducible triplet of or . We start from a renormalisable potential that spontaneously leads to a vacuum with CP-violating phases independent of arbitrary parameters – geometrical CP violation. Then we analyse to arbitrarily high order non-renormalisable terms that are consistent with the symmetry and we demonstrate that inclusion of non-renormalisable terms in the potential can preserve the geometrical CP-violating vacuum. [Copyright &y& Elsevier]

Abstract: We study renormalization group running effects on neutrino mixing patterns when a (type I) seesaw model is implemented by suitable flavour symmetries. We are particularly interested in mass-independent mixing patterns to which the widely studied tribimaximal mixing pattern belongs. In this class of flavour models, the running contribution from neutrino Yukawa coupling, which is generally dominant at energies above the seesaw threshold, can be absorbed by a small shift on neutrino mass eigenvalues leaving mixing angles unchanged. Consequently, in the whole running energy range, the change in mixing angles is due to the contribution coming from charged lepton sector. Subsequently, we analyze in detail these effects in an explicit flavour model for tribimaximal neutrino mixing based on an discrete symmetry group. We find that for normally ordered light neutrinos, the tribimaximal prediction is essentially stable under renormalization group evolution. On the other hand, in the case of inverted hierarchy, the deviation of the solar angle from its TB value can be large depending on mass degeneracy, putting strong constraints on the flavour model. [Copyright &y& Elsevier]

Abstract: We show that Nearest-Neighbour Interaction (NNI) textures for the quark mass matrices can be obtained through the introduction of an Abelian flavour symmetry. The minimal realisation requires a symmetry in the context of a two Higgs doublet model. It is further shown that the NNI textures can be in agreement with all present experimental data on quark masses and mixings, provided one allows for deviations of Hermiticity in the quark mass matrices at the 20% level. [Copyright &y& Elsevier]

Abstract: We propose an extension of the hypothesis of Minimal Flavour Violation (MFV) to general multi-Higgs models without the assumption of Natural Flavour Conservation (NFC) in the Higgs sector. We study in detail under what conditions the neutral Higgs couplings are only functions of and propose a MFV expansion for the neutral Higgs couplings to fermions. [Copyright &y& Elsevier]