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Abstract:We update the constraints on two-Higgs-doublet models (2HDMs) focusing on the parameter space relevant to explain the present muon g − 2 anomaly, ∆a µ , in four different types of models, type I, II, "lepton specific" (or X) and "flipped" (or Y). We show that the strong constraints provided by the electroweak precision data on the mass of the pseudoscalar Higgs, whose contribution may account for ∆a µ , are evaded in regions where the charged scalar is degenerate with the heavy neutral one and the mixing angles α and β satisfy the Standard Model limit β − α ≈ π/2. We combine theoretical constraints from vacuum stability and perturbativity with direct and indirect bounds arising from collider and B physics. Possible future constraints from the electron g − 2 are also considered. If the 126 GeV resonance discovered at the LHC is interpreted as the light CP-even Higgs boson of the 2HDM, we find that only models of type X can satisfy all the considered theoretical and experimental constraints.

An interesting mass relation between down type quarks and charged leptons has been recently predicted within a supersymmetric SU(3)c ⊗ SU(2)L ⊗ U(1)Y model based on the A4 flavor symmetry. Here we propose a simple extension which provides an adequate full description of the quark sector. By adding a pair of vector-like up-quarks we show how the CKM entries V ub , V cb , V td and Vts arise from deviations of the unitarity. We perform an analysis including the most relevant observables in the quark sector, such as oscillations and rare decays of kaons, B d and Bs mesons. In the lepton sector, model predicts an inverted hierarchy for the neutrino masses leading to a potentially observable rate of neutrinoless double beta decay.

We discuss consequences of combining the effective Z 2 Â Z 2 symmetry of the tribimaximal neutrino mass matrix with the CP symmetry. Imposition of such generalized Z 2 Â Z 2 symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to a nonzero 13 and maximal atmospheric mixing angle and CP violating phase. It is shown that an effective generalized Z 2 Â Z 2 symmetry of the mass matrix can arise from the A 4 symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real parameters and leads to determination of the absolute neutrino mass scale as a function of the reactor angle 13 .

Thesymmetry imposed on the neutrino mass matrix in the flavor basis is known to be quite predictive. We integrate this very specific neutrino symmetry into a more general framework based on the supersymmetric SOð10Þ grand unified theory. As in several other models, the fermion mass spectrum is determined by Hermitian mass matrices resulting from the renormalizable Yukawa couplings of the 16plet of fermions with the Higgs fields transforming as 10, 126, and 120 representations of the SOð10Þ group. Thesymmetry is spontaneously broken through the 120-plet. Consequences of this scheme are considered for fermion masses using both a type-I and a type-II seesaw mechanism. This scenario is shown to lead to a generalized CP invariance of the mass matrices and vanishing CP violating phases if the Yukawa couplings are invariant under thesymmetry. Small explicit breaking of thesymmetry is then shown to provide a very good understanding of all of the fermion masses and mixing. Detailed fits to the fermion spectrum are presented in several scenarios. One obtains a very good fit to all observables in the context of the type-I seesaw mechanism, but the type-II seesaw model also provides a good description except for the overall scale of the neutrino masses. Three major predictions on the leptonic mixing parameters in the type-I seesaw case are (i) the atmospheric mixing angle l 23 close to maximal, (ii) l 13 close to the present upper bound, and (iii) a negative but very small Dirac CP violating phase in the neutrino oscillations.