In the original 2004 paper which first derived tribimaximal mixing in the context of A 4 , i.e. the non-Abelian finite symmetry group of the tetrahedron, as its simplest application, it was also pointed out how θ 13 = 0 may be accommodated. On the strength of the new T2K result that 0.03(0.04) ≤ sin 2 2θ 13 ≤ 0.28(0.34) for δ CP = 0 and normal (inverted) neutrino mass hierarchy, we perform a more detailed analysis of how this original idea may be realized in the context of A 4 .

A model based on SU (3) C ×SU (2) L ×U (1) Y ×SU (2) N has recently been proposed, where the SU (2) N vector gauge bosons are neutral, so that a vector dark-matter candidate is possible and constrained by data to be less than about 1 TeV. We explore further implications of this model, including a detailed study of its Higgs sector. We improve on its dark-matter phenomenology, as well as its discovery reach at the LHC (Large Hadron Collider).

If neutrino tribimaximal mixing is explained by a non-Abelian discrete symmetry such as A 4 , T 7 , ∆(27), etc., the charged-lepton Higgs sector has a Z 3 residual symmetry (lepton flavor triality), which may be observed directly in the decay chain, where H 0 is a standard-model-like Higgs boson and ψ 0 2 is a scalar particle needed for realizing the original discrete symmetry. If kinematically allowed, this unusual and easily detectable decay is observable at the LHC with 1 fb −1 for E cm = 7 TeV.

We study one-loop radiative neutrino mass models in which one of the beyond-the-standard model fields is either a hypercharge-zero fermion quintet (minimal dark matter) or a hyperchargezero scalar septet. By systematically classifying all possible one-loop such models we identify various processes that render the neutral component of these representations (dark matter) cosmologically unstable. Thus, our findings show that these scenarios are in general not reconcilable with dark matter stability unless tiny couplings or additional ad hoc symmetries are assumed, in contrast to minimal dark matter models where stability is entirely due to the standard model gauge symmetry. For some variants based on higher-order loops we find that α 2 reaches a Landau pole at rather low scales, a couple orders of magnitude from the characteristic scale of the model itself.Thus, we argue that some of these variations although consistent with dark matter stability and phenomenological constraints are hard to reconcile with perturbativity criteria.

We propose that the observed large leptonic mixing may just reflect a quasidegeneracy of three Majorana neutrinos. The limit of exact degeneracy of Majorana neutrinos is not trivial, as leptonic mixing and even CP violation may occur. We conjecture that the smallness of 1t/131, when compared to the other elements of UPMNS, may be related to the fact that, in the limit of exact mass degeneracy, the leptonic mixing matrix necessarily has a vanishing element. We show that the lifting of the mass degeneracy can lead to the measured value of |C/13| while at the same time accommodating the observed solar and atmospheric mixing angles. In the scenario we consider for the breaking of the mass degeneracy, there is only one CP violating phase, already present in the limit of exact degeneracy, which upon the lifting of the degeneracy generates both Majorana and Dirac-type CP violation in the leptonic sector. We analyze some of the correlations among physical observables and point out that, in most of the cases considered, the implied strength of leptonic Dirac-type CP violation is large enough to be detected in the next round of experiments.