The addition of an A4 family symmetry and extended Higgs sector to the standard model can generate the tribimaximal mixing pattern for leptons, assuming the correct vacuum expectation value alignment of the Higgs scalars. Deviating this alignment affects the predictions for the neutrino oscillation and neutrino mass observables. An attempt is made to classify the plethora of models in the literature, with respect to the chosen A4 particle assignments. Of these models, two particularly popular examples have been analyzed for deviations from tribimaximal mixing by perturbing the vacuum expectation value alignments. The effect of perturbations on the mixing angle observables is studied. However, it is only investigation of the mass-related observables (the effective mass for neutrinoless double beta decay and the sum of masses from cosmology) that can lead to the exclusion of particular models by constraints from future data, which indicates the importance of neutrino mass in disentangling models. The models have also been tested for fine-tuning of the parameters. Furthermore, a well-known seesaw model is generalized to include additional scalars, which transform as representations of A4 not included in the original model.

Kurie-plot experiments allow for neutrino-mass measurements based on kinematics in an almost model-independent manner. A future tritium-based KATRIN-like experiment can be sensitive to light sterile neutrinos with masses below 18 keV, which are among the prime candidates for warm dark matter. Here we consider such keV neutrinos in left-right symmetric extensions, i.e. coupled to right-handed currents, which allow for an enhanced contribution to beta decay even for small active-sterile mixing, without violating astrophysical X-ray constraints. The modified spectral shape is in principle distinguishable from the standard contribution — especially for sterile neutrino masses below 9 keV, which can lead to a distinct peak. We compare the sensitivity to constraints from the LHC and neutrinoless double beta decay.

We construct a flavor symmetry model based on the tetrahedral group A₄ in which the right-handed neutrinos from the seesaw mechanism can be both keV warm dark matter particles and eV-scale sterile neutrinos. This is achieved by giving the right-handed neutrinos appropriate charges under the same Froggatt-Nielsen symmetry responsible for the hierarchy of the charged lepton masses. We discuss the effect of next-to-leading order corrections to deviate the zeroth order tri-bimaximal mixing. Those corrections have two sources: (i) higher order seesaw terms, which are important when the seesaw particles are eV-scale, and (ii) higher-dimensional effective operators suppressed by additional powers of the cut-off scale of the theory. Whereas the mixing angles of the active neutrinos typically receive corrections of the same order, the mixing of the sterile neutrinos with the active ones is rather stable as it is connected with a hierarchy of mass scales. We also modify an effective A₄ model to incorporate keV-scale sterile neutrinos.