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A seesaw mechanism in an extra-dimension, known as the split seesawmechanism, provides a natural way to realize a splitting mass spectrum ofright-handed neutrinos. It leads to one keV sterile neutrino as a dark mattercandidate and two heavy right-handed neutrinos being responsible forleptogenesis to explain the observed baryon asymmetry of the Universe. We studymodels based on $A_4$ flavor symmetry in the context of the split seesawmechanism. It is pointed out that most of known $A_4$ flavor models with threeright-handed neutrinos being $A_4$ triplet suffer from a degeneracy problem forthe bulk mass terms, which disturbs the split mechanism for right-handedneutrino mass spectrum. Then we construct a new $A_4$ flavor model to work inthe split seesaw mechanism. In the model, the experimentally observed neutrinomasses and mixing angles can be realized from both type I+II seesawcontributions. The model predicts the $\mu-\tau$ symmetry in the neutrino massmatrix at the leading order, resulting in the vanishing $\theta_{13}$ andmaximal $\theta_{23}$. The flavor symmetry $A_4$ is broken via the flavonvacuum alignment which can be obtained from the orbifold compactification. Themodel can be consistent with all data of neutrino oscillation experiments,cosmological discussions of dark matter abundance, leptogenesis, and recentastrophysical data.

A4 Flavor Models in Split Seesaw Mechanism