F-theory and Neutrinos: Kaluza-Klein Dilution of Flavor Hierarchy

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We study minimal implementations of Majorana and Dirac neutrino scenarios in F-theory GUT models. In both cases the mass scale of the neutrinos mₙu (Mweak)²/MᵤV arises from integrating out Kaluza-Klein modes, where MᵤV is close to the GUT scale. The participation of non-holomorphic Kaluza-Klein mode wave functions dilutes the mass hierarchy in comparison to the quark and charged lepton sectors, in agreement with experimentally measured mass splittings. The neutrinos are predicted to exhibit a "normal" mass hierarchy, with masses m₃,m₂,m₁.05*(1,(alphaGUT)(1/2),alphaGUT) eV. When the interactions of the neutrino and charged lepton sectors geometrically unify, the neutrino mixing matrix exhibits a mild hierarchical structure such that the mixing angles theta₂3 and theta₁2 are large and comparable, while theta₁3 is expected to be smaller and close to the Cabibbo angle: theta₁3 thetaC (alphaGUT)(1/2) 0.2. This suggests that theta₁3 should be near the current experimental upper bound.