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

Abstract

We study minimal implementations of Majorana and Dirac neutrino scenarios in F-theory GUT models. In both cases the mass scale of the neutrinos (m_{\nu} \sim M_{weak}^2/\land_{UV}) arises from integrating out Kaluza-Klein modes, where (\land_{UV}) 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 (m_3,m_2,m_1 \sim .05 \times (1,\alpha_{GUT}^{1/2},\alpha_{GUT})) 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 (\theta_{23}) and (\theta_{12}) are large and comparable, while (\theta_{13}) is expected to be smaller and close to the Cabibbo angle: (\theta_{13} \sim \theta_{C} \sim \alpha_{GUT}^{1/2} \sim 0.2). This suggests that (\theta_{13}) should be near the current experimental upper bound.