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.