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

TL;DR

This paper explores how Kaluza-Klein modes in F-theory GUT models influence neutrino mass hierarchies and mixing angles, predicting a normal hierarchy and specific mixing angle magnitudes consistent with experiments.

Contribution

It introduces a minimal F-theory GUT framework that explains neutrino masses and mixings via Kaluza-Klein mode effects, linking geometric unification to observable neutrino properties.

Findings

Neutrino masses arise from integrating out Kaluza-Klein modes near the GUT scale.

Neutrino mass hierarchy is normal, with specific mass ratios predicted.

Neutrino mixing angles theta_23 and theta_12 are large, theta_13 is small, near the Cabibbo angle.

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 ~ (M_weak)^2/M_UV arises from integrating out Kaluza-Klein modes, where M_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 ~ .05*(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 ~ theta_C ~ (alpha_GUT)^(1/2) ~ 0.2. This suggests that theta_13 should be near the current experimental upper bound.