Person:

Vafa, Cumrun

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.

In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the mu term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare mu and B mu terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value (\mu \sim 10^2 - 10^3) GeV when the hidden sector scale of supersymmetry breaking is (\sqrt{F} \sim 10^{8.5}) GeV. Further, the B(\mu) problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant (f_a \sim M_{GUT \times \mu/\wedge}), where (\wedge \sim 10^5) GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio (\mu / \wedge \sim M_{GUT}/M_{pl} \sim 10^{-3}). We find (f_a \sim 10^{12}) GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about (10^1 - 10^2) MeV, and a bino-like neutralino is (typically) the NLSP with mass of about (10^2 - 10^3) GeV. Compatibility with electroweak symmetry breaking also determines the value of tan(\beta \sim 30 \pm 7).