F-theory, GUTs, and the Weak Scale

Abstract

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\(\beta \sim 30 \pm 7\).