F-theory, GUTs, and the Weak Scale

TL;DR

This work develops a local F-theory GUT framework in which the μ term is tied to the SUSY-breaking scale, providing a predictive link between high-energy geometry and MSSM soft terms. By leveraging an anomalous U(1)_{PQ} symmetry and a Fayet–Polonyi–type SUSY-breaking sector, the authors realize a GM-like mechanism that yields μ in the weak range while suppressing Bμ, and they identify a QCD axion with f_a ≈ 10^{12} GeV arising from a combination of PQ-phase dynamics. The model naturally places the gravitino as the LSP (m_{3/2} ∼ 10^{1–2} MeV) and a bino-like NLSP (∼ 10^{2–3} GeV), with tanβ ≈ 30±7, and constrains the MSSM spectrum via RG running from a high messenger scale M_{mess} ∼ 10^{11.5–12.5} GeV to the weak scale. These results link GUT-scale geometry to weak-scale phenomenology and axion physics, offering concrete, testable predictions for collider and cosmological observations within a tightly constrained parameter space.

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 ~ 10^2 - 10^3 GeV when the hidden sector scale of supersymmetry breaking is F^(1/2) ~ 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 ~ M_(GUT) * mu / L, where L ~ 10^5 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio μ/ L ~ M_(GUT)/M_(pl) ~ 10^(-3). We find f_a ~ 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) ~ 30 +/- 7.

Figures (9)

• Figure 1: Depiction of the diamond ring model. The GUT model seven-brane wraps the Kähler surface $S$, while the $X$ field localizes at the intersection of two additional seven-branes wrapping the surfaces $S^{\prime}$ and $S^{\prime\prime}$.
• Figure 2: Depiction of the messenger sector of a local $SU(5)$ model where the messengers and $X$ field originate from local enhancements to $E_{7}$ and embed in the $\overline{27}$ of $E_{6}$. The $XYY^{\prime}$ interaction term descends from a local enhancement to $E_{8}$ at a point of triple intersection. The Higgs fields originate from local enhancement to $SU(6)$. In this case, the Higgs fields embed in the $27$ of $E_{6}$ and can therefore only participate in a $27^{3}$ interaction so that a direct coupling with the $X$ field via the superpotential is forbidden, but an interaction term via the Kähler potential is allowed.
• Figure 3: Plot of the effective potential for the saxion. With notation as in section 8.4, the specific choice of parameters used in this plot are $M_{\ast }=10^{17}$ GeV, $M_{X}=10^{15.5}$ GeV, $A=1$, $B=1.425$. By construction, the value of $B$ has been chosen so that the minimum is located at $x_{\ast }=10^{12}$ GeV. The shallow variation of the potential as a function of energy scale illustrates that the mass of this radial mode is much smaller than $10^{12}$ GeV, and is instead closer to the weak scale.
• Figure 4: Plot of $\tan\beta$ at the scale $M_{S}$, the scale at which electroweak symmetry breaking boundary conditions are imposed, as a function of $\log_{10}(\Lambda/$GeV$)$. By inspection, $\tan\beta$ grows logarithmically with the gaugino mass unification scale. The vertical line at the left of the plot ($\Lambda = 10^{5.08}$ GeV) indicates the experimentally excluded region based on current bounds on the mass of the Higgs.
• Figure 5: Plot of the $\mu$ term, stau mass, bino mass and Higgs mass as a function of the gaugino mass unification scale $\Lambda$ in a single messenger model with vanishing PQ deformation. The vertical line at the left ($\Lambda = 10^{5.08}$ GeV) indicates the experimentally excluded region based on bounds on the mass of the Higgs.