Quark and Lepton Flavor Physics from F-Theory

TL;DR

This work connects quark and lepton flavor to local F-theory GUT constructions, showing that wavefunction localization on matter curves and KK-mode mediated effects generate hierarchical Yukawa textures. The authors map the geometry-driven Yukawas onto an effective field theory with two perturbative sources, Y^{\mathrm{FLX}} and Y^{\mathrm{DER}}, whose sum reproduces observed quark masses and CKM mixing when ε ∼ κ ∼ α_{\text{GUT}}^{1/2}. In the neutrino sector, right-handed neutrinos on singlet curves and multiple intersection points naturally lead to an approximately rank-2 Dirac mass matrix, predicting large lepton mixings and a small third eigenvalue, with distinctive implications for |m_{ββ}| and cosmological bounds. Overall, the work provides a geometrical origin for SM flavor patterns via KK-mode mediation and flux-induced distortions, yielding concrete EFT realizations and testable predictions for future experiments.

Abstract

Recent work on local F-theory models shows the potential for new categories of flavor models. In this paper we investigate the perturbative effective theory interpretation of this result. We also show how to extend the model to the neutrino sector.

Figures (6)

• Figure 1: The structure of an F-theory GUT
• Figure 2: An intersection of matter curves giving the down Yukawa.
• Figure 3: An approximately rank-1 Yukawa involving a gauge singlet.
• Figure 4: An approximately rank-2 Yukawa involving a gauge singlet.
• Figure 5: Possible values of $|m_{\beta\beta}|$ versus the smallest mass eigenvalue $m_\mathrm{min}$. The brown shaded region corresponds to the inverted hierarchy, while the blue corresponds to the normal hierarchy. The uncertainty is from a combination of Majorana phases and uncertainty in the known values of $\Delta m^2_{12}, \Delta m^2_{23}$, and the mixing angles. We predict $\frac{m_\mathrm{min}}{m_{\mathrm{max}}}\approx \alpha_\mathrm{GUT} \approx \frac{1}{25}$, so a conservative upper bound for $m_\mathrm{min}$ would be $\frac{m_\mathrm{min}}{m_\mathrm{max}}=\frac{1}{5}$, about 5 times larger allowing for unknown order unity factors. This yields a rough upper bound of $|m_{\beta\beta}|<0.056\,\mathrm{eV}$ (green line, above). A higher measured value for $|m_{\beta\beta}|$ would rule out our model.