CP Violation and F-theory GUTs

TL;DR

This work analyzes CP violation in F-theory GUTs by evaluating the Jarlskog invariant for quark and lepton sectors. It employs the polar decomposition to work with Hermitian Yukawas and expands in the small parameters $\varepsilon$ to expose cancellations in the determinant of commutators, yielding leading scalings $|J_{\text{quark}}^{\mathrm{F-th}}|\sim \alpha_{\rm GUT}^3$ and $|J_{\text{lepton}}^{\mathrm{F-th}}|\sim \alpha_{\rm GUT}$ with $\sin\delta$ of order unity. Numerically, $|J_{\text{quark}}^{\mathrm{F-th}}|\sim 6\times10^{-5}$ and $|J_{\text{lepton}}^{\mathrm{F-th}}|\sim 4\times10^{-2}$, and the observed $|J_{\text{quark}}^{\text{obs}}|\sim 3.08\times10^{-5}$ is consistent with the prediction, suggesting sizable leptonic CP violation may be measurable. The results support the view that CP-violating phases in both sectors can be large in this framework, with potential experimental implications for leptonic CP tests.

Abstract

Recent work on F-theory GUTs has shown that the predicted masses, and magnitudes of the mixing matrix elements in the quark and lepton sectors are in close accord with experiment. In this note we estimate the CP violating phase of the mixing matrices by considering the Jarlskog invariant. We find by carefully treating certain cancellations in the computation of the Jarlskog invariant that |J_quark| ~ alpha_GUT^(3) ~ 6*10^(-5), and that the CP violating phase of the quark sector is large, in accord with experiment. Moreover, we predict (up to order one factors) that |J_lepton| ~ alpha_GUT ~ 4*10^(-2) and that the CP violating phase of the lepton sector is also large.