Geometrical Origin of CP Violation and CKM and MNS Matrices in SU(5) x T'

TL;DR

This paper introduces a novel origin of CP violation based on complex Clebsch-Gordon coefficients in a SUSY SU(5) model with T' symmetry, explaining neutrino mixing and CP phases consistent with experimental data.

Contribution

It proposes a new mechanism for CP violation originating from complex CG coefficients in a SUSY SU(5) x T' model, linking neutrino mixing and leptogenesis.

Findings

Predicts theta_{13} ~ (1/(3√2)) * theta_c

Derives a sum rule relating mixing angles and CP phase

Consistent with current experimental data on CP violation

Abstract

We propose the complex group theoretical Clebsch-Gordon coefficients as a novel origin of CP violation. This is manifest in our model based on SUSY SU(5) combined with the double tetrahedral group, T', as a family symmetry. Due to the presence of the doublet representations in T', there exist complex CG coefficients, leading to explicit CP violation in the model, while the Yukawa couplings and the vacuum expectation values of the scalar fields remain real. The tri-bimaximal neutrino mixing matrix arises from the CG coefficients of T'. In addition to the prediction for theta_{13} ~ (1/ (3\sqrt{2}) theta_{c}, the model gives rise to a sum rule, tan^{2} theta_{sol} ~ tan^{2} theta_{sol, TBM}} + (1/2) theta_{c} cos(delta_{lep}), which is a consequence of the Georgi-Jarlskog relations in the charged fermion sector. The predicted leptonic Dirac CP phase, delta_{lep}, gives the correct value of the solar mixing angle, and the predicted CP violation measures in the quark sector are consistent with the current experimental data. Since the Dirac CP phase is the only non-vanishing phase predicted in the lepton sector, there is a connection between leptogenesis and low energy leptonic CP violating processes in our model.