A Novel Origin of CP Violation

TL;DR

This paper introduces a new origin of CP violation based on complex Clebsch-Gordon coefficients in a model combining SU(5) with the double tetrahedral group T', leading to explicit CP violation without complex Yukawa couplings.

Contribution

It proposes a novel CP violation mechanism via complex CG coefficients in a unified model, connecting neutrino mixing, CP phases, and fermion mass relations.

Findings

Predicts theta_{13} ~ theta_{c}/(3 sqrt{2})

Derives a sum rule for solar mixing angle involving CP phase

Predicts leptonic CP phase delta_{ell} ~ 227 degrees

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 SU(5) combined with the double tetrahedral group, T'. Due to the presence of the doublet representations in $T^{\prime}$, there exist complex CG coefficients, leading to explicit CP violation in the model, while the Yukawa couplings and the vacuum expectation of the scalar fields remain real. The tri-bimaximal neutrino mixing matrix arises from the CG coefficients of the T'. In addition to the prediction for theta_{13} ~ theta_{c}/(3 sqrt{2}), the model gives rise to a sum rule, tan^2 theta_{sol} ~ \tan^2 theta_{sol,TBM} + (1/2) theta_{c} cos(delta), which is a consequence of the Georgi-Jarlskog relations in the charged fermion sector. The leptonic Dirac CP violating phase, delta_{ell}, is predicted to be ~227^{o}, which turns out to be the value needed to account for the difference between the experimental best fit value for the solar mixing angle and the TBM prediction. The predicted CP violation measures in the quark sector are also consistent with the current experimental data.