A novel origin of CP violation

We propose the complex group theoretical Clebsch–Gordan 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 ′ , 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 T ′ . In addition to the prediction for θ 13 ∼ θ c / ( 3 2 ) , the model gives rise to a sum rule, tan 2 θ ⊙ ∼ tan 2 θ ⊙ , TBM + 1 2 θ c cos δ , which is a consequence of the Georgi–Jarlskog relations in the charged fermion sector. The leptonic Dirac CP violating phase, δ ℓ , is predicted to be ∼227∘, 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.