CP破坏的几何起源和SU（5）× T'中的CKM和MNS矩阵
Geometrical Origin of CP Violation and CKM and MNS Matrices in SU(5) x T'
摘要：
我们提出复群理论的Clebsch-Gordon系数作为CP破坏的一个新的起源。这一点在我们的基于超对称SU（5）与双四面体群T '作为族对称相结合的模型中表现得很明显。由于T '中偶重态的存在，使得模型中存在复CG系数，从而导致明显的CP破坏，而Yukawa耦合和标量场的真空期望值仍然是实的.三-双极大中微子混合矩阵来自T '的CG系数。除了对theta_{13} ~（1/（3 \sqrt{2}）theta_{c}的预测之外，该模型还产生了一个求和规则tan^{2} theta_{sol} ~ tan^{2} theta_{sol, TBM} } +（1/2）theta_{c} cos（delta_{lep}），这是带电费米子部门中Georgi-Jarlskog关系的结果。预言的轻子狄拉克CP相位delta_{lep}给出了太阳混合角的正确值，预言的夸克扇区的CP破坏测量与目前的实验数据一致。由于狄拉克CP相位是轻子扇区中唯一预测的非零相位，因此在我们的模型中，轻子生成和低能轻子CP破坏过程之间存在联系。
英文摘要：
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.
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