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arXiv 1306.4138hep-ph
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CKM、PMNS和轻子生成的动力学CP源

A dynamical CP source for CKM, PMNS and Leptogenesis

Y. H. Ahn, Seungwon Baek

备注：
40 pages, 11 figures; version published in Phys. Rev. D. arXiv admin note: substantial text overlap with arXiv:1207.1229, arXiv:1304.0921, arXiv:1303.4863
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摘要：

我们提出了一个简单的模型的基础上$SU(2)_{L}\times U(1)_{Y}\times A_{4}\times CP\times Z_{2}$对称性的夸克和轻子的自发CP破坏的跷跷板框架。在我们的模型CP自发打破在高能量，打破味对称性后，由一个复杂的真空期望值$A_{4}$ -三重态和规范单重标量场。在夸克拉格朗日量中引入有效的5维算符，使夸克混合矩阵等价于Cabibbo-Kobayashi-Maskawa（CKM）混合矩阵，而轻子拉格朗日量是可重整化的，从而得到非简并的Dirac中微子Yukawa矩阵和唯一的CP相位，并由此解释了$θ_{13}\simeq9^{\circ}$的非零值和两个大的混合角$θ_{12}, θ_{23}$ .我们发现，自发产生的CP阶段“$ξ$”可能成为leptogenesis以及在CKM和Pontecorvo-Maki-Nakagawa-Sakata（PMNS）的CP违规的自然来源。此外，我们提供了一个解决方案的强CP问题。有趣的是，我们发现，在$ξ\simeq120^{\circ}$附近，夸克导致正确的CKM CP相对应于$δ^{q}_{CP}\simeq67^{\circ}$，而轻子的测量值的$θ_{13}$有利于$δ_{CP}=$，$|θ_{23}-45^{\circ}|\rightarrow0$正常的质量等级和$δ_{CP}=$，$|θ_{23}-45^{\circ}|\rightarrow5^{\circ}$倒置的。作为轻子部门的数值研究，我们显示了低能量的现象和leptogenesis的正常和倒置的情况下，分别和它们之间的联系。

英文摘要：

We propose a simple model for the spontaneous CP violation based on $SU(2)_{L}\times U(1)_{Y}\times A_{4}\times CP\times Z_{2}$ symmetry for quarks and leptons in a seesaw framework. In our model CP is spontaneously broken at high energies, after breaking of flavor symmetry, by a complex vacuum expectation value of $A_{4}$-triplet and gauge singlet scalar field. And, certain effective dimension-5 operators are introduced in the quark Lagrangian as an equal footing, which lead the quark mixing matrix to the Cabibbo-Kobayashi-Maskawa (CKM) one in the form, while the lepton Lagrangian is renormalizable, which gives rise to a non-degenerate Dirac neutrino Yukawa matrix and an unique CP-phase, and which in turn explains the non-zero value of $θ_{13}\simeq9^{\circ}$ and two large mixing angles $θ_{12}, θ_{23}$. We show that the spontaneously generated CP phase "$ξ$" could become a natural source of leptogenesis as well as CP violations in the CKM and Pontecorvo-Maki-Nakagawa-Sakata (PMNS). Moreover, we provide a solution for the strong CP problem. Interestingly enough, we show that, for around $ξ\simeq120^{\circ}$, the quarks lead to the correct CKM CP-phase corresponding to $δ^{q}_{CP}\simeq67^{\circ}$, while the leptons with the measured value of $θ_{13}$ favor $δ_{CP}=$, $|θ_{23}-45^{\circ}|\rightarrow0$ for normal mass hierarchy and $δ_{CP}=$, $|θ_{23}-45^{\circ}|\rightarrow5^{\circ}$ for inverted one. As a numerical study in the lepton sector, we show low-energy phenomenologies and leptogenesis for the normal and inverted case, respectively, and a link between them.

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