离散对称性、单位根和轻子混合
Discrete symmetries, roots of unity, and lepton mixing
摘要：
我们研究轻子混合矩阵U的第一列由u_1 =（2，-1，-1）^T/sqrt{6}给出的可能性。在一个纯粹的群论的方法，剩余对称性的基础上，在带电轻子和中微子部门和一个定理上消失的总和根的单位，我们讨论了有限的群体，可以强制执行这一点。假设Majorana中微子质量矩阵中只有一个剩余对称性，我们找到了几乎唯一的解Z_q × S_4，其中q = 1，2，3，.对于在U中获得u_1是无关的。我们的讨论也为实现这一目标提供了一个自然的机制。最后，除了真空对齐，我们实现了这一机制在一类可重正化模型。
英文摘要：
We investigate the possibility that the first column of the lepton mixing matrix U is given by u_1 = (2,-1,-1)^T/sqrt{6}. In a purely group-theoretical approach, based on residual symmetries in the charged-lepton and neutrino sectors and on a theorem on vanishing sums of roots of unity, we discuss the finite groups which can enforce this. Assuming that there is only one residual symmetry in the Majorana neutrino mass matrix, we find the almost unique solution Z_q x S_4 where the cyclic factor Z_q with q = 1,2,3,... is irrelevant for obtaining u_1 in U. Our discussion also provides a natural mechanism for achieving this goal. Finally, barring vacuum alignment, we realize this mechanism in a class of renormalizable models.
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