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具有保子群的二面体味对称的费米子质量和混合

Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups

A. Blum, C. Hagedorn, M. Lindner

备注：
25 pages
发表信息：
Phys.Rev.D77:076004,2008
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摘要：

我们对作为味对称的二面体群进行了系统的研究。这里的关键特征是，我们不允许二面角群以任意的方式被破坏，但在所有情况下，必须保留某些（非平凡的）子群。通过这种方式，我们只得到了五种可能的（狄拉克）质量矩阵结构，如果我们要求矩阵必须具有非零行列式，并且三代左手（共轭）费米子中至少有两代被置于味群的不可约二维表示中。我们证明了单值和双值二面体群的质量矩阵结构没有区别。此外，我们评论的可能形式的马约拉纳质量矩阵。作为第一个应用，我们找到了一种表达Cabibbo角的方法，即CKM矩阵元素|V_{us}|，仅根据群论量，群指数n，表示指数j和上夸克扇区和下夸克扇区中不同保留子群的指数m_{u,d}：|V_{us}| =| cos（pi（m_{u}-m_{d}）j/n）|这是|cos（3 pi/7）|= 0.2225，n = 7，j = 1，m_{u} = 3和m_{d} = 0。我们证明了两个成功的模型，导致最大的大气混合和消失theta_{13}在轻子部门的基础上的事实，味对称性被打破的带电轻子，狄拉克中微子和马约拉纳中微子部门下降到不同的保留的子组，其失配的结果，这些混合角的预测。这也证明了保留子群在预测夸克和轻子扇区混合角方面的能力。

英文摘要：

We perform a systematic study of dihedral groups used as flavor symmetry. The key feature here is the fact that we do not allow the dihedral groups to be broken in an arbitrary way, but in all cases some (non-trivial) subgroup has to be preserved. In this way we arrive at only five possible (Dirac) mass matrix structures which can arise, if we require that the matrix has to have a non-vanishing determinant and that at least two of the three generations of left-handed (conjugate) fermions are placed into an irreducible two-dimensional representation of the flavor group. We show that there is no difference between the mass matrix structures for single- and double-valued dihedral groups. Furthermore, we comment on possible forms of Majorana mass matrices. As a first application we find a way to express the Cabibbo angle, i.e. the CKM matrix element |V_{us}|, in terms of group theory quantities only, the group index n, the representation index j and the index m_{u,d} of the different preserved subgroups in the up and down quark sector: |V_{us}|=|cos(pi(m_{u}-m_{d})j/n)| which is |cos(3 pi/7)| = 0.2225 for n=7, j=1, m_{u}=3 and m_{d}=0. We prove that two successful models which lead to maximal atmospheric mixing and vanishing theta_{13} in the lepton sector are based on the fact that the flavor symmetry is broken in the charged lepton, Dirac neutrino and Majorana neutrino sector down to different preserved subgroups whose mismatch results in the prediction of these mixing angles. This also demonstrates the power of preserved subgroups in connection with the prediction of mixing angles in the quark as well as in the lepton sector.

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