A new family symmetry for SO(10)SO(10) GUTs
A new family symmetry for SO(10)SO(10) GUTs
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SO(10)SO(10) GUT 的新族对称性
DOI：
10.1016/j.nuclphysb.2009.05.020
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
C. Luhn
中科院分区：
文献类型：
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作者：
S. King;C. Luhn
我们认为，在SO（10）型统一模型的框架下，投影特殊线性群PSL2（7），也称为PSL2（168），具有独特的性质，使其成为描述夸克和轻子质量和混合的最合适的离散族对称。在这样的模型中，PSL2（7）的六重态表示中的flavon场在获得三双峰中微子混合以及产生第三族带电费米子Yukawa耦合中起着至关重要的作用。为物理应用作准备，我们导出了PSL2（7）在基S，T，U，V中的三重态表示，其中S，T，U是S_4在对角荷电轻子基中常见的三重态生成元，T是对角荷电轻子基。我们还推导出一个类似的基础上的真实的六重表示，并确定真空对齐，导致三双极大中微子混合和大的第三家庭收费费米子汤川耦合。
We argue that the projective special linear group PSL2(7), also known as Σ(168), has unique features which make it the most suitable discrete family symmetry for describing quark and lepton masses and mixing in the framework of SO(10) type unified models. In such models flavon fields in the sextet representation of PSL2(7) play a crucial role both in obtaining tri-bimaximal neutrino mixing as well as in generating the third family charged fermion Yukawa couplings. In preparation for physical applications, we derive the triplet representation of PSL2(7) in the basis S,T,U,V where S,T,U are the familiar triplet generators of S4in the diagonal charged lepton basis where T is diagonal. We also derive an analogous basis for the real sextet representation and identify the vacuum alignments which lead to tri-bimaximal neutrino mixing and large third family charged fermion Yukawa couplings.