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群论中的自然真空排列:最小情形

Natural Vacuum Alignment from Group Theory: The Minimal Case

Martin Holthausen, Michael A. Schmidt

摘要:

离散味对称性已被证明成功地解释轻子味结构。为了解释所观察到的混合模式,味对称性必须在带电和中性轻子扇区中被打破到不同的子组。然而,通过标量势中的非平凡收缩的交叉耦合迫使群分裂为相同的子群。我们提出了一个解决这个问题的方法,通过扩展的味道组在这样一种方式,它保留了味道结构,但导致一个“意外”的对称性的flavon潜力。我们已经寻找了直到1000阶的对称群,它们禁止所有危险的交叉耦合,并扩展了有趣的群A4,T7,S4,T '或Δ(27)之一。我们已经找到了一些候选群体,并提出了一个模型的基础上的最小的扩展A4,即Q8 \rtimes A4。我们表明,最一般的非超对称势允许正确的真空对齐。我们研究了高维算符对真空组态和混合角的影响,给出了一个类似于跷跷板的紫外完备化。最后,我们讨论了模型的超对称化。此外,我们还发布了Mathematica软件包"Discrete",为模型构建提供了各种有用的工具,例如轻松计算离散群和flavon势的不变量。

英文摘要:

Discrete flavour symmetries have been proven successful in explaining the leptonic flavour structure. To account for the observed mixing pattern, the flavour symmetry has to be broken to different subgroups in the charged and neutral lepton sector. However, cross-couplings via non-trivial contractions in the scalar potential force the group to break to the same subgroup. We present a solution to this problem by extending the flavour group in such a way that it preserves the flavour structure, but leads to an 'accidental' symmetry in the flavon potential. We have searched for symmetry groups up to order 1000, which forbid all dangerous cross-couplings and extend one of the interesting groups A4, T7, S4, T' or Δ(27). We have found a number of candidate groups and present a model based on one of the smallest extension of A4, namely Q8 \rtimes A4. We show that the most general non-supersymmetric potential allows for the correct vacuum alignment. We investigate the effects of higher dimensional operators on the vacuum configuration and mixing angles, and give a see-saw-like UV completion. Finally, we discuss the supersymmetrization of the model. Additionally, we release the Mathematica package "Discrete" providing various useful tools for model building such as easily calculating invariants of discrete groups and flavon potentials.

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