arXiv 2001.029542020-01hep-phhep-th

反SU（5）中的四面体对称性A $_{\bf 4}$ GUT

Tetrahedral Symmetry A$_{\bf 4}$ in Anti-SU(5) GUT

Paul H. Frampton, Jihn E. Kim, Se-Jin Kim, Soonkeon Nam

备注：: 14 pages of LaTeX file with 2 figures
发表信息：: Phys. Rev. D 101, 055022 (2020)
DOI：: 10.1103/PhysRevD.101.055022

摘要：

我们在反SU（5）大统一理论中构造了一个具有四面体对称性$A_4$的味模型.我们选择一个基础，其中$Q_{text{em}}=-\frac13$夸克和带电轻子已经是质量本征态。根据$A_4$对称性，可以进行这种选择。然后，物质表象$\overline{10}_{-1}^{\rm\, matter}$同时包含一个夸克二重态和一个重中微子$N$，这使我们能够将$A_4$对称性用于$Q_{text{em}}=+\frac23$夸克质量和中微子质量（通过$N$的跷跷板）。这是可能的，因为反SU（5）破缺是通过希格斯场变换为SU（5）的反对称表示$\overline{10}_{-1}^H\oplus 10_{+1}^H$来实现的，从而将秩5的反SU（5）群降低到秩4的标准模型群\smg。对于可能的质量矩阵，在场论水平上导出了质量矩阵的$A_4$对称性预言。最后给出了一个字符串紧化的例子。

英文摘要：

We construct a flavor model in an anti-SU(5) GUT with a tetrahedral symmetry $A_4$. We choose a basis where $Q_{text{em}}=-\frac13$ quarks and charged leptons are already mass eigenstates. This choice is possible from the $A_4$ symmetry. Then, matter representation $\overline{10}_{-1}^{\rm\, matter}$ contains both a quark doublet and a heavy neutrino $N$, which enables us to use the $A_4$ symmetry to both $Q_{text{em}}=+\frac23$ quark masses and neutrino masses (through the see-saw via $N$). This is made possible because the anti-SU(5) breaking is achieved by the Higgs fields transforming as anti-symmetric representations of SU(5), $\overline{10}_{-1}^H\oplus 10_{+1}^H$, reducing the rank-5 anti-SU(5) group down to the rank-4 standard model group \smg. For possible mass matrices, the $A_4$ symmetry predictions on mass matrices at field theory level are derived. Finally, an illustration from string compactification is presented.

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