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arXiv 1907.09141hep-ph
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由$S_4$模对称性导出的新的$A_4$轻子味模型

New $A_4$ lepton flavor model from $S_4$ modular symmetry

Tatsuo Kobayashi, Yusuke Shimizu, Kenta Takagi, Morimitsu Tanimoto, Takuya H. Tatsuishi

摘要:

研究了一类具有$A_4$对称性的味模型,该味模型起源于$S_4$模群.在$S_4$对称性中,$Z_2$子群可以是反常的,则$S_4$可以被破坏为$A_4$ .从树水平上的$S_4$对称拉格朗日量开始,当$S_4$中的$Z_2$是反常的时,量子水平上的拉格朗日量仅具有$A_4$对称性。通过将$S_4$模形式分解为$A_4$表示,得到了$A_4$的两个单重态和一个三重态表示的模形式.利用这些$A_4$模形式,我们提出了一个新的轻子味模型$A_4$.通过Weinberg算符,我们成功地构造了一个可行的中微子质量矩阵,它适用于中微子质量的正态层次(NH)和逆层次(IH)。我们对CP破坏狄拉克相$δ_{CP}$和混合$\sin^2θ_{23}$的预测依赖于NH中微子质量的总和。

英文摘要:

We study a flavor model with $A_4$ symmetry which originates from $S_4$ modular group. In $S_4$ symmetry, $Z_2$ subgroup can be anomalous, and then $S_4$ can be violated to $A_4$. Starting with a $S_4$ symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only $A_4$ symmetry when $Z_2$ in $S_4$ is anomalous. We obtain modular forms of two singlets and a triplet representations of $A_4$ by decomposing $S_4$ modular forms into $A_4$ representations. We propose a new $A_4$ flavor model of leptons by using those $A_4$ modular forms. We succeed in constructing a viable neutrino mass matrix through the Weinberg operator for both normal hierarchy (NH) and inverted hierarchy (IH) of neutrino masses. Our predictions of the CP violating Dirac phase $δ_{CP}$ and the mixing $\sin^2θ_{23}$ depend on the sum of neutrino masses for NH.

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