Modular invariant quark and lepton models in double covering of S4 modular group
Modular invariant quark and lepton models in double covering of S4 modular group
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DOI：
10.1103/physrevd.103.056013
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发表时间：
2020-06
影响因子：
5
通讯作者：
Xiang-Gan Liu;Chang-Yuan Yao;Gui-Jun Ding
中科院分区：
文献类型：
--
作者：
Xiang-Gan Liu;Chang-Yuan Yao;Gui-Jun Ding
本文对齐次有限模群$\Gamma '_4\equiv S'_4 $进行了全面的分析，它是S '_4 $群的双重覆盖.第4层的权1模形式是根据Dedekind eta函数构造的，它们变换为$S '_4 $的三元组$\mathbf{\hat{3}'}$。直到权重6的积分权重模形式是从权重1模形式的张量积构建的。本文对有/无广义CP的轻子质量和混合的$S '4 $模模型进行了系统的分类，其中左手轻子被分配到$S' 4 $的三重态，右手带电轻子在$S '4 $下变换为单重态，我们考虑了中微子质量由温伯格算符或I型跷跷板机制产生的两种情况。讨论了最小模型对轻子质量、混合角、CP破坏相和无中微子双衰变的唯象意义。将$S '4 $模对称性推广到夸克扇区，提出了几种用包括$\tau$的真实的和虚部在内的9个或10个自由参数来描述夸克质量和CKM混合矩阵的预测模型。我们给出了一个夸克-轻子统一模型，它可以同时解释夸克和轻子的味结构，并且给出了一个共同的$\tau$。
We perform a comprehensive analysis of the homogeneous finite modular group $\Gamma'_4\equiv S'_4$ which is the double covering of $S_4$ group. The weight 1 modular forms of level 4 are constructed in terms of Dedekind eta function, and they transform as a triplet $\mathbf{\hat{3}'}$ of $S'_4$. The integral weight modular forms until weight 6 are built from the tensor products of weight 1 modular forms. We perform a systematical classification of $S'_4$ modular models for lepton masses and mixing with/without generalized CP, where the left-handed leptons are assigned to triplet of $S'_4$ and right-handed charged leptons transform as singlets under $S'_4$, and we consider both scenarios where the neutrino masses arise from Weinberg operator or type I seesaw mechanism. The phenomenological implications of the minimal models for lepton masses, mixing angles, CP violation phases and neutrinoless double decay are discussed. The $S'_4$ modular symmetry is extended to quark sector, we present several predictive models which use nine or ten free parameters including real and imaginary parts of $\tau$ to describe quark masses and CKM mixing matrix. We give a quark-lepton unified model which can explain the flavor structure of quarks and leptons simultaneously for a common value of $\tau$.