Modular symmetry origin of texture zeros and quark-lepton unification
Modular symmetry origin of texture zeros and quark-lepton unification
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DOI：
10.1103/physrevd.101.115020
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发表时间：
2019-12
影响因子：
5
通讯作者：
Jun-Nan Lu;Xiang-Gan Liu;Gui-Jun Ding
中科院分区：
文献类型：
--
作者：
Jun-Nan Lu;Xiang-Gan Liu;Gui-Jun Ding
层N$的偶权模形式可以被安排成非齐次有限模群$Gamma‘N$和齐次有限模群$Gamma’N$的公共不可约表示，它是$Gamma N$的二重覆盖，以及层N$变换的奇权模形式。我们发现，如果适当地分配模群下物质场的表示和权重，上述模形式的结构可以自然地产生费米子质量矩阵的织构零点。我们对模对称性进行了全面的分析。假设三代左撇子夸克变换为双重态和单重态，我们发现了夸克质量矩阵的六种可能的织构零点结构，直至行排列和列排列。我们给出了五个基准夸克模型，它们可以很好地与实验数据相吻合。这些夸克模型被进一步扩展到包括轻子扇区，所得到的模型可以同时给出夸克和轻子质量以及味道混合的统一描述，尽管它们包含的自由参数比可见的少。
The even weight modular forms of level $N$ can be arranged into the common irreducible representations of the inhomogeneous finite modular group $\Gamma_N$ and the homogeneous finite modular group $\Gamma'_N$ which is the double covering of $\Gamma_N$, and the odd weight modular forms of level $N$ transform in the new representations of $\Gamma'_N$. We find that the above structure of modular forms can naturally generate texture zeros of the fermion mass matrices if we properly assign the representations and weights of the matter fields under the modular group. We perform a comprehensive analysis for the $\Gamma'_3\cong T'$ modular symmetry. The three generations of left-handed quarks are assumed to transform as a doublet and a singlet of $T'$, we find six possible texture zeros structures of quark mass matrix up to row and column permutations. We present five benchmark quark models which can produce very good fit to the experimental data. These quark models are further extended to include lepton sector, the resulting models can give a unified description of both quark and lepton masses and flavor mixing simultaneously although they contain less number of free parameters than the observables.