论文标题
模块化不变$ a_ {4} $模型，用于夸克和带有广义CP对称性的Leptons
Modular Invariant $A_{4}$ Models for Quarks and Leptons with Generalized CP Symmetry
论文作者
论文摘要
我们对$ A_4 $模块模型进行了系统分析，该模型具有通用的CP，用于夸克和叶子的质量和风味混合，并给出了夸克和Lepton质量矩阵的最通用形式。 CP不变性需要在所选的基础上进行所有真实的耦合，因此，模量$τ$的真空期望值唯一打破了模块化对称性和CP对称性。出现了具有最小数量的自由参数和拟合结果的现象学上可行的模型。我们找到了20个具有7个实际自由参数的模型，可以容纳Lepton部门的实验数据。然后，我们将$ A_4 $模块化对称性应用于夸克扇区以解释夸克质量和CKM混合矩阵，发现最小可行的夸克模型包含10个免费的真实参数。最后，我们提供了两个预测性的夸克 - 莱普顿统一模型，它们仅使用16个真正的自由参数来解释夸克和叶子的风味模式。
We perform a systematical analysis of the $A_4$ modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus $τ$ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply $A_4$ modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.
