2022 A 4 Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point τ = ω
2022 A 4 Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point τ = ω
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2022 接近定点 τ = ω 的夸克质量层次的 4 模块化风味模型
DOI：
10.1007/jhep06(2020)134
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发表时间：
2022
影响因子：
5.4
通讯作者：
M. Tanimoto
中科院分区：
文献类型：
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作者：
S. Petcov;M. Tanimoto
我们研究了在具有模块A4对称性的夸克flavour模型中无需微调即可描述夸克质量等级以及CKM夸克混合矩阵的可能性。夸克的质量等级被认为是在不动点τ = ω exp（i 2 π/ 3）（模群基本域的左尖点）附近，τ是模的VEV。该模型涉及级别3和权重6、4和2的模形式，并且包含八个常数，除了模的VEV τ = ω + ω，（ω）ω 6 = ω，| ǫ |2001年。我们发现，在下夸克和上夸克扇区中的真实的（CP守恒）g u和g d以及公共τ（τ）的情况下，下型夸克质量等级可以在没有微调的情况下再现，| ǫ |= 0。03，所有其他常数为O（1），并大致对应于1：| ǫ | : | ǫ |二、上型夸克质量等级可以用同样的方法来实现。| ǫ |= 0。03，但允许g u = O（10），并对应于1：| ǫ | / |G u| : | ǫ |2个/|G u|二、在此设置中，CKM值的再现
We investigate the possibility to describe the quark mass hierarchies as well as the CKM quark mixing matrix without fine-tuning in a quark flavour model with modular A 4 symmetry. The quark mass hierarchies are considered in the vicinity of the fixed point τ = ω ≡ exp( i 2 π/ 3) (the left cusp of the fundamental domain of the modular group), τ being the VEV of the modulus. The model involves modular forms of level 3 and weights 6, 4 and 2, and contains eight constants, only two of which, g u and g d , can be a source of CP violation in addition to the VEV of the modulus, τ = ω + ǫ , ( ǫ ) ∗ 6 = ǫ , | ǫ | ≪ 1. We find that in the case of real (CP-conserving) g u and g d and common τ ( ǫ ) in the down-quark and up-quark sectors, the down-type quark mass hierarchies can be reproduced without fine tuning with | ǫ | ∼ = 0 . 03, all other constants being of O (1), and correspond approximately to 1 : | ǫ | : | ǫ | 2 . The up-type quark mass hierarchies can be achieved with the same | ǫ | ∼ = 0 . 03 but allowing g u ∼ O (10) and correspond to 1 : | ǫ | / | g u | : | ǫ | 2 / | g u | 2 . In this setting the reproduction of the value of the CKM