We present a flavor model with |$S_3$| modular invariance in the framework of SU(5) grand unified theory (GUT). The |$S_3$| modular forms of weights |$2$| and |$4$| give the quark and lepton mass matrices with a common complex parameter, the modulus |$au$|?. The GUT relation of down-type quarks and charged leptons is imposed by the vacuum expectation value (VEV) of the adjoint 24-dimensional Higgs multiplet in addition to the VEVs of |$5$| and |$ar 5$| Higgs multiplets of SU(5). The observed Cabibbo–Kobayashi–Maskawa and Pontecorvo–Maki–Nakagawa–Sakata mixing parameters as well as the mass eigenvalues are reproduced properly. We discuss the leptonic charge–parity phase and the effective mass of the neutrinoless double beta decay with the sum of neutrino masses.
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机译：我们提出了一种味道模型| $ S_3 $ |苏（5）统一理论（肠道）框架中的模块化不变性。 The | $ S_3 $ |模块化的重量形式| $ 2 $ |和| $ 4 $ |给出夸克和Lepton大规模矩阵，具有常见的复杂参数，模数| $ tau $ |？除了伴随的VEVS之外，伴随24维HIGGS多重的真空预期值（VEV）施加了下型夸克和带电肝脏的肠道关系和| $ BAR 5 $ | Higgs苏（5）的苏格兰。观察到的Cabibbo-Kobayashi-MaskaWa和Pontecorvo-Maki-Nakagawa-Sakata混合参数以及群众特征值进行了正确。我们讨论了Leptonic电荷阶段和中微子双β衰变的有效质量与中微子质量的总和。
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