Abstract
We propose to construct the finite modular groups from the quotient of two principal congruence subgroups as Γ(N′)/Γ(N″), and the modular group SL(2, ℤ) is ex- tended to a principal congruence subgroup Γ(N′). The original modular invariant theory is reproduced when N′ = 1. We perform a comprehensive study of \( {\Gamma}_6^{\prime } \) modular symmetry corresponding to N′ = 1 and N″ = 6, five types of models for lepton masses and mixing with \( {\Gamma}_6^{\prime } \) modular symmetry are discussed and some example models are studied numerically. The case of N′ = 2 and N″ = 6 is considered, the finite modular group is Γ(2)/Γ(6) ≅ T′, and a benchmark model is constructed.
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Li, CC., Liu, XG. & Ding, GJ. Modular symmetry at level 6 and a new route towards finite modular groups. J. High Energ. Phys. 2021, 238 (2021). https://doi.org/10.1007/JHEP10(2021)238
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DOI: https://doi.org/10.1007/JHEP10(2021)238