Abstract
We have investigated the modular binary octahedral group 2O as a flavor symmetry to explain the structure of Standard Model. The vector-valued modular forms in all irreducible representations of this group are constructed. We have classified all possible fermion mass models based on the modular binary octahedral group 2O. A comprehensive numerical analysis is performed, and we present some benchmark quark/lepton mass models in good agreement with the experimental data. Notably we find a minimal modular invariant model for leptons and quarks, which is able to explain simultaneously the masses and mixing parameters of both quarks and leptons in terms of 14 real free parameters including the modulus τ. The fermion mass hierarchies around the vicinity of the modular fixed points are explored.
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Acknowledgments
GJD is supported by the National Natural Science Foundation of China under Grant Nos. 11975224, 11835013. XGL is supported by U.S. National Science Foundation under Grant No. PHY-2210283. JNL is supported by the Grant No. NSFC-12147110 and the China Post-doctoral Science Foundation under Grant No. 2021M70. MHW is supported by the National Natural Science Foundation of China under Grant No. 12275263. GJD would like to thank the School of Physics and Astronomy at the University of Southampton for hospitality.
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Ding, GJ., Liu, XG., Lu, JN. et al. Modular binary octahedral symmetry for flavor structure of Standard Model. J. High Energ. Phys. 2023, 83 (2023). https://doi.org/10.1007/JHEP11(2023)083
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DOI: https://doi.org/10.1007/JHEP11(2023)083