Abstract
Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D3. After building the vector-valued modular forms in the representations of 2D3 with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D3, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as \({\mathbb{T}}^{2}/{\mathbb{Z}}_{4}\) heterotic orbifold compactifications.
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Acknowledgments
It is a pleasure to thank Ramón Díaz-Castro for useful discussions during this work. We also thank Alexander Baur, Hans Peter Nilles, Patrick K.S. Vaudrevange and Andreas Trautner for enlightening top-down discussions. This work is partially supported by UC-MEXUSCONACyT grant No. CN-20-38. CAO and SRS are supported by UNAM-PAPIIT IN113223, CONACyT grant CB-2017-2018/A1-S-13051, and Marcos Moshinsky Foundation. XGL is supported by U.S. National Science Foundation under Grant No. PHY-2210283.
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Arriaga-Osante, C., Liu, XG. & Ramos-Sánchez, S. Quark and lepton modular models from the binary dihedral flavor symmetry. J. High Energ. Phys. 2024, 119 (2024). https://doi.org/10.1007/JHEP05(2024)119
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DOI: https://doi.org/10.1007/JHEP05(2024)119