{"paper":{"title":"Fermion Hierarchies in $SU(5)$ Grand Unification from $\\Gamma_6^\\prime$ Modular Flavor Symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Junichiro Kawamura, Tatsuo Kobayashi, Tetsutaro Higaki, Yoshihiko Abe","submitted_at":"2023-07-04T01:06:54Z","abstract_excerpt":"We construct a model in which the hierarchies of the quark and lepton masses and mixing are explained by the $\\Gamma_6^\\prime$ modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual $Z^T_6$ symmetry, approximately unbroken at $\\tau \\sim i\\infty.$ We argue that the $\\Gamma_6^{(\\prime)}$ symmetry is the minimal possibility to realize the up-type quark mass hierarchies, since the Yukawa matrix is symmetric. We find a combination of the representations and modular weights and then show numerical values of $\\mathcal{O}(1)$ coefficients for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.01419","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.01419/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}