{"paper":{"title":"Quark and lepton hierarchies from $S_4^\\prime$ modular flavor symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Junichiro Kawamura, Tatsuo Kobayashi, Tetsutaro Higaki, Yoshihiko Abe","submitted_at":"2023-02-22T07:33:59Z","abstract_excerpt":"We propose models in which the hierarchical structures of the masses and mixing in both quark and lepton sectors are explained by the $S_4^\\prime$ modular flavor symmetry near the fixed point $\\tau \\sim i\\infty$. The model provides the first explicit example which explains hierarchies of both quarks and leptons. The hierarchies are realized by powers of $\\epsilon = e^{2\\pi i \\tau/4} = \\mathcal{O}(0.01)$ and $2\\,\\mathrm{Im}\\,\\tau \\sim 5$, where $\\tau$ being the modulus. The small parameter $\\epsilon$ plays a role of flavon in the Froggatt-Nielsen mechanism under the residual $Z_4^T$ symmetry, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11183","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/2302.11183/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"}