{"paper":{"title":"Modular invariant flavor model of $\\rm A_4$ and hierarchical structures at nearby fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hiroshi Okada, Morimitsu Tanimoto","submitted_at":"2020-09-29T18:21:35Z","abstract_excerpt":"In the modular invariant flavor model of $\\rm A_4$, we study the hierarchical structure of lepton/quark flavors at nearby fixed points of $\\tau=i$ and $\\tau=\\omega$ of the modulus, which are in the fundamental domain of $\\rm PSL(2,\\mathbb{Z})$. These fixed points correspond to the residual symmetries $\\mathbb{Z}_2^{S}=\\{I, S \\}$ and $\\mathbb{Z}_3^{S}=\\{ I, ST, (ST)^2 \\}$ of $\\rm A_4$, where $S$ and $T$ are generators of the $A_4$ group. The infinite $\\tau= i \\infty$ also preserves the residual symmetry of the subgroup $\\mathbb{Z}^T_3=\\{ I,T,T^2 \\}$ of $\\rm A_4$. We study typical two-type mass "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.14242","kind":"arxiv","version":2},"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/2009.14242/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"}