{"paper":{"title":"Quark and lepton flavors with common modulus $\\tau$ in $A_4$ modular symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hiroshi Okada, Morimitsu Tanimoto","submitted_at":"2020-05-02T09:58:36Z","abstract_excerpt":"We study quark and lepton mass matrices with the common modulus $\\tau$ in the $A_4$ modular symmetry. The viable quark mass matrices are composed of modular forms of weights $2$, $4$ and $6$. It is remarked that the modulus $\\tau$ is close to $i$, which is a fixed point in the fundamental region of SL$(2,Z)$, and the CP symmetry is not violated. Indeed, the observed CP violation is reproduced at $\\tau$ which is deviated a little bit from $\\tau=i$. The charged lepton mass matrix is also given by using modular forms of weights $2$, $4$ and $6$, where five cases have been examined. The neutrino m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.00775","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/2005.00775/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"}