{"paper":{"title":"Spontaneous CP violation by modulus $\\tau$ in $A_4$ model of lepton flavors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hiroshi Okada, Morimitsu Tanimoto","submitted_at":"2020-12-03T03:50:20Z","abstract_excerpt":"We discuss the modular $A_4$ invariant model of leptons combining with the generalized CP symmetry. In our model, both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus $\\tau$. The source of the CP violation is a non-trivial value of ${\\rm Re} [\\tau]$ while other parameters of the model are real. The allowed region of $\\tau$ is in very narrow one close to the fixed point $\\tau=i$ for both normal hierarchy (NH) and inverted ones (IH) of neutrino masses. The CP violating Dirac phase $\\delta_{CP}$ is predicted clearly in $[98^\\circ,\\,110^\\circ]$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.01688","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/2012.01688/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"}