{"paper":{"title":"Modulus $\\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ex"],"primary_cat":"hep-ph","authors_text":"Hiroshi Okada, Morimitsu Tanimoto, Takahiro Yoshida, Yusuke Shimizu","submitted_at":"2021-05-29T13:06:49Z","abstract_excerpt":"We propose an $A_4$ modular invariant flavor model of leptons, in which both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus $\\tau$. The value of the modulus $\\tau$ is restricted by the observed lepton mixing angles and lepton masses for the normal hierarchy of neutrino masses at $3\\sigma$ confidence level. The predictive Dirac CP phase $\\delta_{CP}$ is in the ranges $[0^\\circ,50^\\circ]$, $[170^\\circ,175^\\circ]$ and $[280^\\circ,360^\\circ]$ for ${\\rm Re}\\, [\\tau]<0$, and $[0^\\circ,80^\\circ]$, $[185^\\circ,190^\\circ]$ and $[310^\\circ,360^\\circ]$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.14292","kind":"arxiv","version":3},"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/2105.14292/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"}