{"paper":{"title":"Direct and Semi-Direct Approaches to Lepton Mixing with a Massless Neutrino","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Patrick Otto Ludl, Stephen F. King","submitted_at":"2016-05-05T18:35:14Z","abstract_excerpt":"We discuss the possibility of enforcing a massless Majorana neutrino in the direct and semi-direct approaches to lepton mixing, in which the PMNS matrix is partly predicted by subgroups of a discrete family symmetry, extending previous group searches up to order 1535. We find a phenomenologically viable scheme for the semi-direct approach based on $Q(648)$ which contains $\\Delta(27)$ and the quaternion group as subgroups. This leads to novel predictions for the first column of the PMNS matrix corresponding to a normal neutrino mass hierarchy with $m_1=0$, and sum rules for the mixing angles an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01683","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":""},"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"}