{"paper":{"title":"Horizontal symmetries of leptons with a massless neutrino","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Anjan S. Joshipura, Ketan M. Patel","submitted_at":"2013-06-08T07:59:12Z","abstract_excerpt":"Residual symmetry $G_\\nu$ of neutrino mass matrix with a massless neutrino and embedding of $G_\\nu$ and the residual symmetry $G_l$ of the charged lepton mass matrix into finite discrete groups $G$ is discussed. Massless neutrino results if $G_\\nu$ and hence $G$ are subgroups of $U(3)$ rather than of $SU(3)$. Structure of the resulting leptonic mixing matrix $U_{PMNS}$ is discussed in three specific examples based on groups (a) $\\Sigma(3N^3)$, (b) $\\Sigma(2N^2)$ and (c) $S_4(2) \\equiv A_4\\rtimes Z_4$. $\\Sigma(3N^3)$ groups are able to reproduce either the second or the third column of $U_{PMNS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1890","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":""},"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"}