{"paper":{"title":"The U(1) symmetry of the non-tribimaximal pattern in the degenerate mass spectrum case of the neutrino mass matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Cairo & Zewail City of Science, E.I. Lashin (Ain Shams U., Giza & ICTP, N. Chamoun (HIAST & Bonn U.), S. Nasri (United Arab Emirates U.), Technology, Trieste)","submitted_at":"2012-09-04T17:18:29Z","abstract_excerpt":"On account of the new neutrino oscillation data signalling a non-zero value for the smallest mixing angle ($\\theta_z$), we present an explicit realization of the underlying U(1) symmetry characterizing the maximal atmospheric mixing angle ($\\theta_y = \\pi / 4$) pattern with two degenerate masses but now with generic values of $\\theta_z$. We study the effects of the form invariance with respect to U(1), and/or $Z_3$, $Z_2$ subgroups, on the Yukawa couplings and the mass terms. Later on, we specify $\\theta_z$ to its experimental best fit value ($ \\sim 8^o$), and impose the symmetry in an entire "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0707","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"}