{"paper":{"title":"A complex-angle rotation and geometric complementarity in fermion mixing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Kee-Hwan Nam, Kim Siyeon, Seungsu Hwang","submitted_at":"2008-08-06T07:38:21Z","abstract_excerpt":"The mixing among flavors in quarks or leptons in terms of a single rotation angle is defined such that three flavor eigenvectors are transformed into three mass eigenvectors by a single rotation about a common axis. We propose that a geometric complementarity condition exists between the complex angle of quarks and that of leptons in $\\mathbb{C}^2$ space. The complementarity constraint has its rise in quark-lepton unification and is reduced to the correlation among $\\theta_{12}, \\theta_{23}, \\theta_{13}$ and the CP phase $\\delta$. The CP phase turns out to have a non-trivial dependence on all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0788","kind":"arxiv","version":1},"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"}