{"paper":{"title":"Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-ph","authors_text":"Shun Zhou","submitted_at":"2020-04-22T13:45:48Z","abstract_excerpt":"Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $\\widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{\\alpha i}$ (for $\\alpha = e, \\mu, \\tau$ and $i = 1, 2, 3$). When the matter parameter $a \\equiv 2\\sqrt{2} G^{}_{\\rm F} N^{}_e E$ is taken as an independent variable, a complete set of first-order ordinary differential equations for $\\widetilde{m}^2_i$ and $|V^{}_{\\alpha i}|^2$ have been derived in the previous works. In the present paper, we point out that such a system of differential equations possesses both the conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.10570","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.10570/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"}