{"paper":{"title":"Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Shun Zhou, Xin Wang","submitted_at":"2019-01-30T15:07:27Z","abstract_excerpt":"Recently, a complete set of differential equations for the effective neutrino masses and mixing parameters in matter have been derived to characterize their evolution with respect to the ordinary matter term $a \\equiv 2\\sqrt{2}G^{}_{\\rm F} N^{}_e E$, in analogy with the renormalization-group equations (RGEs) for running parameters. Via series expansion in terms of the small ratio $\\alpha^{}_{\\rm c} \\equiv \\Delta^{}_{21}/\\Delta^{}_{\\rm c}$, we obtain approximate analytical solutions to the RGEs of the effective neutrino parameters and make several interesting observations. First, at the leading"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10882","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"}