{
  "abstract": "We utilize renormalization group equations (RGEs) for neutrino oscillations in matter to decipher the structure of exact matter invariants. By combining the RGEs with the $S^{}_3$ permutation covariance under relabeling of the neutrino mass eigenstates, we recast all five algebraically independent matter invariants in the three-flavor framework as exact first integrals. Treating the matter potential as a matter spurion and imposing the cancellation conditions for the $1/\\widetildeΔ_{ij}^{}$ poles in the RGEs, we further prove that the three-flavor framework contains only two independent monomial invariants, which can be related to the Naumov and Toshev relations. We then extend the analysis to the four-flavor framework, where we uncover a complete set of eleven algebraically independent matter invariants and prove that the rank-two electron--sterile spurion obstructs the common pole cancellation required for any nontrivial multiplicative monomial invariant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28540",
  "author_total": 2,
  "authors": [
    {
      "name": "Xin Wang"
    },
    {
      "name": "Shun Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqkt7an8r9cb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28540",
  "fulltext_url": null,
  "id": "fqkt7an8r9cb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28540",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "openalex",
      "3106|Neutrino Physics Research"
    ]
  ],
  "openalex": "W7204778320",
  "pdf_url": "https://arxiv.org/pdf/2608.28540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqkt7an8r9cb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28540"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Deciphering Matter Invariants via Renormalization Group Equations for Neutrino Oscillations",
  "title_text": "Deciphering Matter Invariants via Renormalization Group Equations for Neutrino Oscillations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/fqkt7an8r9cb4",
  "venue": "arXiv",
  "versions": []
}