Deciphering Matter Invariants via Renormalization Group Equations for Neutrino Oscillations

@misc{wang2026deciphering,
  title = {{Deciphering Matter Invariants via Renormalization Group Equations for Neutrino Oscillations}},
  author = {Xin Wang and Shun Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28540},
  eprint = {2608.28540},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28540},
}

TY  - UNPB
TI  - Deciphering Matter Invariants via Renormalization Group Equations for Neutrino Oscillations
AU  - Xin Wang
AU  - Shun Zhou
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28540
UR  - https://arxiv.org/abs/2608.28540
AB  - 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/Δ̃_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.
ER  -