Symmetry in neutrino oscillation in matter: New picture and the $\nu$SM -- non-unitarity interplay

TL;DR

This paper explores reparametrization symmetries in neutrino oscillations in matter, introduces a systematic method to find such symmetries, and discusses their implications in the presence of unitarity violation within the neutrino Standard Model.

Contribution

It introduces the 'Symmetry Finder' method to systematically uncover reparametrization symmetries and examines their features and potential larger symmetry structures, especially with unitarity violation.

Findings

Symmetries exist at solar- and atmospheric-resonances.

The DMP perturbation theory has only the 1-2 symmetry.

Reparametrization symmetry can diagnose UV effects in neutrino models.

Abstract

We update and summarize the present status of our understanding of the reparametrization symmetry with $i \leftrightarrow j$ state exchange in neutrino oscillation in matter. We introduce a systematic method called ``Symmetry Finder'' (SF) to uncover such symmetries, demonstrate its efficient hunting capability, and examine their characteristic features. Apparently they have a local nature: The 1-2 and 1-3 state exchange symmetries exist at around the solar- and atmospheric-resonances, respectively, with the level-crossing states exchanged. However, this view is not supported, to date, in the globally valid Denton et al. (DMP) perturbation theory, which possesses the 1-2 exchange symmetry but not the 1-3. It is probably due to lack of our understanding, and we find a clue for a larger symmetry structure than that we know. In the latter part of this article, we introduce non-unitarity, or unitarity violation (UV), into the $\nu$SM neutrino paradigm, a low-energy description of beyond $\nu$SM new physics at high (or low) scale. Based on the analyses of UV extended versions of the atmospheric-resonance and the DMP perturbation theories, we argue that the reparametrization symmetry has a diagnostics capability for the theory with the $\nu$SM and UV sectors. A speculation is given on the topological nature of the identity which determines the transformation property of the UV $\alpha$ parameters.