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Symmetry in Neutrino Oscillation in Matter: New Picture and the νSM–Non-Unitarity Interplay

Abstract:

We update and summarize the present status of our understanding of the reparametrization symmetry with an (Formula presented.) 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, but not the 1–3, exchange symmetry. This is probably due to our lack of understanding, and we find a clue for a larger symmetry structure than we know of. In the latter part of this article, we introduce non-unitarity, or unitarity violation (UV), into the (Formula presented.) SM neutrino paradigm, a low-energy description of beyond (Formula presented.) SM new physics at a 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 diagnostic capability for the theory with the (Formula presented.) SM and UV sectors. Speculation is given on the topological nature of the identity, which determines the transformation property of the UV (Formula presented.) parameters.