物质中中微子振荡的对称性：新的图象和$ν$ SM --非么正性相互作用
Symmetry in neutrino oscillation in matter: New picture and the $ν$SM -- non-unitarity interplay
摘要：
本文对物质中中微子振荡中$i \leftrightarrow j$态交换的重参数化对称性的研究现状进行了更新和总结。我们引入了一个系统的方法，称为“对称发现”（SF），以发现这样的对称性，展示其有效的狩猎能力，并检查其特性。显然，它们具有局部性质：1-2和1-3态交换对称性分别存在于太阳和大气共振附近，并交换了能级交叉态。然而，这种观点不支持，到目前为止，在全球有效的丹顿等人（Denton）微扰理论，它具有1-2交换对称性，但没有1-3。这可能是由于我们缺乏理解，我们发现了一个比我们所知道的更大的对称结构的线索。在本文的后半部分，我们将非么正性或么正性破坏（UV）引入到$ν$ SM中微子范式中，该范式是对高（或低）尺度下超越$ν$ SM的新物理的低能描述。通过对紫外扩展的大气共振理论和微扰理论的分析，指出重参数化对称性对具有$ν$ SM和紫外扇区的理论具有诊断能力.对决定UV $α$参数变换性质的恒等式的拓扑性质进行了推测。
英文摘要：
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 $ν$SM neutrino paradigm, a low-energy description of beyond $ν$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 $ν$SM and UV sectors. A speculation is given on the topological nature of the identity which determines the transformation property of the UV $α$ parameters.
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