Singular values are used to construct physically admissible 3-dimensional mixing matrices characterized as contractions. Depending on the number of singular values strictly less than one, the space of the 3-dimensional mixing matrices can be split into four disjoint subsets, which accordingly corresponds to the minimal number of additional, non-standard neutrinos. We show in numerical analysis that taking into account present experimental precision and fits to different neutrino mass splitting schemes, it is not possible to distinguish, on the level of 3-dimensional mixing matrices, between two and three extra neutrino states. It means that in 3+2 and 3+3 neutrino mixing scenarios, using the so-called α parametrization, ranges of non-unitary mixings are the same. However, on the level of a complete unitary 3+1 neutrino mixing matrix, using the dilation procedure and the Cosine-Sine decomposition, we were able to shrink bounds for the “light-heavy” mixing matrix elements. For instance, in the so-called seesaw mass scheme, a new upper limit on |U e 4 | is about two times stringent than before and equals 0.021. For all considered mass schemes the lowest bounds are also obtained for all mixings, i.e. |U e 4 |, |U μ 4 |, |U τ 4 | . New results obtained in this work are based on analysis of neutrino mixing matrices obtained from the global fits at the 95% CL.

中文翻译：

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基于规定奇异值的中微子非幺正混合的新限制

奇异值用于构造以收缩为特征的物理上可接受的 3 维混合矩阵。根据严格小于 1 的奇异值的数量，3 维混合矩阵的空间可以分成四个不相交的子集，相应地对应于额外的非标准中微子的最少数量。我们在数值分析中表明，考虑到目前的实验精度并适合不同的中微子质量分裂方案，在 3 维混合矩阵的水平上，不可能区分两个和三个额外的中微子态。这意味着在 3+2 和 3+3 中微子混合场景中，使用所谓的 α 参数化，非幺正混合的范围是相同的。然而，在一个完整的酉 3+1 中微子混合矩阵的水平上，使用膨胀过程和余弦-正弦分解，我们能够缩小“轻-重”混合矩阵元素的边界。例如，在所谓的跷跷板质量方案中，|U e 4 | 的新上限。大约是以前严格的两倍，等于 0.021。对于所有考虑的质量方案，还获得了所有混合的最低界限，即 |U e 4 |、|U μ 4 |、|U τ 4 | . 在这项工作中获得的新结果基于对从 95% CL 的全局拟合中获得的中微子混合矩阵的分析。对于所有考虑的质量方案，还获得了所有混合的最低界限，即 |U e 4 |、|U μ 4 |、|U τ 4 | . 在这项工作中获得的新结果基于对从 95% CL 的全局拟合中获得的中微子混合矩阵的分析。对于所有考虑的质量方案，还获得了所有混合的最低界限，即 |U e 4 |、|U μ 4 |、|U τ 4 | . 在这项工作中获得的新结果基于对从 95% CL 的全局拟合中获得的中微子混合矩阵的分析。