New limits on neutrino non-unitary mixings based on prescribed singular values

Singular values are used to construct physically admissible 3-dimensional mix- ing 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 pos- sible 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 jUe4j 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. |Ue4|, |Uμ4|, |Uτ4|. New results obtained in this work are based on analysis of neutrino mixing matrices obtained from the global fits at the 95% CL