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

TL;DR

This paper uses singular value analysis and matrix decompositions to establish new bounds on non-standard neutrino mixings, improving constraints on light-heavy neutrino interactions based on current experimental data.

Contribution

It introduces a novel approach combining singular values and matrix decompositions to refine bounds on non-standard neutrino mixings in 3+1 scenarios.

Findings

New upper limit on |U_{e4}| is approximately 0.021.

Bounds on non-unitary mixings in 3+2 and 3+3 scenarios are indistinguishable.

Shrinking bounds on light-heavy neutrino mixing elements using dilation and Cosine-Sine decomposition.

Abstract

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 $\alpha$ 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_{e4} | $ 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. $| U_{e4} | , | U_{\mu 4} | , | U_{\tau 4} | .$ New results obtained in this work are based on analysis of neutrino mixing matrices obtained from the global fits at the 95% CL.