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

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 α parametrization, ranges of non-standard 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 µ4 |, |U τ 4 |.

Studies of Non-standard Particle Mixings Through Singular Values

“…This implies that |U e4 | behaves in a controllable way. As a consequence, numerical estimations of |U i4 |, i = e, µ, τ given in [19] are stable.…”

“…Quantitative results of mixing matrix analysis by singular values can be found in [5,18,19]. In these works, the estimation of allowed space for additional neutrinos is discussed, along with statistical analysis of physically admissible mixing matrices within experimental bounds, and the possibility to distinguish sets in (12).…”

“…In this way, the mixing between three known active neutrino states can be maintained. However, if instead of the construction of particular complete mixing matrices, we are only interested in the estimation of the mixing between standard and non-standard neutrinos, it is also possible to do so with the help of singular values and the CS decomposition [19]. In this situation, we are interested in estimation of the top right block U 12 of the complete mixing matrix.…”

“…Numerical estimation of these bounds for different mass scenario splittings can be found in [19]. The upper bounds have been obtained by looking for the largest absolute value of w i3 , i = 1, 2, 3, corresponding to allowed singular values for each massive scenario.…”

Neutrinoless double beta decay versus other probes of heavy sterile neutrinos

“…Numerous weak decays have bee used to pin down the CKM elements V ud , V us , V ub and the unitarity condition |V ud | 2 +|V us | 2 +|V ub | 2 = 1. Assuming a single sterile state coupling to just the first generation, all of these measurements enforce a constant bound of 2|η ee | = |V eN | < 0.050 for m N 1 GeV [134][135][136][137][138][139].…”