Matrix norms and search for sterile neutrinos

Flieger, Wojciech; Pindel, Franciszek; Porwit, K.

doi:10.22323/1.347.0050

Cited by 3 publications

(3 citation statements)

References 43 publications

(47 reference statements)

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“…Moreover, matrix norms can be used to measure deviation from unitarity on the different levels of the mixing matrix. More details about the matrix norms applied to neutrino mixings can be found in [32,44]. Further, the number of singular values less than one determines a minimal number of additional neutrinos.…”

Section: Introductionmentioning

confidence: 99%

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

Flieger

Gluza

Porwit

2020

J. High Energ. Phys.

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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 |.

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Section: Introductionmentioning

confidence: 99%

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

Flieger

Gluza

Porwit

2020

J. High Energ. Phys.

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“…• Symmetric gauge functions are strictly connected to the unitary invariant norms. We use unitary invariant norms in our study of the mixing matrices [36,37,98]. The symmetric gauge functions can provide a new perspective into the mixing analysis.…”

Section: Discussionmentioning

confidence: 99%

General neutrino mass spectrum and mixing properties in seesaw mechanisms

Flieger¹,

Gluza²

2020

Preprint

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Neutrinos stand out among elementary particles through their unusually small masses. Various seesaw mechanisms attempt to explain this fact. In this work applying insights from matrix theory we are in a position to treat variants of seesaw mechanisms in a general manner. Specifically, using Weyl's inequalities we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos. We find an estimate on the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos shifted at most by the maximal strength of the coupling to the light neutrino sector. We provide analytical conditions allowing to prescribe that precisely two out of five neutrinos are heavy. For higher-dimensional cases the inverse eigenvalue methods are used. In particular, for the CP invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones, i.e. the respective mass submatrix is positive definite, then large masses are provided by matrices with large elements accumulated on the diagonal. Finally, the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis. This general observation concerning neutrino mixing together with results on the mass spectrum properties opens directions for further neutrino physics studies using matrix analysis.

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“…The rest of the eigenvalues of correspond to those of the submatrix. Our approach will be based on the Davis-Kahan theorem (Theorem C2), which is valid for the CP-conserving case (a generalization to the CP-violating case seems to be possible [91], but it requires a separate study). It allows us to estimate the sine of the angle between subspaces, denoted as , spanned by the eigenvectors.…”

Section: Separation Between Eigenspaces In the Seesaw Scenariomentioning

confidence: 99%

General neutrino mass spectrum and mixing properties in seesaw mechanisms *

Flieger

Gluza

2021

Chinese Phys. C

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Neutrinos stand out among the elementary particles because of their unusually small masses. Various seesaw mechanisms attempt to explain this fact. In this work, applying insights from matrix theory, we are in a position to treat variants of seesaw mechanisms in a general manner. Specifically, using Weyl's inequalities, we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos. We find an estimate of the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos, shifted at most by the maximal strength of the coupling to the light neutrino sector. We provide analytical conditions allowing one to prescribe that precisely two out of five neutrinos are heavy. For higher-dimensional cases the inverse eigenvalue methods are used. In particular, for the CP-invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones, i.e. if the respective mass submatrix is positive definite, then large masses are provided by matrices with large elements accumulated on the diagonal. Finally, the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis. This general observation concerning neutrino mixing, together with results on the mass spectrum properties, opens directions for further neutrino physics studies using matrix analysis.

show abstract

Matrix norms and search for sterile neutrinos

Cited by 3 publications

References 43 publications

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

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

General neutrino mass spectrum and mixing properties in seesaw mechanisms

General neutrino mass spectrum and mixing properties in seesaw mechanisms *

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