Majorana neutrino mass matrices with three texture zeros and the sterile neutrino

TL;DR

This paper analyzes Majorana neutrino mass matrices with three texture zeros within the (3+1) model, identifying feasible textures compatible with experimental data and predicting active neutrino masses around 0.01 eV, with implications for future neutrinoless double beta decay experiments.

Contribution

It systematically classifies all three-zero textures in the (3+1) neutrino model and identifies which are compatible with current experimental constraints.

Findings

100 textures with zeros in the fourth row and column are incompatible with experiments.

19 out of 20 other textures are feasible under current experimental data.

Active neutrino masses are predicted to be around 0.01 eV.

Abstract

As a consequence of the LSND anomaly and other hints of an eV scale sterile neutrino from particle physics and cosmology, the neutrino sector of the standard model of particle physics has to be extended and the smallest extension is the (3+1) model, i.e. three active neutrinos plus one sterile one. In this work we study the neutrino mass matrix $M_\nu$ with three texture zeros in the (3+1) model, assuming all the neutrino states are of Majorana type. With the mass hierarchy between the active and sterile neutrinos as well as the smallness of the reactor neutrino mixing and active-sterile mixing, the analytical expressions can be greatly simplified. We systematically examine all the 120 texture zeros, via both analytical and numerical analysis, and find that the 100 textures with zeros in the fourth column and row of $M_\nu$ can hardly be compatible with experiments whereas 19 of the other 20 are feasible. We can foresee that the active neutrino masses are required to be around 0.01 eV and the next generation neutrinoless double beta decay experiments are promising to test these textures. Many other phenomenologically meaningful predictions are also obtained. All the CP conserving (3+1) textures with three zeros are excluded by experiments.