Small entries of neutrino mass matrices

TL;DR

This paper analyzes the structure of neutrino mass matrices considering experimental constraints, focusing on small entries and their impact on neutrino masses and mixing angles, for both hierarchical and quasi-degenerate cases.

Contribution

It provides simplified expressions for neutrino masses and mixing angles based on the mass matrix entries, emphasizing the role of small entries and their stability.

Findings

Derived approximate formulas for neutrino masses and mixing angles.

Analyzed the stability of neutrino parameters against small matrix entries.

Discussed implications for hierarchical and quasi-degenerate neutrino mass scenarios.

Abstract

We consider phenomenologically allowed structures of the neutrino mass matrix in the case of three light neutrino species. Constraints from the solar, atmospheric and reactor neutrino experiments as well as those from the neutrinoless double beta decay are taken into account. Both hierarchical and quasi-degenerate neutrino mass cases are studied. Assuming maximal $\nu_\mu-\nu_\tau$ mixing we derive simple approximate expressions giving the values of the neutrino masses and remaining lepton mixing angles in terms of the entries of the neutrino mass matrix. Special attention is paid to the small entries which are usually not specified in discussions of the neutrino mass matrix textures. We specifically discuss the stability of neutrino masses and lepton mixing angles with respect to the choice and variations of these small entries.