Maximal mixing as a `sum' of small mixings

TL;DR

This paper investigates how small mixing angles in two or three sources of neutrino masses can combine to produce large or maximal mixing angles in the total neutrino mass matrix, especially in degenerate spectra.

Contribution

It demonstrates that maximal mixing naturally arises from quasi-degenerate spectra decomposed into hierarchical or inverse-hierarchical matrices with small mixing, extending to three generations and multiple sources.

Findings

Maximal mixing occurs mainly in quasi-degenerate neutrino spectra.

Decomposition into hierarchical matrices explains the emergence of large mixing angles.

Multiple sources can produce large mixing angles from small initial mixings.

Abstract

In models with two sources of neutrino masses, we look at the possibility of generating maximal/large mixing angles in the total mass matrix, where both the sources have only small mixing angles. We show that in the two generation case, maximal mixing can naturally arise only when the total neutrino mass matrix has a quasi-degenerate pattern. The best way to demonstrate this is by decomposing the quasi-degenerate spectrum in to hierarchial and inverse-hierarchial mass matrices, both with small mixing. Such a decomposition of the quasi-degenerate spectra is in fact very general and can be done irrespective of the mixing present in the mass matrices. With three generations, and two sources, we show that only one or all the three small mixing angles in the total neutrino mass matrix can be converted to maximal/large mixing angles. The decomposition of the degenerate pattern in this case is best realised in to sub-matrices whose dominant eigenvalues have an alternating pattern. On the other hand, it is possible to generate two large and one small mixing angle if either one or both of the sub-matrices contain maximal mixing. We present example textures of this. With three sources of neutrino masses, the results remain almost the same as long as all the sub-matrices contribute equally. The Left-Right Symmetric model where Type I and Type II seesaw mechanisms are related provides a framework where small mixings can be converted to large mixing angles, for degenerate neutrinos.