Neutrino Mass Hierarchies in a Mass Matrix Form Versus its Inverse Form

TL;DR

This paper explores how neutrino mass matrices and their inverses can produce different mass hierarchies, analyzing the conditions under which normal and inverted hierarchies arise in such models.

Contribution

It demonstrates that models with a neutrino mass matrix and its inverse can be diagonalized by the same mixing matrix, linking different mass hierarchy scenarios.

Findings

Normal hierarchy can be achieved with the original mass matrix.

Inverted hierarchy can be obtained via the inverse matrix form.

Both hierarchies share the same mixing matrix U_ν.

Abstract

A neutrino mass matrix model M_\nu with M_\nu^T =M_\nu and a model with its inverse matrix form \widetilde{M}_\nu = m_0^2 (M_\nu^*)^{-1} can be diagonalized by the same mixing matrix U_\nu. It is investigated whether a scenario which provides a matrix model M_\nu with normal mass hierarchy can also give a model with an inverted mass hierarchy by considering a model with an inverse form of M_\nu.