Neutrino Mass Matrix from Seesaw Mechanism with Heavy Majorana Neutrino Subject to Texture Zero and Invariant Under a Cyclic Permutation

TL;DR

This paper investigates neutrino mass matrices derived from the seesaw mechanism with heavy Majorana neutrinos, focusing on texture zeros and cyclic permutation invariance, to explain solar and atmospheric neutrino mixing.

Contribution

It identifies specific invariant heavy Majorana neutrino mass matrix patterns that can qualitatively explain neutrino mixing phenomena.

Findings

No invariant heavy Majorana neutrino mass matrix under cyclic permutation without additional assumptions.

Two patterns satisfy invariance when a sub-matrix inverse has zero determinant.

One invariant pattern successfully explains solar and atmospheric neutrino mixing qualitatively.

Abstract

We evaluate the predictive power of the neutrino mass matrices arising from seesaw mechanism with heavy Majorana mass matrices subject to texture zero and satisfy a cyclic permutation invariant form to the solar neutrino mixing phenomena. From eight possible patterns of heavy Majorana neutrino mass matrix, we found that there is no heavy Majorana neutrino mass matrix to be invariant in form under a cyclic permutation. But, by imposing an additional assumption that at least one of the 2x2 sub-matrices of heavy Majorana neutrino mass matrix inverse having zero determinant, we found that only two of the eight possible patterns for heavy Majorana neutrino mass matrices to be invariant under a cyclic permutation. One of the two invariant heavy Majorana neutrino mass matrices could produces neutrino mass matrix $M_{\nu}$ that can be used to explain the neutrino mixing phenomena for both solar and atmospheric neutrinos qualitatively.