Neutrino Mass Matrices with Two Equalities Between the Elements or Cofactors

TL;DR

This paper explores specific structured neutrino mass matrices with two equalities, analyzing their phenomenological implications and providing a model realization, to better understand neutrino properties and CP violation.

Contribution

It classifies sixty-five possible structures of neutrino mass matrices with two equalities and examines their phenomenological viability, including model realization with an $A_4$ symmetry.

Findings

Certain structures are compatible with current neutrino data.

Predictions for Majorana mass and CP phases are derived.

A simple $A_4$ model realizes one viable structure.

Abstract

We study the implications of the existence of two equalities between the elements or cofactors of the neutrino mass matrix. There are sixty five structures of this type for each case. Phenomenological implications for unknown parameters like the effective Majorana mass of the electron neutrino and CP-violating phases are examined for the viable cases. To illustrate how such forms of the neutrino mass matrices may be realized, we also present a simple $A_4$ model for one of the classes in each case.