Masses, mixing angles and phases of general Majorana neutrino mass matrix

TL;DR

This paper provides a comprehensive analysis of the general Majorana neutrino mass matrix, expressing physical parameters in terms of matrix elements, and applies it to a cyclic symmetry-based model consistent with neutrino oscillation data.

Contribution

It derives explicit relations between neutrino parameters and mass matrix elements and applies these to a specific symmetry-based model, exploring parameter space compatibility.

Findings

Normal mass hierarchy is the only allowed scenario.

The model satisfies neutrino oscillation data with minimal symmetry breaking.

Numerical estimates of CP phases and neutrino mass observables are provided.

Abstract

General Majorana neutrino mass matrix is complex symmetric and for three generations of neutrinos it contains 12 real parameters. We diagonalize this general neutrino mass matrix and express the three neutrino masses, three mixing angles, one Dirac CP phase and two Majorana phases (removing three unphysical phases) in terms of the neutrino mass matrix elements. We apply the results in the context of a neutrino mass matrix derived from a broken cyclic symmetry invoking type-I seesaw mechanism. Phenomenological study of the above mass matrix allows enough parameter space to satisfy the neutrino oscillation data with only 10% breaking of this symmetry. In this model only normal mass hierarchy is allowed. In addition, the Dirac CP phase and the Majorana phases are numerically estimated. $\Sigma m_i$ and $|m_{\nu_{ee}}|$ are also calculated.