Quasi-Degenerate Neutrino Masses with Normal and Inverted Hierarchy

Ng K Francis,N Nimai Singh

doi:10.4236/jmp.2011.211158

Abstract

The effects of CP-phases on the three absolute quasi-degenerate Majorana neutrino (QDN) masses are studied with neutrino mass matrices obeying µ – τ symmetry for normal as well as inverted hierarchical mass patterns. We have made further investigations on 1) the prediction of solar mixing angle which lies below tri-bimaximal mixing value in consistent with neutrino oscillation observational data, 2) the prediction on absolute neutrino mass parameter (mee) in 0νββ decay, and 3) cosmological bound on the sum of the three absolute neutrino masses . The numerical analysis is carried out through the parameterization of neutrino mass matrices using only two unknown parameters (ε, η) within µ – τ symmetry. The results show the validity of QDN mass models in both normal and inverted hierarchical patterns. These models are far from discrimination and hence not yet ruled out. The results presented in this article are new and have subtle ef- fects in the discrimination of neutrino mass models.

Highlights

The presently available neutrino oscillation observational data [1,2,3,4,5] on two neutrino mass-squared differences ( m221, m223 ), is found to be insufficient to predict the three absolute neutrino masses in case of quasi-degenerate neutrino (QDN) mass models [6,7,8,9,10,11,12,13,14], as three independent equations are required for solving three unknown values of absolute neutrino masses
Investigations on QDN models for both normal hierarchical (NH) and inverted hierarchical (IH) patterns of the three absolute neutrino masses, require detailed numerical analysis to check whether such QDN models can really accommodate lower values of absolute neutrino masses mi ≤ 0.09 eV which is consistent with the above cosmological bound
The solar mixing angle lying below the tri-bimaximal mixing (TBM) [19,20,21], which is consistent with present observational data [1,2,3,4,5] and the effects of CP-phases on three absolute neutrino masses, are important ingredients for further analysis of QDN models

Summary

Introduction

The presently available neutrino oscillation observational data [1,2,3,4,5] on two neutrino mass-squared differences ( m221, m223 ), is found to be insufficient to predict the three absolute neutrino masses in case of quasi-degenerate neutrino (QDN) mass models [6,7,8,9,10,11,12,13,14], as three independent equations are required for solving three unknown values of absolute neutrino masses. The solar mixing angle lying below the tri-bimaximal mixing (TBM) [19,20,21], which is consistent with present observational data [1,2,3,4,5] and the effects of CP-phases on three absolute neutrino masses, are important ingredients for further analysis of QDN models. We address all these issues in the present work and show the validity of the quasi-degenerate models for lower values of neutrino masses mi ≤ 0.09 eV.

Parameterizations of Neutrino Mass Matrix

Numerical Analysis and Results

Conclusions