Neutrino mass spectrum and neutrinoless double beta decay

Abstract

The relations between the effective Majorana mass of the electron neutrino, $m_{ee}$, responsible for neutrinoless double beta decay, and the neutrino oscillation parameters are considered. We show that for any specific oscillation pattern $m_{ee}$ can take any value (from zero to the existing upper bound) for normal mass hierarchy and it can have a minimum for inverse hierarchy. This means that oscillation experiments cannot fix in general $m_{ee}$. Mass ranges for $m_{ee}$ can be predicted in terms of oscillation parameters with additional assumptions about the level of degeneracy and the type of hierarchy of the neutrino mass spectrum. These predictions for $m_{ee}$ are systematically studied in the specific schemes of neutrino mass and flavor which explain the solar and atmospheric neutrino data. The contributions from individual mass eigenstates in terms of oscillation parameters have been quantified. We study the dependence of $m_{ee}$ on the non-oscillation parameters: the overall scale of the neutrino mass and the relative mass phases. We analyze how forthcoming oscillation experiments will improve the predictions for $m_{ee}$. On the basis of these studies we evaluate the discovery potential of future \znbb decay searches. The role \znbb decay searches will play in the reconstruction of the neutrino mass spectrum is clarified. The key scales of $m_{ee}$, which will lead to the discrimination among various schemes are: $m_{ee} \sim 0.1$ eV and $m_{ee} \sim 0.005$ eV.