Constraints from Neutrino Oscillation Experiments on the Effective Majorana Mass in Neutrinoless Double $\beta$-Decay

TL;DR

This paper analyzes how neutrino oscillation data constrains the effective Majorana neutrino mass relevant for neutrinoless double beta decay across different neutrino models, highlighting potential for future discoveries and CP phase determination.

Contribution

It provides a comprehensive evaluation of the possible values of the Majorana mass in three- and four-neutrino scenarios based on current oscillation constraints.

Findings

In four-neutrino Scheme A, |< m >| can reach 1 eV, enabling potential detection.

In four-neutrino Scheme B, |< m >| is limited to about 0.01 eV.

In three-neutrino models, hierarchical spectra imply small |< m >|, but quasi-degenerate neutrinos allow larger values (~0.1 eV).

Abstract

We determine the possible values of the effective Majorana neutrino mass $|< m > |= |\sum_j U_{ej}^2 m_j|$ in the different phenomenologically viable three and four-neutrino scenarios. The quantities $U_{\alpha j}$ ($\alpha = e,\mu,\tau,...$) denote the elements of the neutrino mixing matrix and the Majorana neutrino masses $m_j$ ($j=1,2,3,...$) are ordered as $m_1 < m_2 < ... $ Assuming $m_1 \ll m_3$ in the three-neutrino case and $m_1 \ll m_4$ in the four-neutrino case, we discuss, in particular, how constraints on $| < m > |$ depend on the mixing angle relevant in solar neutrino oscillations and on the three mass-squared differences obtained from the analyses of the solar, atmospheric and LSND data. If neutrinoless double $\beta$-decay proceeds via the mechanism involving $|< m >|$, conclusions about neutrinoless double $\beta$-decay can be drawn. If one of the two viable four-neutrino schemes (Scheme A) is realized in nature, $|< m >|$ can be as large as 1 eV and neutrinoless double $\beta$-decay could possibly be discovered in the near future. In this case a Majorana CP phase of the mixing matrix $U$ could be determined. In the other four-neutrino scheme (Scheme B) there is an upper bound on $|< m >|$ of the order of $10^{-2}$ eV. In the case of three-neutrino mixing the same is true if the neutrino mass spectrum is hierarchical, however, if there exist two quasi-degenerate neutrinos and the first neutrino has a much smaller mass, values of $|< m >|$ as large as $\sim 0.1$ eV are possible.