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

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.

15 pages, REVTEX, 2 figures, final version to be published in Phys. Lett. B