Constraints from neutrino oscillation experiments on the effective Majorana mass in neutrinoless double β-decay

Abstract

We determine the possible values of the effective Majorana neutrino mass |〈m〉|=| ∑ j U ej 2m j| in the different phenomenologically viable three and four-neutrino scenarios. The quantities U αj ( α= e, μ, τ,…) 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≪ m 3 in the three-neutrino case and m 1≪ 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 β-decay proceeds via the mechanism involving |〈 m〉|, conclusions about neutrinoless double β-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 β-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 ∼0.1 eV are possible.