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

We determine the possible values of the effective Majorana neutrino mass \[ m]\ = \Sigma(j)U(ej)(2)m(j)\ in the different phenomenologically viable thr ee and four-neutrino scenarios. The quantities U-alpha j (alpha = e,mu,tau, ...) denote the elements of the neutrino mixing matrix and the Majorana neu trino 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-neutr ino 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 a nd LSND data. If neutrinoless double beta-decay proceeds via the mechanism involving \[m]\, conclusions about neutrinoless double beta-decay can be dr awn. 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 C P phase of the mixing matrix U could be determined. In the other four-neutr ino 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 neutrin o mass spectrum is hierarchical, however, if there exist two quasi-degenera te neutrinos and the first neutrino has a much smaller mass, values of \[m] \ as large as similar to 0.1 eV are possible. (C) 1999 Elsevier Science B.V . All rights reserved.