Neutrino oscillation constraints on neutrinoless double-beta decay

We have studied the constraints imposed by the results of neutrino oscillation experiments on the effective Majorana mass $|〈m〉|$ that characterizes the contribution of Majorana neutrino masses to the matrix element of neutrinoless double-beta decay. We have shown that in a general scheme with three Majorana neutrinos and a hierarchy of neutrino masses (which corresponds to the standard seesaw mechanism) the results of neutrino oscillation experiments imply rather strong constraints on the parameter $|〈m〉|.$ From the results of the first reactor long-baseline experiment CHOOZ and the Bugey experiment it follows that $|〈m〉|\lesssim 3\times {10}^{-2}\mathrm{eV}$ if $\Delta m^2\lesssim 2{\mathrm{eV}}^2$ $(\Delta m^2$ is the largest mass-squared difference). Hence, we conclude that the observation of neutrinoless double-beta decay with a probability that corresponds to $|〈m〉|\gtrsim {10}^{-1}\mathrm{eV}$ would be a signal for a nonhierarchical neutrino mass spectrum and/or nonstandard mechanisms of lepton number violation.