From the standard seesaw mechanism of neutrino mass generation, which is
based on the assumption that the lepton number is violated at a large
(~10exp(+15) GeV) scale, follows that the neutrinoless double-beta decay is
ruled by the Majorana neutrino mass mechanism. Within this notion, for the
inverted neutrino-mass hierarchy we derive allowed ranges of half-lives of the
neutrinoless double-beta decay for nuclei of experimental interest with
different sets of nuclear matrix elements. The present-day results of the
calculation of the neutrinoless double-beta decay nuclear matrix elements are
briefly discussed. We argue that if neutrinoless double-beta decay will be
observed in future experiments sensitive to the effective Majorana mass in the
inverted mass hierarchy region, a comparison of the derived ranges with
measured half-lives will allow us to probe the standard seesaw mechanism
assuming that future cosmological data will establish the sum of neutrino
masses to be about 0.2 eV.Comment: Some changes in sections I, II, IV, and V; two new figures;
additional reference