  The experimental rate of neutrinoless double beta decay can be saturated by
the exchange of virtual sterile neutrinos, that mix with the ordinary neutrinos
and are heavier than 200 MeV. Interestingly, this hypothesis is subject only to
marginal experimental constraints, because of the new nuclear matrix elements.
This possibility is analyzed in the context of the Type I seesaw model,
performing also exploratory investigations of the implications for heavy
neutrino mass spectra, rare decays of mesons as well as neutrino-decay search,
LHC, and lepton flavor violation. The heavy sterile neutrinos can saturate the
rate only when their masses are below some 10 TeV, but in this case, the
suppression of the light-neutrino masses has to be more than the ratio of the
electroweak scale and the heavy-neutrino scale; i.e., more suppressed than the
naive seesaw expectation. We classify the cases when this condition holds true
in the minimal version of the seesaw model, showing its compatibility (1) with
neutrinoless double beta rate being dominated by heavy neutrinos and (2) with
any light neutrino mass spectra. The absence of excessive fine-tunings and the
radiative stability of light neutrino mass matrices, together with a saturating
sterile neutrino contribution, imply an upper bound on the heavy neutrino
masses of about 10 GeV. We extend our analysis to the Extended seesaw scenario,
where the light and the heavy sterile neutrino contributions are completely
decoupled, allowing the sterile neutrinos to saturate the present experimental
bound on neutrinoless double beta decay. In the models analyzed, the rate of
this process is not strictly connected with the values of the light neutrino
masses, and a fast transition rate is compatible with neutrinos lighter than
100 meV.
