  The lower and upper bounds on the neutrinoless double beta (0nu-2beta) decay
rate are obtained, as functions of the parameters of neutrino oscillations and
of the lightest neutrino mass. The constraints on these parameters from the
search for the 0nu-2beta transition, as well as from the interpretation of
solar and atmospheric neutrino data in terms of oscillations, can be
conveniently represented in one unitarity triangle. This representation helps
to clarify the cases when the 0nu-2beta rate is small; the crucial dependence
on the scenarios assumed for solar neutrino oscillations and on the neutrino
spectrum is emphasized. We consider hierarchical and non-hierarchical neutrino
spectra, and discuss their interest in view of future searches of the 0nu-2beta
decay.
