  We investigate numerically how accurately one could constrain the strengths
of different short-range contributions to neutrino-less double beta decay in
effective field theory. Depending on the outcome of near-future experiments
yielding information on the neutrino masses, the corresponding bounds or
estimates can be stronger or weaker. A particularly interesting case, resulting
in strong bounds, would be a positive signal of neutrino-less double beta decay
that is consistent with complementary information from neutrino oscillation
experiments, kinematical determinations of the neutrino mass, and measurements
of the sum of light neutrino masses from cosmological observations. The keys to
more robust bounds are improvements of the knowledge of the nuclear physics
involved and a better experimental accuracy.
