Neutrinoless double beta (\znbb) decay is considered within bilinear
R-parity breaking supersymmetry, including the full one-loop corrections to the
neutrino-neutralino mass matrix. Expected rates for \znbb decay in this model
are discussed in light of recent atmospheric and solar neutrino data. We
conclude that (a) tree-level calculations for \znbb decay within the bilinear
model are not reliable in the range of parameters preferred by current solar
and atmospheric neutrino problems. And (b) if the solar and atmospheric
neutrino problems are to be solved within bilinear R-parity violating SUSY the
expected rates for \znbb decay are very low; the effective Majorana neutrino
mass at most 0.01 eV and typical values being one order of magnitude lower.
Observing \znbb decay in the next round of experiments therefore would rule
out the bilinear R-parity violating supersymmetric model as an explanation for
solar and atmospheric neutrino oscillations, as well as any hierarchical scheme
for neutrino masses, unless new neutrino interactions are present.Comment: 1 reference added, enlarged discussion of loop
