The minimal Standard Model extension with the Weinberg operator does
accommodate the observed neutrino masses and mixing, but predicts a
neutrinoless double beta (0νββ) decay rate proportional to the
effective electron neutrino mass, which can be then arbitrarily small within
present experimental limits. However, in general 0νββ decay can
have an independent origin and be near its present experimental bound; whereas
neutrino masses are generated radiatively, contributing negligibly to
0νββ decay. We provide a realization of this scenario in a simple,
well defined and testable model, with potential LHC effects and calculable
neutrino masses, whose two-loop expression we derive exactly. We also discuss
the connection of this model to others that have appeared in the literature,
and remark on the significant differences that result from various choices of
quantum number assignments and symmetry assumptions. In this type of models
lepton flavor violating rates are also preferred to be relatively large, at the
reach of foreseen experiments. Interestingly enough, in our model this stands
for a large third mixing angle, sin2θ13≳0.008, when μ→eee is required to lie below its present experimental limit.Comment: Published extended version with further reference