Long-range contributions to double beta decay revisited

We discuss the systematic decomposition of all dimension-7 (d=7) lepton number violating operators. These d=7 operators produce momentum enhanced contributions to the long-range part of the neutrinoless double beta decay amplitude and thus are severely constrained by existing half-live limits. In our list of possible models one can find contributions to the long-range amplitude discussed previously in the literature, such as the left-right symmetric model or scalar leptoquarks, as well as some new models not considered before. The d=7 operators generate Majorana neutrino mass terms either at tree-level, 1-loop or 2-loop level. We systematically compare constraints derived from the mass mechanism to those derived from the long-range double beta decay amplitude and classify our list of models accordingly. We also study one particular example decomposition, which produces neutrino masses at 2-loop level, can fit oscillation data and yields a large contribution to the long-range double beta decay amplitude, in some detail.