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 0νββ 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 0νββ 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 0νββ decay amplitude, in some detail.