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Neutrinoless double beta ($0\nu\beta\beta$) decay can in general produceelectrons of either chirality, in contrast with the minimal Standard Model (SM)extension with only the addition of the Weinberg operator, which predicts twoleft-handed electrons in the final state. We classify the lepton numberviolating (LNV) effective operators with two leptons of either chirality but noquarks, ordered according to the magnitude of their contribution to \znbbdecay. We point out that, for each of the three chirality assignments, $e_Le_L,e_Le_R$ and $e_Re_R$, there is only one LNV operator of the corresponding typeto lowest order, and these have dimensions 5, 7 and 9, respectively. Neutrinomasses are always induced by these extra operators but can be delayed to one ortwo loops, depending on the number of RH leptons entering in the operator.Then, the comparison of the $0\nu\beta\beta$ decay rate and neutrino massesshould indicate the effective scenario at work, which confronted with the LHCsearches should also eventually decide on the specific model elected by nature.We also list the SM additions generating these operators upon integration ofthe heavy modes, and discuss simple realistic examples of renormalizabletheories for each case.

Effective Lagrangian approach to neutrinoless double beta decay and neutrino masses