Neutrinoless double $\beta$ decay with small neutrino masses

Understand

If the only contribution to neutrinoless double beta decay (NLDBD) are neutrino masses its discovery may be very difficult, especially if neutrinos present a normal hierarchy spectrum.

• However, this is not the only possibility; NLDBD can in general produce electrons of either chirality, in contrast with the neutrino induced NLDBD which predicts two left-handed electrons.
• Using an effective Lagrangian approach we classify the lepton number violating (LNV) effective operators with two leptons of either chirality but no quarks, ordered according to the magnitude of their contribution to NLDBD.
• We point out that, for each of the three chirality assignments, $e_{L}e_{L},e_{L}e_{R}$ and $e_{R}e_{R}$, there is only one LNV operator of the corresponding type to lowest order, and these have dimensions 5, 7 and 9, respectively.