Neutrinoless double-beta decay at colliders: interference between Majorana states

Heavy neutral leptons (HNLs) are hypothetical particles able to explain several puzzles of fundamental physics, first and foremost - neutrino oscillations. Being sterile with respect to Standard Model interactions, these particles admit Majorana masses, allowing for violation of the total lepton number. Lepton number violating (LNV) processes thus become a key signature of HNLs, pursued by many experiments. In this work, we demonstrate that if HNLs are the sole origin of neutrino masses, destructive interference between Majorana states suppresses the same-sign di-lepton signal. In the phenomenologically interesting case of large HNL couplings, such suppression is akin to the cancellation of HNLs' contributions to neutrino masses. Nevertheless, the signal can be much larger than coming from the Weinberg operator alone. We identify regions of the parameter space of such realistic HNL models where the LNV signal is maximised at the LHC and future FCC-hh. Our results are obtained within the effective W approximation which allows for analytic treatment and gives a clear dependence on the model parameters. Although approximate, they are argued to be correct within a factor of a few.