On Lepton Number Violation in Heavy Neutrino Decays at Colliders

We study the perspective to observe lepton number violating signatures from heavy Majorana neutrino decays at colliders in view of the requirement to explain the light neutrino masses via the seesaw mechanism. In the minimal model with only two heavy neutrinos and in the $\nu$MSM one can identify three distinct regions in the mass-mixing plane. For Majorana masses above the electroweak scale the branching ratio for lepton number violating processes at the LHC is generically suppressed. For masses well below the electroweak scale that are probed in displaced vertex searches or at fixed target experiments lepton number violation is the rule and can only be avoided at the cost of fine tuning. In between there is a mass regime where both possibilities coexist. In models with more than two heavy neutrinos the larger parameter space allows for more freedom, but our results remain qualitatively correct unless there is a mass degeneracy amongst more than two of the heavy neutrinos.