Abstract
We discuss the potential to observe lepton number violation (LNV) in displaced vertex searches for heavy neutral leptons (HNLs) at future lepton colliders. Even though a direct detection of LNV is impossible for the dominant production channel because lepton number is carried away by an unobservable neutrino, there are several signatures of LNV that can be searched for. They include the angular distribution and spectrum of decay products as well as the HNL lifetime. We comment on the perspectives to observe LNV in realistic neutrino mass models and argue that the dichotomy of Dirac vs Majorana HNLs is in general not sufficient to effectively capture their phenomenology, but these extreme cases nevertheless represent well-defined benchmarks for experimental searches. Finally, we present accurate analytic estimates for the number of events and sensitivity regions during the $Z$-pole run for both Majorana and Dirac HNLs.
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