# On Lepton Number Violation in Heavy Neutrino Decays at Colliders

## TL;DR

This paper investigates the potential to detect lepton number violation from heavy Majorana neutrino decays at colliders, analyzing different mass regimes and model complexities to identify observable signatures and parameter space constraints.

## Contribution

It provides a detailed analysis of lepton number violating signatures across various heavy neutrino mass ranges and model configurations, highlighting conditions for observability and fine-tuning.

## Key findings

- Lepton number violation is suppressed above the electroweak scale at the LHC.
- Below the electroweak scale, lepton number violation is prevalent unless fine-tuning occurs.
- A mixed regime exists where both violation and conservation are possible depending on parameters.

## Abstract

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.