$\Delta L \ge 4$ lepton number violating processes

We discuss the experimental prospects for observing processes which violate lepton number ($\Delta L$) in four units (or more). First, we reconsider neutrinoless quadruple beta decay, deriving a model independent and very conservative lower limit on its half-life of the order of $10^{41}$ ys for $^{150}$Nd. This renders quadruple beta decay unobservable for any feasible experiment. We then turn to a more general discussion of different possible low-energy processes with values of $\Delta L \ge 4$. A simple operator analysis leads to rather pessimistic conclusions about the observability at low-energy experiments in all cases we study. However, the situation looks much brighter for accelerator experiments. For two example models with $\Delta L=4$ and another one with $\Delta L=5$, we show how the LHC or a hypothetical future pp-collider, such as the FCC, could probe multi-lepton number violating operators at the TeV scale.