$\Delta L \ge 4$ processes

TL;DR

This paper evaluates the experimental prospects for observing lepton number violating processes with $$ units, concluding that low-energy experiments are unlikely to detect such processes, but high-energy collider experiments could potentially observe them.

Contribution

It provides a model-independent lower limit on quadruple beta decay half-life and explores collider capabilities to detect $$ and $$ lepton number violation.

Findings

Quadruple beta decay is unobservable with current experiments.

Low-energy processes with $$ or more lepton number violation are unlikely to be detected.

High-energy colliders like the LHC or FCC could probe these processes at the TeV scale.

Abstract

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.