$\Delta L = 3$ processes: Proton decay and LHC

TL;DR

This paper explores lepton number violation by three units through high-dimensional operators, linking proton decay and LHC searches, and presents a model with testable low- and high-energy signatures.

Contribution

It identifies and analyzes dimension 9, 11, and 13 operators causing $ riangle L=3$ processes and constructs a simple model with observable phenomenology.

Findings

High-dimensional operators can induce observable proton decay.

New physics scale for $ riangle L=3$ processes can be as low as 1 TeV.

The constructed model predicts signatures accessible at current experiments.

Abstract

We discuss lepton number violation in three units. From an effective field theory point of view, $\Delta L=3$ processes can only arise from dimension 9 or higher operators. These operators also violate baryon number, hence many of them will induce proton decay. Given the high dimensionality of these operators, in order to have a proton half-life in the observable range, the new physics associated to $\Delta L=3$ processes should be at a scale as low as 1 TeV. This opens up the possibility of searching for such processes not only in proton decay experiments but also at the LHC. In this work we analyze the relevant $d=9,11,13$ operators which violate lepton number in three units. We then construct one simple concrete model with interesting low- and high-energy phenomenology.