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

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.