Left-Right Symmetry and Lepton Number Violation at the Large Hadron Electron Collider

We show that the proposed Large Hadron electron Collider (LHeC) will provide a great opportunity to search for left-right symmetry and establish lepton number violation, complementing current and planned searches based on LHC data and neutrinoless double beta decay. We consider several plausible configurations for the LHeC -- including different electron energies and polarizations, as well as distinct values for the charge misidentification rate. Within left-right symmetric theories we determine the values of right-handed neutrino and gauge boson masses that could be tested at the LHeC after one, five and ten years of operation. Our results indicate that this collider might probe, via the $\Delta L =2$ signal $e^-p\to e^+jjj$, Majorana neutrino masses up to $1$ TeV and $W_R$ masses up to $\sim 6.5$ TeV. Interestingly, part of this parameter space is beyond the expected reach of the LHC and of future neutrinoless double beta decay experiments