Low Scale Seesaw with Local Lepton Number

Abstract: We discuss a class of theories for Majorana neutrinos where the total lepton number is a local gauge symmetry. These theories predict a dark matter candidate from anomaly cancellation. We discuss the properties of the dark matter candidate and using the cosmological bounds, we obtain the upper bound on the lepton number symmetry breaking scale. The dark matter candidate has unique annihilation channels due to the fact that the theory predicts a light pseudo-Goldstone boson, the Majoron, and one can obtain the correct relic density in a large fraction of the parameter space. In this context, the seesaw scale is below the ${\cal{O}}(10^2)$TeV scale and one can hope to test the origin of neutrino masses at current or future colliders. We discuss the lepton number violating Higgs decays and the possibility to observe lepton number violation at the Large Hadron Collider.