Seesaw theories at LHC and warm dark matter

Explaining the origin of neutrino masses clearly requires new physics beyond the Standard Model. I focus on the Seesaw paradigm and discuss a few simplest extensions of the SM that give Majorana masses to the active neutrinos. If realized at TeV scale, seesaw theories could manifest themselves in lepton number violating signatures at both low-energy processes and high-energy collider experiments. I summarize the constraints on the seesaw scales using the current LHC data. The left-right symmetric model connects the seesaw mechanism with the origin of parity symmetry breaking, and provides a unified framework for the simplest seesaw types. With new right-handed charged-current interactions, a TeV such model offers a plethora of new particles and exotic signatures at the LHC, and also accommodates a dark matter candidate, the lightest right-handed neutrino. A challenging question is the dark matter relic density which is typically over-produced in the early universe. The late decays of two heavier right-handed neutrinos can produce entropy and dilute the dark matter number. The key observation for this picture to work is the interplay between the freeze temperature of TeV right-handed gauge interaction and the QCD phase transition. The resulting dark matter mass is predicted to be around keV which makes the left-right model also a theory of warm dark matter. I will also comment on the fate of cosmic baryon asymmetry in this scenario.