LHC and the neutrino paradigm

<!--HTML-->I argue that LHC may shed light on the nature of neutrino mass through the probe of the seesaw mechanism. The smoking gun signature is lepton number violation through the production of same sign lepton pairs, a collider analogy of the neutrinoless double beta decay. I discuss this in the context of L-R symmetric theories, which predicted neutrino mass long before experiment and led to the seesaw mechanism. A WR gauge boson with a mass in a few TeV region could easily dominate neutrinoless double beta decay, and its discovery at LHC would have spectacular signatures of parity restoration and lepton number violation. I also discuss the collider signatures of the three types of seesaw mechanism, and show how in the case of Type II one can measure the PMNS mixing matrix at the LHC, complementing the low energy probes. Finally, I give an example of a simple realistic SU(5) grand unified theory that predicts the hybrid Type I + III seesaw with a weak fermion triplet at the LHC energies. The seminar will be followed by a round table discussion on the theme "Future Neutrino Facilities in the Global Physics Environment". The panel composed of the following members -- S. Bertolucci (CERN) -- K. Nishikawa (KEK) -- J. Strait (Fermilab) -- M. Spiro (CERN Council) -- J. Womersley (STFC) -- T. Nakada (ECFA) -- S. Myers (CERN) -- S. Komamya (ICFA) will be chaired by J. Ellis (CERN).