Seesaw Type I and III at the LHeC

We study the potential of testing the seesaw type I and III models at the LHeC, an e-p collision mode at the CERN collider. The e-p collision mode provides an excellent place to study lepton number violating process e^- p \to N j + X \to l^+ W^- j + X with W^- into hadron jets. Here N is a heavy Majorana neutrino and j is a hard hadron jet. With the electron energy E_e = 140 GeV and proton energy E_p = 7 TeV, we find that the cross section for the heavy neutrino N production can be as large as a few fb for the mass scale as high as 1 TeV, higher than what can be achieved by the p-p collision mode of LHC with the same related heavy neutrino couplings.