Search for heavy Majorana neutrinos at electron-proton colliders

We develop a search strategy for a heavy Majorana neutrino via the lepton number violation signal process pe(-) -> mu(+)jjj at future electron-proton colliders. The signal and dominant standard model background events are generated with a fast detector simulation. We apply the preselection criteria and perform a multivariate analysis based on machine learning to reject the background. Distributions of representative kinematic observables are presented for both signal and background processes, and effects on final limits are compared by inputting two different sets of observables when performing multivariate analysis. The 2s and 5s limits on the mixing parameter vertical bar V-lN vertical bar(2) are predicted for the heavy neutrino mass mN in the range of 10-1000 GeV. At the LHeC (FCC-eh) with an electron beam energy of 60 GeV, a proton beam energy of 7 (50) TeV, and an integrated luminosity of 1 o3THORN ab(-1), the mixing parameter vertical bar V-lN vertical bar(2) can be constrained to be below similar to 3.0(1.0) x 10(-6) for m(N) around O(100) GeV at 2 sigma level. The limits are much stronger than the current experiment limits at the LHC for m(N) above 30 GeV. The positron signal final state and the effect of long-lived cases of heavy neutrinos are also checked and commented.