Signatures of Dirac and Majorana Sterile Neutrinos in Trilepton Events at the LHC

Heavy sterile neutrinos with masses below $M_W$ can induce trilepton events at the 14 TeV LHC through purely leptonic $W$ decays of $W^\pm \to e^\pm e^\pm \mu^\mp \nu$ and $\mu^\pm \mu^\pm e^\mp \nu$ where the heavy neutrino will be in an intermediate state on its mass shell. Discovery and exclusion limits for the heavy neutrinos are found using both Cut-and-Count (CC) and a Multi-Variate Analysis (MVA) methods in this study. We also show that it is possible to discriminate between a Dirac and a Majorana heavy neutrino, even when lepton number conservation cannot be directly tested due to unobservability of the final state neutrino. This discrimination is done by exploiting a combined set of kinematic observables that differ between the Majorana vs. Dirac cases. We find that the MVA method can greatly enhance the discovering and discrimination limits in comparison with the CC method. For a 14-TeV $pp$ collider with integrated luminosity of 3000 ${\rm fb}^{-1}$, sterile neutrinos can be found with 5$\sigma$ significance if heavy-to-light neutrino mixings $|U_{Ne}|^2 \sim |U_{N\mu}|^2 \sim 10^{-6}$, while the Majorana vs. Dirac type can be distinguished if $|U_{Ne}|^2 \sim |U_{N\mu}|^2 \sim 10^{-5}$ or even $|U_{N\ell}|^2\sim 10^{-6}$ if one of the mixing elements is at least an order of magnitude smaller than the other.