Probing the Dirac or Majorana nature of the Heavy Neutrinos in pure leptonic decays at the LHC

We propose a strategy for distinguishing the Dirac / Majorana character of heavy neutrinos with masses below the $W$ boson mass, using purely leptonic decays at the LHC. The strategy makes use of a forward-backward asymmetry of the opposite charge lepton in the $W^{+}\to l^{+}{l}^{+}{l}^{{}^{\mathrm{\prime }}-}\nu$ decay. In order to check the experimental feasibility of the model, we show, through a numerical analysis, that in the decay $W^{+}\to e^{+}{e}^{+}{\mu }^{-}\nu$ the two positrons in the final state can be distinguished for different ranges of the heavy neutrino masses. Finally, we estimated the number of events of $W^{+}\to e^{+}{e}^{+}{\mu }^{-}\nu$ for a Dirac and Majorana $N$ neutrino. For an integrated luminosity of 120 fb${}^{-1}$ at LHC RUN II, signals can be found if heavy-to-light neutrino mixings are $ |U_{N \mu}|^2,|U_{N e}|^2 \gtrsim 10^{-6} $.