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 $W^{+}\rightarrow l^{+}l^{+}l^{'-}ν$ decay. In order to check the experimental feasibility of the model, we show, through a numerical analysis, that in the decay $W^{+}\rightarrow e^{+}e^{+}μ^{-}ν$ 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 $W^{+}\rightarrow e^{+}e^{+}μ^{-}ν$ 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 μ}|^2,|U_{N e}|^2 \gtrsim 10^{-6} $.