Z-boson decays into Majorana or Dirac heavy neutrinos

We computed the kinematics of Z-boson decay into a heavy-light neutrino pair when the Z-boson is produced at rest in e(+)e(-) collisions, including the subsequent decay of the heavy neutrino into a visible final state containing a charged-lepton. We concentrated on heavy-neutrino masses of order dozens of GeV and the issue of addressing the nature of the neutrinos-Dirac fermions or Majorana fermions. We find that while it is not possible to tell the nature of the heavy and light neutrinos on an event-by-event basis, the nature of the neutrinos can nonetheless be inferred given a large-enough sample of heavy-light neutrino pairs. We identify two observables sensitive to the nature of neutrinos. One is the forward-backward asymmetry of the daughter-charged-leptons. This asymmetry is exactly zero if the neutrinos are Majorana fermions and is nonzero (and opposite) for positively- and negatively-charged daughter-leptons if the neutrinos are Dirac fennions. The other observable is the polarization of the heavy neutrino, imprinted in the laboratory-frame energy distribution of the daughter-charged-leptons. Dirac neutrinos and antineutrinos produced in e(+)e(-) collisions at the Z-pole are strongly polarized while Majorana neutrinos are at most as polarized as the Z-bosons.