  We computed the kinematics of Z-boson decay into a heavy-light neutrino pair
when the Z-boson is produced at rest in electron-positron 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 non-zero (and opposite) for positively- and
negatively-charged daughter-leptons if the neutrinos are Dirac fermions. 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 electron-positron collisions at the
Z-pole are strongly polarized while Majorana neutrinos are at most as polarized
as the $Z$-bosons.

High Energy Physics - Phenomenology;High Energy Physics - Experiment