  The nature of a neutrino, whether it is a Dirac type or Majorana type, may be
comprehensively probed using their quantum statistical properties. If the
neutrino is a Majorana fermion, then by definition it is identical and
indistinguishable from the corresponding antineutrino. When a Majorana neutrino
and antineutrino are pair produced, the corresponding state has to obey the
Pauli principle unlike in the Dirac case. We use this property to distinguish
between the two cases using the process $B^0 \to
\mu^-\,\mu^+\,\nu_\mu\,\bar{\nu}_\mu$. We show that the two cases differ
dramatically in a special kinematic scenario where, in the rest frame of the
parent $B$ meson, the muons fly away back-to-back (i.e. fly with 3-momenta of
equal magnitudes but opposite directions), and so do the neutrino and
antineutrino. Unlike any other scenario, we know the energies and magnitudes of
$3$-momenta of both the neutrino and the antineutrino in this back-to-back
configuration without even directly measuring them. This provides a way of
avoiding the constraint imposed by the `practical Dirac-Majorana confusion
theorem', as one need not fully integrate over neutrino and antineutrino in
this case. As a true signature of the universal principle of quantum statistics
which does not depend on the size of the mass of the particle but its spin, the
difference between Dirac and Majorana cases in this special kinematic
configuration does survive independent of the neutrino mass as long as neutrino
mass is nonzero. The analysis presented here is applicable immediately to
several other processes with the same final state as in the case of $B^0$ decay
without any major change.
