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 B0→μ−μ+νμν¯μ. 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 B0 decay without any major change.

• Received 3 July 2021
• Accepted 3 June 2022

DOI:https://doi.org/10.1103/PhysRevD.105.113006

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society