- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Exploring quantum statistics for massive Dirac and Majorana neutrinos using spinor-helicity techniques

Innes Bigaran1,2,*, Stephen J. Parke1,†, and Pedro Pasquini3,‡

  • *Contact author: ibigaran@fnal.gov
  • †Contact author: parke@fnal.gov
  • ‡Contact author: pasquini@ifi.unicamp.br
PDF

Phys. Rev. D 112, 053008 – Published 30 September, 2025

DOI: https://doi.org/10.1103/23ks-btx5

Abstract

Recently, there has been interest in the applicability of quantum statistics to distinguish Dirac from Majorana neutrinos in multineutrino final states. In particular, debate has arisen over the validity of the Dirac-Majorana confusion theorem in these processes, i.e., that any distinction between the Dirac and Majorana processes goes to zero as the neutrino mass goes to zero. Here we approach this problem equipped with spinor-helicity methods generalized for massive Dirac and Majorana fermions. We explicitly calculate all helicity amplitudes, and their squares, for the decay of a light scalar particle to two neutrinos and two oppositely charged leptons. This allows us to pinpoint the crucial steps which could lead to claims of a violation of the confusion theorem. We show that, if the correct antisymmetrization of Dirac to Majorana amplitudes is used, identification of which is clear in this framework, and all relevant contributions are appropriately summed, a scalar decay into two charged leptons and two neutrinos satisfies the Dirac-Majorana confusion theorem.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (21)

  1. B. Kayser, Majorana neutrinos and their electromagnetic properties, Phys. Rev. D 26, 1662 (1982).
  2. R. E. Shrock, Electromagnetic properties and decays of Dirac and Majorana neutrinos in a general class of gauge theories, Nucl. Phys. B206, 359 (1982).
  3. J. Schechter and J. W. F. Valle, Neutrinoless double beta decay in SU(2)×U(1) theories, Phys. Rev. D 25, 2951 (1982).
  4. J. F. Nieves, Dirac and pseudo-Dirac neutrinos and neutrinoless double beta decay, Phys. Lett. 147B, 375 (1984).
  5. E. Takasugi, Can the neutrinoless double beta decay take place in the case of Dirac neutrinos?, Phys. Lett. 149B, 372 (1984).
  6. B. Kayser and S. Loken, in Proceedings of the XXIII International Conference on High Energy Physics (World Scientific, Singapore, 1987).
  7. S. P. Rosen, Double beta decay, in The Benjamin Franklin Symposium in Celebration of the Discovery of the Neutrino (1992), p. 9, arXiv:hep-ph/9210202.
  8. C. S. Kim, M. V. N. Murthy, and D. Sahoo, Inferring the nature of active neutrinos: Dirac or Majorana?, Phys. Rev. D 105, 113006 (2022).
  9. C. S. Kim, Practical Dirac Majorana confusion theorem: Issues and applicability, Eur. Phys. J. C 83, 972 (2023).
  10. C. S. Kim, D. Sahoo, and K. N. Vishnudath, Searching for signatures of new physics in B→Kνν¯ to distinguish between Dirac and Majorana neutrinos, Eur. Phys. J. C 84, 882 (2024).
  11. J. M. Márquez, D. Portillo-Sánchez, and P. Roig, Dirac-Majorana neutrinos distinction in four-body decays, Phys. Rev. D 109, 033005 (2024).
  12. E. Akhmedov and A. Trautner, Can quantum statistics help distinguish Dirac from Majorana neutrinos?, J. High Energy Phys. 05 (2024) 156.
  13. G. Mahlon and S. J. Parke, Angular correlations in top quark pair production and decay at hadron colliders, Phys. Rev. D 53, 4886 (1996).
  14. M. L. Mangano and S. J. Parke, Multiparton amplitudes in gauge theories, Phys. Rep. 200, 301 (1991).
  15. H. K. Dreiner, H. E. Haber, and S. P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rep. 494, 1 (2010).
  16. R. Kleiss and W. J. Stirling, Spinor Techniques for Calculating pp¯→W±/Z0+Jets, Nucl. Phys. B262, 235 (1985).
  17. G. Mahlon and S. J. Parke, Deconstructing angular correlations in ZH, ZZ, and WW production at LEP-2, Phys. Rev. D 58, 054015 (1998).
  18. E. Ma and J. T. Pantaleone, Heavy Majorana neutrino production, Phys. Rev. D 40, 2172 (1989).
  19. F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics (John Wiley & Sons, New York, 1984), pp. 120–121.
  20. W. Rodejohann, X.-J. Xu, and C. E. Yaguna, Distinguishing between Dirac and Majorana neutrinos in the presence of general interactions, J. High Energy Phys. 05 (2017) 024.
  21. C. S. Kim, M. V. N. Murthy, and D. Sahoo, Comments on exploring quantum statistics for Dirac and Majorana neutrinos using spinor-helicity technique, arXiv:2507.07180.

Outline

Information

Phys. Rev. D 112, 053008– Published 30 September, 2025
  • Received 18 July 2025
  • Accepted 19 August 2025
Crossmark - Check for updates button
Creative Commons Logo

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

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation