Can quantum statistics help distinguish Dirac from Majorana neutrinos?

TL;DR

This paper investigates whether quantum statistical effects can distinguish Dirac from Majorana neutrinos, concluding that within the Standard Model, such effects do not provide a practical way to differentiate them at small neutrino masses.

Contribution

The paper provides a rigorous proof that quantum statistics cannot distinguish Dirac from Majorana neutrinos within the Standard Model at small neutrino masses.

Findings

Quantum statistics do not differentiate Dirac and Majorana neutrinos in the Standard Model.

Differences in cross sections due to quantum indistinguishability vanish as neutrino mass approaches zero.

Theoretical proof confirms the indistinguishability of neutrino types via quantum statistics in relevant limits.

Abstract

Finding out if neutrinos are Dirac or Majorana particles is known to be extremely difficult due to the smallness of neutrino mass and the fact that in the limit $m_\nu=0$ both Dirac and Majorana neutrinos become Weyl particles, i.e. are indistinguishable. There have been suggestions in the literature that in the case of processes with production of a neutrino-antineutrino pair (if neutrinos are Dirac particles) or two neutrinos (if they are of Majorana nature) quantum statistics may be of help. This is because for Majorana neutrinos quantum indistinguishability of identical particles requires the amplitude of the process to be antisymmetrized with respect to the interchange of the final-state neutrinos, whereas no such antisymmetrization must be done for Dirac neutrinos. It has been claimed that the resulting differences between the cross sections for Dirac and Majorana neutrinos persist even for arbitrarily small but not exactly vanishing neutrino mass. We demonstrate that, at least in the framework of the Standard Model, this is not the case. We also give a general proof that within the Standard Model quantum statistics does not help tell Dirac and Majorana neutrinos apart in the limit of negligibly small $m_\nu/E$.