Addressing the Majorana vs. Dirac question with neutrino decays

The Majorana versus Dirac nature of neutrinos remains an open question. This is due, in part, to the fact that virtually all the experimentally accessible neutrinos are ultra-relativistic. Noting that Majorana neutrinos can behave quite differently from Dirac ones when they are non-relativistic, we show that, at leading order, the angular distribution of the daughters in the decay of a heavy neutrino into a lighter one and a self-conjugate boson is isotropic in the parent's rest frame if the neutrinos are Majorana fermions, independent of the parent's polarization. This result follows from CPT invariance and is independent of the details of the physics responsible for the decay. In contrast, if the neutrinos are Dirac fermions, the angular distribution in such a decay is, in general, not isotropic. We explore the feasibility of using these angular distributions—or, equivalently, the energy distributions of the daughters in the laboratory frame—in order to address the Majorana versus Dirac nature of neutrinos if a fourth, heavier neutrino mass eigenstate reveals itself in the current or next-generation of high-energy colliders, intense meson facilities, or neutrino beam experiments. We also point out how the related decays of a heavy neutrino into charged daughters can be used for the same purpose.