Deciphering Majorana nature of sub-eV neutrinos by using their quantum statistical property

TL;DR

This paper proposes a novel method to identify Majorana neutrinos by analyzing their quantum statistical properties in specific three-body decay processes, overcoming the limitations of traditional kinematic tests.

Contribution

It introduces a new approach based on event distribution symmetry in effective Dalitz plots to distinguish Majorana from Dirac neutrinos, even for very small neutrino masses.

Findings

Event distribution symmetry indicates Majorana nature

Method applicable even in the massless neutrino limit

Potential to experimentally identify Majorana neutrinos

Abstract

Neutrinos are the only known elementary fermions that can exhibit Majorana nature. As per the "practical Dirac-Majorana confusion theorem" it is impossible to distinguish between Dirac and Majorana neutrinos via any kinematic tests when their masses are very small. However, it is also well known that Majorana neutrino and anti-neutrino present in the final state must obey the Fermi-Dirac statistics, irrespective of how small the mass of neutrino is. We propose a new method to search for Majorana neutrinos by exploiting their quantum statistical property. We analyse `effective' three-body decays of the kind $X \to Y \nu \overline{\nu}$ (e.g.\ $X \left[ B^0 \right] \to \pi^+ \big( \to \mu^+ \nu_{\mu} \big) \mu^- \overline{\nu}_{\mu} \equiv Y \left[ \mu^+ \mu^-\right] \nu_{\mu} \overline{\nu}_{\mu}$), with 4-momenta of $X$ and $Y$ experimentally known, such that the 4-momenta of both neutrino and anti-neutrino can be deduced. For Majorana neutrinos the distribution of events in the `effective' Dalitz plot for such a well chosen process would be fully symmetric under exchange of the neutrino and anti-neutrino. Unlike the neutrinoless double-beta decay or other lepton-number violating modes, this distinction between Majorana and Dirac neutrinos survives even in the almost massless neutrino limit due to the quantum statistical property.