Distinguishing between Dirac and Majorana neutrinos using temporal correlations

TL;DR

This paper proposes using Leggett-Garg Inequalities to distinguish Dirac from Majorana neutrinos by analyzing temporal correlations affected by neutrino decay and mixing parameters.

Contribution

It introduces a novel approach employing LGI violations in a non-Hermitian PT-symmetric Hamiltonian framework to differentiate neutrino types.

Findings

LGI violations differ by about 15% for Dirac and Majorana neutrinos.

Optimal parameters enhance the distinguishability of neutrino types.

Temporal correlations can serve as a new probe for neutrino nature.

Abstract

In the context of two flavour neutrino oscillations, it is understood that the $2\times 2$ mixing matrix is parameterized by one angle and a Majorana phase. However, this phase does not impact the oscillation probabilities in vacuum or in matter with constant density. Interestingly, the Majorana phase becomes relevant when we describe neutrino oscillations along with neutrino decay. This is due to the fact that effective Hamiltonian has Hermitian and anti-Hermitian components which cannot be simultaneously diagonalized (resulting in decay eigenstates being different from the mass eigenstates). We consider the $\cal PT$ symmetric non-Hermitian Hamiltonian describing two flavour neutrino case and study the violation of Leggett-Garg Inequalities (LGI) in this context for the first time. We demonstrate that temporal correlations in the form of LGI allow us to probe whether neutrinos are Dirac or Majorana. We elucidate the role played by the mixing and decay parameters on the extent of violation of LGI. We emphasize that for optimized choice of parameters, the difference in $K_4$ ($K_3$) for Dirac and Majorana case is $\sim 15\%$ ($\sim 10\%$).