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arXiv:1710.11182 · Physical review. D/Physical review. D.

Leggett-Garg K3 quantity discriminates between Dirac and Majorana neutrinos

M. Richter, Bartosz Dziewit, Jerzy Dajka

Published Oct 16, 2017• 17 citations
arXivHTMLPDF

Abstract

The ${K}_{3}$ quantity, introduced in a context of the Leggett-Garg inequality violation, is studied for the neutrino oscillations in matter with a phenomenologically modeled dissipative environment. It is shown that the ${K}_{3}$ function acquires different values depending on whether the neutrino is a Dirac or Majorana particle, provided that there is a dissipative interaction between matter and neutrinos. The difference occurs for various matter densities and can serve as a potential quantifier verifying the neutrino nature. Moreover, working within a phenomenological model one can suggest the values of the matter density and dissipation for which the difference is the most visible. There exist also special conditions in which the violation of the Leggett-Garg inequality, to a different extent for both kinds of neutrino, is observed.

DOI
10.1103/physrevd.96.076008

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The K3{K}_{3}K3​ quantity, introduced in a context of the Leggett-Garg inequality violation, is studied for the neutrino oscillations in matter with a phenomenologically modeled dissipative environment. It is shown that the K3{K}_{3}K3​ function acquires different values depending on whether the neutrino is a Dirac or Majorana particle, provided that there is a dissipative interaction between matter and neutrinos. The difference occurs for various matter densities and can serve as a potential quantifier verifying the neutrino nature. Moreover, working within a phenomenological model one can suggest the values of the matter density and dissipation for which the difference is the most visible. There exist also special conditions in which the violation of the Leggett-Garg inequality, to a different extent for both kinds of neutrino, is observed.
In the context of two flavour neutrino oscillations, it is understood that the 2×22\times 22×2 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 PT\cal PTPT 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 K4K_4K4​ (K3K_3K3​) for Dirac and Majorana case is ∼15%\sim 15\%∼15% (∼10%\sim 10\%∼10%).
The present work is devoted to the characterization of the Leggett-Garg inequality (LGI) for three flavored neutrino oscillations in the presence of both matter and charge-conjugation and parity violating effects. This study complements and completes the recent one put forward in arXiv:1710.05562 by relaxing the stationary condition. At variance with the latter case, the LGI contains interference terms which cannot be expressed in terms of experimentally measurable quantities, thus drawing a clear-cut distinction between the two scenarios, as well as highlighting the role of the stationary assumption on such systems. We find that the additional terms are small for a high energy neutrino beam compared to the maximum value attained by the Leggett-Garg parameter.
Neutrinos, due to their weakly interacting nature, provide us with a unique opportunity to test foundations of quantum mechanics over macroscopic distances. There has been considerable theoretical and experimental interest in examining the extent of violation of Leggett-Garg inequalities (LGI) in the context of neutrino flavour oscillations. While it is established that neutrino oscillations occur due to mass and mixing among the three generations of neutrinos, sub-dominant effects due to physics beyond the Standard Model (SM) are not yet ruled out. As we are entering the precision era in neutrino physics, it is possible that some of these effects may leave an imprint on data. Thus, it is worthwhile to investigate different physics scenarios beyond the SM and study their impact on oscillation probabilities. In the present work, we invoke damping effects (including decoherence and decay) on oscillation probabilities and study their implications on the LGI.
The Leggett-Garg inequality (LGI) as a temporal analog of Bell's inequality, derived using the notion of realism, is studied in a hitherto unexplored context involving weak-interaction-induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of the LGI obtained from the relevant quantum mechanical results is significantly higher for oscillating neutrinos compared to that for kaons. Interestingly, the effect of CP noninvariance for the kaon oscillation is to enhance this violation, while, for neutrinos, the violation is sensitive to the value of mixing parameter.
The Leggett--Garg inequality (LGI) constrains temporal correlations under the assumptions of macrorealism and noninvasive measurability. We study the four-time quantity K4K_4K4​ for two-flavor neutrino oscillations using a pseudo-density matrix (PDM) under static conditions, instead of non-invasive measurement. With this approach, it becomes possible to examine a Horodecki-type criterion for the temporal Pauli-correlation tensor. The Horodecki criterion had been proven for CHSH inequality (R. Horodecki et al. Phys. Lett. \textbf{A200}, 340), For any unitary qubit evolution, the corresponding scalar is MR=2M_R=2MR​=2. Although, this result characterizes the correlation tensor and the optimized temporal construction, it does not imply that a fixed flavor observable violates the LGI at every neutrino energy or baseline. We therefore evaluate K4K_4K4​ explicitly for flavor measurements in matter of constant density. The numerical examples illustrate how matter effects modify the temporal correlations, with a pronounced matter--vacuum separation near the MSW resonance for the chosen parameters and generally smaller differences in the selected off-resonance cases. This finding motivates further investigation of matter-induced temporal correlations in atmospheric neutrinos and their potential relevance to future studies with long-baseline and atmospheric-neutrino experiments, including DUNE and Hyper-Kamiokande.
Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral BdB_dBd​ , BsB_sBs​ and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter D[n]\mathscr {D}^{[n]}D[n] closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in BdB_dBd​ and BsB_sBs​ systems.