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arXiv:1702.04646 · The European Physical Journal C

Three-flavoured neutrino oscillations and the Leggett–Garg inequality

Debashis Gangopadhyay, Animesh Sinha Roy

Published Apr 1, 2017• 33 citations
arXivHTMLPDF

Abstract

Three-flavoured neutrino oscillations are investigated in the light of the Leggett–Garg inequality (LGI). The results obtained are: (a) The maximum violation of the LGI is 2.17036 for neutrino path length $$L_{1}=140.15 $$ km and $$\Delta L=1255.7 $$ km. (b) The presence of the mixing angle $$\theta _{13}$$ enhances the maximum violation of LGI by $$4.6\%$$ . (c) The currently known mass hierarchy parameter $$\alpha = 0.0305$$ increases the maximum violation of LGI by $$3.7\%$$ . (d) The presence of a CP-violating phase parameter enhances the maximum violation of LGI by $$0.24\%$$ , thus providing an alternative indicator of CP violation in three-flavoured neutrino oscillations. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified.

DOI
10.1140/epjc/s10052-017-4837-2

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Three-flavoured neutrino oscillations are investigated in the light of the Leggett–Garg inequality (LGI). The results obtained are: (a) The maximum violation of the LGI is 2.17036 for neutrino path length L1=140.15L_{1}=140.15 L1​=140.15 km and ΔL=1255.7\Delta L=1255.7 ΔL=1255.7 km. (b) The presence of the mixing angle θ13\theta _{13}θ13​ enhances the maximum violation of LGI by 4.6%4.6\%4.6% . (c) The currently known mass hierarchy parameter α=0.0305\alpha = 0.0305α=0.0305 increases the maximum violation of LGI by 3.7%3.7\%3.7% . (d) The presence of a CP-violating phase parameter enhances the maximum violation of LGI by 0.24%0.24\%0.24% , thus providing an alternative indicator of CP violation in three-flavoured neutrino oscillations. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified.
Abstract Neutrino oscillations occur due to non-zero masses and mixings and most importantly they are believed to maintain quantum coherence even over astrophysical length scales. In the present study, we explore the quantumness of three flavour neutrino oscillations by studying the extent of violation of Leggett–Garg inequalities (LGI) if non-standard interactions (NSI) are taken into account. We report an enhancement in violation of LGI with respect to the standard scenario for appropriate choice of NSI parameters.
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 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.
The Leggett-Garg inequality (LGI), an analogue of Bellś inequality involving correlations of measurements of one observable on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. In this work, we investigate its implications in the context of neutrino flavour (νeL↔νμLν_{e}^{L}\leftrightarrowν_μ^{L}νeL​↔νμL​) and spin (νeL↔νeRν_{e}^{L}\leftrightarrowν_{e}^{R}νeL​↔νeR​) oscillations in the presence of a constant transverse magnetic field. For systems with strong magnetic fields, we show that, for both cases, there are length regions ΔLΔLΔL where the LGI is violated, as quantified by the correlator functions K3K_{3}K3​ and K4K_{4}K4​.
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.
This project examines the quantum mechanical nature of neutrino oscillations through the Leggett-Garg Inequality (LGI), a test for temporal correlations that distinguishes quantum mechanics from classical hidden-variable theories. Using data from the MINOS experiment, which measures neutrino survival probabilities across a 735 km baseline, two methods were employed to calculate LGI violations: a conventional approach and an overlap method. While both are valid, the overlap method is theoretically more accurate as it incorporates uncertainties in energy. The conventional method identified 80 triplets with 62 LGI violations, while the overlap method identified 780 triplets with an average of 528 LGI violations. These results demonstrate significant LGI violations, affirming quantum coherence in neutrino oscillations and challenging classical macrorealism. This study advances our understanding of quantum behavior in macroscopic systems, offering robust evidence for the quantum mechanical framework of neutrino physics.