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arXiv:2606.04412 · Acta Physica Polonica B

Leggett-Garg test inequality with spin and flavour neutrino oscillations in a constant magnetic field

I. A. Monroy, S. D. Madrid

quant-phgr-qchep-phSubmitted Jun 3, 2026• Announced Jun 4, 2026• 0 citations
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Abstract

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 ($ν_{e}^{L}\leftrightarrowν_μ^{L}$) and spin ($ν_{e}^{L}\leftrightarrowν_{e}^{R}$) 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 $ΔL$ where the LGI is violated, as quantified by the correlator functions $K_{3}$ and $K_{4}$.

Journal reference
Acta Phys. Pol. B 57, 7-A3 (2026)
DOI
10.5506/APhysPolB.57.7-A3
Comments
11 pages, 4 figures

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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, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6 σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
Abstract Leggett–Garg inequality (LGI) is a time analogue of Bell’s inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett–Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of over 10σ10\sigma 10σ 10σ , and of over 90 %\%% % of theoretical predictions, while the KamLAND data exhibit violation of 1.9σ1.9\sigma 1.9σ 1.9σ , being of 58 %\%% % of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
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.
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