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arXiv · 2610.34832

A General Framework for Leggett--Garg Violation in Neutrino Oscillations and Matter Effects

M. M. Ettefaghi·H. Hajipour
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Abstract

The Leggett--Garg inequality (LGI) constrains temporal correlations under the assumptions of macrorealism and noninvasive measurability. We study the four-time quantity \(K_4\) 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 \(M_R=2\). 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 \(K_4\) 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.

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M. M. Ettefaghi, H. Hajipour. 2026-10-26. A General Framework for Leggett--Garg Violation in Neutrino Oscillations and Matter Effects. https://arxiv.org/abs/2610.34832

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