Leggett-Garg inequality violation in muong-2 experiments

We present the first study of Leggett-Garg inequality (LGI) violation in polarized muon spin precession. We formulate a procedure to reconstruct temporal correlators of the longitudinal muon polarization from measured time-dependent muon decay spectra and apply it to publicly available Fermilab Muondata corresponding to approximatelybillion muon decays. Using a simplified model of the detector acceptance and efficiency, the LGI is found to be violated with a single-bin significance of, while combining neighboring bins further increases the significance. While our analysis is limited by systematic uncertainties associated with the detector modeling, a dedicated experimental analysis could reduce these uncertainties toward the statistical level,, potentially enabling one of the most precise measurements of temporal quantum correlations.