Violation of LGtI inequalities in the light of NO$ν$A and T2K anomaly
The recent anomaly observed in NO$ν$A and T2K experiments in standard three-flavor neutrino oscillation could potentially signal physics extending beyond the standard model (SM). For the NSI parameters that can accommodate this anomaly, we explore the violation of Leggett-Garg type inequalities (LGtI) within the context of three-flavor neutrino oscillations. Our analysis focuses on LGtI violations in scenarios involving complex NSI with $ε_{eμ}$ or $ε_{eτ}$ coupling in long baseline accelerator experiments for normal and inverted mass ordering.LGtI violation is significantly enhanced in normal ordering (NO) for $ε_{eτ}$ scenario for T2K, NO$ν$A, and DUNE experiment set-up. We find that for inverted ordering (IO), in the DUNE experimental set-up above $8.5$ GeV, the LGtI violation can be an indication of $ε_{eτ}$ new physics scenario.