Violation of LGtI inequalities in the light of NO $$\nu $$ ν A and T2K anomaly

Abstract

Abstract The recent anomaly observed in NO $$\nu $$ 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 $$\epsilon _{e\mu }$$ ϵ e μ or $$\epsilon _{e\tau }$$ ϵ e τ coupling in long baseline accelerator experiments for normal and inverted mass ordering. LGtI violation is significantly enhanced in normal ordering (NO) for $$\epsilon _{e\tau }$$ ϵ e τ scenario for T2K, NO $$\nu $$ 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 $$\epsilon _{e\tau }$$ ϵ e τ new physics scenario.