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

Abstract

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

Comments: 7 pages, 2 figure