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

Abstract The recent anomaly observed in NO $$\nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ν</mml:mi> </mml:math> 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 $$\epsilon _{e\mu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msub> </mml:math> or $$\epsilon _{e\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>τ</mml:mi> </mml:mrow> </mml:msub> </mml:math> coupling in long baseline accelerator experiments for normal and inverted mass ordering. LGtI violation is significantly enhanced in normal ordering (NO) for $$\epsilon _{e\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>τ</mml:mi> </mml:mrow> </mml:msub> </mml:math> scenario for T2K, NO $$\nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ν</mml:mi> </mml:math> 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 $$\epsilon _{e\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>τ</mml:mi> </mml:mrow> </mml:msub> </mml:math> new physics scenario.