# Leggett-Garg inequality in the context of three flavour neutrino oscillation

## TL;DR

This paper investigates the Leggett-Garg inequality in three-flavor neutrino oscillations, considering matter effects and CP violation, revealing the impact of non-stationary conditions on quantum coherence tests.

## Contribution

It extends previous work by analyzing non-stationary conditions, showing how interference terms affect the Leggett-Garg inequality in neutrino oscillations.

## Key findings

- Interference terms are small at high neutrino energies.
- Non-stationary conditions introduce measurable differences in LGI.
- Stationary assumption simplifies the LGI analysis.

## Abstract

The present work is devoted to the characterization of the Leggett-Garg inequality for three-flavoured neutrino oscillations in presence of both matter and Charge-Conjugation and Parity violating (CP) effects. This study complements and completes the recent one put forward in [17] by relaxing the stationary condition. At variance with the latter case, the LGI contains interference terms which cannot be expressed in terms of experimentally measurable quantities, thus drawing a clear-cut distinction between the two scenarios, as well as highlighting the role of the stationary assumption on such systems. We find that the additional terms are small for high energy neutrino beam compared to the maximum value attained by the Leggett-Garg parameter.