Leggett-Garg inequality in the context of three flavor neutrino oscillation

The present work is devoted to the characterization of the Leggett-Garg inequality (LGI) for three flavored neutrino oscillations in the presence of both matter and charge-conjugation and parity violating effects. This study complements and completes the recent one put forward in arXiv:1710.05562 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 a high energy neutrino beam compared to the maximum value attained by the Leggett-Garg parameter.