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.
Highlights
One of the most characterizing aspects of quantum mechanics is the principle of superposition, according to which a system exists simultaneously in different states until a measurement is performed on it
LeggettGarg inequalities (LGIs) investigate the nature of correlations among measurements performed on the same system but at different instants of time
In [2], the intuition about our view of macroscopic systems was formalized in terms of two principles, namely (i) macroscopic realism and (ii) noninvasive measurability (NIM) [3,4,5]
Summary
One of the most characterizing aspects of quantum mechanics is the principle of superposition, according to which a system exists simultaneously in different states until a measurement is performed on it. Quantum coherences extended over macroscopic distances have been in the spotlight in the context of flavor oscillations in neutrinos and mesons [6,7,8,9,10,11,12] This provides ample reason for promoting such systems as candidates to study LGI. This leads to a modified version of the LGIs called Leggett-Garg-type inequalities (LGtIs), where all the intermediate nonmeasurable correlations are replaced by measurable ones [13,14,15,16] Such approach was recently used in [17], where the resulting LGtI can be recast in terms of experimentally measurable quantities such as neutrino flavor oscillation probabilities. We make use of the experimental input parameters like energy and baseline of the two ongoing experiments NOνA (NuMI Off-axis νe Appearance) [24,25] and T2K (Tokai to Kamioka) [26] and the future experiment DUNE (Deep Underground Neutrino Experiment) [27]
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