A quantum information theoretic quantity sensitive to the neutrino mass-hierarchy. (English) Zbl 1472.81294
Summary: In this work, we derive a quantum information theoretic quantity similar to the Leggett-Garg inequality, which can be defined in terms of neutrino transition probabilities. For the case of \(\nu_\mu \to \nu_e / \bar{\nu}_\mu \to \bar{\nu}_e\) transitions, this quantity is sensitive to CP violating effects as well as the neutrino mass-hierarchy, namely which neutrino mass eigenstate is heavier than the other ones. The violation of the inequality for this quantity shows an interesting dependence on mass-hierarchy. For normal (inverted) mass-hierarchy, it is significant for \(\nu_\mu \to \nu_e (\bar{\nu}_\mu \to \bar{\nu}_e)\) transitions. This is applied to the two ongoing accelerator experiments T2K and NO\(\nu\)A as well as the future experiment DUNE.
MSC:
| 81V15 | Weak interaction in quantum theory |
| 81U90 | Particle decays |
| 81V45 | Atomic physics |
| 47A63 | Linear operator inequalities |
Keywords:
neutrino mass-hierarchyReferences:
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