A quantum information theoretic quantity sensitive to the neutrino mass-hierarchy

Abstract

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 T$2$K and NO$\nu$A as well as the future experiment DUNE.

Comments: 6 pages, 5 figures