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

TL;DR

This paper introduces a quantum information measure based on a Leggett-Garg-like inequality that can detect neutrino mass hierarchy and CP violation effects, with implications for current and future neutrino experiments.

Contribution

It develops a novel quantum information theoretic quantity sensitive to neutrino mass hierarchy and CP violation, applicable to experimental neutrino transition data.

Findings

The quantity shows significant violation depending on mass hierarchy.

It can distinguish between normal and inverted hierarchy in neutrino oscillations.

Application to T2K, NOvA, and DUNE demonstrates experimental relevance.

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.