New Test of Neutrino Oscillation Coherence with Leggett-Garg Inequality

TL;DR

This paper introduces a generalized Leggett-Garg inequality to test quantum coherence in neutrino oscillations, applying it to experimental data and considering energy uncertainties, revealing significant violations indicating coherence.

Contribution

It develops a new LGI compatible with neutrino frameworks, incorporating decoherence and energy uncertainties, and applies it to multiple experiments for the first time.

Findings

Daya Bay and MINOS data violate LGI over 10σ

KamLAND data shows 1.9σ violation

Results suggest strong neutrino coherence presence

Abstract

Leggett-Garg Inequality~(LGI) is a time analogue of Bell's inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett-Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of over $10\sigma$, and of over 90$\%$ of theoretical predictions, while the KamLAND data exhibit violation of $1.9\sigma$, being of 58$\%$ of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.