Probing the Leggett-Garg Inequality for Oscillating Neutral Kaons and Neutrinos

TL;DR

This paper investigates the violation of the Leggett-Garg inequality in the context of neutral kaons and neutrinos, revealing significant quantum effects and the influence of CP violation and mixing parameters.

Contribution

It applies the Leggett-Garg inequality to neutral kaons and neutrinos, exploring quantum violations in these oscillating systems for the first time.

Findings

Neutrinos show higher LGI violation than kaons.

CP non-invariance enhances LGI violation in kaons.

LGI violation depends on neutrino mixing parameters.

Abstract

The Leggett-Garg inequality (LGI) as a temporal analogue of Bell's inequality, derived using the notion of realism, is applied in a hitherto unexplored context involving the weak interaction induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of LGI obtained from the quantum mechanical results is significantly higher for the oscillating neutrinos compared to that for the kaons. Interestingly, the effect of CP non-invariance for the kaon oscillation is to enhance this violation while, for neutrinos, it is sensitive to the value of the mixing parameter.