Entropic Leggett-Garg inequality in neutrinos and B (K) meson systems

TL;DR

This paper investigates the violation of entropic Leggett-Garg inequalities in neutrino oscillations and meson systems, considering effects like matter interaction, decoherence, and CP violation, revealing longer violation durations in K mesons.

Contribution

It introduces an analysis of entropic Leggett-Garg inequalities in neutrino and meson systems, incorporating matter effects, decoherence, and CP violation, and compares violation durations across different meson types.

Findings

Violation increases with more measurements, consistent with spin-$s$ systems.

Decoherence reduces the violation, aligning with classical expectations.

K mesons exhibit longer violation durations than B mesons.

Abstract

Entropic Leggett-Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral $B_d$, $B_s$ and $K$ mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering $B/K$ meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-$s$ systems. The effect of decoherence is found to bring the deficit parameter $\mathcal{D}^{[n]}$ closer to its classical value zero, as expected. The violation of entropic Leggett-Garg inequality lasts for a much longer time in $K$ meson system than in $B_d$ and $B_s$ systems.