The signal of ill-defined CPT weakening entanglement in the $B_d$ system

TL;DR

This paper proposes a method to detect the complex $$-effect, a potential signature of quantum gravity fluctuations, in entangled $B_d$ meson systems by analyzing decay correlations and disentangling it from CPT violation.

Contribution

It introduces a novel approach to measure the complex $$-effect in $B_d$ meson entanglement, separating it from CPT violation effects using decay channel correlations.

Findings

Identifies how to probe Re($$) and Im($$) independently.

Shows uncorrelated 2-$$ tensions for Re($$) and Im($$).

Provides observables for experimental determination of the $$-effect.

Abstract

In the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the $\omega$-effect. In the current paper we identify how to probe the complex $\omega$ in the entangled $B_d$-system using Flavour(f)-CP(g) eigenstate decay channels: the connection between the Intensities for the two time-ordered decays (f, g) and (g, f) is lost. Appropriate observables are constructed allowing independent experimental determinations of Re($\omega$) and Im($\omega$), disentangled from CPT violation in the evolution Hamiltonian Re($\theta$) and Im($\theta$). 2-$\sigma$ tensions for both Re($\theta$) and Im($\omega$) are shown to be uncorrelated.