The signal of ill-defined CPT weakening entanglement in the B d system

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 the 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.