The signal of ill-defined CPT weakening entanglement in the $${B_d}$$ B d system

Abstract

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 $$\omega $$ ω -effect. In the current paper we identify how to probe the complex $$\omega $$ ω in the entangled $$B_d$$ 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( $$\omega $$ ω ) and Im( $$\omega $$ ω ), disentangled from CPT violation in the evolution Hamiltonian Re( $$\theta $$ θ ) and Im( $$\theta $$ θ ). $$2\sigma $$ 2 σ tensions for both Re( $$\theta $$ θ ) and Im( $$\omega $$ ω ) are shown to be uncorrelated.