Probing violations of CPT with $B_d$ mesons

Abstract

We establish the precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the neutral meson B d states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-Factory of entangled states. Genuine asymmetry parameters in the time distribution of the asymmetries are identified and their measurability analysed, disentangling genuine and possible fake terms. The nine asymmetry parameters -three different observables for each one of the three symmetries -are expressed in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled for the diagonal flavour terms of the mass matrix. Finally, we consider scenarios where, 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 ω-effect. The analysis is extended to identify how to probe the complex ω when the connection between the Intensities for the two time-ordered decays ( f , g) and (g, f ) is lost ( f flavour and g CP eigenstate decay channels), and how the ω-effect is disentangled from CPT violation in the evolution Hamiltonian.