We discuss the demise of flavour tagging due to the loss of the particle–antiparticle identity of neutral B -mesons in the Einstein–Podolsky–Rosen correlated states. Such a situation occurs in cases where the CPT operator is ill-defined, as happens, for example, in quantum gravity models with induced decoherence in the matter sector. The time evolution of the perturbed B 0 – B ¯ 0 initial state, as produced in B -factories, is sufficient to generate new two-body states. For flavour specific decays at equal times, we discuss two definite tests of the two body entanglement: (i) search for the would-be forbidden B 0 B 0 and B ¯ 0 B ¯ 0 states; (ii) deviations from the indistinguishable probability between the permuted states B ¯ 0 B 0 and B 0 B ¯ 0 .
We discuss the demise of flavour tagging due to the loss of the particle–antiparticle identity of neutral B -mesons in the Einstein–Podolsky–Rosen correlated states. Such a situation occurs in cases where the CPT operator is ill-defined, as happens, for example, in quantum gravity models with induced decoherence in the matter sector. The time evolution of the perturbed B 0 – B ¯ 0 initial state, as produced in B -factories, is sufficient to generate new two-body states. For flavour specific decays at equal times, we discuss two definite tests of the two body entanglement: (i) search for the would-be forbidden B 0 B 0 and B ¯ 0 B ¯ 0 states; (ii) deviations from the indistinguishable probability between the permuted states B ¯ 0 B 0 and B 0 B ¯ 0 .
Genuine tests of an asymmetry under T and/or CPT transformations imply the interchange between in-states and out-states. I explain a methodology to perform model-independent separate measurements of the three CP, T and CPT symmetry violations for transitions involving the decay of the neutral meson systems in B- and Φ-factories. It makes use of the quantum-mechanical entanglement only, for which the individual state of each neutral meson is not defined before the decay of its orthogonal partner. The final proof of the independence of the three asymmetries is that no other theoretical ingredient is involved and that the event sample corresponding to each case is different from the other two. The experimental analysis for the measurements of these three asymmetries as function of the time interval Δt > 0 between the first and second decays is discussed, as well as the significance of the expected results. In particular, one may advance a first observation of true, direct, evidence of Time-Reserval-Violation in B-factories by many standard deviations from zero, without any reference to, and independent of, CP-Violation. In some quantum gravity framework the CPT-transformation is ill-defined, so there is a resulting loss of particle-antiparticle identity. This mechanism induces a breaking of the EPR correlation in the entanglement imposed by Bose statistics to the neutral meson system, the so-called ω -effect. I present results and prospects for the ω -parameter in the correlated neutral meson-antimeson states.
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 B d -meson states and we obtain a global fit to their values from the BaBar Collaboration experimental results. The possible fake terms are all compatible with zero. The information content of the nine asymmetry parameters is indeed different. The non-vanishing and are impressive separate direct evidence of Time-Reversal-Violation and CP-Violation in these transitions (and compatible with Standard Model expectations). A 2σ effect for the Re(θ) parameter responsible of CPT-Violation appears; interpreted as an upper limit, it leads to eV at 95% C.L. 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.
The signal of ill-defined CPT weakening entanglement in the Bd B d system
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. In the current paper we identify how to probe the complex ω in the entangled Bd -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( ω ) and Im( ω ), disentangled from CPT violation in the evolution Hamiltonian Re( θ ) and Im( θ ). 2σ tensions for both Re( θ ) and Im( ω ) are shown to be uncorrelated.
In this brief review I discuss ways and tests of CPT-Violation in the context of quantum gravity theories with space-time foam vacua, which entail quantum decoherence of matter propagating in such backgrounds. I cover a wide variety of sensitive probes, ranging from cosmic neutrinos to meson factories. I pay particular emphasis on associating the latter with specific, probably unique ('smoking-gun'), effects of this type of CPT Violation, related to a modification of Einstein-Podolsky-Rosen (EPR) correlations in the entangled states of the relevant neutral mesons. I also present some semi-microscopic estimates of these latter effects, in the context of a specific string-inspired model of space-time foam ('D-particle foam').
In a ϕ factory, neutral kaons are produced in Einstein-Podolsky-Rosen (EPR) states, furthermore, a KS is tagged if its entangled partner is detected as KL, and vice versa. Here we point out that upon its detection as KL, one of the EPR-entangled particles is projected into one of the orthogonal basis states, consequently the other particle should be projected to the state orthogonal to KL, denoted as K⊥L, rather than KS, because KS is not orthogonal to KL. Therefore the semileptonic charge asymmetry of what was previously regarded as KS is really that of K⊥L. Based on this re-tagging, we modify the experimentally determined values of several parameters, including the one describing the violation of ΔS=ΔQ rule, the one describing CPT violation for ΔS=ΔQ transitions, and the time-like CPT- and Lorentz-violating coefficient for the two valence quarks in a kaon.
The quantum interference between the decays of entangled neutral kaons is a very powerful tool for testing the quantum coherence of the entangled kaon pair state. The studied process ϕ→KSKL→π+π−π+π− exhibits the characteristic Einstein-Podolsky-Rosen correlations that prevent both kaons to decay into π+π− at the same time. The newly published result is based on data sample collected with the KLOE detector at DAΦNE and corresponds to an integrated luminosity of about 1.7 fb−1 , i.e. to ∼ 1.7 × 109ϕ→KSKL decays. From the fit to the observed time difference distribution of the two kaon decays, the decoherence and CPT violation parameters of various phenomenological models are measured. A stringent upper limit on the branching ratio of the ϕ→KSKS,KLKL decay is also derived. Independently, the comparison of neutral meson transition rates between flavour and CP eigenstates allows direct and model independent tests of time-reversal T and CPT symmetries to be conducted, through ratios of rates of two classes of processes: KSKL→(π±e∓ν)(3π0) and KSKL→(π+π−)(π±e∓ν). In addition to this a straightforward extension to the case of CPT symmetry is performed providing the first model independent test of CPT symmetry violation in transitions of neutral kaons.