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arXiv:hep-ph/9712274

epsilon'/epsilon violates Bell's inequality

Fabio Benatti, Roberto Floreanini B

Published Dec 5, 1997• 1 citation
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Abstract

We formulate a set of Bell's inequalities for the system of two correlated neutral kaons coming from the decay of a phi-meson, without assuming CP and CPT invariance. We show that a non-vanishing value of the phenomenological parameter epsilon' would violate such inequalities, ruling out Bell's locality.
DOI
10.48550/arxiv.hep-ph/9712274

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We formulate a set of Bell's inequalities for the system of two correlated neutral kaons coming from the decay of a \ensuremath{\varphi} meson, without assuming CP\mathrm{CP}CP and CPT\mathrm{CPT}CPT invariance. We show that a nonvanishing value of the phenomenological parameter ${\mathrm{\ensuremath{\varepsilon}}}^{\ensuremath{'}}$ would violate such inequalities, ruling out Bell's locality.
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A local realistic theory of single neutral kaons and of correlated neutral kaon pairs is formulated by deducing the most general consequences of three assumptions: (i) the Einstein-Podolsky-Rosen (EPR) reality criterion, (ii) locality, and (iii) no retroactive causality. Variables must be introduced for every kaon determining the stable CP\mathrm{CP}CP value and the variable value of strangeness S.S.S. Instantaneous SSS jumps are shown to take place. If kaon pairs are produced in \ensuremath{\Phi} meson decays, the local realistic probability of observing K‾0K‾0{\overline{K}}^{0}{\overline{K}}^{0}K0K0 pairs at certain different proper times necessarily differs by 30% from the quantum-mechanical predictions. The size of this difference justifies our systematic neglect of CP\mathrm{CP}CP violation. A \ensuremath{\Phi} factory is thus shown to provide a unique tool for the study of the EPR problem
We point out that decoherence parameters in the correlated two neutral kaon system breaks the transformation invariance of basis and their magnitude are stringently limited by the experimentally measured magnitudes of CP violation and of the strangeness non conserving ΔS=±2ΔS = \pm 2ΔS=±2 transitions.
We analyze the premises of recent propositions to test local realism via the Bell inequalities using neutral kaons from $\ensuremath{\Phi}$ resonance decays as entangled Einstein-Podolsky-Rosen pairs. We pay special attention to the derivation of the Bell inequalities, or related expressions, for unstable and oscillating kaon ``quasispin'' states and to the possibility of the actual identification of these states through their associated decay modes. We discuss an indirect method to extract probabilities to find these states by combining experimental information with theoretical input. However, we still find inconsistencies in previous derivations of the Bell inequalities. We show that the identification of the quasispin states via their associated decay mode does not allow the free choice to perform different tests on them, a property which is crucial to establish the validity of any Bell inequality in the context of local realism. In view of this we propose a different kind of Bell inequality in which the free choice or adjustability of the experimental setup is guaranteed. We also show that the proposed inequalities are violated by quantum mechanics.
The nonlocal property of quantum mechanics can be nicely tested in high energy physics; in particular, the neutral kaon pairs as produced at DAΦΦΦNE, Frascati, are very well suited. The analogies of kaons as compared to polarized photons or spin--1/2 particles --the kaonic qubit feature-- are reviewed. However, there are also fundamental differences which occur due to the kaon time evolution and due to internal symmetries; in particular, the violation of CP symmetry is related to the violation of Bell inequalities. Two type of Bell inequalities for kaons are presented, one for the variation of the ``quasi--spin'' and the other for different detection times of the kaon.