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arXiv:hep-ph/9211203

Bell's Inequality and τττ-Physics at LEP

Herbert Karl Dreiner

Published Nov 2, 1992• 0 citations
arXivHTMLPDF

Abstract

In this talk given at the TAU92 Workshop, Columbus, OH, Sept. 92, we summarize results presented in more detail in a recent paper by S. Abel, M. Dittmar and the author where we gave a general proof that Bell's inequality can not be tested at a collider experiment. In particular, a measurement of correlated tau-spins at LEP does not constitute a test of local realistic theories via Bell's inequality. The central point of the argument is that such tests, where the spins of two particles are inferred from a scattering distribution, can always be described by a local hidden variable theory. In response to questions at the workshop we go beyond the paper and show that an old experiment involving the measurement of the correlated spins of the two photons emitted in positronium decay via Compton-scattering is also not a viable test of Bell's inequality.

DOI
10.48550/arxiv.hep-ph/9211203

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In this talk given at the TAU92 Workshop, Columbus, OH, Sept. 92, we summarize results presented in more detail in a recent paper by S. Abel, M. Dittmar and the author where we gave a general proof that Bell's inequality can not be tested at a collider experiment. In particular, a measurement of correlated tau-spins at LEP does not constitute a test of local realistic theories via Bell's inequality. The central point of the argument is that such tests, where the spins of two particles are inferred from a scattering distribution, can always be described by a local hidden variable theory. In response to questions at the workshop we go beyond the paper and show that an old experiment involving the measurement of the correlated spins of the two photons emitted in positronium decay via Compton-scattering is also not a viable test of Bell's inequality.
A bstract Recently there has been an increased interest in possible tests of locality via Bell’s inequalities, as well as separately tests of entanglement at colliders, in particular at the LHC. These have involved various physical processes, such as tt‾ t\overline{t} tt t t ¯ , or τ + τ − production, or the decay of a Higgs boson to two vector bosons H → VV ∗ . We argue that none of these proposals constitute a test of locality via Bell’s inequality or promise unconditional observational evidence of entanglement. In all cases what is measured are the momenta of the final state particles. Using the construction proposed by Kasday (1971) in a different context, and adapted to collider scenarios by Abel, Dittmar, and Dreiner (1992), it is straightforward to construct a local hidden variable theory (LHVT) which exactly reproduces the data. This construction is only possible as the final state momenta all commute. We show that this LHVT satisfies Bell’s inequality or the related CHSH inequality as appropriate for all the proposed LHC collider tests in the literature. Thus a test of locality via Bell’s inequality is not possible at colliders. The LHVT is also by construction local, i.e. all correlations are separable. Thus an unconditional proof of entanglement is also inherently not possible at colliders. It can only be shown that the entanglement within the Standard Model consistently describes the data.
Abstract For decades, it has been known that generic local hidden-variable theories cannot be disproved by collider experiments involving decaying particles. However, if these theories satisfy a small set of mild assumptions, they become testable. In particular, this class of theories can be disproved using Bell-like inequalities for μ+μ−\mu ^+ \mu ^-μ+μ− μ + μ - and τ+τ−\tau ^+ \tau ^-τ+τ− τ + τ - pairs.
For decades, it has been known that local hidden variable theories cannot be disproved by collider experiments involving decaying particles. However, if these theories satisfy a small set of mild assumptions, they become testable. In particular, they can be disproved using Bell-like inequalities for μ+μ−μ^+ μ^-μ+μ− and τ+τ−τ^+ τ^-τ+τ− pairs.
Abstract In current studies for testing Bell inequalities at colliders, the reconstruction of spin correlations from scattering cross-sections relies on the bilinear form of the spin correlations, but not all local hidden variable models (LHVMs) have such a property. To demonstrate that a general LHVM cannot be rule out via scattering cross-section data, we propose a specific LHVM, which can exactly duplicate the same scattering cross-section for particle production and decay as the standard quantum theory, making it indistinguishable at colliders in principle. Despite of this, we find that reconstructing spin correlations through scattering cross-sections can still exclude a broad class of LHVMs, e.g., those models employing classical spin correlations as a surrogate for quantum spin correlations.
We review in this paper the research status on testing the completeness of Quantum mechanics in High Energy Physics, especially on the Bell Inequalities. We briefly introduce the basic idea of Einstein, Podolsky, and Rosen paradox and the results obtained in photon experiments. In the tests of Bell inequalities in high energy physics, the early attempts of using spin correlations in particle decays and later on the mixing of neutral mesons used to form the quasi-spin entangled states are covered. The related experimental results in K^0 and B^0 systems are presented and discussed. We introduce the new scheme, which is based on the non-maximally entangled state and proposed to implement in ϕfactory, in testing the Local Hidden Variable Theory. And, we also discuss the possibility in generalizing it to the tau charm factory.
Testing Bell inequality through h→ττh\toττh→ττ at CEPC
The decay of Higgs boson into two spin-1/2 particles provides an ideal system to reveal quantum entanglement and Bell-nonlocality. Future e+e−e^+e^-e+e− colliders can improve the measurement accuracy of the spin correlation of tau lepton pairs from Higgs boson decay. We show the testability of Bell inequality through h→ττh\to ττh→ττ at Circular Electron Positron Collider (CEPC). Two realistic methods of testing Bell inequality are investigated, i.e., Törnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the simulation, we take into account the detector effects of CEPC including uncertainties for tracks and jets from ZZZ boson in the production of e+e−→Zhe^+e^-\to Zhe+e−→Zh. Necessary reconstruction approaches are described to measure quantum entanglement between τ+τ^+τ+ and τ−τ^-τ−. Finally, we show the sensitivity of CEPC to the Bell inequality violation for the two methods.