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The European Physical Journal C

Understanding Bell locality tests at colliders

J. A. Aguilar–Saavedra, J.A. Casas, Jesús M. Moreno

Published Jul 25, 2026• 0 citations
Publisher

Abstract

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 $$\mu ^+ \mu ^-$$ μ + μ - and $$\tau ^+ \tau ^-$$ τ + τ - pairs.

DOI
10.1140/epjc/s10052-026-16099-9

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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.
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.
Tests of Bell's theorem rule out local hidden variables theories. But any theorem is only as good as the assumptions that go into it, and one of these assumptions is that the experimenter can freely choose the detector settings. Without this assumption, one enters the realm of superdeterministic hidden variables theories and can no longer use Bell's theorem as a criterion. One can like or not like such superdeterministic hidden variables theories and their inevitable nonlocality, the real question is how one can test them. Here, we propose a possible experiment that could reveal superdeterminism.
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.
Abstract Bell inequalities are consequences of local realism while violated by quantum mechanics. In particle physics, entangled high energy particles can be produced from a common source, and the decay of each particle plays the role of measurement. However, in a hidden variable theory, the decay could be determined by hidden variables. This loophole killed such approaches to Bell test in particle physics. It is a special form of measurement-setting or free-will loophole, which also exists in other systems. Using entangled baryons, we present new inequalities of local realism with the explicit assumption of the dependence of the decays on hidden variables, as well as the consideration of the statistical mixture of polarizations and the separation of local hidden variables for objects with spacelike distances. These violations closes the measurement-setting loophole once and for all. We propose to use the processes ηc→ΛΛˉ\eta _c\rightarrow \varLambda {\bar{\varLambda }}ηc​→ΛΛˉ ηc→ΛΛ¯ and χc0→ΛΛˉ\chi _{c0} \rightarrow \varLambda {\bar{\varLambda }}χc0​→ΛΛˉ χc0→ΛΛ¯ to test our inequalities, and show that their violations are likely to be observed with the data already collected in BESIII.