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arXiv:2603.19389

Understanding Bell locality tests at colliders

J. A. Aguilar-Saavedra, J. A. Casas, J. M. Moreno

hep-phhep-exquant-phSubmitted Mar 19, 2026• Announced Mar 23, 2026• 0 citations
v1 · Mar 19, 2026v2 · Apr 10, 2026
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Abstract

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 $μ^+ μ^-$ and $τ^+ τ^-$ pairs.

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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 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.
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.
It is commonly believed that the local hidden variable theories (LHVTs) can be tested through measuring the Bell inequalities. This scheme, for the massive particle system, was originally set up for the entangled K0K‾0{K}^{0}{\overline{K}}^{0}K0K0 pair system from the $\ensuremath{\phi}$ factory. In this paper we show that the $J/\ensuremath{\Psi}\ensuremath{\rightarrow}{K}^{0}{\overline{K}}^{0}$ process is even more realistic for this goal. We analyze the unique properties of $J/\ensuremath{\Psi}$ in the detection of basic quantum effects, and find that it is possible to use $J/\ensuremath{\Psi}$ decay as a test of LHVTs in the future $\ensuremath{\tau}$-charm factory. Our analyses and conclusions are generally also true for other heavy onium decays.
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.