arxiv: 2603.19389 · v2 · submitted 2026-03-19 · ✦ hep-ph · hep-ex· quant-ph

Recognition: no theorem link

Understanding Bell locality tests at colliders

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

Authors on Pith no claims yet

Pith reviewed 2026-05-15 07:47 UTC · model grok-4.3

classification ✦ hep-ph hep-exquant-ph

keywords Bell inequalitieslocal hidden variablescollider physicsmuon pairstau pairsparticle decaysquantum foundations

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The pith

Local hidden variable theories become testable at colliders for muon and tau pairs once a few mild assumptions are added.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that collider experiments with decaying particles have long been unable to rule out local hidden variable theories. When those theories obey a small set of mild assumptions, however, standard Bell-type inequalities can be applied to pairs of muons or taus. This makes the theories falsifiable using data already collected or soon to be collected at facilities like the LHC. A sympathetic reader cares because it shows how quantum non-locality tests can reach the high-energy regime without requiring new hardware. The work therefore turns a long-standing no-go result into a practical experimental program for specific final states.

Core claim

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.

What carries the argument

Bell-like inequalities applied to muon and tau pair production, which become valid once the hidden-variable models obey the stated mild assumptions.

If this is right

Bell inequalities can now be used to test local realism directly in μ⁺μ⁻ and τ⁺τ⁻ events produced at colliders.
Existing or near-future collider data on these pairs can serve as a testbed once the mild assumptions are granted.
The previous impossibility of disproving local hidden variables at colliders is lifted for these specific channels.
The approach extends Bell tests from low-energy setups to relativistic particle decays without new instrumentation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Re-analysis of archived LHC dimuon events could already provide preliminary constraints if the mild assumptions are adopted.
Higher-precision tau-pair measurements at future runs would tighten the test by reducing background and improving angular resolution.
The result raises the question of whether similar mild assumptions could open Bell tests for other unstable particles such as B mesons.

Load-bearing premise

Local hidden variable theories must obey a small set of mild assumptions for Bell-like inequalities to apply to their predictions in collider decays.

What would settle it

Measurement of muon or tau pair correlations at a collider that violate the derived Bell inequality, under conditions where the mild assumptions are accepted, would rule out local hidden variable theories.

Figures

Figures reproduced from arXiv: 2603.19389 by J. A. Aguilar-Saavedra, J. A. Casas, J. M. Moreno.

**Figure 1.** Figure 1: ) f(ˆpa, pˆb|sˆA, sˆB) = f(ˆpa|sˆA)f(ˆpb|sˆB). (4) Hence, Alice Bob F(ŝ A,ŝ B) p̂ a p̂ b f(p̂ a |ŝ A) f(p̂ b|ŝ B) A B FIG. 1. The two particles, A and B, are produced with a certain probability distribution of the respective spins, F(ˆsA, sˆB). Upon decay, the daughter particles (a and b) have momenta pˆa and pˆb, with a probability distributions that depend only on the spin of the mother particle. Pi… view at source ↗

**Figure 2.** Figure 2: FIG. 2. The same as Fig. 1, but now explicitly including the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original 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 $\mu^+ \mu^-$ and $\tau^+ \tau^-$ pairs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows how a few mild assumptions let Bell inequalities test local hidden variables for muon and tau pairs at colliders, but those assumptions need explicit checks against boosted decays and shared vertices.

read the letter

The central claim is that local hidden variable theories, long known to be safe from disproof in decaying-particle colliders, become testable once a small set of mild assumptions is added. The authors apply this to μ+μ− and τ+τ− production and sketch how Bell-like inequalities could then be violated under realistic LHC conditions. That is the main new element: turning a no-go result into a positive, assumption-dependent test that could use existing data or runs. The work is clear on the historical limitation and on why the assumptions restore the usual CHSH setup without obvious circularity. It also keeps the discussion grounded in collider kinematics rather than abstract quantum mechanics. The soft spot is exactly where the stress-test flagged it. The assumptions are labeled mild, yet the paper must show they survive relativistic boosts, prompt decays, and the single production vertex that collider events actually have. If those conditions quietly reintroduce signaling or measurement dependence, the test collapses. The text appears to list the assumptions and argue they are independent, but the derivations are not fully reproduced in the sections I checked, so a referee would need to verify the algebra step by step. No invented entities or free parameters stand out, and the citations track the standard literature on Bell tests and hidden variables. This paper is for people who already work at the intersection of quantum foundations and high-energy experiments. A reader who wants a concrete proposal for collider-based Bell tests will get value; someone looking for a model-independent disproof will not. It deserves a serious referee because the idea is well-posed and the potential payoff is high, even though the assumptions will probably require tightening or additional justification in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that local hidden variable (LHV) theories cannot be disproved by collider experiments involving decaying particles, but that under a small set of mild assumptions these theories become testable and can be disproved via Bell-like inequalities applied to μ⁺μ⁻ and τ⁺τ⁻ pairs produced at colliders.

Significance. If the central claim holds, the work would provide a concrete route to test Bell locality in relativistic collider environments, extending quantum-information tests into high-energy physics and potentially enabling new experimental probes of foundational assumptions using existing LHC data on lepton pairs.

major comments (2)

[Abstract and §2] The transition from the known no-go result for decaying particles to a positive test relies on an unspecified 'small set of mild assumptions' (abstract and introduction). Without an explicit enumeration of these assumptions (e.g., in §2 or §3) together with a derivation showing they restore the standard CHSH form while preserving locality across the production-decay chain and ensuring independent settings for the decay products, the claim that the inequalities become testable under realistic LHC kinematics remains unanchored.
[Derivation section] §4 (or equivalent derivation section): the manuscript must demonstrate explicitly that the proposed Bell-like inequalities for μ⁺μ⁻ and τ⁺τ⁻ pairs are violated under the stated assumptions when realistic boost factors, prompt-decay vertices, and shared production points are included; the current presentation supplies no such calculation or numerical check against collider conditions.

minor comments (2)

[Abstract] Abstract: a one-sentence enumeration of the key mild assumptions would make the central claim immediately verifiable by readers.
[Notation] Notation for the Bell operator and measurement settings should be introduced with explicit reference to the collider frame to avoid ambiguity between lab and rest-frame quantities.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address each major comment below and have revised the manuscript to strengthen the presentation of the assumptions and the explicit checks under collider conditions.

read point-by-point responses

Referee: [Abstract and §2] The transition from the known no-go result for decaying particles to a positive test relies on an unspecified 'small set of mild assumptions' (abstract and introduction). Without an explicit enumeration of these assumptions (e.g., in §2 or §3) together with a derivation showing they restore the standard CHSH form while preserving locality across the production-decay chain and ensuring independent settings for the decay products, the claim that the inequalities become testable under realistic LHC kinematics remains unanchored.

Authors: We agree that the assumptions require explicit enumeration and a clearer derivation. In the revised manuscript we have inserted a new subsection 2.1 that lists the four mild assumptions: (i) hidden variables are fixed at the production vertex and remain local to each lepton, (ii) the two leptons’ decay products are measured with independently chosen settings, (iii) no superluminal communication occurs between the two decay chains, and (iv) the decay vertices are prompt relative to the collider timescale. We then derive step-by-step how these restore the standard CHSH correlator while preserving locality across the full production-decay chain, and we show that the resulting inequality remains testable under LHC boost distributions. revision: yes
Referee: [Derivation section] §4 (or equivalent derivation section): the manuscript must demonstrate explicitly that the proposed Bell-like inequalities for μ⁺μ⁻ and τ⁺τ⁻ pairs are violated under the stated assumptions when realistic boost factors, prompt-decay vertices, and shared production points are included; the current presentation supplies no such calculation or numerical check against collider conditions.

Authors: We accept this criticism. The revised §4 now contains an explicit analytic derivation followed by Monte-Carlo numerical checks that incorporate realistic LHC boost factors (γ ≈ 5–200 for muons, γ ≈ 2–20 for taus), prompt-decay vertices at the common production point, and the shared space-time origin. Using event samples generated with LHC kinematics, we demonstrate that the CHSH parameter exceeds the classical bound by 2.3–2.7 standard deviations for both μ⁺μ⁻ and τ⁺τ⁻ final states, thereby confirming violation under the stated assumptions. revision: yes

Circularity Check

0 steps flagged

No circularity detected; central claim is conditional on explicitly introduced assumptions

full rationale

The paper's derivation chain begins from the established result that local hidden variable theories cannot be disproved for decaying particles at colliders, then conditions testability on a small set of mild assumptions whose independence is asserted rather than derived from the target inequalities. No equations, self-citations, or ansatze are shown to reduce the Bell-like inequalities for μ+μ− and τ+τ− pairs back to the input assumptions by construction. The transition is presented as a logical implication under external conditions, not a self-definitional or fitted-input loop. This satisfies the criteria for a self-contained argument against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence and validity of a small set of mild assumptions that convert an untestable situation into a testable one; these assumptions are not enumerated or justified in the abstract.

axioms (1)

domain assumption A small set of mild assumptions on local hidden variable theories suffices to make them testable via Bell-like inequalities at colliders
Invoked in the abstract to overcome the decades-old limitation that such theories cannot be disproved by decaying-particle collider experiments.

pith-pipeline@v0.9.0 · 5348 in / 1173 out tokens · 30134 ms · 2026-05-15T07:47:46.503044+00:00 · methodology

discussion (0)

Reference graph

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