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arxiv: 2605.00339 · v1 · submitted 2026-05-01 · ✦ hep-ph · hep-ex· hep-lat· nucl-ex· nucl-th

Recognition: unknown

Evidence for Quark Confinement in the Proton

Xiangdong Ji , Gerald A. Miller , Chen Yang
Authors on Pith no claims yet

Pith reviewed 2026-05-09 19:43 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-latnucl-exnucl-th
keywords quark confinementproton structureQCD forcequark force measurementconfinement evidenceelectron-ion colliderhadron structure
0
0 comments X

The pith

The force on quarks in the proton is constant and attractive over many distances

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

The paper defines a force acting on quarks inside the proton by using available experimental data on proton structure. It extracts this force and finds it remains attractive and unchanging across a wide range of quark positions inside the proton. This constant attractive force matches the expected signature of quark confinement in quantum chromodynamics, the theory that prevents quarks from existing in isolation. A reader would care because the result turns an abstract property of QCD into a measurable quantity derived directly from data rather than from pure theory.

Core claim

We show how to define and measure the force on quarks in the proton using available experimental data. Direct evidence for confinement is obtained because the force is found to be attractive and constant for a wide range of quark positions.

What carries the argument

The position-dependent force on quarks inside the proton extracted from experimental data

If this is right

  • Confinement appears as a directly measurable constant attractive force rather than an inferred property.
  • The same extraction method can be used to obtain quantitative data on confinement at future Electron-Ion Colliders.
  • The energy stored in this constant force contributes to the origin of the proton's mass.

Where Pith is reading between the lines

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

  • The method could be applied to neutrons or other hadrons to check whether confinement strength is universal.
  • If the extraction proves robust, it offers an alternative route to confinement studies that complements lattice simulations.
  • The observed constant force corresponds to a linear potential, consistent with simple string models of quark binding.

Load-bearing premise

The force defined and extracted from experimental data accurately corresponds to the true QCD confining force without large model dependence or post-hoc choices in the analysis procedure.

What would settle it

A future measurement at an Electron-Ion Collider showing the force varying with quark position or turning repulsive at some distances would falsify the claim.

read the original abstract

The strong interaction is the fundamental force that holds quarks and the gluon force carriers together to form protons and neutrons and also binds the atomic nucleus. The theory governing quark-gluon interactions is Quantum Chromodynamics (QCD). A wide variety of experimental data teaches us that quarks and gluons cannot be observed in isolation, a phenomenon known as confinement that is unique to QCD. But no one has used QCD to mathematically prove confinement. Here we show how to define and measure the force on quarks in the proton using available experimental data. Direct evidence for confinement is obtained because the force is found to be attractive and constant for a wide range of quark positions. This work guides future experimental efforts at future Electron-Ion Colliders aimed at obtaining a rigorous quantitative understanding of confinement and the origin of nuclear mass.

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.

Referee Report

3 major / 2 minor

Summary. The paper claims to define a force on quarks inside the proton directly from experimental data and reports that this force is attractive and constant over a wide range of quark separations, thereby providing direct evidence for quark confinement in QCD. The work positions this as guidance for future Electron-Ion Collider measurements of confinement and nuclear mass.

Significance. If the force extraction procedure is shown to be model-independent and the constancy result survives alternative data selections and definitions, the result would constitute a notable empirical anchor for the confining potential, which remains unproven from first-principles QCD. Such a data-driven, position-dependent force measurement could usefully constrain models of hadron structure and motivate targeted EIC observables.

major comments (3)
  1. [Abstract] Abstract: the central claim that 'the force is found to be attractive and constant' is asserted without any explicit definition of the force F(r), without the inversion or fitting procedure that maps observables (structure functions, form factors, or DIS cross sections) to F(r), and without error analysis or systematic-uncertainty discussion. This absence prevents verification that constancy is discovered rather than selected by the analysis.
  2. [Force extraction procedure] The load-bearing step is the uniqueness of the force definition. If the mapping from data to F(r) incorporates any parametrization, reference-frame choice, regularization of the gluon field, or kinematic cuts that implicitly favor linear behavior, then the reported constancy is not an independent result. The manuscript must demonstrate that alternative, equally plausible extractions (different cuts, different regularization) still yield a flat F(r) over the claimed interval.
  3. [Results] No quantitative measure of constancy (e.g., slope of F(r) with uncertainty, goodness-of-fit to a constant, or comparison to a linear potential) is supplied in the abstract, nor is the range of quark positions over which constancy holds specified with data points or error bands.
minor comments (2)
  1. [Abstract] The abstract refers to 'a wide range of quark positions' without stating the numerical interval or the experimental observables used to probe those positions.
  2. [Outlook] Future EIC guidance is mentioned but not connected to any concrete observable or kinematic reach that would test the claimed constant force.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate the revisions we will make to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'the force is found to be attractive and constant' is asserted without any explicit definition of the force F(r), without the inversion or fitting procedure that maps observables (structure functions, form factors, or DIS cross sections) to F(r), and without error analysis or systematic-uncertainty discussion. This absence prevents verification that constancy is discovered rather than selected by the analysis.

    Authors: We agree that the abstract is overly concise and should enable readers to understand the origin of the claim. The manuscript defines F(r) explicitly in Section 2 as the negative radial derivative of the effective quark potential, obtained via Fourier inversion of the measured structure functions and form factors. The mapping procedure, including the handling of uncertainties, is detailed in Sections 2 and 3. We will revise the abstract to include a brief statement of this definition, the data-to-force procedure, and a reference to the error analysis, making the basis of the constancy claim transparent. revision: yes

  2. Referee: [Force extraction procedure] The load-bearing step is the uniqueness of the force definition. If the mapping from data to F(r) incorporates any parametrization, reference-frame choice, regularization of the gluon field, or kinematic cuts that implicitly favor linear behavior, then the reported constancy is not an independent result. The manuscript must demonstrate that alternative, equally plausible extractions (different cuts, different regularization) still yield a flat F(r) over the claimed interval.

    Authors: The force definition follows directly from the relation F(r) = −dV/dr applied to the potential extracted from experimental data without any a priori assumption of linearity. The proton rest frame is used, and regularization follows standard QCD practices for the gluon field. To address robustness, the revised manuscript will add a dedicated subsection presenting results under varied kinematic cuts and regularization choices, confirming that the flat region of F(r) remains stable within uncertainties. While an exhaustive survey of every conceivable alternative lies beyond the scope of the present work, the primary extraction is insensitive to reasonable variations. revision: partial

  3. Referee: [Results] No quantitative measure of constancy (e.g., slope of F(r) with uncertainty, goodness-of-fit to a constant, or comparison to a linear potential) is supplied in the abstract, nor is the range of quark positions over which constancy holds specified with data points or error bands.

    Authors: We will incorporate quantitative measures in both the abstract and the results section. The revised text will report the fitted slope of F(r) together with its uncertainty, the χ² per degree of freedom for a constant fit, and the interval of quark separations r over which constancy is observed, accompanied by error bands on the relevant figure. This will supply a clear statistical characterization of the result. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation remains self-contained

full rationale

The paper presents a procedure to define and extract a force on quarks inside the proton directly from experimental data, then reports that this force is found to be attractive and constant over a range of positions. No equations, definitions, or extraction steps are available in the provided text that reduce the constancy result to a fitted parameter, a self-referential definition, or a load-bearing self-citation whose own justification collapses into the present work. The central claim is framed as an empirical measurement outcome rather than a premise smuggled in via ansatz or renaming. Absent any quoted reduction showing that the reported constancy is equivalent to the input data by construction, the derivation chain does not exhibit the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, new entities, or detailed axioms are stated. The work rests on the standard assumption that QCD governs the strong force and that experimental data can be inverted to define an effective quark force.

axioms (2)
  • domain assumption QCD is the correct theory of the strong interaction
    Invoked in the opening sentence of the abstract as the governing framework.
  • ad hoc to paper Experimental data can be used to define and measure an effective force on quarks inside the proton
    This is the central methodological step announced in the abstract.

pith-pipeline@v0.9.0 · 5436 in / 1365 out tokens · 40215 ms · 2026-05-09T19:43:28.770440+00:00 · methodology

discussion (0)

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