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arxiv: 2504.08631 · v2 · submitted 2025-04-11 · ⚛️ nucl-th · hep-ex· hep-lat· hep-ph· nucl-ex

Can the strong interactions between hadrons be determined using femtoscopy?

Evgeny Epelbaum , Sven Heihoff , Ulf-G. Mei{\ss}ner , Alexander Tscherwon This is my paper

Pith reviewed 2026-05-22 20:34 UTC · model grok-4.3

classification ⚛️ nucl-th hep-exhep-lathep-phnucl-ex
keywords femtoscopyhadron interactionscorrelation functionsKoonin-Pratt formulastrong interactionsheavy-ion collisionssource termnuclear forces
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The pith

Femtoscopic measurements of strong hadron interactions suffer from large intrinsic uncertainties due to non-universal source terms.

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

The paper examines whether femtoscopic data from heavy-ion collisions can reliably determine the strong interactions between hadrons. It centers on the Koonin-Pratt formula that links observed correlation functions to the final-state wave function and a source term for pair production. The analysis demonstrates that the common assumption of a universal source introduces potentially large uncertainties when the particles interact strongly, as with nucleons. A reader would care because this technique is widely applied to study hadron forces, yet the results may not be as clean as assumed. The work also notes ongoing attempts to apply the same method to three-body interactions.

Core claim

The interpretation of femtoscopic measurements suffers from a potentially large intrinsic uncertainty for strongly interacting particles such as nucleons, because the source term describing the production mechanism of hadron pairs cannot be treated as universal without introducing significant errors in the extracted interactions.

What carries the argument

The Koonin-Pratt formula, which relates measured two-hadron correlation functions to the relative wave function of an outgoing pair and a source term assumed to be universal across different interactions.

If this is right

  • Extracted two-body strong interactions from femtoscopic data carry potentially large errors for nucleons and similar particles.
  • The same source-term uncertainty affects attempts to determine three-body interactions using this technique.
  • Phenomenological modeling of the source must be refined to account for dependence on the final-state interaction strength.
  • Results for weakly interacting pairs may remain more reliable than those for strongly interacting ones.

Where Pith is reading between the lines

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

  • Direct lattice QCD calculations of correlation functions without an assumed source could provide an independent check on extracted interactions.
  • Varying collision systems or energies to map source variations experimentally might quantify the size of the uncertainty.
  • Combining femtoscopic data with other observables, such as scattering lengths from different experiments, could help isolate interaction effects from source effects.

Load-bearing premise

The source term describing the production mechanism of hadron pairs is universal and can be modeled phenomenologically without introducing large uncertainties in the extracted interactions for strongly interacting particles.

What would settle it

A direct comparison of source parameters extracted from correlation data for nucleon pairs versus non-interacting pairs, or a microscopic calculation showing interaction-dependent changes in the effective source size or shape exceeding a few percent, would test whether the universality assumption holds.

Figures

Figures reproduced from arXiv: 2504.08631 by Alexander Tscherwon, Evgeny Epelbaum, Sven Heihoff, Ulf-G. Mei{\ss}ner.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color online). S-, P-, D- and F-wave phase shifts [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (Color online). Correlation functions calculated by [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (Color online). S-wave momentum-space matrix el [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (Color online). Neutron-deuteron total cross section [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

In the last decades, femtoscopic measurements from heavy-ion collisions have become a popular tool to investigate the strong interactions between hadrons. The key observables measured in such experiments are the two-hadron momentum correlations, which depend on the production mechanism of hadron pairs and the final-state interactions. Given the complexity of ultra-relativistic collision experiments, the source term describing the production mechanism can only be modeled phenomenologically based on numerous assumptions. The commonly employed approach for analyzing femtoscopic data relies on the Koonin-Pratt formula, which relates the measured correlation functions with the relative wave function of an outgoing hadron pair and a source term that is assumed to be universal. Here, we critically examine this universality assumption and show that for strongly interacting particles such as nucleons, the interpretation of femtoscopic measurements suffers from a potentially large intrinsic uncertainty. We also comment on the ongoing efforts to explore three-body interactions using this experimental technique.

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

1 major / 2 minor

Summary. The manuscript critically examines the Koonin-Pratt formula employed in femtoscopic analyses of heavy-ion collisions. It argues that the assumption of a universal source term for the production mechanism of hadron pairs is invalid for strongly interacting particles such as nucleons, leading to potentially large intrinsic uncertainties in the extracted strong-interaction parameters. The work contrasts phenomenological source modeling with the requirements imposed by final-state interactions and offers comments on ongoing three-body interaction studies.

Significance. If the non-universality argument holds, the result would caution against over-interpreting femtoscopic correlation functions as direct probes of strong hadron interactions, particularly for nucleons, and would motivate more careful source modeling or alternative extraction methods. The paper provides a timely critical perspective on a widely used technique without introducing new data or derivations.

major comments (1)
  1. [§4] §4 (or equivalent section presenting the nucleon example): the claim of 'potentially large intrinsic uncertainty' is supported by contrasting source assumptions but would benefit from a quantitative bound or sensitivity study showing how much the extracted scattering length or effective range shifts under plausible non-universal source variations.
minor comments (2)
  1. [Abstract] The abstract states the conclusion without referencing the specific section or figure that demonstrates the non-universality; a cross-reference would improve readability.
  2. [Introduction] Notation for the source function S(r) and the wave function should be defined explicitly at first use to avoid ambiguity with standard femtoscopy literature.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the point raised below.

read point-by-point responses

  1. Referee: [§4] §4 (or equivalent section presenting the nucleon example): the claim of 'potentially large intrinsic uncertainty' is supported by contrasting source assumptions but would benefit from a quantitative bound or sensitivity study showing how much the extracted scattering length or effective range shifts under plausible non-universal source variations.

    Authors: We agree that a quantitative sensitivity study would strengthen the presentation of the intrinsic uncertainty. In the revised manuscript we will augment §4 with an explicit sensitivity analysis for the nucleon example. This will report the variation in the extracted scattering length and effective range obtained when the source function is varied across the range of non-universal profiles already contrasted in the text, thereby providing the requested quantitative bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper critically examines the universality assumption in the Koonin-Pratt formula without presenting any derivation that reduces to fitted inputs or self-citations by construction. Its central argument contrasts phenomenological source modeling with final-state interaction requirements for nucleons to highlight potential uncertainty, relying on physical reasoning rather than self-definitional steps, fitted predictions, or load-bearing self-citations. No equations or claims in the provided text exhibit the enumerated circularity patterns, making the analysis self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the source term is not universal for strongly interacting hadrons, which is invoked to conclude large intrinsic uncertainty in interaction extraction.

axioms (1)
  • domain assumption The Koonin-Pratt formula relates measured correlation functions to the relative wave function and a universal source term.
    Stated in the abstract as the commonly employed approach for analyzing femtoscopic data.

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discussion (0)

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