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arxiv: 2504.04655 · v1 · submitted 2025-04-07 · ⚛️ nucl-th · hep-lat

Examination of the lattice QCD-motivated strong attractive Ω N potentials in the Ω^- n p system

I. Filikhin , R. Ya. Kezerashvili , B. Vlahovic This is my paper

Pith reviewed 2026-05-22 21:27 UTC · model grok-4.3

classification ⚛️ nucl-th hep-lat
keywords Omega N potentialsFaddeev equationsthree-body bindinglattice QCDCoulomb forcehyperon interactionsABC modelshort-range attraction
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0 comments X

The pith

The large binding energy of the Ω−np system arises from the short-range behavior of the ΩN potentials.

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

The authors solve the Faddeev equations in configuration space for the Ω− n p system using lattice HAL QCD and Yukawa-type potentials for the ΩN interaction. They treat the particles as non-identical to include the attractive Coulomb force between Ω− and the proton. Results show that this Coulomb force has only a small perturbative effect, mainly shifting the binding energy by the two-body Coulomb contribution without much changing the spatial symmetry. The calculations differ from prior AAC model results and indicate that the strong short-range attraction in the ΩN potentials is what produces the large three-body binding energy.

Core claim

Within the ABC model for three non-identical particles, the Faddeev calculations demonstrate that the Ω−np system exhibits large binding driven by the short-range part of the strongly attractive ΩN potentials from lattice QCD, while the Coulomb interaction contributes only marginally by shifting the binding energy approximately equal to the Coulomb energy of the Ω−p pair and causing minor deviation from isosceles symmetry.

What carries the argument

The ABC model in Faddeev equations in configuration space applied to lattice-motivated ΩN potentials with included Coulomb force.

If this is right

  • The ABC model yields different low-energy characteristics for the ΩNN system than previous AAC calculations.
  • The Coulomb potential shifts the three-body binding energy by the Coulomb energy of the two-body BC subsystem.
  • The spatial configuration deviates only slightly from isosceles triangle symmetry due to the Coulomb force.
  • The strong ΩN interaction is the primary driver of both the binding energy and the spatial effects.

Where Pith is reading between the lines

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

  • If the short-range behavior dominates, refining lattice QCD potentials at short distances could significantly impact predictions for other hypernuclear systems.
  • Similar three-body calculations could test whether other meson-exchange or lattice potentials produce comparable binding without adjustable parameters.
  • The marginal role of Coulomb suggests that electromagnetic effects can be treated perturbatively in such systems for first approximations.

Load-bearing premise

The lattice HAL QCD and Yukawa-type potentials accurately describe the short-range ΩN interaction and the ABC Faddeev treatment correctly models the low-energy three-body physics including Coulomb.

What would settle it

An experimental measurement of the binding energy of the Ω−np system or a more precise lattice QCD simulation resolving different short-range potential details that leads to substantially lower binding energy.

Figures

Figures reproduced from arXiv: 2504.04655 by B. Vlahovic, I. Filikhin, R. Ya. Kezerashvili.

Figure 1
Figure 1. Figure 1: FIG. 1: The comparison of the Coulomb force and the Ω [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The schematics for the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The schematic representation of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The schematic representation of the Ω [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Within the framework of the Faddeev equations in configuration space, we examine the $\Omega^{-} np$ system, employing strongly attractive lattice HAL QCD and Yukawa-type meson exchange potentials for the $\Omega N$ interaction. Our formalism incorporates the attractive Coulomb force between the $\Omega^{-}$ and proton, treating the system as three non-identical particle pairs (the $ABC$ model). In this study, we assess the impact of the Coulomb interaction on the system and compare our results with recent $\Omega NN$ ($AAC$ model) calculations obtained using various approaches. The $ABC$ model yields low-energy characteristics for the \(\Omega NN\) system that differ from previous calculations. The Coulomb potential has a marginal perturbative effect on the $AAC$ system, shifting the three-body binding energy by the Coulomb energy of the two-body $BC$ subsystem, but only slightly deviating the spatial configuration from isosceles triangle symmetry. These effects are primarily driven by the strong \(\Omega N\) interaction. We demonstrate that the large binding energy of the $\Omega^{-} np$ system arises from the short-range behavior of the $\Omega N$ potentials.

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

2 major / 3 minor

Summary. The manuscript solves the Faddeev equations in configuration space for the Ω−np system (ABC model with non-identical particles) using lattice HAL QCD and Yukawa-type ΩN potentials that include strong short-range attraction. It incorporates the Ω−p Coulomb interaction, compares the resulting low-energy properties and binding energies to prior AAC-model calculations, assesses the perturbative role of Coulomb, and concludes that the large three-body binding energy is driven by the short-range part of the ΩN potentials.

Significance. If the central attribution holds, the work supplies a concrete numerical illustration of how lattice-QCD-motivated short-range ΩN attraction can produce substantial ΩNN binding, while clarifying the limited impact of Coulomb in the ABC versus AAC treatments. The direct use of externally supplied potentials and the Faddeev configuration-space approach are standard and reproducible in principle; the comparison across models adds value for the few-body community.

major comments (2)
  1. [Abstract / Conclusion] Abstract and concluding section: the central claim that 'the large binding energy of the Ω−np system arises from the short-range behavior of the ΩN potentials' is not secured by an explicit isolation of short-range versus long-range contributions. The calculations employ the full potentials and compare ABC versus AAC models, but contain no sensitivity test (e.g., short-range cutoff variation, core repulsion modification, or long-range tail truncation while holding the other fixed). Without such a test the attribution remains an interpretation rather than a demonstrated result.
  2. [Numerical results] Numerical results section: the reported binding energies and low-energy characteristics lack explicit error bars, convergence checks with respect to basis size or integration cutoff, and quantitative assessment of numerical stability. These omissions weaken in the quantitative differences quoted between ABC and AAC models and in the statement that Coulomb effects are 'marginal'.
minor comments (3)
  1. [Potential definitions] The manuscript should specify the precise functional forms and parameter values of the HAL QCD and Yukawa potentials (including any regularization) so that the calculations can be reproduced.
  2. [Introduction / Formalism] Notation for the ABC versus AAC models and for the particle labels (Ω−, n, p) should be introduced once and used consistently; occasional shifts between 'ΩNN' and 'Ω−np' are confusing.
  3. [Figures] Figure captions and axis labels should state the units and the precise observable plotted (e.g., binding energy in MeV, wave-function components).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment in turn below.

read point-by-point responses

  1. Referee: [Abstract / Conclusion] Abstract and concluding section: the central claim that 'the large binding energy of the Ω−np system arises from the short-range behavior of the ΩN potentials' is not secured by an explicit isolation of short-range versus long-range contributions. The calculations employ the full potentials and compare ABC versus AAC models, but contain no sensitivity test (e.g., short-range cutoff variation, core repulsion modification, or long-range tail truncation while holding the other fixed). Without such a test the attribution remains an interpretation rather than a demonstrated result.

    Authors: We thank the referee for this observation. The attribution in the abstract and conclusion rests on the fact that both the lattice HAL QCD and Yukawa potentials employed are dominated by strong short-range attraction, as motivated by the underlying lattice data, while the long-range parts are comparatively weak. The ABC versus AAC comparison and the marginal role of the long-range Coulomb force further support that the binding is driven by the short-range ΩN component. Nevertheless, we agree that an explicit sensitivity test would make the claim more robust. In the revised manuscript we will therefore add a brief paragraph discussing the potential shapes and the expected dominance of the short-range region, and we will soften the wording in the abstract and conclusion from 'demonstrate' to 'indicate'. revision: partial

  2. Referee: [Numerical results] Numerical results section: the reported binding energies and low-energy characteristics lack explicit error bars, convergence checks with respect to basis size or integration cutoff, and quantitative assessment of numerical stability. These omissions weaken in the quantitative differences quoted between ABC and AAC models and in the statement that Coulomb effects are 'marginal'.

    Authors: We agree that explicit convergence and stability information would strengthen the quantitative statements. In the revised manuscript we will add a dedicated subsection (or appendix) presenting convergence tests with respect to basis size and integration cutoff, together with an assessment of numerical stability under small parameter variations. Where feasible we will also supply estimated uncertainties on the binding energies and low-energy observables to support the reported differences between the ABC and AAC models and the assessment of Coulomb effects. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper obtains binding energies and spatial configurations by direct numerical solution of the Faddeev equations in configuration space, using externally supplied lattice HAL QCD and Yukawa-type ΩN potentials together with the Coulomb interaction. No parameter is fitted to three-body observables and then relabeled as a prediction; no quantity is defined in terms of itself; and no load-bearing step reduces to a self-citation chain or an ansatz smuggled from prior work by the same authors. The demonstration that binding arises from short-range behavior is an interpretation of the numerical output rather than a reduction by construction, leaving the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard few-body quantum mechanics and externally generated potentials; no new free parameters or postulated entities are introduced beyond the choice of input potentials.

axioms (2)
  • domain assumption The Faddeev equations in configuration space provide an accurate description of the three-body dynamics for the chosen potentials and Coulomb interaction.
    Invoked as the primary computational framework throughout the study.
  • domain assumption The lattice HAL QCD and Yukawa potentials faithfully represent the ΩN strong interaction at the distances relevant for binding.
    Used directly as input without further adjustment in the abstract description.

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