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REVIEW 4 major objections 4 minor 52 references

On $\Omega_{3c}NN$ and $\Omega_{3c} \Omega_{3c} N$ systems with HAL QCD potentials

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read No bound Ω3cNN tribaryon; near-threshold resonances appear instead.

desk verdict The no-bound-state Faddeev result is solid, but the resonance energies are unstable extrapolations that the paper itself undermines; treat the headline as an estimate, not a prediction. read the letter →

arxiv 2509.01902 v1 pith:C7FYYKRN submitted 2025-09-02 nucl-th hep-lat

Igor Filikhin , Roman Ya. Kezerashvili , Branislav Vlahovic This is my paper
classification nucl-thhep-lat
keywords triplycharmedOmegabaryontribaryonHALQCDpotentialFaddeevequationsnear-thresholdresonancelatticeΩ3cNNsystemΩ3cΩ3cN
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether a triply charmed omega baryon (Ω3c) can form a three-body bound cluster with two nucleons, or with another Ω3c plus a nucleon. Using S-wave Ω3cN potentials derived from lattice QCD, the standard MT-I-III nucleon-nucleon potential, and Faddeev equations in configuration space, it finds no bound states in either system, with the Coulomb force neglected. It does predict near-threshold resonances for Ω3cnp: about 1.1 MeV below the three-body breakup threshold in the maximal-spin 5/2+ state and essentially at threshold in the 1/2+ state, at lattice time t/a=16; for Ω3cΩ3cN the possible resonance sits well above threshold. The paper also argues that the deep short-range attraction of the input Ω3cN potential, on length scales inside a nucleon, is physically suspect and may be replaced by a repulsive core in the real interaction.

What carries the argument

The load-bearing input is the two-range Gaussian fit VΩ3cN(r) = α1 e^{-(r/β1)^2} + α2 e^{-(r/β2)^2} to the lattice Ω3cN interaction, with a deep, narrow attractive well (α1 ≈ -119 MeV, β1 ≈ 0.14 fm in the 3S1 channel) that determines whether three-body binding is possible. The three-body dynamics are handled by the Faddeev equations in configuration space, with a two-channel decomposition into (Ω3c)(NN) and (Ω3cN)N rearrangements, and resonance energies are extracted by analytic continuation in the coupling constant: scaling the potential by (1+γ), locating bound states for γ > 0, and exponentially interpolating back to γ = 0.

What would settle it

A higher-resolution lattice QCD calculation of the Ω3cN potential at r < 0.5 fm would settle the short-range question: a repulsive core instead of the Table I well would remove the resonances. Alternatively, a direct three-body scattering calculation with the same potentials should reproduce the same near-threshold poles; if no poles appear in the physical amplitude, the extrapolated resonance claim fails.

Watch

Extended reading notes

Core claim

The paper's central finding is that the charm-3 tribaryon Ω3cnp is not bound: solving the Faddeev equations in configuration space with the HAL QCD Ω3cN potentials in the 3S1 and 5S2 channels and the MT-I-III NN potential yields no bound-state solution for the 1/2+ and 5/2+ spin states at t/a = 16, 17, or 18. Instead, by scaling the Ω3cN potential and extrapolating three-body energies back to the physical coupling, the paper finds near-threshold resonances: 1.1 MeV below the breakup threshold for Jπ=5/2+ and 0.0 MeV at threshold for Jπ=1/2+ at t/a=16, with values drifting by about a MeV across lattice times. The same analysis of Ω3cΩ3cN gives no bound state and only a tentative resonance rou

Load-bearing premise

The near-threshold resonance prediction rests on trusting the very deep attractive core of the lattice Ω3cN potential at separations below about 0.8 fm; if the true interaction is repulsive there, the resonances can disappear.

Editorial extensions

If this is right

  • The Ω3cnp system should not be hunted as a sharp bound tribaryon; the expected signal is an enhancement within about 1 MeV of the three-body breakup threshold.
  • The resonance positions shift by roughly 1 MeV between t/a = 16 and 18, so the quantitative energies are not converged and need larger Euclidean-time potentials.
  • If the true short-range Ω3cN interaction is repulsive rather than deeply attractive, the near-threshold resonances disappear, making the prediction a direct probe of the short-distance part of the potential.
  • The Ω3cΩ3cN system appears unbound at this level; its possible resonance sits far above threshold and is a much weaker prediction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the authors' short-range repulsion argument is right, a modified Ω3cN potential with the same scattering length but a repulsive core should be tested in the same Faddeev calculation; the expectation is that the near-threshold resonances vanish.
  • A femtoscopic measurement of Ω3c-deuteron or Ω3c-pn correlations in heavy-ion collisions would be a natural experimental test, but the paper computes only resonance energies, not correlation functions.
  • The no-bound conclusion is tied to the HAL QCD Ω3cN potential; using a quark-model Ω3cN interaction that already binds the two-body system would likely produce a bound tribaryon, so the result is potential-specific.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This paper reports configuration-space Faddeev calculations for the Ω3cN N and Ω3cΩ3cN tribaryon systems, using the HAL QCD Ω3cN potentials of Ref. [25], the Ω3cΩ3c potential of Ref. [26], and the MT-I–III NN potential, with Coulomb neglected. The direct calculations find no bound Ω3cnp state for t/a = 16, 17, 18, nor a bound Ω3cΩ3cN state. To explore resonances, the authors scale the Ω3cN potential by (1+γ), compute three-body bound-state energies for γ > 0, and extrapolate to γ = 0 with f(γ) = A e^{αγ}+B. This yields the paper's central quantitative claims: near-threshold resonances in the Jπ = 1/2+ and 5/2+ channels, with energies at t/a = 16 of -1.1 MeV and 0.0 MeV relative to threshold, and a possible Ω3cΩ3cN resonance near 9.5 MeV. The paper also discusses why the short-range part of the HAL QCD Ω3cN potential is physically questionable, presenting a modified potential with reduced short-range attraction.

Significance. The no-bound-state result for Ω3cnp with the given potentials is a useful, concrete benchmark, and the Faddeev implementation appears standard and reproducible from the cited potentials. If the near-threshold resonances were established, they would be of genuine interest for heavy-flavor few-body physics. However, the resonance prediction rests on an exponential extrapolation in the coupling constant whose numerical results change sign across the three lattice Euclidean times, and the paper's own short-distance discussion undermines the very part of the input that controls the near-threshold behavior. The manuscript therefore does not currently establish its headline quantitative claim, though the underlying calculation and the critical discussion of the potential are valuable.

major comments (4)
  1. [Abstract, Summary, and Table II] The spin assignments in the Abstract and Summary are reversed relative to Table II. For t/a = 16, Table II gives -1.1 MeV for (0)1/2+ and 0.0 MeV for (0)5/2+. The Abstract instead states that 5/2+ has the 1.1 MeV resonance and 1/2+ is at threshold, and the Summary repeats this mismatch. This is a factual error in the paper's headline result and must be corrected.
  2. [Eq. (4) and Fig. 2] The resonance energies are not computed directly but are the γ = 0 values of f(γ) = A e^{αγ}+B fitted to bound-state energies for scaled attractive potentials. The paper does not report the number or range of γ values used, the fit quality, or uncertainties. Table II shows that the extrapolated values change sign across t/a: -1.1, -0.7, 0.1 and 0.0, -0.5, 0.2. A prediction that switches from below to above threshold depending on t/a is not stable enough to support the stated quantitative claim.
  3. [Fig. 3 and Summary] The paper itself argues that a repulsive core should appear at short distances in the Ω3cN potential and constructs a modified two-range Gaussian with compatible low-energy parameters (a0 ≈ 0.57 fm, reff ≈ 1.77 fm) but substantially reduced short-range attraction. This modified potential is never propagated through the Faddeev equations. Since the text notes that a three-body bound state appears only for γ ≤ 0.2, the physical point is close to critical binding; a modest reduction of the deep attractive core could move the extrapolated state across threshold. The resonance claim therefore rests on the least-trusted part of the input, and the proposed test is left undone.
  4. [Table II and sign convention] Negative energies in Table II are labeled 'resonance energies' relative to the three-body breakup threshold. A negative energy relative to the three-body breakup threshold is a bound state, not a resonance, and would contradict the paper's no-bound-state conclusion. If the energies are instead relative to the Ω3c-d two-body threshold, that must be stated in Table II and used consistently in the Abstract and Summary. As written, the sign convention and reference threshold are internally inconsistent.
minor comments (4)
  1. [Summary] The Summary says 't/a = 1.6'; this should be 't/a = 16'.
  2. [Theoretical approach] There is a typo: 'presnts' should be 'presents'.
  3. [Fig. 1/Fig. 2 cross-reference] In the interaction section, the sentence 'The HAL QCD Ω3cΩ3c potential ... are shown in Fig. 2' appears to refer to Fig. 1, since Fig. 2 displays the resonance-energy extrapolations; the cross-reference should be corrected.
  4. [Table I caption] The caption contains 'tlattice Euclidean time' and a period in 'Table.'; these are typographical errors.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: inputs are external HAL QCD potentials; resonance extraction is an extrapolation, not a fitted prediction; self-citations are non-load-bearing.

full rationale

The paper's chain is: take HAL QCD Ω3cN and Ω3cΩ3c potentials from Refs [25,26] and the MT-I-III NN potential; solve the Faddeev equations in configuration space; solve for bound states; and use analytic continuation in the coupling constant (ACCC) to locate near-threshold resonances. Each stage uses external inputs and standard, independently documented methods (Faddeev refs [28,31,32]; ACCC refs [50-52]). The no-bound-state statement is a direct solution of the coupled equations, not a fit. The resonance energies are extrapolated from bound-state energies computed for deepened potentials Vγ=V(1+γ) using f(γ)=Ae^{αγ}+B; the constants A, B, and α are determined from computed E3 at nonzero γ, and the physical γ=0 value is not used as a fitting datum. This is an extrapolation, not a fitted parameter renamed as a prediction. Self-citations (Refs [18,42-48]) supply the authors' prior Faddeev implementations and applications, but the formalism is also supported by standard external references, so they are not load-bearing. The paper itself flags the interpolation sensitivity and the expected short-range repulsive core; these are genuine robustness caveats about the input potential and extrapolation, not circularity. No reduction of the central claim to its inputs by definition or self-citation was found.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central numbers rest on fitted potentials imported from two lattice papers [25,26] and on an exponential extrapolation defined in this paper. The no-bound-state result is a direct Faddeev consequence and is robust across t/a; the resonance energies are extrapolations of fitted curves. No new entities are postulated.

free parameters (4)
  • VΩ3cN two-range Gaussian parameters (α1, β1, α2, β2), 3S1 and 5S2 at t/a=16,17,18 = e.g., 3S1 at t/a=16: α1=-118.9(1.6) MeV, β1=0.142(7) fm, α2=-85.7(2.6) MeV, β2=0.633(33) fm
    Fitted in Ref. [25] to lattice HAL QCD potentials; the three-body resonance energies in Table II vary from -1.1 to +0.2 MeV across the t/a values, so the results depend critically on which fitted set is used.
  • VΩ3cΩ3c three-range Gaussian parameters = α1=239, β1=48.5, α2=-62.7, β2=7.8, α3=-98.8, β3=3.4 (MeV and fm units, t/a=26)
    Fitted in Ref. [26]; drives the Ω3cΩ3cN calculation.
  • Exponential interpolation parameters A, α, B in f(γ)=A exp(α γ)+B = not quoted in paper
    Fitted to computed three-body energies at several γ values; the reported resonance energies are the value of this fitted curve at γ=0, and the paper states the Ω3cΩ3cN estimate (~9.5 MeV) depends sensitively on the interpolation choice.
  • Hypothetical modified Ω3cN potential parameters (Fig. 3) = chosen to give a0=0.57 fm, reff=1.77 fm
    Ad hoc potential used only for the short-distance discussion to illustrate what a potential with reduced short-range attraction looks like; not used for the main three-body results.
assumptions (6)
  • domain assumption Faddeev equations in configuration space with S-wave truncation (all orbital angular momenta zero) describe the three-body dynamics
    Used throughout 'Theoretical approach'; higher partial waves and tensor forces are omitted; for near-threshold S-wave states this is customary but not justified in the text.
  • domain assumption HAL QCD potentials are local, energy-independent two-body potentials valid as inputs to nonrelativistic Schrödinger/Faddeev equations
    VΩ3cN from Ref. [25] and VΩ3cΩ3c from Ref. [26] are used as local Gaussians; HAL QCD extractions carry systematic uncertainties from the derivative expansion and time dependence, discussed only briefly.
  • domain assumption Coulomb interaction between Ω3c (charge +2) and proton can be neglected
    Stated in the Abstract ('neglecting the Coulomb force'); for near-threshold resonances within 1 MeV of threshold, the repulsive Coulomb barrier could be relevant, but no estimate is given.
  • domain assumption MT-I-III NN potential is adequate in this S-wave three-body model
    Used for VNN; the paper notes it reproduces low-energy NN parameters and three-nucleon properties within an S-wave model (Introduction/Interactions).
  • ad hoc to paper Analytic continuation in the coupling constant with exponential interpolation f(γ)=A e^{αγ}+B recovers the physical resonance energy at γ=0
    Equations (4) and the interpolation in Fig. 2; the extrapolated values are used as 'predicted' resonance energies, while the paper acknowledges sensitivity to the interpolation choice and instability across t/a.
  • standard math The two nucleons in Ω3cnp can be treated as identical fermions via isospin with antisymmetrization operator P
    Faddeev system (3) with Ψ = Φ1 + Φ2 - P Φ2; standard isospin treatment, but n and p are physically distinct and charge effects beyond Coulomb are ignored.

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Pith. "Pith review of On $\Omega_{3c}NN$ and $\Omega_{3c} \Omega_{3c} N$ systems with HAL QCD potentials." pith.science (2026). https://pith.science/paper/C7FYYKRN

@misc{pith2026250901902,
  author       = {Pith},
  title        = {Pith review of: On $\Omega_3cNN$ and $\Omega_3c \Omega_3c N$ systems with HAL QCD potentials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C7FYYKRN}},
  note         = {Machine review of arXiv:2509.01902}
}
abstract

This study employs the Faddeev formalism in configuration space to investigate the $\Omega_{3c}NN$ cluster containing a triply charmed Omega baryon ($\Omega_{3c}$). Using the recently reported HAL QCD $S$-wave $\Omega_{3c}N$ potentials in the $^3S_1$ and $^5S_2$ channels, together with the MT-I--III nucleon--nucleon potential and neglecting the Coulomb force, we find no bound state for the $\Omega_{3c}np$ system. We predict near-threshold resonances in the $J^{\pi}=5/2^{+}$ (maximal total spin) and $J^{\pi}=1/2^{+}$ (minimal total spin) states, with resonance energies of $1.1~\mathrm{MeV}$ below and $0.0~\mathrm{MeV}$ at the three-body breakup threshold, respectively, at Euclidean time $t/a = 16$. A similar analysis of the $\Omega_{3c}\Omega_{3c}N$ system likewise reveals no bound states, though a possible resonance is indicated. The short-distance behavior of the HAL QCD $\Omega_{3c}N$ potential is also discussed.

Figures

Figures reproduced from arXiv: 2509.01902 by the authors.

Figure 1
Figure 1. FIG. 1. HAL QCD Ω [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Modified Ω [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.