{"id":"4076ab69-e2ad-413e-8b66-6e43ab4101ac","arxiv_id":"2509.01902","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Ω3cNN and Ω3cΩ3cN are found unbound in S-wave Faddeev calculations with HAL QCD potentials, with only fragile near-threshold resonance estimates for Ω3cnp.","lead":"This paper runs three-body Faddeev calculations with lattice QCD-derived two-body potentials to test whether a triply charmed Omega baryon can form a tribaryon with two nucleons, or with another Omega and a nucleon. It finds no bound states and estimates near-threshold resonances for the charm-3 system, though the quoted resonance energies shift across the lattice-time parameter and the text and table disagree on which spin state is which.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Short-range attraction in the HAL QCD Ω3cN potential is the load-bearing input: the predicted resonances sit within ~20% of critical binding, and the paper's own modified potential (Fig. 3) is never tested in the Faddeev equations.","rationale":"The reader's weakest assumption correctly identifies the short-range Ω3cN interaction. I agree that the no-bound-state part of the paper is the stable core: it follows directly from the unbound two-body Ω3cN system plus the NN attraction being insufficient to bind, and it is consistent across t/a. The fragile part is the near-threshold resonance claim. The paper's own Fig. 3 and Summary concede that a repulsive core is expected from QCD, yet the reported resonance energies are computed only with the HAL QCD potential with its deep attractive core. Because the system is within ~20% of critical coupling, a small change in core strength can change the qualitative conclusion. The proposed Faddeev test with the Fig. 3 potential is the missing computation that would settle the concern. I also note minor reporting issues (abstract vs Table II state assignment, 't/a=1.6' typo, and the reference frame for the -1.1 MeV value), but these are secondary to the short-distance sensitivity. The conditional verdict is therefore appropriate; no further adjustment is needed.","tokens_in":10648,"tokens_out":9295,"duration_ms":104334,"concrete_test":"Re-run the configuration-space Faddeev calculation of Sec. III using the modified Ω3cN potential displayed in Fig. 3 (or a one-parameter family of two-range Gaussians constrained to the same a0 and reff but with the r≲0.5 fm core strength capped or sign-flipped), and extract the resonance energy by the same ACCC exponential extrapolation at t/a=16. If the (0)1/2+ and (0)5/2+ states cease to be near-threshold, the headline resonance claim is driven by the unphysical short-range core; if they persist, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claims are the near-threshold resonances in Table II. These are controlled by the deep, narrow attractive core of the Ω3cN potential: for the 3S1 channel at t/a=16, Table I gives α1=-118.9 MeV with β1=0.142 fm, i.e. a strong short-range attraction at r far below the hadron size (~0.8 fm). The paper itself argues in the Fig. 3 discussion and in the Summary that QCD color-field overlap should produce a repulsive core, and it constructs a modified two-range Gaussian with the same low-energy parameters (a0≈0.57 fm, reff≈1.77 fm) but substantially reduced short-range attraction. However, that modified potential is never propagated through the Faddeev equations. This matters because the physical point is close to critical: the text states that a bound three-body state appears only for γ≤0.2 in Eq. (4), so a modest reduction of the short-range attraction can push the extrapolated state across threshold or remove the pole. The no-bound-state statement is robust, but the 'prediction' of near-threshold resonances rests on the least-trusted part of the input potential, and the paper explicitly flags that part as expected to be repulsive.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":11036,"tokens_out":4994,"duration_ms":53640,"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":[{"comment":"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.","section":"Abstract, Summary, and Table II"},{"comment":"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.","section":"Eq. (4) and Fig. 2"},{"comment":"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.","section":"Fig. 3 and Summary"},{"comment":"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.","section":"Table II and sign convention"}],"minor_comments":[{"comment":"The Summary says 't/a = 1.6'; this should be 't/a = 16'.","section":"Summary"},{"comment":"There is a typo: 'presnts' should be 'presents'.","section":"Theoretical approach"},{"comment":"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.","section":"Fig. 1/Fig. 2 cross-reference"},{"comment":"The caption contains 'tlattice Euclidean time' and a period in 'Table.'; these are typographical errors.","section":"Table I caption"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"We've been going back and forth on this one. The direct result—no bound Ω3cnp or Ω3cΩ3cN in the Faddeev calculation with the HAL QCD potentials—is straightforward and, as far as I can tell, correct. It holds at all three t/a values. That part deserves to be published. What doesn't sit well is the headline resonance claim.\n\nThe resonances are extracted by scaling the Ω3cN potential by (1+γ), computing bound three-body energies for γ>0, and fitting f(γ)=Ae^{αγ}+B to extrapolate to γ=0. That's the analytic-continuation-in-coupling-constant trick, which can work, but here the values are unstable: the extracted energy changes sign across t/a=16,17,18. When your 'prediction' flips from -1.1 to +0.1 MeV across equivalent lattice times, you have an uncertainty estimate problem, not a prediction. The paper acknowledges the instability but then insists on 'predict' in the abstract.\n\nWorse, the abstract and summary say the 5/2+ state sits at -1.1 MeV and the 1/2+ at 0.0, while Table II has the opposite assignment. And -1.1 MeV relative to the three-body breakup threshold is literally a bound state, contradicting the paper's own no-bound-state conclusion. There's a reference-frame ambiguity (Fig. 2 plots relative to the Ω3c-d threshold), but as written it reads as an internal contradiction.\n\nThe stress-test is right about the short-distance behavior. The Ω3cN potential has a deep narrow attractive core at r<0.8 fm. The resonances live within ~20% of critical binding. The paper itself argues that color-field overlap should produce a repulsive core, constructs a modified potential in Fig. 3 with the same low-energy parameters, and then never runs it through the Faddeev equations. That is the obvious next step, and its absence leaves the resonance claim resting on the least-trusted part of the input.\n\nThe Faddeev machinery, the treatment of identical particles, and the use of external lattice potentials are all competent. The citation to Refs. [25,26] is proper. This is honest work; it just overreaches in the resonance claim.\n\nSo: send it to peer review, but the referee should insist on fixing the state assignment and reference frame, adding error bars from the exponential-fit instability, and either testing the modified potential or dropping 'predict' to 'estimate'. For the audience—people doing heavy-quark few-body and femtoscopy—the no-bound-state result is the useful part.","headline":"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.","tokens_in":11600,"tokens_out":4771,"would_cite":false,"duration_ms":50438,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"No bound Ω3cNN tribaryon; near-threshold resonances appear instead.","keywords":["triply charmed Omega baryon","tribaryon","HAL QCD potential","Faddeev equations","near-threshold resonance","lattice QCD","Ω3cNN system","Ω3cΩ3cN system"],"falsifier":"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.","tokens_in":10503,"feed_emoji":"⚛️","tokens_out":8969,"duration_ms":91292,"temperature":0.7,"pith_summary":"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.","feed_headline":"Triply charmed Omega plus two nucleons refuses to bind","feed_subtitle":"Faddeev calculation with lattice potentials finds only near-threshold resonances, not a bound tribaryon.","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the S-wave Ω3cN potentials in the 3S1 and 5S2 channels, the central two-body input for both tribaryon systems.","marker":"[25]"},{"why":"Supplies the Ω3cΩ3c potential in the 1S0 channel and the bound dibaryon used in the Ω3cΩ3cN calculation.","marker":"[26]"},{"why":"Supplies the MT-I-III nucleon-nucleon potential used as the identical-particle interaction in the Ω3cnp Faddeev equations.","marker":"[33]"},{"why":"Introduces the Faddeev equations for the three-particle problem that the calculation solves.","marker":"[28]"},{"why":"Provides the configuration-space solution method for three-body scattering used to obtain the numerical results.","marker":"[31]"},{"why":"Supplies the analytic continuation in the coupling constant, the method used to locate and extrapolate the near-threshold resonances.","marker":"[50]"}],"fun_headline_variants":["Charm-3 Omega tribaryon refuses to bind","No bound Ω3cNN from lattice QCD potentials","Ω3cNN: only near-threshold resonances, no binding","Triply charmed Omega + double nucleon: no bound state","Faddeev with HAL QCD: no Ω3cNN bound"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Charm-3 Omega tribaryon refuses to bind","No bound Ω3cNN from lattice QCD potentials","Ω3cNN: only near-threshold resonances, no binding","Triply charmed Omega + double nucleon: no bound state","Faddeev with HAL QCD: no Ω3cNN bound"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000317,"raw_usage":{"total_tokens":1674,"prompt_tokens":834,"completion_tokens":840,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":578,"completion_tokens_details":{"reasoning_tokens":750}},"tokens_in":578,"tokens_out":840,"duration_ms":7347,"temperature":1.0,"reasoning_tokens":750,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T12:05:11.129914+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Malfliet and J","cited_arxiv_id":null,"evidence_quote":"Supplies the MT-I-III nucleon-nucleon potential used as the identical-particle interaction in the Ω3cnp Faddeev equations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the Faddeev equations for the three-particle problem that the calculation solves."},{"cited_title":"Gignoux, C","cited_arxiv_id":null,"evidence_quote":"Provides the configuration-space solution method for three-body scattering used to obtain the numerical results."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the analytic continuation in the coupling constant, the method used to locate and extrapolate the near-threshold resonances."}],"review_version":1}