{"id":"223524d7-f4db-4085-b8ae-0c34838e8b0a","arxiv_id":"2509.01195","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The Omega_b* -> Omega_c* l nu semileptonic decay widths are predicted with QCD sum rules: about 2.5e-12 GeV for electron/muon channels and 0.71e-12 GeV for the tau channel, with R = 0.29.","lead":"This paper predicts how often an as-yet-unseen heavy particle, excited Omega_b, turns into a similar heavy particle, excited Omega_c, while emitting an electron, muon, or tau and a neutrino. It gives concrete numbers that a future collider experiment could check.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lorentz-structure set spread (~1.8x in Γ) is not included in the quoted errors, so the averaged widths are not robust SM benchmarks.","rationale":"The reader's weakest assumption was the spin-1/2 removal. That is a valid structural concern, but the paper's spin-1/2 isolation procedure is standard and the chosen structures appear to satisfy the stated criterion. The more immediate, observable threat to the central claim is the factor-1.8 spread among the three Lorentz-structure sets in Table 5, which the paper does not incorporate as a systematic uncertainty. This spread directly affects the quoted benchmark widths and their precision, and it is not explained or reproduced because fit parameters for sets 2 and 3 are missing. The proposed test (recomputing widths with published parameters and propagating uncertainties per set) would settle whether the spread is a genuine inconsistency or an artifact of the reported error bars. The reader's conditional verdict already requires addressing systematic errors, so the verdict remains CONDITIONAL; no change is needed.","tokens_in":26541,"tokens_out":14416,"duration_ms":162873,"concrete_test":"Provide the q^2 fit parameters (F(0), a, b, c, d) for structure sets 2 and 3 and recompute Γ_ℓ from each set using a common integration code. Then perform a Monte Carlo propagation of the input and auxiliary-parameter uncertainties for each set. If the 1σ bands of the three sets do not overlap, the set-to-set spread is a systematic discrepancy that must be folded into the error; if they overlap after correct propagation, the average may be defensible.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the QCD sum-rule extraction yields the SM benchmark widths for Ω_b^*→Ω_c^*ℓν. The paper extracts form factors from three different Lorentz-structure sets (Sec. 3.1) and averages the resulting widths (Table 5). The spread is large: in units of 10^-12 GeV, Γ_e = 2.78 (set1), 2.97 (set2), 1.65 (set3); Γ_τ = 0.76, 0.86, 0.51. The reported 'average' 2.47 ± 0.64 and 0.71 ± 0.19 does not include the between-set spread; e.g., set3's Γ_e is ~1.3σ below the lower edge of the average error bar. Since all sets are asserted to be valid after spin-1/2 removal and Borel stabilization, the disagreement implies the extraction is not unique under the paper's own criteria. Fit parameters are provided only for set1 (Tables 3,4), so the other sets are not independently checkable. The central claim therefore rests on an unjustified average, not on a demonstrably convergent sum rule.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper analyzes the semileptonic weak transition Ω_b^*(3/2^+, bss) → Ω_c^*(3/2^+, css) ℓ ν̄_ℓ using three-point QCD sum rules. A correlation function is matched between a phenomenological side parametrized by seven vector (F_i) and seven axial (G_i) form factors and an OPE side computed through dimension-six condensates. Borel windows (M^2 = 9–12 GeV^2, M'^2 = 6–9 GeV^2) are fixed by pole dominance (≥ 0.5) and OPE convergence (≤ 0.05), with continuum thresholds selected by stability. The q^2 dependence is fitted with the rational function of Eq. (34) for three different sets of Lorentz structures, although fit parameters are tabulated only for set 1 (Tables 3 and 4). The resulting widths, averaged over the three sets, are Γ_e = 2.47 × 10^-12 GeV, Γ_μ = 2.46 × 10^-12 GeV, Γ_τ = 0.71 × 10^-12 GeV, giving R = Γ_τ/Γ_e = 0.29 ± 0.01 (Eq. (42)). The paper presents these as Standard Model benchmark values.","tokens_in":26887,"tokens_out":11863,"duration_ms":140175,"significance":"If substantiated, this is the first QCD sum-rule treatment of the 3/2→3/2 Ω_b^*→Ω_c^* transition and provides falsifiable predictions for a channel that will be difficult but not impossible to probe at future LHC runs. The paper follows the standard machinery of the field: explicit interpolating currents, OPE through dimension six, pole-dominance and OPE-convergence criteria, stability plots, and three alternative structure sets as a cross-check. The cross-check is a strength, but it exposes a factor-1.8 spread in the widths that is not reflected in the quoted errors, and the extraction is therefore not yet demonstrated to be unique. The analysis is not fully reproducible from the text alone because the spectral densities are not given explicitly and the fit parameters are shown for only one of the three structure sets; no code or supplementary material is provided. Nevertheless, the central derivation is a standard three-point sum rule and, if the identified issues are resolved, the paper would be a useful benchmark calculation for the community.","major_comments":[{"comment":"The three Lorentz-structure sets give Γ_e = 2.78, 2.97, 1.65 (×10^-12 GeV), a spread of about a factor 1.8. The quoted average, 2.47^{+0.64}_{-0.49}, has a 68% lower edge of 1.98 × 10^-12 GeV, which is above the set-3 central value; the between-set disagreement is therefore not covered by the reported uncertainty. Since §3.1 asserts that all three sets are acceptable after spin-1/2 removal and Borel stabilization, the extraction is not unique under the paper's own criteria, and the 'SM benchmark' claim rests on an unjustified average. The same issue affects R: values for the three sets are 0.273, 0.290, 0.309, a spread larger than the quoted ±0.01. Please provide fit parameters for sets 2 and 3, quote each set separately, and include the between-set variance as a systematic error, or justify selecting a preferred set.","section":"§3.2, Table 5"},{"comment":"Fit parameters are given only for set 1, and only F(0)/G(0) carry uncertainties; the shape parameters a, b, c, d are quoted without errors and no covariance with F(0) is provided. The decay width in Eq. (40) is an integral over q^2 up to m_-^2 ≈ 11 GeV^2, so the shape parameters contribute directly to the uncertainty. The errors in Table 5 therefore omit an entire error source even for set 1. Please propagate uncertainties in all fit parameters, or supply a covariance matrix, so that the quoted width errors are not optimistic by construction.","section":"Tables 3, 4 and Eq. (34)"},{"comment":"The prefactor 1/2 in Eq. (40) equals 1/(2J_i+1) for an initial spin-1/2 state. For the initial spin 3/2^+ baryon, the conventional spin-average factor is 1/4. The helicity sum H^{3/2→3/2} in Eq. (41) already sums over positive and negative final-state and W helicities, hence over all four initial polarizations, so no additional factor of 2 is apparent. Unless H is defined with an extra factor of 2 (not stated), all entries in Table 5 are too large by a factor of 2. Please confirm the normalization against Ref. [44]. R is unaffected, but Γ_e, Γ_μ, and Γ_τ would each halve if the concern is correct.","section":"Eq. (40)"},{"comment":"The removal of spin-1/2 contamination is asserted by dropping structures containing γ_ρ at the far left, γ_ν at the far right, and terms proportional to p'_ρ and p_ν. This assumption is not independently tested. The three-set comparison in §3.1 is in fact the natural test, and it shows a factor-1.8 disagreement, so residual spin-1/2 pollution cannot be excluded on the evidence presented. Please quantify the effect—for example, by repeating the extraction with a different interpolating current, or by checking that the extracted form factors are independent of the chosen structure set within a common error—or state this limitation explicitly in the error budget.","section":"Sec. 2.2, Eq. (11)"}],"minor_comments":[{"comment":"Typo: 'QCD sun rule' should be 'QCD sum rule'.","section":"Sec. 2.3, first paragraph"},{"comment":"The integration limits are written as 'm^2_- to m^2_ℓ', which is ambiguous. Presumably the physical range is m_ℓ^2 ≤ q^2 ≤ m_-^2; please clarify the order of the limits.","section":"Eq. (40)"},{"comment":"The value m_{Ω_b^*} = (6084 ± 84) MeV and the residue λ_{Ω_b^*} are taken from Ref. [6], but Ω_b^*(1S,3/2^+) is not an established PDG state. The 84 MeV uncertainty is a large phase-space input; please justify the identification and discuss the sensitivity of Table 5 to this mass.","section":"Table 2"},{"comment":"The stability plots and the pole-dominance/OPE-convergence diagnostics are shown only for set 1. Please show the same diagnostics for sets 2 and 3, or at least tabulate the pole-dominance and OPE-convergence ratios, so that the acceptance of all three sets can be assessed.","section":"Figs. 1–3"},{"comment":"The appendix lists only the Lorentz-structure decomposition of the QCD correlation function. The spectral densities ρ_i(s,s',q^2) and the non-imaginary pieces Γ_i are not given explicitly. A supplementary file with these expressions would make the calculation reproducible and allow independent checks.","section":"Appendix A"},{"comment":"Phrases such as 'useful theoretical benchmarks' and 'pioneering' overstate the robustness of the results given the structure-set spread and the normalization question in Eq. (40). Suggest tempering these claims until the systematic issues are resolved.","section":"Abstract and Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and uses standard methods that the authors' group has applied successfully before. The editorial decision hinges on two points: (i) whether the factor-1.8 spread among the three structure sets can be folded into a defensible error budget or resolved by an explicit selection criterion, and (ii) whether the normalization of Eq. (40) is correct—this is a quick check against Ref. [44] and, if the 1/2 factor is wrong, all widths in Table 5 halve. The spin-1/2 contamination concern is a common working assumption in the literature and I would not reject on that basis alone, but it should be discussed openly. If the authors fix the average procedure and the normalization, I would view this as publishable after a standard revision cycle. The absence of spectral density expressions and fit parameters for sets 2 and 3 is a reproducibility weakness that should also be addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Punchline: this is the first QCD sum-rule calculation of the Omega_b^* -> Omega_c^* semileptonic transition, and as a benchmark estimate it is probably in the right ballpark, but the quoted errors are too narrow because the spread among three Lorentz-structure sets is not folded into the average.\n\nWhat is actually new is the channel. The paper applies the standard three-point sum-rule machinery to a 3/2+ -> 3/2+ b-to-c transition that no one has computed before. It gives fourteen form factors, fit functions, e/mu/tau widths, and R = 0.29. The method is standard, the stability analysis is standard, and the presentation is reasonably clear for this genre. Credit where due: they report three sets of structures rather than cherry-picking one, and they choose Borel windows using pole dominance and OPE convergence.\n\nWhere it gets soft. The three sets do not agree: Gamma_e ranges from 1.65 to 2.97 (in units of 10^-12 GeV), and the quoted average 2.47 +/- 0.64 does not include that between-set spread. Set3 lies outside the average error bar. If all three sets pass the stated criteria, the sum-rule extraction is not uniquely convergent, and the average is an unjustified procedure. This is the main issue, and it is answerable: publish the fit parameters for sets 2 and 3, treat the spread as a systematic uncertainty, and state which set is preferred and why.\n\nSecond, the spin-1/2 contamination in the spin-3/2 currents is removed by dropping specific Lorentz structures. That is a standard assumption, but it is not independently tested here. If any spin-1/2 contribution leaks through, all fourteen form factors shift. Not fatal, but it deserves a sentence of sensitivity check.\n\nThird, the OPE side is not transparent enough for a referee to check. Appendix A lists the Lorentz structures but not the explicit spectral densities or non-imaginary terms. For a sum-rule paper, that is the actual calculational content. I would ask for supplementary material.\n\nFourth, the uncertainties in the widths and in R come only from the first structure set. The q^2-shape coefficients and Borel/continuum choices also contribute, and R = 0.29 +/- 0.01 looks too precise. This is partly a consequence of the first issue.\n\nWho it is for: QCD sum-rule practitioners and heavy-baryon phenomenologists who want a first benchmark for this transition. The Omega_b^* itself is not yet observed and probably radiates dominantly, so data will not come soon. The paper does not fit data, so circularity is low.\n\nRecommendation: yes, send it to referees, but ask for the structure-set spread to be handled properly, for complete fitting information, and for the OPE detail. The core derivation looks serious, but the central benchmark is not robust until the systematic spread is addressed.","headline":"First QCD sum-rule estimate of Omega_b^* -> Omega_c^* semileptonic widths, likely right in spirit but the quoted errors are too narrow because the between-structure-set spread is not included in the average.","tokens_in":27375,"tokens_out":2675,"would_cite":true,"duration_ms":34679,"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":"QCD sum rules yield all fourteen form factors and decay widths of the Ω_b^*→Ω_c^* ℓν̄_ℓ transition: 2.5, 2.5 and 0.71 × 10⁻¹² GeV (e, μ, τ).","keywords":["QCD sum rules","semileptonic weak decay","Omega_b^* baryon","Omega_c^* baryon","spin-3/2 baryons","b to c transition","transition form factors","helicity amplitudes"],"falsifier":"A lattice QCD computation of a single form factor at q² = 0 — for instance the vector form factor F₁(0) ≈ 8.7 or the axial G₁(0) ≈ 4.9 — would settle the sum-rule extraction, because the fitted q² functions are anchored to those values; agreement within errors would validate the predicted widths. Experimentally, a measurement of R = Γ(Ω_b^*→Ω_c^* τν̄_τ)/Γ(Ω_b^*→Ω_c^* eν̄_e) from b-baryon samples would directly test the predicted 0.29.","tokens_in":26423,"feed_emoji":"⚛️","tokens_out":19675,"duration_ms":188601,"temperature":0.7,"pith_summary":"The paper tries to establish the Standard Model benchmark values for the semileptonic weak decay of the excited bottom baryon Ω_b^* (spin 3/2) into the excited charmed baryon Ω_c^* (spin 3/2) — a 3/2 → 3/2 b→c transition that has never been measured. Using three-point QCD sum rules, the authors extract all fourteen form factors (seven vector, seven axial-vector) that parametrize the transition matrix element, working to mass dimension six in the operator product expansion, and fit their q² dependence. Feeding the fitted form factors into the standard helicity-amplitude formalism gives predicted widths of 2.47 × 10⁻¹² GeV (electron), 2.46 × 10⁻¹² GeV (muon) and 0.71 × 10⁻¹² GeV (tau), with tau-to-electron ratio R = 0.29 ± 0.01. If these numbers are right, future hadron-collider measurements should reproduce them, and any deviation would signal new physics in the b→c sector; the results also give a quantitative handle on the weak dynamics of an excited bottom baryon whose dominant radiative decay is nearly undetectable because its photon is so soft.","feed_headline":"Omega_b* weak decay widths: ~2.5e-12 GeV, tau ratio 0.29","feed_subtitle":"Standard Model benchmarks for the excited Omega_b's b-to-c weak decay, testable at hadron colliders.","key_machinery":"The load-bearing object is the three-point correlation function Π_{ρμν}(p, p′, q²) of the transition current c̄γ_μ(1−γ₅)b between spin-3/2 interpolating currents (quark-field operators with the baryons' quantum numbers). On the hadronic side, saturating with the two baryon states turns it into the fourteen form factors; on the QCD side the same function is evaluated by the operator product expansion (short-distance expansion into perturbative plus condensate terms) through dimension-six condensates. A double Borel transformation suppresses excited states and continuum; quark-hadron duality with thresholds s₀, s′₀ completes each sum rule. Spin-1/2 contamination, the hazard specific to 3/2 cur","core_discovery":"The central claim is a complete sum-rule determination of the Ω_b^* → Ω_c^* ℓν̄_ℓ transition. The authors compute the three-point correlation function of spin-3/2 interpolating currents on both the hadronic and quark-gluon sides, discard the Lorentz structures that carry spin-1/2 contamination, and extract fourteen q²-dependent form factors — F₁…F₇ (vector) and G₁…G₇ (axial-vector) — each fitted by the rational function of Eq. (34). Averaged over three sets of Lorentz structures, the predicted widths are 2.47 × 10⁻¹² GeV (electron), 2.46 × 10⁻¹² GeV (muon) and 0.71 × 10⁻¹² GeV (tau), with R = Γ(τ)/Γ(e or μ) = 0.29 ± 0.01. These are presented as theoretical benchmarks for forthcoming measurem","pith_inferences":["Editorial extension: the uncertainty quoted on R (±0.01) is far smaller than the ~25% uncertainties on the individual widths, because most QCD inputs cancel in the ratio; a lattice or experimental determination of R alone would therefore be the sharpest test of this calculation.","Editorial extension: heavy-quark spin symmetry relates the ground-state Ω_b → Ω_c transition of the companion sum-rule study [41] to this 3/2 → 3/2 transition at leading order in 1/m_Q; comparing the two form-factor sets, both now available from the same method, would quantify spin-symmetry breaking.","Editorial extension: the tau channel, though phase-space suppressed, leaves a displaced-vertex signature that colliders can trigger on, so R = 0.29 might be measured even if the tiny electron and muon channels individually are not; a measured ratio well above 0.29 would mimic the pattern of the b→cτν anomalies seen in B-meson decays."],"forward_implications":["The averaged electron and muon widths (2.47 and 2.46 × 10⁻¹² GeV) and the tau width (0.71 × 10⁻¹² GeV) become the Standard Model expectations that future hadron-collider measurements of this transition should be compared against.","The complete set of q²-dependent form factors permits computation of differential distributions and lepton-side observables for all three channels, not just integrated widths.","Since Ω_b^* is expected to decay predominantly via the radiative mode Ω_b^* → Ω_b γ with a photon of only tens of MeV, these weak widths are among the few testable predictions for the excited bottom baryon's decay dynamics.","The three sets of Lorentz structures yield mutually consistent widths (1.65–2.97 × 10⁻¹² GeV for the electron channel), and their average is the paper's quoted benchmark."],"supporting_citations":[{"why":"Supplies the spin-3/2 interpolating currents for heavy baryons (Eq. 14) and the form of spin-1/2 contamination that the analysis removes.","marker":"[2]"},{"why":"Provides the Ω_b^* and Ω_c^* masses and residues used as numerical input (Table 2).","marker":"[6]"},{"why":"PDG values for quark and lepton masses, G_F and V_cb entering the numerical analysis and the widths.","marker":"[34]"},{"why":"Introduces the QCD sum-rule framework on which the three-point calculation rests.","marker":"[36]"},{"why":"The companion sum-rule computation of the ground-state Ω_b → Ω_c ℓν̄_ℓ transition; template and comparison point for this excited-state extension.","marker":"[41]"},{"why":"Supplies the helicity-amplitude decomposition of 3/2 → 3/2 transitions and the decay-width formula (Eqs. 36–41).","marker":"[44]"},{"why":"Supplies the Rarita-Schwinger spinor completeness relations and the spin-1/2 contamination analysis for spin-3/2 currents.","marker":"[45]"},{"why":"Provides the light- and heavy-quark propagators, including condensate terms up to dimension six, used in the QCD side.","marker":"[47]"},{"why":"Supplies the integral identities (Eqs. 22–26) used to extract the spectral densities of the sum rules.","marker":"[48]"},{"why":"Provides the quark condensate values and m₀² used as non-perturbative inputs.","marker":"[49]"}],"fun_headline_variants":["QCD sum rules pin down Omega_b* weak decay to Omega_c*","Excited bottom baryon decay: QCD sum rule benchmarks","Omega_b* to Omega_c* weak decay: QCD sum rule predictions","Spin-3/2 heavy baryon decay calculated with QCD sum rules","Benchmarks for Omega_b* semileptonic decay to Omega_c*"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The extraction assumes that dropping the Lorentz structures containing γ_ρ, γ_ν, p′_ρ and p_ν (Eq. 11) removes the spin-1/2 contamination completely; if any spin-1/2 contribution survives, all fourteen form factors and every decay width shift.","fun_headline_variants_meta":{"raw":{"variants":["QCD sum rules pin down Omega_b* weak decay to Omega_c*","Excited bottom baryon decay: QCD sum rule benchmarks","Omega_b* to Omega_c* weak decay: QCD sum rule predictions","Spin-3/2 heavy baryon decay calculated with QCD sum rules","Benchmarks for Omega_b* semileptonic decay to Omega_c*"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000761,"raw_usage":{"total_tokens":3266,"prompt_tokens":845,"completion_tokens":2421,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":589,"completion_tokens_details":{"reasoning_tokens":2333}},"tokens_in":589,"tokens_out":2421,"duration_ms":20102,"temperature":1.0,"reasoning_tokens":2333,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T12:46:51.953688+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A lattice QCD computation of a single form factor at q² = 0 — for instance the vector form factor F₁(0) ≈ 8.7 or the axial G₁(0) ≈ 4.9 — would settle the sum-rule extraction, because the fitted q² functions are anchored to those values; agreement within errors would validate the predicted widths. Experimentally, a measurement of R = Γ(Ω_b^*→Ω_c^* τν̄_τ)/Γ(Ω_b^*→Ω_c^* eν̄_e) from b-baryon samples would directly test the predicted 0.29.","supporting_citations":[{"cited_title":"Mass and Magnetic Moments of the Heavy Flavored Baryons with $J=3/2$ in Light Cone QCD Sum Rules","cited_arxiv_id":"0807.3481","evidence_quote":"Supplies the spin-3/2 interpolating currents for heavy baryons (Eq. 14) and the form of spin-1/2 contamination that the analysis removes."},{"cited_title":"On the nature of the newly discovered $\\Omega_c^{0}$ states","cited_arxiv_id":"1703.07091","evidence_quote":"Provides the Ω_b^* and Ω_c^* masses and residues used as numerical input (Table 2)."},{"cited_title":"QCD and R esonance Physics. Theoretical Foundations,","cited_arxiv_id":null,"evidence_quote":"Introduces the QCD sum-rule framework on which the three-point calculation rests."},{"cited_title":"Determination of Baryon and Bar yonic Resonance Masses from QCD Sum Rules. 1. Nonstrange Baryons,","cited_arxiv_id":null,"evidence_quote":"Provides the quark condensate values and m₀² used as non-perturbative inputs."}],"review_version":1}