{"id":"4c234c21-793a-4836-be25-bc6d71899e6c","arxiv_id":"2608.04105","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A QCD-constrained Born-Oppenheimer calculation organizes most observed quarkoniumlike states above open-flavor thresholds into heavy-quark-spin-symmetry multiplets and predicts a shallow X_b.","lead":"This paper uses Born-Oppenheimer effective field theory to compute hidden-charm and hidden-bottom states above open-flavor thresholds, with only one parameter tuned to experiment. It proposes a common multiplet organization for many exotic hadron candidates and predicts a shallow bottomoniumlike state, X_b.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Predicted X_b binding and open-flavor widths rest on the unconstrained V_Pi_g potential; a sensitivity scan is needed to test the quantitative central claim.","rationale":"The reader's weakest_assumption correctly identifies the unconstrained V_Pi_g potential and the modeled short-distance part of V_Sigma'_g as the load-bearing soft spot. The central claim is not merely qualitative multiplet organization; it includes specific numbers for near-threshold open-flavor-dominated states and for widths of resonances with sizable tetraquark components. Those numbers are computed with a potential that the paper itself admits is unknown. A sensitivity scan is the minimal computational check that would show whether the quoted numbers are accidental outputs of the chosen parametrization or robust consequences of the QCD constraints. The paper's own sensitivity study of the adjoint meson mass demonstrates that shallow-state properties can vary strongly with a single parameter; the same must be done for V_Pi_g before the quantitative predictions, especially for X_b, can be considered reliable. The CONDITIONAL verdict is appropriate.","tokens_in":54196,"tokens_out":5918,"duration_ms":55018,"concrete_test":"Perform a sensitivity scan of the coupled-channel calculation in which V_Pi_g is varied between (i) the degenerate limit V_Pi_g = V_Sigma'_g and (ii) the Eq. (2.11) form with A_Pi_g and B_Pi_g changed by ±50% and with the sign of B_Pi_g flipped, re-calibrating the adjoint meson mass in each case so the spin-averaged charmonium 2P multiplet remains 96 keV below threshold. Compare the resulting X_b binding energy, radius, and quarkonium probability and the charmonium 3P and bottomonium 3D pole masses and widths with Tables II, III, and XII. If the X_b binding changes by more than about 1 MeV or the 3P width by more than 10 MeV, the quantitative predictions are not robust to the unknown V_Pi_g; if the multiplet ordering and open-flavor dominance of the shallow states persist, the qualitative organization claim is corroborated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II C parameterizes the tetraquark potentials with Eq. (2.11), and the text explicitly states that \"the parametrization of the presently unknown V_Pi_g potential and of the short-distance part of V_Sigma'_g introduces a model uncertainty.\" V_Pi_g is completely unconstrained by lattice data, while the short-distance part of V_Sigma'_g is modeled on the quenched hybrid form with the gluelump mass replaced by the adjoint meson mass. The central claim includes quantitative predictions for open-flavor-dominated states: the X_b binding energy of 233 keV, radius 4.9 fm, and about 1% bottomonium probability, alongside the 3P and 3D pole widths. For l=1, the tetraquark S-wave potential that supports the shallow 2P and 4P multiplets is (1/3)V_Sigma'_g + (2/3)V_Pi_g, so the shape and depth of V_Pi_g directly control these near-threshold states. The calibration of the adjoint meson mass can compensate for an overall shift of the charmonium 2P level, but it cannot absorb the effect of an incorrectly modeled V_Pi_g on the bottomonium X_b or on the widths and compositions of resonances with sizable tetraquark components. If V_Pi_g differs materially from the assumed functional form, the quantitative predictions shift, even if the HQSS multiplet organization survives.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies Born-Oppenheimer effective field theory (BOEFT) to isoscalar hidden-charm and hidden-bottom spectroscopy between the spin–isospin averaged nonstrange S+S and S+P open-flavor thresholds. At leading order in the heavy-quark expansion, heavy-quark spin decouples, and the quarkonium static potential mixes through string breaking with the lowest isoscalar tetraquark/open-flavor Born–Oppenheimer potentials of the same quantum numbers. The potentials are constrained by QCD symmetries, short- and long-distance behavior, and lattice data; the only parameter calibrated to experimental spectroscopy is the lowest 1−− adjoint meson mass, fixed so that the spin-averaged multiplet associated with the χc1(3872) lies 96 keV below the spin–isospin averaged D(*)D̄(*) threshold. Using analytic continuation of the T-matrix, K-matrix analysis, and complex scaling, the authors find four charmoniumlike and five bottomoniumlike resonance multiplets, together with shallow bound multiplets: the χc1(3872)-associated 2P multiplet (binding energy 96 keV, rms radius 10.8 fm, 3% quarkonium probability) and a predicted bottomoniumlike 4P multiplet X_b (binding energy 233 keV, radius 4.9 fm, 1% bottomonium probability). The paper also presents phase shifts, effective-range parameters, prescription-dependent composition measures, uncoupled hybrid reference levels, and comparisons with the experimental spectrum and lattice QCD.","tokens_in":54506,"tokens_out":5807,"duration_ms":58176,"significance":"If the quantitative predictions hold, the paper is significant: it offers a single QCD-constrained coupled-channel framework that organizes most established isoscalar hidden-charm and hidden-bottom candidates into HQSS multiplets, connects compact-quarkonium and molecular-open-flavor pictures within one dynamical setup, and makes a falsifiable prediction for X_b. The technical execution is strong in several respects: the pole extraction is cross-checked with three complementary methods (T-matrix, K-matrix, complex scaling), the complex-scaled eigenvalues agree with the analytically continued T-matrix poles, the K-matrix diagnostics behave as expected for broad resonances and threshold backgrounds, and the effective-range analysis correctly reproduces the bound-state binding momentum while demonstrating that inverting the leading Weinberg relation without finite-range corrections is unreliable. The paper is also careful to distinguish pole widths from physical total widths and to label resonance composition measures as prescription-dependent rather than probabilities.","major_comments":[{"comment":"The central quantitative claims for open-flavor-dominated states rest on the unconstrained V_Πg potential. In Eq. (2.11), the parameters A_Πg and B_Πg are not constrained by lattice data, and the text explicitly states that the parametrization of V_Πg and of the short-distance part of V_Σg′ introduces a model uncertainty. The l=1 shallow multiplets that produce the χc1(3872) and X_b are supported by the combination (1/3)V_Σg′ + (2/3)V_Πg, so the shape and depth of V_Πg directly control the X_b binding energy, radius, and quarkonium probability reported in Table XII. The calibration of the adjoint meson mass can absorb an overall shift of the charmonium 2P level, but it cannot compensate for a materially different V_Πg in the bottomonium sector or in the widths and compositions of the 3P and 3D resonances. The paper acknowledges this limitation, but it does not provide a sensitivity scan over A_Πg, B_Πg, or the matching radius R_Πg. A quantitative assessment of how the X_b binding and the 3P/3D pole widths vary under plausible variations of these parameters is required before these are presented as central predictions.","section":"Section II C, Eq. (2.11), and Tables II, III, XII"},{"comment":"The quoted pole widths and compositions carry no uncertainty estimates, yet the T-matrix and K-matrix determinations differ substantially for two of the most open-flavor-sensitive multiplets: the charmoniumlike 3P width is 28 MeV from the T-matrix versus 50 MeV from the K-matrix, and the bottomoniumlike 3D width is 32 MeV versus 58 MeV. The paper attributes these differences to nonresonant threshold background, which is physically plausible, but the central values are then used in the experimental comparisons as if they had no systematic uncertainty. In addition, the model uncertainty from V_Πg is not propagated into any of the numerical tables. The paper should state the dominant systematic uncertainty on the pole masses, widths, and composition measures, at least in the form of a range obtained from varying the unconstrained potential parameters and from the T/K prescription difference.","section":"Section V A, Tables II and III"},{"comment":"The claim that the same equations 'generate' the shallow charmoniumlike multiplet associated with χc1(3872) should be formulated more carefully. The adjoint meson mass is calibrated so that this multiplet lies 96 keV below threshold, so the shallow charmonium 2P binding is an input constraint rather than an independent output. The genuine predictions are the higher quarkonium-dominated spectrum, the X_b multiplet, the compositions, and the relative organization. The distinction is stated in Section V D, but the abstract and conclusions sometimes present the 2P multiplet as a dynamical output of the coupled equations. Rephrasing these passages would avoid giving the impression that the χc1(3872) binding energy is predicted rather than imposed.","section":"Section II C and Section V D"}],"minor_comments":[{"comment":"The notation g²_{l−1} is not defined for the l=0 multiplets 3S and 5S, where there is only a single open channel with l_QbarQ = l+1; the columns should be labeled consistently for the l=0 case.","section":"Tables II and III"},{"comment":"The phrase 'the only calibrated parameter' is potentially misleading: V_Σg′, V_Πg, and the mixing-potential parameters are modeling inputs that are not independently constrained by data, even if they are not calibrated to experimental spectroscopy. The sentence at the end of Section II C clarifies this, but the abstract and introduction could state 'only parameter calibrated to experimental spectroscopy' more consistently.","section":"Section II C"},{"comment":"The effective-range fit interval k ∈ [1.4 keV, 14.0 keV] is extremely narrow and close to threshold; it would be helpful to show explicitly that the phase shift is numerically stable in this regime and that the extraction of a0 = 15.2 fm is not dominated by numerical artifacts at such low momenta.","section":"Section V C"},{"comment":"The scalar and tensor assignments in the 2P/3P region are presented as ambiguous, which is appropriate. However, the text says one organization 'may be somewhat preferred based on the mass' without giving a quantitative measure of preference; adding the mass differences in MeV would make this statement more concrete.","section":"Section VII A"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is careful and the framework is promising, but the central quantitative claims—especially the X_b prediction and the widths of open-flavor-sensitive resonances—require a sensitivity analysis over the unconstrained V_Πg potential before publication. I recommend major revision focused on propagating and quantifying that model uncertainty; I do not see grounds for rejection if that can be addressed convincingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know up front: this is the first BOEFT calculation that carries the quarkonium–tetraquark coupled-channel machinery across the full S+S to S+P window and claims a common HQSS multiplet organization for most hidden-charm and hidden-bottom candidates. The calculation is done carefully, the paper is unusually explicit about what it does not include, and the X_b prediction is a real output of the framework rather than a hand-assembled molecule. That alone makes it worth a serious referee.\n\nWhat the paper does well is the internal consistency work. T-matrix poles, K-matrix diagnostics, and complex scaling agree where they should; the effective-range analysis reproduces the bound-state binding momentum; the phase-shift and Argand-trajectory discussion tying the shallow 2P state to the broad 3P resonance is illuminating. The paper also repeatedly states that resonance composition is prescription dependent and that the quoted widths are not physical total widths. That level of honesty is genuine, not a disclaimer ritual.\n\nThe soft spot is exactly the one the authors name but do not quantify. V_Pi_g is completely unconstrained by lattice data, and the l=1 tetraquark S-wave potential that supports both the chi_c1(3872) multiplet and X_b is (1/3)V_Sigma_g' + (2/3)V_Pi_g. The calibration of the adjoint meson mass can absorb an overall shift in the charmonium 2P level, but it cannot correct a wrongly modeled V_Pi_g in the bottom sector or in the widths of quarkoniumlike resonances with large open-flavor components. The paper reports 233 keV binding for X_b as a central prediction, then does a sensitivity test on the adjoint meson mass only. A sensitivity scan over the V_Pi_g coefficients—even a crude one with the A and B parameters varied within a plausible range—would materially change how much weight the X_b prediction can carry. The absence of propagated uncertainties in the numerical tables is a related but secondary issue. No code or data release is included, which makes the sensitivity question harder to answer independently.\n\nAlso worth noting: the assignment of X(3940) to the 3S multiplet is off by roughly 200 MeV, and the paper tolerates that with an order-of-magnitude band. The band is honestly labeled as not a statistical uncertainty, but the association is correspondingly weak. Similarly, the lattice comparison in the 0++/2++ sector shows that the number of scalar poles is not yet settled. These are not fatal; they are places where the framework's predictive power is currently limited.\n\nBottom line: the HQSS multiplet organization and the qualitative message—quarkonium-dominated resonances plus a few exceptional shallow open-flavor-dominated states from the same equations—are likely to survive improved modeling. The quantitative X_b binding energy and the near-threshold widths should not be quoted as predictions until the V_Pi_g sensitivity is explored. This paper deserves peer review, and the referee should ask for that sensitivity scan and at least an estimate of the model uncertainty in the quoted tables. I would take it to reading group.","headline":"A serious QCD-constrained spectroscopy paper whose multiplet organization is likely robust, but whose headline X_b binding energy rest on an unconstrained potential that needs a sensitivity scan before the numbers are trusted.","tokens_in":55078,"tokens_out":1631,"would_cite":true,"duration_ms":18265,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that one calibrated adjoint-meson mass, inside a QCD-constrained Born–Oppenheimer effective field theory, organizes most quarkoniumlike states above open-flavor thresholds into heavy-quark-spin-symmetry multiplets.","keywords":["quantum chromodynamics","exotic hadrons","quarkonium","Born-Oppenheimer effective field theory","heavy-quark spin symmetry","tetraquarks","hadronic molecules","threshold resonances"],"falsifier":"A lattice QCD determination of the lowest 1-- adjoint meson mass in a comparable heavy-light scheme would be decisive: if it disagrees substantially with the calibrated value, the predicted shallow binding energies, radii, and quarkonium probabilities of the chi_c1(3872) multiplet and the X_b would not survive.","tokens_in":53947,"feed_emoji":"⚛️","tokens_out":6269,"duration_ms":59123,"temperature":0.7,"pith_summary":"This paper attempts to show that the many quarkoniumlike states observed above open-flavor thresholds are not a random collection of unrelated exotic mechanisms. It claims that a single leading-order Born–Oppenheimer effective field theory, with only one parameter calibrated to experiment, generates the hidden-charm and hidden-bottom spectrum between the spin–isospin averaged S+S and S+P thresholds. The result is a common heavy-quark-spin-symmetry multiplet organization: most poles are quarkonium-dominated resonances, while the same coupled equations also produce shallow, spatially extended, open-flavor-dominated states such as the multiplet associated with the chi_c1(3872) and a predicted bottomonium counterpart, X_b. If right, this would mean conventional quarkonia, molecular-like states, and hybrids are organized by the same QCD symmetries rather than by separate dynamical descriptions.","feed_headline":"One parameter organizes the quarkoniumlike spectrum","feed_subtitle":"BOEFT predicts a common multiplet structure for hidden-charm and hidden-bottom candidates, including a shallow X_b bound state.","key_machinery":"The central object is the leading-order diabatic coupled Schrödinger equation in which the quarkonium static potential, carrying Sigma_g^+ quantum numbers, mixes through string breaking with tetraquark/open-flavor Born–Oppenheimer potentials of the same quantum numbers (Sigma_g^+' and Pi_g). The potentials are constrained by QCD symmetries, their short- and long-distance behavior, and lattice QCD static energies in the string-breaking region; the only calibrated parameter is the lowest 1-- adjoint meson mass. This single Hamiltonian, solved with T-matrix analytic continuation, K-matrix poles, and complex scaling, generates all the predicted bound states and resonance poles, with the string-breaking mixing potential and the adjoint meson mass carrying the main quantitative weight.","core_discovery":"The central claim is that, at leading order in the heavy-quark expansion, the coupled Born–Oppenheimer Schrödinger equations—with the quarkonium potential mixed through string breaking with the lowest tetraquark/open-flavor potentials—reproduce the isoscalar hidden-charm and hidden-bottom spectrum above the open-flavor thresholds. With only the lowest 1-- adjoint meson mass calibrated so that the spin-averaged 2P multiplet of the chi_c1(3872) binds at 96 keV below the spin-averaged D(*)D(*) threshold, the equations yield four charmoniumlike resonance multiplets (3P, 3S, 2D, 4P) and five bottomoniumlike resonance multiplets (3D, 5P, 5S, 4D, 6P) between the two thresholds. Most of these poles are predominantly quarkonium, with the largest open-flavor components closest to threshold; the same dynamics also generates a shallow 4P bottomonium multiplet, X_b, with binding energy 233 keV, root-mean-square heavy-quark separation 4.9 fm, and about 1% bottomonium probability. The paper argues that this global multiplet organization, together with uncoupled hybrid reference levels, accommodates most established isoscalar candidates, while the remaining ones point to hidden-strange and S+P tetraquark/open-flavor sectors and to hybrid–quarkonium or hybrid–tetraquark mixings.","pith_inferences":["The paper's logic implies that compact-tetraquark and molecular descriptions are not separate hypotheses: the same open-flavor Born–Oppenheimer channel interpolates from short-distance adjoint-hadron configurations to long-distance meson–antimeson pairs, so any state samples both regimes dynamically.","A lattice QCD determination of the lowest 1-- adjoint meson mass in a comparable scheme would turn the X_b prediction into a sharp test: if the lattice value differs from the calibration used here, the shallow binding energies and radii should change substantially while the higher spectrum remains stable.","The predicted non-vector bottomonium multiplets (for example, the 5P and 6P multiplets with no 1-- member) indicate that future searches in non-vector channels could discriminate between the proposed HQSS organization and alternative interpretations."],"forward_implications":["If the central claim is correct, the chi_c1(3872) sits in a spin-averaged 2P multiplet whose scalar and tensor partners are resolved only after spin-dependent corrections, leaving two possible assignments for the 0++ and 2++ candidates in that region.","A shallow bottomonium state X_b should exist as the 4P counterpart, with a binding energy of about 233 keV, an rms heavy-quark separation of about 4.9 fm, and a bottomonium probability of about 1%; its properties are highly sensitive to the adjoint meson mass.","The higher quarkonium-dominated multiplets are comparatively stable against changes in the adjoint meson mass, so their masses and dominant channel content are more reliable than the near-threshold states' binding energies and radii.","States such as the chi_c1(4140), psi(4230), and psi(4360) are not naturally accommodated by the included channels, which indicates that hidden-strange and S+P tetraquark/open-flavor sectors, plus hybrid mixing terms, are needed for a complete description.","The open-flavor pole widths are leading-order estimates only and may be qualitatively different from physical total widths, especially when the pole sits near a node of the transition amplitude."],"supporting_citations":[{"why":"Supplies the lattice QCD static energies in the string-breaking region used to constrain the quarkonium–tetraquark mixing and the Sigma_g^+' potential.","marker":"[43]"},{"why":"Provides the previous below-threshold BOEFT analysis, including the heavy-light mass scheme and the calibration convention for the adjoint meson mass.","marker":"[45]"},{"why":"Establishes the Born–Oppenheimer quantum numbers, the static-energy classification, and the mixing constraints between quarkonium and tetraquark channels.","marker":"[37]"},{"why":"Supplies the earlier BOEFT treatment of threshold effects and the treatment of the chi_c1(3872) and T_cc+ states used as the starting point of this calculation.","marker":"[44]"},{"why":"Provides a lattice result for a near-threshold 1++ charmoniumlike state used as qualitative support for the shallow bound-state multiplet.","marker":"[30]"},{"why":"Supplies the quenched hybrid potential parametrization used for the uncoupled hybrid reference levels.","marker":"[58]"}],"fun_headline_variants":["One dial tunes the whole quarkoniumlike spectrum","BOEFT: single calibration predicts hidden-charm and bottom poles","One adjoint mass shapes the quarkoniumlike zoo","Shallow X_b emerges from one-parameter BOEFT","Single parameter reproduces quarkoniumlike multiplets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation's load-bearing premise is that the two least-constrained open-flavor potentials—the unmeasured Pi_g potential and the modeled short-distance part of the tetraquark Sigma_g^+ potential—are parametrized accurately enough for quantitative predictions; the paper itself flags this as a model uncertainty.","fun_headline_variants_meta":{"raw":{"variants":["One dial tunes the whole quarkoniumlike spectrum","BOEFT: single calibration predicts hidden-charm and bottom poles","One adjoint mass shapes the quarkoniumlike zoo","Shallow X_b emerges from one-parameter BOEFT","Single parameter reproduces quarkoniumlike multiplets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000255,"raw_usage":{"total_tokens":1709,"prompt_tokens":1217,"completion_tokens":492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":833,"completion_tokens_details":{"reasoning_tokens":415}},"tokens_in":833,"tokens_out":492,"duration_ms":5710,"temperature":1.0,"reasoning_tokens":415,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:44:09.028839+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A lattice QCD determination of the lowest 1-- adjoint meson mass in a comparable heavy-light scheme would be decisive: if it disagrees substantially with the calibrated value, the predicted shallow binding energies, radii, and quarkonium probabilities of the chi_c1(3872) multiplet and the X_b would not survive.","supporting_citations":[],"review_version":1}