{"id":"4abc1839-6e25-42e5-bf8e-b71f70896b6a","arxiv_id":"2509.01289","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Compositeness values for X(3872), Zb(10610), Zb(10650), and Tcc are extracted from CDD-pole fits to published spectra; X(3872) is unconstrained (0 to 1), Tcc is found at 0.23 with large errors.","lead":"A hadron physicist applies a CDD-pole scattering framework to four exotic hadron states and extracts their 'compositeness', the molecular weight. The paper is a short conference proceedings; the quoted values mostly come from fits already published by the same author, and for X(3872) the extracted compositeness spans the entire range from 0 to 1.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The compositeness extraction assumes the observed spectrum is exactly |d(E)|²; a coherent direct-production component would change pole residues and X, and the paper does not test this.","rationale":"The reader's verdict is CONDITIONAL, and the weakest assumption identified by the reader is exactly the production-model assumption: the spectrum is parameterized by |d(E)|², so if direct production or other channels contribute, the extracted pole residue and hence compositeness are not physical probabilities. This is the most load-bearing concern because every central compositeness value (X(3872), Zb, Tcc) is derived from fits that depend on this mapping, and the paper provides no test of it. The paper itself flags the provisional nature of the Tcc analysis by stating that a more rigorous coupled-channel study is ongoing, which supports treating the extracted values as conditional rather than definitive. I do not find an internal mathematical inconsistency in the CDD-pole parameterization itself; the method is physically motivated and consistent with unitarity and analyticity. The weakness is the missing production-model robustness check. Since the reader already assigned CONDITIONAL with the same core concern, my stress-test does not move the verdict; it confirms it. I would keep the verdict as CONDITIONAL, not REJECT, because the concern is about the interpretation/robustness of the extracted compositeness, not about a demonstrated mathematical error. A single targeted fit with a coherent direct-production term could settle whether the concern is substantive or whether the extracted X is stable.","tokens_in":4680,"tokens_out":4018,"duration_ms":55559,"concrete_test":"Refit the LHCb Tcc spectrum with a production amplitude that includes a coherent direct-production term, e.g. A(E) = N[d(E) + c e^{iφ}], keeping d(E) in Eq. (8) and letting c, φ, and all previous parameters float. Re-extract the pole residue and recompute X = |γ² dG/ds|. Repeat the same exercise for the X(3872) spectrum (BESIII data) with the same coherent term. If the resulting X moves outside the quoted intervals (Tcc: 0.23+0.40-0.09; X(3872): 0–1) or if the fit quality cannot distinguish A(E) from pure d(E), then the reported compositeness values are not robust to the production assumption. If X stays stable within errors, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central values of X for X(3872), Zb(10610/10650), and Tcc are obtained by fitting the measured invariant-mass spectra with |d(E)|² as the signal shape, where d(E) is defined in Eq. (8) from a single-channel scattering amplitude with one CDD pole and one subtraction constant. This is a strong production-model assumption: it equates the observable spectrum with the two-hadron final-state interaction alone, with no coherent direct-production amplitude for a compact component and no explicit coupled-channel production. If direct production of an elementary/tetraquark component contributes (or if other channels feed the same final state), the amplitude that fits the spectrum is not proportional to the scattering t-matrix; the fitted pole residue γ², and therefore X = |γ² dG/ds|, is not the physical compositeness. The paper's Fig. 2 includes an additive background, but an additive background does not cure a coherent direct-production term. The Tcc conclusion that \"both poles are found in the physical and unphysical Riemann sheets... indicates that Tcc has large portion of elementary degree of freedom\" rests precisely on this assumption. The author's own closing caveat in Sec. 4 — \"A detailed and more rigorous study in the coupled channel is ongoing\" — concedes that the present single-channel FSI-only extraction is provisional. The abstract's \"deeper insights\" therefore overstate the robustness of the numbers, and the reader's weakest_assumption correctly identifies this as the load-bearing point.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings paper introduces a CDD-pole-modified two-body scattering amplitude (Eq. (1), with non-relativistic form Eq. (4)) and uses it to extract compositeness values for the exotic candidates X(3872), Zb(10610), Zb(10650), and Tcc. The signal shape is taken as |d(E)|^2, where d(E) is defined in Eq. (8), with an additive background in the spectral fits. The paper reports that X(3872) can be bound or virtual with compositeness from 0 to 1, that Zb states have compositeness 0.4--1, and that Tcc has compositeness 0.23^{+0.40}_{-0.09}, which is interpreted as indicating a large elementary/tetraquark component because both physical and unphysical Riemann sheet poles are found. The quantitative support for these claims is largely delegated to cited papers.","tokens_in":5043,"tokens_out":3312,"duration_ms":43689,"significance":"The CDD-pole parameterization itself is a standard and internally consistent extension of the effective-range expansion, and the paper honestly acknowledges the wide ranges obtained for X(3872) and Zb. If the extracted compositeness values were robust, they would give useful constraints on the nature of these states. However, the central numerical claims are not verifiable from this manuscript: the fits, pole searches, and uncertainties are in Refs. [14,15,17,19,21], and this paper does not provide the fitted parameters, residues, pole positions, or error budgets. In addition, the extraction rests on the production-model assumption that the observed spectrum is, up to an additive background, exactly |d(E)|^2, with no coherent direct-production amplitude. The paper's own closing caveat in Sec. 4 that a more rigorous coupled-channel study is ongoing signals that the present numbers are provisional. The abstract's claim of 'deeper insights' therefore overstates the robustness of the reported compositeness values.","major_comments":[{"comment":"The central quantitative claim is obtained by setting the signal shape equal to |d(E)|^2, where d(E) is a single-channel final-state interaction with one CDD pole and one subtraction constant. This equates the observable spectrum with the two-hadron FSI alone, plus an additive background. A coherent direct-production amplitude for a compact/tetraquark component, or an additional coupled-channel production mechanism, would interfere with this term and change the fitted pole residue gamma^2, and hence X = |gamma^2 dG/ds|. The additive background in Fig. 2 does not cure this. This is not a testable assumption as presented; the paper would need, at minimum, a comparison with an alternative production parameterization or an explicit statement of the production model's experimental validity. This point is load-bearing because the Tcc conclusion about a large elementary component depends direct","section":"Sec. 4, Eq. (8)"},{"comment":"The abstract promises compositeness values and deeper insights, but the support is not in this paper. For X(3872) the text says only that 'the compositeness could range from 0 to 1'; for Zb the manuscript states that M_CDD can vary over a wide range and gives no fit uncertainties; for Tcc only the central value and asymmetric uncertainty of X are given. There is no table of fitted parameters, pole positions, residues, chi^2 values, or correlation matrices. Figures 1 and 2 show curves and data, but a reader cannot check whether the claimed compositeness values follow from the displayed fits. The provenance of the numbers in Refs. [14,19,21] is fine, but for a paper whose stated purpose is to report these values, the omission makes the central claims unverifiable from the manuscript itself.","section":"Sec. 4"},{"comment":"The text calls the value 0.23^{+0.40}_{-0.09} a 'predicted' compositeness, but it is an output of the fit to the same data from which M_CDD and the residue are determined (Eqs. (1)--(8)). It is therefore a fit result, not a prediction in the sense of a parameter fixed independently of the fitted spectrum. The subsequent inference 'both poles are found in the physical and unphysical Riemann sheets, which indicates that Tcc has large portion of elementary degree of freedom' rests on the Morgan rule and on the production-model assumption in the previous comment. The manuscript itself notes 'A detailed and more rigorous study in the coupled channel is ongoing', which is an explicit admission that the present single-channel FSI-only extraction is provisional. This caveat should be reflected in the abstract and conclusions.","section":"Sec. 4, Tcc paragraph"}],"minor_comments":[{"comment":"The formula for kappa_± is garbled by typesetting; as printed it reads 'kappa_± = ...' with the square-root argument split across lines in an ambiguous way. Please rewrite the equation cleanly.","section":"Eq. (3)"},{"comment":"The horizontal axis label appears as an encoded string ('/s32/s116/...') rather than readable text, and the axis label 'Events(/500keV)' is not standard notation. Please fix the figure text.","section":"Fig. 2"},{"comment":"The phrase 'meadited' should be 'mediated'; other typos include 'compositenss', 'quantatified', and 'interpretated'. A careful proofread is needed.","section":"Sec. 4"},{"comment":"The two scenarios for Zb are described with M_CDD values and X values, but the figure does not show which curve corresponds to which parameter set beyond the solid/dashed distinction. Please give the exact parameters or a small table in the caption or text.","section":"Sec. 4, Zb paragraph"},{"comment":"The statement that X(3872) can be a bound and/or virtual state, and possibly a higher-order virtual-state pole in the limit of vanishing D*0 width, is an important caveat, but it is stated without references to the specific pole positions or compositeness values. A brief numerical summary would make the 'range 0 to 1' claim concrete.","section":"Sec. 4, X(3872) paragraph"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings-style contribution, and the report treats it as a standalone manuscript. The main obstacle is not the formalism, which is standard, but the absence of the underlying fit details and the untested production-model assumption. If the journal allows, requesting supplementary tables of the fit parameters, pole positions, and residues for each state would make the manuscript self-contained enough for the central claims to be judged. The paper's own 'coupled channel is ongoing' caveat should be elevated to a visible limitation in the abstract or conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is exactly what it looks like: a conference proceedings that re-runs the author's earlier published analyses of X(3872), Z_b, and T_cc in a common CDD-pole framework. There is no new derivation, data set, or extraction here. What it does well: it lays out the N/D-based amplitude and the compositeness formula in a compact way, and it is honest about the wide ranges in the results—X(3872) compositeness spans 0 to 1, Z_b spans 0.4 to 1, T_cc is 0.23(+0.40,-0.09). The text does not hide those uncertainties.\n\nThe soft spot is the load-bearing production assumption. The signal shape is fitted as |d(E)|^2, with d(E) the single-channel final-state interaction from Eq. (8), one CDD pole plus one subtraction. That equates the measured spectrum with the two-hadron FSI alone, leaving out a coherent direct-production amplitude for an elementary/tetraquark component or any coupled-channel feeding. If such a component is present, the fitted pole residue is not the physical compositeness. The author's own closing sentence in Sec. 4—'a detailed and more rigorous study in the coupled channel is ongoing'—concedes exactly this. Given that, the abstract's 'deeper insights' is too strong a claim; the numbers are input-dependent, not insight.\n\nTwo smaller complaints. First, the T_cc compositeness is called a 'prediction' in Sec. 4, but it is computed from parameters fitted to the same LHCb spectrum; that is an extraction, and over-calling it a prediction invites trouble. Second, the paper does not include the fit parameters or enough information for a reader to reproduce the amplitudes; that is typical for proceedings but it means the central results sit entirely in Refs. [14,15,17,19,21]. For a standalone research paper, this would be a problem; for a proceedings summary, it is acceptable.\n\nWho is this for? A reader who wants a quick map of one group's CDD-pole approach to compositeness in exotics, and who is willing to go to the cited papers for the details. It is not a journal-article-quality research contribution. But it deserves a serious referee if submitted as a proceedings or mini-review: the framework is standard, the results are honest, and the production-model assumption is precisely the kind of thing referees should push on. I would not desk-reject it.","headline":"A conference proceedings that usefully compacts the author's own CDD-pole compositeness analyses, but the 'deeper insights' claim outruns what the production model can actually support.","tokens_in":5528,"tokens_out":2543,"would_cite":false,"duration_ms":30145,"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":"CDD-pole fits to X(3872), Zb, and Tcc spectra quantify their hadronic-molecule content","keywords":["compositeness","CDD pole","exotic hadrons","hadronic molecules","X(3872)","Zb(10610)","Zb(10650)","Tcc"],"falsifier":"Fit the same Tcc spectrum after adding a second subtraction constant or a second channel, and check whether the pole residue (hence X) moves outside the quoted errors; if it does, the single-pole |d(E)|² ansatz is incomplete. Separately, measure the near-threshold effective range r for Tcc: Eq. (7) predicts r from the fitted CDD-pole position, so a precise measured r that disagrees with that prediction would falsify the amplitude.","tokens_in":4575,"feed_emoji":"⚛️","tokens_out":14186,"duration_ms":146353,"temperature":0.7,"pith_summary":"The paper proposes that a two-hadron scattering amplitude with exactly one Castillejo-Dalitz-Dyson (CDD) pole—an extra zero of the amplitude that unitarity and analyticity do not fix—plus the standard two-point loop function can describe the measured spectra of near-threshold exotic hadrons, even where the effective-range expansion fails. From the fitted amplitude one reads the compositeness, the weight of the two-hadron (molecule) component in the state's wave function. Applied to X(3872), Zb(10610), Zb(10650), and Tcc, the method reports that Tcc has a two-hadron weight of 0.23 (+0.40/−0.09) and therefore a large elementary (tetraquark-like) component, that the two Zb states have weights between 0.4 and 1, and that X(3872) data alone leave its weight anywhere from 0 to 1. This matters because it turns ordinary line-shape data into a structural statement about what these states are made of, without committing to a specific quark model.","feed_headline":"23 percent of Tcc is molecule, new fit says","feed_subtitle":"Same amplitude gives Zb states 0.4–1 molecular weight and X(3872) anywhere from 0 to 1.","key_machinery":"The load-bearing object is the CDD pole—an extra zero of the scattering amplitude whose position and residue are not fixed by unitarity and analyticity. The amplitude is t(s) = [γ²/(s−M_CDD²)+G(s)]⁻¹, with G the two-point loop function; non-relativistically it becomes t(E) = 8π m_th [λ/(E−M_CDD)+β−ik]⁻¹. The quantity fitted to data is |d(E)|², with d(E) = [1+(E−M_CDD)(β−ik)/λ]⁻¹, which removes the zero at the CDD pole. Compositeness is X = |γ² dG(s_R)/ds_R| at the resonance pole. Thus the CDD-pole location sets the molecule-versus-elementary mix: far from threshold gives molecule-dominated, near threshold gives elementary-dominated.","core_discovery":"The central claim is that the position of the CDD pole, not only the proximity of a pole to a two-hadron threshold, controls whether a near-threshold state is a hadronic molecule or an elementary object. For Tcc, the fit yields poles on both the physical and unphysical Riemann sheets and, invoking Morgan's rule, the paper concludes that Tcc has a large elementary (tetraquark-like) component; the compositeness is quoted as 0.23 (+0.40/−0.09). For Zb(10610) and Zb(10650), moving the CDD pole from threshold to farther away changes the compositeness from 0.39/0.36 up to 1. For X(3872), bound, virtual, and higher-order virtual-pole scenarios all fit the data, leaving the compositeness anywhere be","pith_inferences":["A natural test the paper does not report is to fit Tcc again with a second channel or a second subtraction constant; if the extracted residue changes beyond the quoted errors, the 0.23 value is parameterization-dependent rather than intrinsic.","If CDD-pole distance from threshold is the controlling variable, then other near-threshold exotics—such as charmed pentaquark candidates—could be classified by the same line-shape analysis instead of by quark-model prejudice.","The Tcc result implies that a sharp peak sitting exactly at a threshold is not by itself evidence for a molecule; a compact state with a near-threshold CDD pole can produce a similar line shape, so threshold proximity alone should not drive molecule claims."],"forward_implications":["Tcc's two-hadron component is 0.23 central, so the state is mostly not a D-D* molecule; the dominant part is elementary/tetraquark-like.","Zb(10610) and Zb(10650) are molecule-dominated but not pinned: compositeness ranges from 0.39/0.36 to 1 as the CDD pole moves.","X(3872)'s line shape is compatible with compositeness anywhere from 0 to 1, including bound, virtual, and higher-order virtual poles; current data do not decide.","When the CDD pole sits near threshold, the effective range becomes huge, so effective-range expansion fails just where these states live; the CDD-pole parameterization stays valid.","The fitting procedure turns any measured two-body line shape into a pole residue and a compositeness value, so improved spectra will directly sharpen these numbers."],"supporting_citations":[{"why":"Generalizes the compositeness definition to resonances as X = |γ² dG/ds|, used for all four states.","marker":"[4]"},{"why":"Introduces the CDD pole as an adjustable zero of the amplitude that unitarity and analyticity do not fix; it is the basis of the parameterization.","marker":"[8]"},{"why":"Provides the N/D method from which the scattering amplitude in Eq. (1) is derived.","marker":"[9]"},{"why":"Supplies the CDD-pole parameterization of the |d(E)|² signal shape and its comparison to a Breit-Wigner.","marker":"[12]"},{"why":"Earlier X(3872) analysis whose bound/virtual scenarios and compositeness range 0–1 are summarized as the X(3872) result.","marker":"[14]"},{"why":"Gives the Zb(10610)/Zb(10650) fits from which the compositeness range 0.4–1 is taken.","marker":"[19]"},{"why":"Provides the Zb mass spectra reproduced by the fits in Fig. 1.","marker":"[20]"},{"why":"Carries out the Tcc data analysis that yields the compositeness 0.23 (+0.40/−0.09) and the two-sheet pole structure.","marker":"[21]"},{"why":"Provides the D0D0π+ data used for the Tcc spectrum in Fig. 2.","marker":"[22]"},{"why":"Supplies Morgan's rule, used to read a large elementary component from poles on both physical and unphysical sheets.","marker":"[23]"}],"fun_headline_variants":["CDD pole position decides molecule vs elementary","Tcc is 23% molecule, mostly tetraquark","Fit: Zb states can be 100% molecule with CDD shift","X(3872) composition stays ambiguous: 0 to 1","New fit: CDD pole controls hadron molecular weight"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The extraction assumes that the measured signal shape is produced entirely by the two-hadron rescattering function d(E) of Eq. (8), which contains one CDD pole and one subtraction constant; if direct production of a compact state or additional channels shape the spectrum, the quoted compositeness values are not physical probabilities.","fun_headline_variants_meta":{"raw":{"variants":["CDD pole position decides molecule vs elementary","Tcc is 23% molecule, mostly tetraquark","Fit: Zb states can be 100% molecule with CDD shift","X(3872) composition stays ambiguous: 0 to 1","New fit: CDD pole controls hadron molecular weight"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000525,"raw_usage":{"total_tokens":2306,"prompt_tokens":610,"completion_tokens":1696,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":354,"completion_tokens_details":{"reasoning_tokens":1624}},"tokens_in":354,"tokens_out":1696,"duration_ms":12096,"temperature":1.0,"reasoning_tokens":1624,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T12:40:15.460951+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fit the same Tcc spectrum after adding a second subtraction constant or a second channel, and check whether the pole residue (hence X) moves outside the quoted errors; if it does, the single-pole |d(E)|² ansatz is incomplete. Separately, measure the near-threshold effective range r for Tcc: Eq. (7) predicts r from the fitted CDD-pole position, so a precise measured r that disagrees with that prediction would falsify the amplitude.","supporting_citations":[{"cited_title":"Castillejo, R","cited_arxiv_id":null,"evidence_quote":"Introduces the CDD pole as an adjustable zero of the amplitude that unitarity and analyticity do not fix; it is the basis of the parameterization."},{"cited_title":"Resonance on top of thresholds: the $\\Lambda_c(2595)^+$ as an extremely fine-tuned state","cited_arxiv_id":"1601.00862","evidence_quote":"Supplies the CDD-pole parameterization of the |d(E)|² signal shape and its comparison to a Breit-Wigner."},{"cited_title":"Different pole structures in line shapes of the $X(3872)$","cited_arxiv_id":"1612.08420","evidence_quote":"Earlier X(3872) analysis whose bound/virtual scenarios and compositeness range 0–1 are summarized as the X(3872) result."},{"cited_title":"Composite nature of the $T_{cc}$ state","cited_arxiv_id":"2412.19597","evidence_quote":"Carries out the Tcc data analysis that yields the compositeness 0.23 (+0.40/−0.09) and the two-sheet pole structure."},{"cited_title":"Morgan, Nucl","cited_arxiv_id":null,"evidence_quote":"Supplies Morgan's rule, used to read a large elementary component from poles on both physical and unphysical sheets."}],"review_version":1}