{"id":"61b42133-13ff-4da3-a925-335542f0bebe","arxiv_id":"1908.07914","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A QCD sum rule analysis assigns many observed hidden-charm exotic states to specific diquark-antidiquark tetraquark structures, with masses matched via a tuned energy-scale formula.","lead":"This paper calculates masses for 20 hidden-charm tetraquark current configurations using QCD sum rules and assigns many observed X, Y, Z exotic states to particular tetraquark structures. It also argues that QCD sum rules can describe tetraquark states at leading order in the strong coupling, countering a recent claim by Lucha, Melikhov and Sazdjian.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The mass extraction is not an independent prediction: Eq. (2) sets μ from the experimental M_and √s0 is set to M+0.58/0.59 GeV, so Table 5 is largely a restatement of inputs.","rationale":"The reader's weakest_assumption identifies the same issue: the energy-scale formula and threshold prescription are fitted to the target states. I agree this is the load-bearing point. The central numerical result—Table 4 and the assignment Table 5—is exactly as secure as the claim that a different M_c or threshold rule would not move the masses by hundreds of MeV. The paper reports good OPE convergence and pole dominance, and it is honest about the failures of Zc(4100)/Zc(4200) under the standard recipe, but those quality checks do not address input dependence. The test above would discriminate 'calibrated to input' from 'genuinely predictive' in one experiment. Since this concern is the same one the reader already used to issue a conditional verdict, my assessment does not change the verdict; it reinforces it. I also note the spectral densities are not printed, which makes independent verification impossible without contacting the author; this is an additional reason the claim should remain conditional.","tokens_in":23337,"tokens_out":4811,"duration_ms":49668,"concrete_test":"Fix one channel, e.g. [uc]S[dc]A − [uc]A[dc]S (JPC = 1+−), and recompute M_Z from Eq. (15) for a grid of trial masses M_trial = 3.7, 3.8, 3.9, 4.0 GeV, setting μ = sqrt(M_trial^2 − (2 × 1.82 GeV)^2) and sqrt(s0) = M_trial + 0.58 GeV, keeping the paper's Borel-window criteria. Plot the extracted mass versus M_trial. If the output is essentially the identity, with slope near 1 and scatter below 50 MeV, the 'prediction' is calibrated to the input and Table 5 does not independently support the assignments. If the output remains near 3.90 GeV for all trial masses, the method has predictive content and this concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"For the central claim of this paper—that the Table 4 masses are reliable ground-state tetraquark predictions and justify the Table 5 assignments—the extraction must have predictive content: the output of Eq. (15) should be governed by the OPE, not by a target mass inserted through the external parameters. That condition is not met as presented. In Sec. 3 the energy scale is fixed by μ = sqrt(M^2 - (2M_c)^2) with M_c = 1.82 GeV, where M is the experimental mass of the candidate state being assigned, and the continuum threshold is chosen as sqrt(s0) = M + 0.58/0.59 GeV 'via trial and error'. Both dials are functions of the same experimental mass. Because s0 lies only roughly 0.6 GeV above the target and the Borel window is then selected so the pole contribution is 40–60%, the mass ratio in Eq. (15) is effectively anchored by input-controlled threshold and scale choices. The paper's own admission that abandoning the formula and hand-setting μ=1.2 GeV reproduces Zc(4200) while μ=1.4 GeV reproduces Zc(4100) shows how much assignment power is carried by this unconstrained parameter. That the explicit spectral densities are withheld ('available upon request') prevents an independent check of whether the OPE, rather than the fitted μ and s0, controls the result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript constructs twenty local diquark-antidiquark interpolating currents for hidden-charm tetraquark states with quantum numbers 0++, 1+-, 1++, and 2++, performs QCD sum-rule analyses with the operator product expansion carried to dimension 10, and extracts ground-state masses and pole residues. It then assigns the known X and Z states to the currents whose predicted masses are closest, and argues that tetraquark and color-singlet-color-singlet (molecular) currents receive contributions at O(alpha_s^0) rather than O(alpha_s^2).","tokens_in":23663,"tokens_out":5580,"duration_ms":57839,"significance":"A reliable comprehensive QCD sum-rule survey of twenty tetraquark currents would be a useful contribution, and the paper does check the four standard sum-rule criteria, reporting pole contributions around 40-60%, |D(10)| mostly below 1%, and Borel windows. The OPE to dimension 10 and the systematic treatment of the current set are positive technical features. However, the predictive content of the mass extraction is compromised by the way the energy scale and continuum threshold are fixed, and the spectral densities are not displayed, so the central assignment claims are not supported as they stand.","major_comments":[{"comment":"The mass extraction is not independent of the states it is used to assign. The energy scale is fixed by mu = sqrt(M^2 - (2M_c)^2) with M_c = 1.82 GeV, where M is the mass of the experimental candidate being assigned, and the continuum threshold is chosen as sqrt(s0) = M + 0.58/0.59 GeV 'via trial and error.' The Borel window is then selected so that the pole contribution is 40-60%. Because the same experimental mass enters through mu and s0 and only then leaves through Eq. (15), the agreement in Table 5 is largely a restatement of inputs. The four criteria constrain the window but not the mean value. To support the assignments, the paper must show that the masses in Table 4 are stable under independent variation of mu and s0, for example by scanning these parameters without reference to the target masses or by adopting a fixed threshold prescription.","section":"Sec. 3, Eqs. (2) and (15), Tables 3 and 5"},{"comment":"The QCD spectral densities rho(s) are not given; the text states that they are 'available upon request.' Since Eq. (15) is determined by these densities, the central numerical results cannot be checked or reproduced from the paper. The manuscript should include the explicit spectral functions in an appendix or as supplementary material.","section":"Sec. 2, after Eq. (14)"},{"comment":"The paper itself demonstrates the sensitivity of the assignments to the energy-scale parameter by noting that hand-setting mu = 1.2 GeV reproduces Zc(4200) and mu = 1.4 GeV reproduces Zc(4100). This shows that the energy-scale prescription, not the OPE alone, controls which experimental states are selected. Combined with the first comment, it also makes the 'no room' conclusions for Zc(4100) and Zc(4200) conditional on the same fitted input, so those conclusions cannot be presented as robust predictions of the method.","section":"Sec. 3, final paragraph, and Sec. 4"},{"comment":"The claim that color-singlet-color-singlet type tetraquark currents begin to receive contributions at O(alpha_s^0), which appears in the abstract, is not derived in this paper but is asserted on the basis of Refs. [37,39]. Since this is one of the advertised conclusions, it should either be substantiated with the relevant calculation here or explicitly presented as a review of previous work rather than a new result of this analysis.","section":"Sec. 2, digression on O(alpha_s^0) contributions"}],"minor_comments":[{"comment":"The horizontal-axis labels in Fig. 1 appear garbled in the manuscript; the figure should be regenerated so that the Borel-parameter values are legible.","section":"Fig. 1"},{"comment":"The column header 'pole' is not defined in the table; the pole contribution PC is defined in Eq. (21), but the table should identify the column as the pole contribution for clarity.","section":"Table 3"},{"comment":"The digression on Fierz rearrangement and the O(alpha_s) counting is long and uses the auxiliary notation gamma^t_mu, gamma^v_mu, sigma^t, and sigma^v that is not needed in the main sum-rule derivation; consider moving this discussion to an appendix or substantially shortening it.","section":"Sec. 2, around Eq. (13)"},{"comment":"The effective charm-quark mass M_c = 1.82 GeV is introduced as 'updated' with reference [41], but no uncertainty or derivation is given; since this value is a central input to the energy-scale formula, its origin and uncertainty should be stated.","section":"Sec. 3, paragraph after Eq. (16)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is essentially a compilation and extension of the author's previous QCD sum-rule studies. The main technical content, the OPE to dimension 10 for twenty currents, is not independently checkable because the spectral densities are withheld. I would ask the editor to insist on the explicit spectral densities and on a non-circular extraction, such as a scan over energy scales and thresholds not targeted at the experimental masses, before reconsidering the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a workmanlike QCD sum rule survey of twenty diquark-antidiquark currents. What is actually new: eleven of those currents have OPE results presented here for the first time, all carried to dimension 10 with the usual pole-dominance and convergence checks. The organization by J^PC is useful. The author also deserves credit for honest caveats: he states plainly that Zc(4100) and Zc(4200) do not fit without mixing or hand-picked scales, and that X(3940)/X(4160) have no tetraquark room without fine tuning.\n\nThe soft spot is the one the reader flagged. The mass extraction is not a clean prediction. The energy scale mu is fixed by the target mass through mu = sqrt(M^2 - (2Mc)^2) with Mc = 1.82 GeV, and the continuum threshold is set to sqrt(s0) = M + 0.58/0.59 GeV. Both dials are functions of the same experimental M, and the Borel window is then selected by trial and error. The paper's own admission that hand-setting mu=1.2 GeV reproduces Zc(4200) and mu=1.4 GeV reproduces Zc(4100) shows how much assignment power lives in that parameter. In addition, the QCD spectral densities are withheld (\"available upon request\"), so an independent check of whether the OPE controls the result is impossible from the manuscript. That is a real deficiency for a paper whose central claim is the mass spectrum.\n\nThe O(alpha_s^0) argument about tetraquark currents is interesting but is a citation to the author's prior Ref. [37]; it is not re-derived here. Self-citation is not itself a problem, but it means this paper does not independently establish that point.\n\nWho this is for: hadron spectroscopists working with QCD sum rules on tetraquarks. The new OPE results and the pole residues are useful reference material even if the assignments in Table 5 remain plausible rather than demonstrated. I would send it to peer review, with the requirement that the spectral densities be included or deposited and that the sensitivity to Mc and the threshold prescription be quantified. If those are not provided, the mass predictions should be presented as conditional.","headline":"The paper's value is the new OPE work for eleven tetraquark currents; the mass table is plausible but not an independent prediction because the scale and threshold are fitted to the experimental states.","tokens_in":24184,"tokens_out":2256,"would_cite":true,"duration_ms":21727,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.39.Mk","12.38.Lg"],"model":"deepseek-v4-flash","headline":"A twenty-current QCD sum-rule analysis assigns a dozen observed X and Z states to hidden-charm tetraquarks, and argues the method is valid from zeroth order in the strong coupling.","keywords":["Tetraquark state","QCD sum rules","hidden-charm states","X(3872)","Zc(3900)","diquark-antidiquark currents","energy-scale formula","operator product expansion"],"falsifier":"Measure the spin-parity of Zc(4050) and Zc(4055): the scheme requires Zc(4050) to be $1^{++}$ or $2^{++}$ and Zc(4055) to be $1^{+-}$, so a confirmed $1^{+-}$ for Zc(4050) or a $1^{++}$ for Zc(4055) would rule out Table 5. A purely calculational check would be to repeat the twenty sum rules with $M_c = 1.275$ GeV instead of $1.82$ GeV and see whether the mass agreement survives.","tokens_in":23084,"feed_emoji":"⚛️","tokens_out":18099,"duration_ms":161747,"temperature":0.7,"pith_summary":"This paper tries to establish that the observed hidden-charm X and Z states can be understood, in one consistent QCD sum-rule treatment, as ground-state tetraquarks built from diquark-antidiquark currents. It constructs twenty scalar, axialvector, and tensor tetraquark currents, carries the operator product expansion through vacuum condensates of dimension 10, and fixes the Borel scale with the formula $\\mu = \\sqrt{M^2 - (2M_c)^2}$ using a universal effective charm-quark mass $M_c = 1.82$ GeV. The resulting masses match X(3860), X(3872), X(3915), Zc(3900), Zc(4020), Zc(4050), Zc(4055), Zc(4430), and Zc(4600) with specific diquark spin structures, while leaving no pure-tetraquark room for X(3940), X(4160), Zc(4100), and Zc(4200) without extra mixing. It also argues that tetraquark QCD sum rules are feasible and that color-singlet tetraquark currents begin contributing at order $\\mathcal{O}(\\alpha_s^0)$, not $\\mathcal{O}(\\alpha_s^2)$. A sympathetic reader would care because this offers a unified and testable assignment scheme for exotic states that the two-quark model cannot place.","feed_headline":"Tetraquark sum rules match X and Z states from 3.88 to 5.49 GeV","feed_subtitle":"One universal charm-quark mass and energy-scale rule place a dozen charmonium-like states on a tetraquark mass ladder.","key_machinery":"The carrying object is the interpolating tetraquark current: a local four-quark operator built from two color-antitriplet diquarks in scalar, pseudoscalar, axialvector, vector, or tensor Dirac structures and their antidiquark counterparts, giving twenty currents with $0^{++}$, $1^{+-}$, $1^{++}$, and $2^{++}$ quantum numbers. Its two-point correlation function is expanded on the quark side in vacuum condensates up to dimension 10 and matched, after a Borel transform (a Laplace-like operation that suppresses excited states), to a single ground-state pole on the hadron side. The carrying identity is the energy-scale formula $\\mu = \\sqrt{M^2 - (2M_c)^2}$ with $M_c = 1.82$ GeV, which sets the renormalization scale for each channel and is checked together with pole dominance, OPE convergence, and the appearance of Borel platforms.","core_discovery":"The paper's central claim is that a QCD sum-rule calculation using twenty local diquark-antidiquark currents predicts ground-state hidden-charm tetraquark masses that coincide with a specific set of experimental X and Z states. The calculation takes scalar, pseudoscalar, axialvector, vector, and tensor diquark operators as building blocks, evaluates two-point correlators with the operator product expansion carried through dimension-10 condensates, and selects Borel windows and continuum thresholds with the energy-scale formula $\\mu = \\sqrt{M^2 - (2M_c)^2}$, $M_c = 1.82$ GeV. In this scheme X(3860) is a $[uc]_S[dc]_S$ scalar, X(3915) a $[uc]_A[dc]_A$ scalar, X(3872) the symmetric $[uc]_S[dc]_A + [uc]_A[dc]_S$ axialvector, Zc(3900) the antisymmetric $[uc]_S[dc]_A - [uc]_A[dc]_S$ axialvector, while Zc(4020)/Zc(4055), Zc(4050), Zc(4430), and Zc(4600) are assigned to axialvector and tensor currents or to radial excitations. The paper further claims that four of the observed states, X(3940), X(4160), Zc(4100), and Zc(4200), cannot be accommodated as pure tetraquarks without fine-tuning, and that the sum-rule treatment of both diquark-antidiquark and color-singlet tetraquark currents is valid because these states receive leading contributions at order $\\mathcal{O}(\\alpha_s^0)$, not $\\mathcal{O}(\\alpha_s^2)$.","pith_inferences":["Inference: The paper's stated rule that $M_c$ is simply replaced by $M_b$ for bottom quarks implies the same twenty-current machinery predicts a hidden-bottom analogue spectrum; comparing those predictions with the observed $Z_b$ states would test whether the effective heavy-quark mass is universal.","Inference: The threshold choice $\\sqrt{s_0} = M_Z + 0.58/0.59$ GeV acts as an implicit prediction that each assigned ground state has a radial partner roughly $0.5$--$0.6$ GeV higher, so the same final states should show additional peaks at those energies.","Inference: The paper notes that hand-picked scales $\\mu = 1.2$ GeV and $1.4$ GeV reproduce Zc(4200) and Zc(4100); this flexibility suggests the central assignment table would be more decisive if the energy scale were fixed by an independent observable, such as a conventional charmonium mass or decay width, rather than by the target mass itself.","Inference: The pole residues computed here are not yet used, although the decay channels are listed; feeding them into three-point sum rules would turn each mass assignment into a width prediction that experiments can check."],"forward_implications":["If the assignments are right, X(3860), X(3915), and X(3872) are compact tetraquarks with definite diquark spin couplings: scalar-scalar, axialvector-axialvector, and symmetric scalar-axialvector, respectively.","Zc(3900) and Zc(4430) form a ground-state and first-radial-excitation pair in the same antisymmetric scalar-axialvector channel, with the mass gap mirroring the $J/\\psi$--$\\psi'$ splitting.","Zc(4020), Zc(4055), and Zc(4600) are assigned to nearly degenerate $1^{+-}$ axialvector or tensor diquark currents, with Zc(4600) possibly the first radial excitation of Zc(4020).","The pure-tetraquark scenario is disfavored for X(3940), X(4160), Zc(4100), and Zc(4200), leaning instead toward conventional $\\eta_c(3S)$/$\\eta_c(4S)$ assignments for the X states and toward mixing or color-octet-octet currents for the Z states.","Diquark-antidiquark and color-singlet tetraquark currents become legitimate objects for QCD sum rules, with leading contributions starting at $\\mathcal{O}(\\alpha_s^0)$ rather than $\\mathcal{O}(\\alpha_s^2)$."],"supporting_citations":[{"why":"Establishes the QCD sum-rule formalism, including the dispersion relation and condensate parametrization used in every correlator.","marker":"[13]"},{"why":"Provides the standard sum-rule technology for hadron masses and the values of the vacuum condensates adopted as input.","marker":"[14]"},{"why":"Supplies the diquark-antidiquark analysis of X(3872) and Zc(3900) that this paper updates, along with the OPE technical details.","marker":"[17]"},{"why":"Introduces the energy-scale formula $\\mu = \\sqrt{M^2 - (2M_c)^2}$ that fixes the Borel scales for each channel.","marker":"[19]"},{"why":"Compiles the experimental masses, widths, and quantum numbers that serve as both targets and threshold inputs.","marker":"[2]"},{"why":"Reports the evidence for the Zc(4100) state that the assignment discussion must either accommodate or exclude.","marker":"[3]"},{"why":"Presents the claim that color-singlet tetraquark currents begin contributing only at $\\mathcal{O}(\\alpha_s^2)$, the assertion the paper contests.","marker":"[36]"},{"why":"Gives the detailed counter-argument that factorizable diagrams also carry Landau singularities and that tetraquark contributions begin at $\\mathcal{O}(\\alpha_s^0/\\alpha_s^1)$.","marker":"[37]"},{"why":"Shows through the Zc(3900) analysis that two-meson scattering states do not saturate the sum rules, supporting the feasibility claim.","marker":"[39]"},{"why":"Supplies the updated effective charm-quark mass $M_c = 1.82$ GeV used in the energy-scale formula.","marker":"[41]"}],"fun_headline_variants":["QCD sum rules match X, Z tetraquark masses from 3.88 to 5.49 GeV","One charm mass rule: QCD sum rules match a dozen hidden-charm states","Hidden-charm tetraquarks identified: QCD sum rules match X, Y, Z spectrum","Twenty diquark currents, one charm mass: QCD sum rules match hidden-charm states"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the QCD energy scale in every channel is set by the formula $\\mu = \\sqrt{M^2 - (2M_c)^2}$ with a single effective charm-quark mass $M_c = 1.82$ GeV, and that each continuum threshold can be placed about $0.58$--$0.59$ GeV above the target mass; both choices are tuned so the extracted masses land on the experimental states, so if either prescription is changed the Table 5 assignments do not follow.","fun_headline_variants_meta":{"raw":{"variants":["QCD sum rules match X, Z tetraquark masses from 3.88 to 5.49 GeV","One charm mass rule: QCD sum rules match a dozen hidden-charm states","Hidden-charm tetraquarks identified: QCD sum rules match X, Y, Z spectrum","Twenty diquark currents, one charm mass: QCD sum rules match hidden-charm states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001697,"raw_usage":{"total_tokens":6842,"prompt_tokens":1188,"completion_tokens":5654,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":804,"completion_tokens_details":{"reasoning_tokens":5554}},"tokens_in":804,"tokens_out":5654,"duration_ms":42962,"temperature":1.0,"reasoning_tokens":5554,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:24:36.200354+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the spin-parity of Zc(4050) and Zc(4055): the scheme requires Zc(4050) to be $1^{++}$ or $2^{++}$ and Zc(4055) to be $1^{+-}$, so a confirmed $1^{+-}$ for Zc(4050) or a $1^{++}$ for Zc(4055) would rule out Table 5. A purely calculational check would be to repeat the twenty sum rules with $M_c = 1.275$ GeV instead of $1.82$ GeV and see whether the mass agreement survives.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the energy-scale formula $\\mu = \\sqrt{M^2 - (2M_c)^2}$ that fixes the Borel scales for each channel."},{"cited_title":"Tanabashi et al, Phys","cited_arxiv_id":null,"evidence_quote":"Compiles the experimental masses, widths, and quantum numbers that serve as both targets and threshold inputs."},{"cited_title":"Aaij et al, Eur","cited_arxiv_id":null,"evidence_quote":"Reports the evidence for the Zc(4100) state that the assignment discussion must either accommodate or exclude."},{"cited_title":"Lucha, D","cited_arxiv_id":null,"evidence_quote":"Presents the claim that color-singlet tetraquark currents begin contributing only at $\\mathcal{O}(\\alpha_s^2)$, the assertion the paper contests."},{"cited_title":"Two-particle contributions and nonlocal effects in the QCD sum rules for the axialvector tetraquark candidate $Z_c(3900)$","cited_arxiv_id":"1910.09981","evidence_quote":"Shows through the Zc(3900) analysis that two-meson scattering states do not saturate the sum rules, supporting the feasibility claim."}],"review_version":1}