{"id":"4aca601f-f3d5-470a-8f72-a04cdf563764","arxiv_id":"2411.10123","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The ratio method, tuned with twisted boundary conditions, extracts a psi(3770) -> D D mixing amplitude from two N_f=2 ensembles and gives Gamma = 24.2(6.4) MeV, but with unquantified systematic errors.","lead":"This paper tests a cheaper lattice QCD method, the 'ratio method', to compute the decay psi(3770) -> D D on two small, non-physical ensembles, and reports a decay width of 24.2 ± 6.4 MeV, close to the experimental value. It matters because this method could avoid the costly multi-volume simulations normally needed for hadronic decays, but its systematic error is not yet quantified.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The finite-volume conversion formula Γ = L^3/(24π) pE |x31|^2 is asserted, not demonstrated; volume cancellation is untested, so the quoted Γ is not yet a controlled physics result.","rationale":"The reader's CONDITIONAL verdict is well supported. The most load-bearing step is not the spectroscopy (which is standard and internally consistent) but the finite-volume to infinite-volume conversion of the extracted mixing matrix element. The paper's own text identifies this: the method 'does not attempt to connect the finite-volume matrix elements to an infinite-volume process' (Section 2), and the conversion relies on a volume cancellation that is only 'expected' rather than demonstrated (Eq. 2.11). Because the headline result is a decay width, every other element (GEVP, PTBC tuning, fit of Eq. 2.6) feeds into the matrix element; if the conversion is uncontrolled, the width quoted in Table 7 is not a physical prediction. The two available volumes do not settle the question: they differ in the chosen on-shell momentum, and the 25%-level statistical errors on Γ permit a wide range of residual volume dependence. A meaningful test exists without new simulations: use the authors' own parabolic momentum fits to compare L^3|x31|^2 at a common p on both ensembles. This would directly probe the assumed L^{-3/2} scaling. I agree with the reader's identification of the weakest assumption. I do not see an internal inconsistency; the paper is honest about its exploratory status, and the methodological proposal remains plausible. The correct verdict remains CONDITIONAL, pending a controlled test of the conversion formula or an explicit systematic error on Γ from the volume dependence.","tokens_in":18608,"tokens_out":6311,"duration_ms":60295,"concrete_test":"Use the parabolic fits of Eq. (4.3) to evaluate |x31(p)| on D5 and E5 at a common momentum, e.g., p=350 MeV (inside both fit ranges), and check whether L^3 |x31(p)|^2 is volume-independent within errors; repeat at two more p values. In parallel, re-derive the finite-volume normalization of x31 from the two-level model of Section 2, including the un-GEVP'd D D tower, to verify the L^{-3/2} scaling and quantify O(1/L) corrections. If the L^3-scaled product varies by more than the statistical error across volumes, Eq. (2.11) is not under control and Γ must carry a systematic error or be withheld.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative result Γ=(24.2±6.4) MeV (Table 7) is obtained by inserting a single-volume lattice matrix element |x31| into Γ = L^3/(24π) p_i E_i |x31|^2 (Eq. 2.11). The paper states only that cancellation of the L^3 factor with the matrix-element volume dependence is 'expected to be exact for sufficiently large volumes' (Section 2); no derivation or scaling test is given. The two ensembles D5 (L/a=24) and E5 (L/a=32) have different tuned momenta (p=329 vs 468 MeV) and slightly different pion masses, so their Γ agreement (26.8±6.2 vs 24.2±6.4 MeV) does not by itself verify the L^{-3/2} scaling. The formula (2.11) was derived in [12,13] for ground-state transitions; this paper re-derives the correlator ratios (2.5)-(2.6) for an excited initial state but not the conversion formula. The paper concedes the method 'does not attempt to connect the finite-volume matrix elements to an infinite-volume process' (Section 2) and that the systematic error is 'difficult to estimate' (Section 5). If x31(L) does not scale as L^{-3/2}, or if there are residual O(1/L) corrections from the un-GEVP'd D D tower and final-state interactions, the quoted width is not the physical decay width. This is the load-bearing step: without controlling Eq. (2.11), compatibility with experiment concerns a lattice matrix element, not Γ.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript applies the ratio method of Pennanen/Michael and McNeile/Michael to the hadronic decay ψ(3770)→D̄D on two N_f=2 CLS ensembles. By forming ratios of the triangle and two-point correlation functions and using partially twisted boundary conditions to tune the D-meson momentum to the on-shell point, it extracts the transition amplitude x31 = ⟨D̄D|ψ(3770)⟩ from the slope of the ratio R(t). The on-shell amplitude is then converted through Γ = L^3/(24π) p_i E_i |x31|^2, yielding Γ=(26.8±6.2) MeV on D5 and Γ=(24.2±6.4) MeV on E5, compatible with the experimental Γ(ψ(3770)→D̄D)=(27.2±1.0) MeV. The paper also computes the energy shift ε of the charmonium spectrum and compares the momentum dependence of the amplitude with the 3P0 quark model. The authors explicitly label the study exploratory: no continuum limit is taken, pion masses are unphysical, and the systematic error from the finite-volume conversion is described as difficult to estimate.","tokens_in":18923,"tokens_out":5758,"duration_ms":56599,"significance":"If the extraction is controlled, the paper would demonstrate an attractive alternative to the Lüscher method for near-threshold decay widths: a single volume plus twisted boundary conditions, with the decay width obtained directly from correlator ratios rather than from a scattering phase-shift scan. The generalization of the ratio method to an excited initial state and the explicit treatment of the off-shell momentum dependence are useful method developments. The paper is transparent about fit intervals, energies, and amplitudes, and it clearly identifies several limitations. The strengths are the clean derivation of the ratio formulae in Section 2, the use of PTBCs to reach the on-shell point, and the direct comparison with a simple quark model. The main caveat is that the central finite-volume conversion formula and the selection of fit windows are not yet fully controlled, so the method is promising rather than established.","major_comments":[{"comment":"The central result Γ=(24.2±6.4) MeV in Table 7 is obtained by inserting a single-volume lattice matrix element |x31| into Eq. (2.11). This finite-volume-to-infinite-volume conversion is asserted, not derived: the text only states that the cancellation of the L^3 factor with the matrix-element volume dependence is 'expected to be exact for sufficiently large volumes', and Section 2 concedes that the method 'does not attempt to connect the finite-volume matrix elements to an infinite-volume process'. The formula was derived in Refs. [12,13] for ground-state transitions, and this paper does not re-derive it for the excited-state case. The agreement between ensembles D5 and E5 cannot verify the required L^{-3/2} scaling because the two ensembles differ in tuned momentum (329 vs 468 MeV) and in pion mass (449 vs 437 MeV). Unless the conversion is derived from a proper quantization condition or tested with a controlled volume scan, the quoted Γ is not a controlled prediction of the physical decay width but a model-dependent conversion of a matrix element. This is load-bearing for the paper's main claim.","section":"Section 2, Eq. (2.11)"},{"comment":"The values of |x31| are extracted from linear fits to R(t) over short time intervals (t/a=2–7 on D5 and 4–10 on E5), and the text states that the final intervals were chosen after generating 10,000 random choices of fit intervals from the same data and using the resulting distributions of c1, c2 and χ² as a guide. This is a post-hoc selection procedure on the same dataset; it can bias the extracted slopes and understate the uncertainty. Since Γ is quadratic in |x31|, the central number inherits this risk. Please demonstrate stability of the result under a fixed selection rule, cross-validation, or a systematic scan over a range of intervals reported as a systematic error. The current presentation does not allow the reader to assess how much of the quoted error is statistical and how much is selection.","section":"Section 4, Tables 5 and 6"},{"comment":"Equation (2.4) expresses the correlator as a sum over all D̄D levels β, and the text notes that this sum can be removed by solving a GEVP for the final state. In the analysis, however, only a single D̄D interpolator is used, so the contribution of the un-GEVP'd higher D̄D tower is assumed to be negligible without a quantitative estimate. Given the short fit windows used for R(t), the linear slope that defines |x31| could receive unidentified contamination. The authors should provide an estimate of the size of the neglected terms, for instance by fitting with an additional exponential or by comparing with the xT(t) result over the same windows.","section":"Section 2, Eqs. (2.4)–(2.6)"}],"minor_comments":[{"comment":"The notation x31 is used for ⟨D̄D|ψ(3770)⟩, but the meaning of the subscripts is not defined; please state explicitly that 3 refers to the third charmonium level and 1 to the D̄D ground state.","section":"Section 2"},{"comment":"The parabola parameters are reported as ac1 and c2/a, but the units of p0 are not explicit; please state the momentum units used in the fit.","section":"Section 4, Eq. (4.3)"},{"comment":"The caption says that the band fits only the dark points, but the figure legend does not clearly distinguish the two sets of points; please clarify the legend or caption.","section":"Figure 5"},{"comment":"The phrase 'fully compatible' with the experimental result in the abstract is stronger than the body's careful caveats, since no systematic error estimate is included; suggest softening the wording.","section":"Abstract and Section 5"},{"comment":"The 3P0 quark-model comparison uses experimental values for the oscillator parameters ω and γ, while the lattice data are at unphysical quark masses; the text notes this, but a direct restatement in the main text would avoid confusion in the comparison of Figs. 6 and 8.","section":"Appendix A"}],"recommendation":"major_revision","confidential_remarks":"This is a method-development paper, and the two-volume comparison is encouraging but not a substitute for a controlled test of the finite-volume scaling. The main issues are fixable: either derive the conversion formula from a scattering framework or add a quantitative systematic estimate, and impose a more defensible fit-window selection. With those additions, the paper could become a useful methodological contribution to the lattice study of near-threshold hadronic decays."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the methodological step is real, the central number is not yet a controlled prediction. The authors generalize the McNeile-Michael ratio method to a GEVP-isolated excited charmonium state, and they use twisted boundary conditions to tune the DD pair to on-shell kinematics. That is a genuine extension — the previous literature only treated ground-state transitions, and the derived formulas (2.5)-(2.6) look right. The analysis is transparent: fits are shown, the momentum dependence is summarized by a parabola, and the 3P0 comparison is a nice sanity check. They also state the assumptions plainly: narrow width, no scattering, no attempt to connect finite-volume matrix elements to infinite-volume processes. Credit where due.\n\nThe soft spot is exactly where the stress-test puts it. Eq. (2.11) — Γ = L^3/(24π) pE |x31|^2 — is asserted, not derived for this setup, and the claimed cancellation of the L^3 factor is untested. The two ensembles have different tuned momenta and slightly different pion masses, so their agreement (26.8 vs 24.2 MeV) does not verify the L^{-3/2} scaling. If x31(L) carries O(1/L) corrections from the un-GEVP'd DD tower or from final-state interactions, the quoted width is a lattice matrix element dressed as a physical decay width. The authors concede the method 'does not attempt to connect the finite-volume matrix elements to an infinite-volume process,' so this is a caveat they know about, not a hidden flaw.\n\nTwo smaller things. First, the ratio fits are short (t/a = 2..7) and the fit windows were selected after a random scan of 10000 options guided by χ². That is post-hoc selection; it should be treated as a systematic. Second, Nf=2 at mπ≈450 MeV with no continuum limit means the numbers are exploratory by design. The abstract's 'fully compatible' is stronger than what the evidence supports without those systematics.\n\nBottom line: this is a worthwhile paper for lattice hadron people. The method extension is real, the presentation is honest, and the comparison with experiment is suggestive, not conclusive. A serious referee should engage with it — and the main revision should be to either derive or test the volume-cancellation, or to put a clear systematic-error bar on Γ. I would not cite the width as a lattice prediction yet, but I would cite the ratio-method extension.","headline":"Useful extension of the ratio method to an excited initial state, but the quoted width rests on an untested volume-cancellation assumption and should be read as exploratory.","tokens_in":19527,"tokens_out":4130,"would_cite":true,"duration_ms":41525,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.Gc","14.40.Pq"],"model":"deepseek-v4-flash","headline":"The paper claims that a generalized ratio method extracts $\\Gamma(\\psi(3770)\\to \\bar{D}D) = (24.2\\pm 6.4)\\ \\mathrm{MeV}$ from a single lattice volume, compatible with the experimental $(27.2\\pm 1.0)\\ \\mathrm{MeV}$.","keywords":["lattice QCD","charmonium","hadronic decay width","psi(3770)","ratio method","twisted boundary conditions","energy shift","correlation functions"],"falsifier":"Compute the same $|x_{31}|$ on these ensembles after enlarging the GEVP to include the $\\bar{D}D$ interpolators, as the paper itself suggests; if the amplitude shifts by more than the quoted errors, the ratio does not isolate the wanted transition. Alternatively, repeat the measurement on a third volume at the same lattice spacing and pion mass: the width from $\\Gamma = \\frac{L^3}{24\\pi} p_i E_i |x_{31}|^2$ should be volume-independent if the cancellation is exact.","tokens_in":18357,"feed_emoji":"⚛️","tokens_out":19927,"duration_ms":160415,"temperature":0.7,"pith_summary":"This paper argues that a hadronic decay width can be extracted from lattice QCD using the ratio method rather than the costly multi-volume finite-volume scattering program. The authors generalize the ratio method to an excited initial state and apply it to $\\psi(3770)\\to \\bar{D}D$, using twisted boundary conditions to tune the kinematics to the on-shell point. From ratios of three-point and two-point correlation functions on two $N_f=2$ ensembles they obtain $\\Gamma=(24.2\\pm 6.4)\\ \\mathrm{MeV}$, consistent with the experimental $(27.2\\pm 1.0)\\ \\mathrm{MeV}$, together with an energy shift for the $\\psi(3770)$ and $\\bar{D}D$ levels. The significance is that a single volume and a scan over twist angles may be enough to predict near-threshold decay parameters.","feed_headline":"24.2 ± 6.4 MeV: ψ(3770) decay width from a single lattice volume","feed_subtitle":"It avoids the costly multi-volume scattering program that lattice decay widths normally require.","key_machinery":"The carrying object is the ratio $R(t) = |\\bar{T}_3(t,t_0)| / \\sqrt{P^{\\bar{D}D}(t)\\,\\lambda_3(t,t_0)}$, built from the GEVP-projected charmonium-to-$\\bar{D}D$ triangle correlator, the $\\bar{D}D$ two-point function, and the $\\psi(3770)$ eigenvalue. In the degenerate (on-shell) limit this ratio behaves as $|x_{31}|\\,t + A$; off-shell it becomes $|x_{31}|\\,\\sinh(t\\Delta)/\\Delta + A e^{-t\\Delta}$. The linear-in-$t$ (or hyperbolic-sine) enhancement suppresses other states, so a fit at long times isolates the mixing amplitude $x_{31}=\\langle \\bar{D}D|\\psi(3770)\\rangle$. Twist angles on the charm quark continuously vary the $\\bar{D}D$ momentum to reach or scan around the on-shell point, and a two-level Hamiltonian with entries $\\pm\\delta/2$ and $x_{31}$, $x_{31}^*$ converts the same amplitude into an energy shift $\\epsilon^2 = |x_{31}|^2 + \\delta^2/4$.","core_discovery":"The paper's central claim is that the ratio $R(t)$ built from the GEVP-isolated charmonium three-point function, the $\\bar{D}D$ two-point function, and the charmonium eigenvalue acquires a time enhancement linear in $t$ (or, off-shell, proportional to $\\sinh(t\\Delta)/\\Delta$) that isolates the hadronic transition amplitude $x_{31}=\\langle \\bar{D}D|\\psi(3770)\\rangle$. Fitting $R(t)$ at several twist angles yields the momentum dependence of $|x_{31}|$, and its on-shell value inserted into $\\Gamma = \\frac{L^3}{24\\pi}\\, p_i E_i |x_{31}|^2$ gives the decay width. The paper reports $\\Gamma = (24.2\\pm 6.4)\\ \\mathrm{MeV}$ on the larger E5 ensemble ($26.8\\pm 6.2$ on D5), compatible with the experimental $27.2\\pm 1.0\\ \\mathrm{MeV}$, and an energy shift $\\epsilon = 28.5\\pm 4.9\\ \\mathrm{MeV}$ ($55.1\\pm 2.2$ on D5) that would appear in a fully dynamical simulation. This is offered as evidence that near-threshold decay parameters can be obtained from a single volume and a few momenta, without multiple volumes or irreducible representations.","pith_inferences":["Finite-volume effects seem to shift the on-shell kinematics substantially (the on-shell twist angle differs by a factor of two between the two ensembles); a three-volume study would test whether the $L^3$ cancellation in the width formula holds at the precision claimed.","The approach likely works best near threshold, where the narrow-width approximation and the assumption that the resonance is an asymptotic state are safest; broad resonances far above threshold may need additional control.","A direct cross-check on the same ensembles with the standard finite-volume scattering formalism would quantify the narrow-width systematic error that this paper leaves unestimated.","The qualitative agreement with the ${}^3P_0$ quark model suggests the momentum dependence of the amplitude is dominated by non-relativistic pair-creation kinematics, which could guide model-informed extrapolations to the on-shell point."],"forward_implications":["The hadronic decay width of $\\psi(3770)$ can be obtained from one lattice volume and a scan over twist angles, without the multi-volume, multi-representation program of the standard finite-volume method.","The energy shift $\\epsilon = |x_{31}|$ at the on-shell point predicts how much the charmonium and $\\bar{D}D$ levels would separate in a fully dynamical simulation where the mixing is active.","The momentum dependence of $|x_{31}|$ is well described by a parabola $|x_{31}|(p)=c_1 - c_2(p-p_0)^2$ that vanishes at zero momentum, giving a compact parametrization of the off-shell behavior.","Near-threshold decays in other heavy-quark systems, such as $\\phi\\to K\\bar{K}$ for a lighter effective charm mass and $\\Upsilon(4S)\\to B\\bar{B}$ for a heavier one, are expected to be reachable by the same ratio method."],"supporting_citations":[{"why":"Introduces the ratio method that this paper applies and extends.","marker":"[10]"},{"why":"Supplies the ratio-method formulas for hadronic mixing, adapted here to an excited initial state.","marker":"[11]"},{"why":"Provides the decay-width conversion formula and ratio relations that the paper generalizes.","marker":"[12]"},{"why":"Applies the ratio method to a vector-meson decay between ground states, the direct predecessor of this work.","marker":"[13]"},{"why":"The standard finite-volume scattering formalism that the ratio method avoids because of its computational cost.","marker":"[4–7]"},{"why":"Earlier lattice determinations of the same charmonium decay channel with the standard formalism.","marker":"[8, 9]"},{"why":"Supplies the experimental value used as the comparison target for the lattice decay width.","marker":"[1]"},{"why":"Establishes the partially twisted boundary conditions used to tune the D-meson momentum.","marker":"[34]"},{"why":"Provides the gauge ensembles and scale setting used to convert lattice results to physical units.","marker":"[28]"},{"why":"Supplies the generalized eigenvalue method used to isolate the ψ(3770) state.","marker":"[40]"}],"fun_headline_variants":["ψ(3770) decay width from a single lattice volume","Lattice ratio method yields ψ(3770) width without multi-volume","One lattice volume pins down ψ(3770) decay width","Single-volume lattice estimate matches ψ(3770) decay experiment","New ratio method extracts charmonium decay width on one volume"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result stands on two linked assumptions: the fitted ratio isolates the $\\psi(3770)\\leftrightarrow \\bar{D}D$ mixing with negligible contamination from other $\\bar{D}D$ levels and other charmonium states, and the finite-volume matrix element converts to the physical width through $\\Gamma = \\frac{L^3}{24\\pi} p_i E_i |x_{31}|^2$, whose volume cancellation is expected but not proven to be exact.","fun_headline_variants_meta":{"raw":{"variants":["ψ(3770) decay width from a single lattice volume","Lattice ratio method yields ψ(3770) width without multi-volume","One lattice volume pins down ψ(3770) decay width","Single-volume lattice estimate matches ψ(3770) decay experiment","New ratio method extracts charmonium decay width on one volume"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000846,"raw_usage":{"total_tokens":3732,"prompt_tokens":1045,"completion_tokens":2687,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":661,"completion_tokens_details":{"reasoning_tokens":2599}},"tokens_in":661,"tokens_out":2687,"duration_ms":21196,"temperature":1.0,"reasoning_tokens":2599,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T19:57:24.755914+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the same $|x_{31}|$ on these ensembles after enlarging the GEVP to include the $\\bar{D}D$ interpolators, as the paper itself suggests; if the amplitude shifts by more than the quoted errors, the ratio does not isolate the wanted transition. Alternatively, repeat the measurement on a third volume at the same lattice spacing and pion mass: the width from $\\Gamma = \\frac{L^3}{24\\pi} p_i E_i |x_{31}|^2$ should be volume-independent if the cancellation is exact.","supporting_citations":[{"cited_title":"Workman et al., Review of Particle Physics , PTEP 2022 (2022) 083C01","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental value used as the comparison target for the lattice decay width."}],"review_version":1}