{"id":"21469d1e-9c09-4cb1-ab40-7c553d7f1de5","arxiv_id":"2412.15915","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The authors extract the psi(3770) to D Dbar hadronic mixing and a decay width compatible with experiment using a narrow-width ratio method on two CLS ensembles.","lead":"Lattice QCD simulation extracts the hadronic mixing between the charmonium state psi(3770) and a pair of D mesons, using a cheaper narrow-width ratio method instead of the standard multi-volume scattering analysis. The resulting decay width, about 24 MeV, is compatible with experiment and supports wider use of the method.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (6) does not reproduce the quoted width: with Table 4 values it gives ~7 MeV, not 24.2 MeV; the table matches Γ = L^3 p m/(24π)|x|^2. The central conversion is internally inconsistent.","rationale":"The reader's weakest assumption identified the unproven conversion in Eq. (6) as the main risk. My stress-test confirms this and sharpens it: the printed Eq. (6) is not merely unproven but inconsistent with the numbers in Table 4. The dimensions of the printed formula are wrong (energy^{-3}), and evaluating it with the E5 inputs gives a decay width about three times smaller than quoted, while the tabulated value is reproduced by moving p_i m_ψ to the numerator. This is a concrete, checkable failure of the central derivation rather than a disagreement with standard methodology. The paper deserves credit for explicitly flagging that no infinite-volume connection is established and for presenting the lattice data transparently, but as written the central claim cannot be reproduced. A corrected formula, a derivation of the normalization, or a reference to the full paper [8] with the correct expression is required before the quoted agreement with experiment can be accepted. The reader's CONDITIONAL verdict is therefore appropriate, but the condition should include fixing this internal inconsistency, not only stating the physical limitation.","tokens_in":7118,"tokens_out":12218,"duration_ms":115079,"concrete_test":"Recompute the E5 row of Table 4 by inserting the tabulated L/a = 32, a p = 0.157, a m_ψ = 1.315, and a|x31| = 0.0095 into Eq. (6) exactly as printed: the result is Γ/a ≈ 0.190, not the quoted 0.0081(21); the same inputs inserted into Γ = L^3 p m/(24π)|x|^2 reproduce the table entry. This arithmetic check settles whether the proceedings contain an internally consistent conversion formula.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central result Γ(ψ(3770)→D Dbar)=24.2(6.4) MeV (Table 4) is not produced by the conversion formula stated in Eq. (6), which reads Γ = L^3/(24π p_i m_ψ) |x31|^2. Since x31 has mass dimension one (see Eq. (4)), the right-hand side has dimension L^3 x^2/(p m) = E^{-3}·E^2/(E^2) = E^{-3}, not energy. In lattice units on E5, the printed formula gives Γ/a ≈ 0.190, whereas Table 4 quotes Γ/a = 0.0081(21). Evaluated in physical units with L = 10.67 GeV^{-1}, p = 0.468 GeV, m_ψ = 3.946 GeV, and x = 0.0284 GeV, it gives about 7 MeV. The quoted 24.2 MeV is instead reproduced by Γ = L^3 p_i m_ψ/(24π)|x|^2 (lattice check: 32^3/(24π)·0.157·1.315·0.0095^2 = 0.0081). Thus the printed equation and the tabulated result contradict each other; either the formula is misprinted or the extracted x31 carries an undocumented normalization. Since the whole claim rests on this finite-volume-to-infinite-volume conversion, which Section 2 explicitly says is not established, the compatibility with experiment cannot be checked from this manuscript as written.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The proceedings paper applies the Michael–Pennanen ratio method to extract the finite-volume hadronic mixing x31 = <DD|psi(3770)> on two Nf=2 CLS ensembles at a single lattice spacing (a ~ 0.066 fm) and an unphysical pion mass (m_pi ~ 440 MeV). Using partially twisted boundary conditions to tune the D-meson pair to near on-shell kinematics, the authors fit the ratio R(t) of Eq. (4) to a parabola in the D-meson momentum, evaluate the on-shell point, and convert the mixing to a decay width with Eq. (6). The main result is Gamma(psi(3770) -> DD) = 24.2(6.4) MeV on the larger E5 ensemble, quoted as compatible with the experimental width, and the paper also compares the lattice mixing with the ^3P_0 quark model.","tokens_in":7462,"tokens_out":8054,"duration_ms":75301,"significance":"If the method is quantitatively sound, it offers a computationally cheaper alternative to Lüscher-type finite-volume analyses for narrow hadronic resonances, and the paper is explicit about the practical ingredients: GEVP spectroscopy, PTBC kinematics, and the ratio estimators of Eqs. (4) and (5). The strength of the paper is its concrete presentation of the lattice setup and of the Wick contractions, which makes the numerical procedure reproducible in principle. The explicit admission that no connection to the infinite-volume decay is established (Section 2) is an honest statement of the main limitation. However, the central numerical claim is currently undermined by an apparent inconsistency between the printed conversion formula and the tabulated decay width, and the absence of continuum, chiral, and systematic uncertainties prevents the quoted compatibility with experiment from being conclusive.","major_comments":[{"comment":"The printed formula Gamma = L^3/(24 pi p_i m_psi) |x31|^2 is dimensionally inconsistent (|x31| has mass dimension one, so the right-hand side has dimension E^-3) and does not reproduce the quoted width. With the E5 numbers L = 10.67 GeV^-1, p = 0.468 GeV, m_psi = 3.946 GeV, and x31 = 0.0284 GeV, Eq. (6) gives about 7 MeV, while Table 4 quotes Gamma = 24.2(6.4) MeV; in lattice units the same formula gives Gamma/a ~ 0.19 against the tabulated Gamma/a = 0.0081(21). The tabulated value is instead reproduced by Gamma = L^3 p_i m_psi/(24 pi) |x31|^2. The authors must correct Eq. (6) or, if x31 carries an undocumented normalization, must state that normalization explicitly. Because this conversion is the only bridge between the lattice extraction and the physical width, the manuscript as written does not allow the central claim to be checked.","section":"Section 2, Eq. (6), and Table 4"},{"comment":"The paper states that 'at no point we establish an explicit connection to the infinite volume decay'. This is a load-bearing gap: the method assumes that the finite-volume mixing extracted with non-interacting plane-wave D mesons is the coupling entering Fermi's golden rule, and that the L^3 factor provides the correct compensation. Since the key result is the decay width, the authors should either provide a derivation of Eq. (6) in the context of their non-relativistic two-level system, or perform a cross-check (for instance, comparing with a Lüscher-type analysis at the same lattice parameters or at least demonstrating volume independence with more than the two ensembles used here). Without such a check, the compatibility with experiment could be coincidental.","section":"Section 2, after Eq. (6)"},{"comment":"The quoted result is obtained at a single lattice spacing and a single unphysical pion mass, and only statistical errors are reported. The central claim of compatibility with experiment would require an estimate of systematic uncertainties from, at minimum, the GEVP fit ranges, the smearing choices, the twist-angle interpolation, finite-volume effects, and the dependence on m_pi and a. As it stands, the agreement of the E5 central value with experiment is suggestive but not yet a quantitative validation of the method.","section":"Sections 3 and 4, Table 4"}],"minor_comments":[{"comment":"The ^3P_0 quark-model comparison fits the coupling beta to the same lattice data (as stated in the text), so the 'remarkable agreement' is a fitted reproduction rather than an independent prediction; the wording should make this explicit.","section":"Section 4, Figure 5"},{"comment":"The notation is inconsistent: the text defines p = sqrt(3) theta/L, while Eq. (8) writes sqrt(3) a theta_0/L; the factors of the lattice spacing should be made uniform.","section":"Equation (8)"},{"comment":"The text describing the figure refers to 'red lines' while the caption says 'solid line'; the color and line-style descriptions should be aligned.","section":"Figure 1"},{"comment":"The phrase 'compatible with experiment' should be qualified by noting that the comparison is made at an unphysical pion mass, one lattice spacing, and with statistical errors only, so the compatibility does not yet establish a precision prediction.","section":"Abstract and Conclusions"},{"comment":"The level-2 mass, m_cc = 3859(52) MeV, is close to the DD threshold and has a large uncertainty; a comment on how the level-3 identification with psi(3770) is justified would help the reader assess the GEVP analysis.","section":"Table 2"}],"recommendation":"major_revision","confidential_remarks":"The decisive issue is the inconsistency between Eq. (6) and Table 4. If the companion paper [8] contains the corrected derivation and normalization, a focused revision of this proceedings could resolve the problem. I recommend asking the authors to correct the formula, justify the finite-volume-to-infinite-volume conversion, and add at least a systematic-error estimate for the quoted width before the manuscript is accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—\n\nShort version: this proceedings applies the Pennanen–Michael ratio method to ψ(3770)→DD with PTBC and a GEVP, and reports Γ=24.2(6.4) MeV, compatible with experiment. That is a genuine new application. But the central conversion formula as printed is wrong: Eq. (6) has dimensions of energy^{-3} and, evaluated with the paper's own Table 4 numbers, gives about 7 MeV (Γ/a ≈ 0.19 in lattice units), not the quoted 24.2 MeV (Γ/a ≈ 0.0081). The table is instead reproduced by Γ = L^3 p m/(24π)|x|^2, which differs from Eq. (6) by a factor (p m_ψ)^2. So the paper's headline agreement with experiment cannot be verified from the manuscript as written.\n\nWhat is good: the ratio method itself is a legitimate, cheaper alternative to Lüscher analyses for narrow resonances; the setup with two ensembles, explicit GEVP, PTBC, and honest error bars is transparent; and the authors state plainly in Section 2 that they do not establish the finite-volume to infinite-volume connection. The 3P0 model comparison is qualitatively interesting, but the quark-pair creation strength β is fitted to the same lattice data, so that agreement is a fitted reproduction, not an independent prediction.\n\nOther soft spots: one lattice spacing, mπ≈440 MeV, no continuum or chiral extrapolation, and only statistical errors quoted. These are normal for an exploratory proceedings, and the authors say so.\n\nBottom line: the underlying idea and data are plausible, but as written the central equation contradicts the table. A serious referee should see this, and the authors should fix Eq. (6) or document the normalization of x31. If this is simply a typo, the result is likely okay; if not, the quoted width needs re-derivation. Until then, treat the experimental agreement as unverified. I would not cite this proceedings in its current form; the companion paper (arXiv:2411.10123) is the one to read. For a referee, yes—this deserves review, but with a demand for a corrected conversion and a clear statement of how x31 is normalized.","headline":"The ratio-method application is promising, but the printed decay-width formula contradicts the paper's own table, so the headline agreement with experiment is currently unverifiable.","tokens_in":8000,"tokens_out":5021,"would_cite":false,"duration_ms":44807,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper extracts the hadronic decay width of ψ(3770) to a D-meson pair from lattice QCD using a narrow-width ratio method, obtaining 24.2(6.4) MeV, compatible with experiment.","keywords":["lattice QCD","hadronic decay","charmonium","psi(3770)","narrow-width approximation","finite volume","ratio method","3P0 quark model"],"falsifier":"Compute the width on a third lattice volume at the same pion mass, keeping the on-shell momentum fixed: if the width from Eq (6) changes with $L$ beyond statistical error, the assumed $L^3$ compensation is wrong. A complementary test is a full finite-volume scattering analysis on the same ensembles, which would give an independent width to compare against.","tokens_in":6934,"feed_emoji":"⚛️","tokens_out":9660,"duration_ms":75881,"temperature":0.7,"pith_summary":"This paper argues that a narrow-width ratio method, computationally cheaper than standard multi-volume scattering analyses, can extract the hadronic decay width of an excited quarkonium state directly from lattice QCD. The key step is to isolate the finite-volume mixing $\\langle \\bar D D | \\psi(3770)\\rangle$ from correlator ratios, then convert it to the decay width $\\Gamma(\\psi(3770)\\to D\\bar D)$ through Fermi's golden rule. On two ensembles at $m_\\pi\\sim 440\\,\\mathrm{MeV}$ the extracted width is compatible with experiment, with the larger volume giving $\\Gamma=24.2(6.4)\\,\\mathrm{MeV}$. The paper further shows that the ${}^3P_0$ quark model reproduces the momentum dependence of the extracted mixing, suggesting the quark-rearrangement mechanism is qualitatively correct. If correct, the method gives a practical alternative for decays where the narrow-width approximation holds.","feed_headline":"Lattice ratio method yields psi(3770) width close to experiment","feed_subtitle":"A narrow-width approximation extracts the DD mixing and reproduces the measured decay width on two volumes.","key_machinery":"The central object is the hadronic mixing element $x_{31}\\equiv \\langle \\bar D D | \\psi(3770)\\rangle$ in a finite box. It is isolated from the long-time behavior of the ratio $R(t)=|\\bar T_3(t)|/\\sqrt{\\bar P^\\psi_{33}(t) P_{DD}(t)}$, whose spectral decomposition at large $t$ is $|x_{31}|/\\big(\\Delta\\sinh(t\\Delta)+A e^{-t\\Delta}\\big)$, where $\\Delta=(m_\\psi-E_{DD})/2$ is half the energy gap. The conversion to the decay width assumes non-interacting plane-wave $D$ mesons and uses Fermi's golden rule, $\\Gamma = \\frac{L^3}{24\\pi p_i m_\\psi}|x_{31}|^2$, with $p_i^2=m_\\psi^2/4-m_D^2$. Partially twisted boundary conditions on the charm quarks set the $D$-meson momenta so the on-shell condition $m_\\psi=2E_D$ can be reached, and the $\\bar D D$ operator is projected to a $p$-wave.","core_discovery":"The central claim is that the finite-volume hadronic mixing between the $\\psi(3770)$ charmonium state and a $D\\bar D$ pair in a $p$-wave, extracted from the ratio $R(t)$ of Eq (4), is the same quantity that enters Fermi's golden rule for the physical decay, so the decay width can be written as $\\Gamma = \\frac{L^3}{24\\pi p_i m_\\psi} |x_{31}|^2$ at the on-shell momentum. Inserting the lattice-determined mixing, the paper obtains $\\Gamma(\\psi(3770)\\to D\\bar D) = 24.2(6.4)\\,\\mathrm{MeV}$ on the larger ensemble, consistent with the experimental value. This is presented as evidence that the narrow-width ratio method is a viable alternative to standard finite-volume scattering analyses for this decay. The paper also extracts the mixing for off-shell momenta and compares the resulting width function with the ${}^3P_0$ quark-model prediction, finding qualitative agreement, particularly on the larger volume.","pith_inferences":["The method's validity hinges on the narrow-width approximation; for broader resonances or decays further from threshold, the assumed two-level system would be a poorer approximation, and the extracted width would need to be cross-checked against a full finite-volume analysis.","A natural next test is to apply the same ratio method to a decay with a known but wider resonance to see how the quality of the width degrades as the width-to-mass gap grows.","The explicit caveat that no infinite-volume connection is established suggests a possible follow-up derivation: a rigorous relation between this ratio-extracted mixing and the infinite-volume coupling, analogous to the quantization condition for two-particle energies, would place the method on firmer theoretical ground.","If the $L^3$ compensation is exact, the ratio method could also be used to extract decay couplings for states above multiple thresholds, where standard single-channel finite-volume analyses become complicated."],"forward_implications":["The narrow-width ratio method offers a computationally cheaper path to hadronic decay widths of narrow excited states, avoiding the need for several lattice volumes and group irreps required by standard scattering analyses.","The extraction is not restricted to on-shell kinematics: the lattice provides the mixing as a function of $D$-meson momentum, enabling direct comparison with quark-model predictions over a range of momenta.","Because the method works at unphysical pion mass ($m_\\pi\\sim 440\\,\\mathrm{MeV}$), a continuum extrapolation and a move to physical quark masses would test whether the agreement with experiment persists away from this single point.","The ${}^3P_0$ quark model, with parameters fixed by the lattice spectroscopy, reproduces the momentum dependence of the mixing, supporting the quark-pair-creation picture as a useful effective description."],"supporting_citations":[{"why":"Supplies the ratio method used to extract the hadronic mixing between a static quark-antiquark pair and a meson pair.","marker":"[9]"},{"why":"Provides the ratio formulas (4) and (5) and the golden-rule conversion to a decay width.","marker":"[15]"},{"why":"The companion full study this proceedings summarizes, including the detailed extraction and quark-model comparison.","marker":"[8]"},{"why":"Defines the ${}^3P_0$ quark-pair-creation model used for the analytic comparison.","marker":"[13]"},{"why":"Supplies the experimental decay width against which the lattice result is compared.","marker":"[1]"}],"fun_headline_variants":["psi(3770) width from lattice ratio matches experiment","Lattice ratio yields psi(3770) decay width consistent with experiment","Narrow-width method extracts psi(3770) width on lattice","Ratio method on lattice reproduces psi(3770) width","Charmonium decay width from lattice: ratio method works"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that the finite-volume mixing extracted with non-interacting plane-wave $D$ mesons, divided by the $L^3$ factor in the golden-rule formula, is exactly the same coupling that drives the decay in infinite volume; the paper explicitly notes it never establishes this connection.","fun_headline_variants_meta":{"raw":{"variants":["psi(3770) width from lattice ratio matches experiment","Lattice ratio yields psi(3770) decay width consistent with experiment","Narrow-width method extracts psi(3770) width on lattice","Ratio method on lattice reproduces psi(3770) width","Charmonium decay width from lattice: ratio method works"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00127,"raw_usage":{"total_tokens":5178,"prompt_tokens":906,"completion_tokens":4272,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":522,"completion_tokens_details":{"reasoning_tokens":4185}},"tokens_in":522,"tokens_out":4272,"duration_ms":26435,"temperature":1.0,"reasoning_tokens":4185,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T10:58:12.534810+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the width on a third lattice volume at the same pion mass, keeping the on-shell momentum fixed: if the width from Eq (6) changes with $L$ beyond statistical error, the assumed $L^3$ compensation is wrong. A complementary test is a full finite-volume scattering analysis on the same ensembles, which would give an independent width to compare against.","supporting_citations":[{"cited_title":"Le Yaouanc, L","cited_arxiv_id":null,"evidence_quote":"Defines the ${}^3P_0$ quark-pair-creation model used for the analytic comparison."}],"review_version":1}