{"id":"6d645f39-5fba-4de9-88fc-d98d56f1ef8c","arxiv_id":"2506.09306","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The first 2+1 flavor lattice QCD calculation of J/psi to gamma eta and gamma eta' form factors finds an enhanced eta'/eta ratio but absolute rates below experiment at m_pi around 391 MeV.","lead":"Using a supercomputer model of quarks and gluons called lattice QCD, the authors computed how often the J/psi particle decays into a photon plus either an eta or eta' meson. The calculation is the first to treat the strange quark distinctly and resolve the eta' as an excited state, giving a benchmark for the large BESIII data set.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central result assumes the electromagnetic current is purely charm; the light-quark current is omitted with justification deferred, so the reported F(0) values and eta'/eta ratio may not be the full physical amplitudes.","rationale":"I agree with the reader's weakest-assumption identification: the charm-only approximation to the electromagnetic current is the most load-bearing condition for the central claim. The calculation is ostensibly of the full transition matrix element in Eq. (1), but only the charm piece of j_mu is evaluated. The paper states the light-quark piece is negligible without showing an estimate, deferring to a longer write-up (Footnote 1). This matters because the results are compared to experiment at the few-percent level, and because the eta and eta' differ in flavor structure, so the omitted operator could affect the ratio. The authors' own Outlook, noting the unexpectedly small eta' mass (945(9) MeV at m_pi ~ 391 MeV) and the possibility of an underestimated axial U(1)/topological contribution, is a second, related limitation: the same singlet physics that produces the eta' also governs its radiative production, so the two issues compound. The rest of the calculation—variational extraction of eta' as an excited state, Wigner-Eckart averaging, AIC-based fits, and the consistency of the Q^2 dependence across multiple parameterizations—appears internally sound. No circularity or inconsistency in the use of experimental numbers was found. The proposed lattice check, computing the disconnected light-quark current diagrams on the same ensemble, would directly settle whether the omitted contribution is within the quoted errors. If it is, the conditional accept is justified; if not, the numerical claims and their comparison to experiment would need revision. I therefore see no reason to change the reader's conditional verdict.","tokens_in":9380,"tokens_out":17295,"duration_ms":194196,"concrete_test":"On the same 20^3 x 256 ensemble (288 configurations, Nvec=128), compute the three-point functions for J/psi -> gamma eta^(prime) with the light-quark part of the electromagnetic current, j_mu^light = (2/3)ubar gamma_mu u - (1/3)dbar gamma_mu d - (1/3)sbar gamma_mu s, using the same variationally optimized meson operators, source-sink separations, and two-stage averaging. Add these contributions to the charm-only results and re-extract |F_{J/psi eta}(0)|, |F_{J/psi eta'}(0)|, and their ratio from the same Q^2 parameterizations. If the light-quark part shifts any |F(0)| by more than its quoted statistical error, or shifts the ratio by more than 0.29, the charm-only approximation is invalid at the claimed precision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claims are the real-photon form factors |F_{J/psi eta}(0)| = 0.00235(18) GeV^-1, |F_{J/psi eta'}(0)| = 0.00777(37) GeV^-1, and the ratio 3.30(29), presented as first-principles lattice QCD results and compared to BESIII/PDG. The computation evaluates only the charm-quark part of the electromagnetic current: 'To a very good approximation, the radiative decay processes considered in this letter are dominated by the photon coupling only to the charm quark in the J/psi, and as such we will compute only the charm part of the electromagnetic current,' with justification deferred to Footnote 1 ('associated longer write-up'). The omitted pieces are the light-quark vector-current matrix elements <eta^(prime)| (2/3)ubar gamma_mu u - (1/3)dbar gamma_mu d - (1/3)sbar gamma_mu s |J/psi>, disconnected loop diagrams that are not reported. Because eta' is dominantly a flavor singlet while eta is dominantly octet, these omitted matrix elements enter with different charge-weighted flavor traces, so absolute amplitudes and the eta'/eta ratio could shift beyond the quoted errors, which cover only statistics and anisotropy variation. The Outlook also notes an unexpectedly small eta' mass (945(9) MeV at m_pi ~ 391 MeV), suggesting a possibly underestimated axial U(1) contribution that would affect the singlet-dominated production mechanism. Thus the reported F(0) values may not be the complete first-principles amplitudes for these decays.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This letter reports the first 2+1-flavor lattice QCD calculation of the transition form factors for J/ψ → γ η and J/ψ → γ η′, performed on a single anisotropic ensemble with a_s ≈ 0.12 fm, a_t^{−1} ≈ 5.7 GeV, and m_π ≈ 391 MeV. The η and η′ are isolated with variationally optimized operators (the η′ as the first excited state in the isoscalar pseudoscalar channel), and a two-stage averaging procedure — Wigner-Eckart subduction of symmetry-related correlators, followed by an over-constrained fit imposing a single F(Q^2) per kinematical point — yields 70 values of Q^2 for each channel. Three-point functions are computed at source-sink separations Δt/a_t = 12, 16, 20, 24, with time-window fits combined via AIC weighting. The real-photon amplitudes are extracted from several Q^2 parameterizations and from linear interpolation near Q^2 = 0, giving |F_{J/ψη}(0)| = 0.00235(18) GeV^{−1}, |F_{J/ψη′}(0)| = 0.00777(37) GeV^{−1}, and a ratio 3.30(29). Only the charm-quark part of the electromagnetic current is evaluated, with justification deferred to a companion write-up; the resulting values lie below the BESIII/PDG rates, and the computed ratio is larger than the experimental ratio.","tokens_in":9689,"tokens_out":20238,"duration_ms":214383,"significance":"If the omitted light- and strange-quark pieces of the electromagnetic current are indeed negligible at the few-percent level, this is a landmark calculation: it demonstrates that the η′ can be accessed as an excited state with variational operators, that the disconnected-process signal can be controlled by symmetry-based averaging, and that a wide range of Q^2 can be covered with a single ensemble. The technical care is evident and is a genuine strength: multiple source-sink separations, AIC-based averaging over time windows, consistency between irreps and between neighboring Q^2 values, agreement among several functional forms for the Q^2 dependence, and an explicit statement of the pion-mass and single-spacing limitations. The principal caveat is that the computation evaluates the charm-current contribution to the amplitude rather than the full electromagnetic amplitude, and the size of the omitted disconnected light-current contributions is not estimated in the letter.","major_comments":[{"comment":"The central quantitative results are obtained with only the charm-quark part of the electromagnetic current. The omitted light- and strange-quark pieces, <η^(′)|(2/3) ū γ_μ u − (1/3) d̄ γ_μ d − (1/3) s̄ γ_μ s |J/ψ>, are disconnected diagrams whose size is not estimated anywhere; the sentence 'To a very good approximation, ... we will compute only the charm part of the electromagnetic current' defers the justification entirely to the 'associated longer write-up' (footnote 1). For the η′, which has a substantial strange-quark component, and for the η, whose octet component carries the net charge factor, these contributions need not be negligible at the level of the quoted 4–8% errors, and they enter with different charge factors for the two mesons, so both |F(0)| values and the ratio 3.30(29) (quoted against the PDG value 2.44(4)) could shift. Because the abstract claims a 'first principles calculation of the radiative decays', and because Fig. 3 and the Outlook compare the computed values with the BESIII/PDG rates and interpret the disagreement as a 'mystery', the manuscript currently presents the charm-current contribution as the full physical amplitude. The authors should either include in the letter a quantitative estimate or upper bound of the light-current contribution (for example, by evaluating the light-quark disconnected diagram on a subset of configurations, or by a model-based estimate anchored to the known flavor content of η and η′), or reframe the abstract, the results, and the Outlook explicitly and consistently as the charm-current contribution to the transition form factors, with the comparison to experiment qualified accordingly. This is load-bearing because it affects the absolute amplitudes, the ratio, and the central comparison with experiment.","section":"Calculation (charm-current paragraph, footnote 1); Results; Outlook"},{"comment":"The overall normalization of every extracted form factor is set by the multiplicative renormalization of the O(a)-improved charm vector current, which is fixed by matching to the η_c form factor at Q^2 = 0 from Ref. [28], plus a tree-level improvement term that is not specified in the letter. The precision of this renormalization is not stated, and its uncertainty is not propagated into |F_{J/ψη}(0)| and |F_{J/ψη′}(0)|; the quoted errors appear to include statistics and anisotropy variation only, yet the F(0) values are compared with experiment at the 5–8% level. The renormalization uncertainty should be quantified, or at least argued to be negligible, in the error budget, since it rescales the absolute values that enter the central claims.","section":"Calculation (renormalization paragraph); Results (final F(0) values)"}],"minor_comments":[{"comment":"The sign convention for Q^2 used in Eq. (1) and in the figures is not stated; since the text refers to the timelike region (the Dalitz decay) while the figure axes run over negative Q^2, the convention should be given explicitly in the text.","section":"Calculation; Figure 2"},{"comment":"The 'somewhat unexpectedly small' η′ mass, 945(9) MeV, is used to motivate a possible underestimate of the axial U(1) contribution, but the letter does not show or cite where this mass is determined; a one-line statement of the extraction, or a reference to the spectrum analysis, is needed for this claim to be evaluable.","section":"Outlook"},{"comment":"The two-stage averaging procedure is described in detail, but the 'novel' aspect would be easier to judge if the statistical gain were quantified (for example, the variance reduction or the effective number of independent correlators) relative to un-averaged correlators.","section":"Calculation"},{"comment":"Minor typography and completeness issues: χ2/Ndof should be typeset as χ²/N_dof; the width formula following Eq. (1) has no reference, and the factor 4/27 (which combines the charm charge and phase space) is not derived; the acronym PDG is introduced only in the caption of Fig. 3.","section":"Results"}],"recommendation":"major_revision","confidential_remarks":"The main technical justification — that the charm-only electromagnetic current is 'a very good approximation' — is deferred to an 'associated longer write-up' that is not part of this submission; if that document is not available to the referee, this load-bearing approximation cannot be verified from the letter alone. The editor may want to request the companion write-up, or an explicit estimate of the light-quark current contribution, as part of the revision. The paper is otherwise careful and honest about its known limitations (single lattice spacing, m_π ≈ 391 MeV, no continuum extrapolation), and the internal consistency checks are convincing."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, what's new: this is the first lattice QCD calculation of J/psi -> gamma eta(eta') with 2+1 flavors, where the eta' appears as the first excited state in the isoscalar pseudoscalar channel. The authors achieve this with variational operators and a Wigner-Eckart averaging scheme that tames the disconnected-diagram noise well enough to get 70 Q^2 points. That is genuine technical progress. The statistical analysis is careful: AIC-based averaging over time windows, multiple source-sink separations, and consistency checks between irreps and extraction methods. The central qualitative result—enhanced eta' production relative to eta—matches the singlet/octet picture and looks robust.\n\nThe soft spot that matters is the charm-only electromagnetic current. The paper evaluates only the charm-quark part of j_mu, with the justification deferred to an associated longer write-up. The light-quark disconnected diagrams, where the photon couples to the sea-quark loop that forms the eta or eta', are not computed. The authors call this a very good approximation, but no quantitative evidence appears in this letter. Since eta' is flavor-singlet while eta is mostly octet, the omitted charge-weighted traces enter differently, so neither the absolute F(0) values nor the ratio are automatically protected. This is a load-bearing approximation for the headline numbers, and the stress-test concern is legitimate.\n\nOther limitations are less severe: one lattice spacing (no continuum extrapolation), m_pi ~391 MeV, and errors that cover statistics and anisotropy variation only. The authors themselves flag the low eta' mass on this ensemble, 945(9) MeV, as a possible sign that the axial U(1) contribution is underestimated. They stay appropriately cautious about comparing to experiment.\n\nThe paper deserves a serious referee. It is the first calculation of its kind, technically credible, and it opens the door to more complex radiative decays like J/psi -> gamma(pi pi, K Kbar). A referee should require the longer write-up, the form-factor tables, and at least a crude estimate of the light-quark current contribution. The citation pattern looks fine; the renormalization using a previous eta_c form factor on the same lattice is a reasonable calibration.\n\nWho should read it: lattice QCD practitioners working on charmonium or disconnected correlators, and phenomenologists following BESIII. I would bring it to a reading group and cite it once the supporting material is available.","headline":"A solid first 2+1 flavor lattice QCD calculation of J/psi -> gamma eta(eta'), but the charm-only current approximation needs quantitative support before the absolute amplitudes are taken as benchmarks.","tokens_in":10261,"tokens_out":3428,"would_cite":true,"duration_ms":37289,"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":"Lattice QCD yields first-principles amplitudes for J/psi decaying to eta and eta'.","keywords":["lattice QCD","radiative decay","J/psi","eta-eta' mixing","transition form factor","variational analysis","disconnected diagram","charmonium"],"falsifier":"Recompute the amplitudes on the same lattice including the full electromagnetic current (light and charm quarks) and compare |F(0)| for both mesons; if the values move toward the experimental ones, the charm-only approximation was responsible, whereas if they do not, a measurement of the topological-charge distribution or a physical-pion-mass ensemble would discriminate the quark-mass and axial-anomaly explanations.","tokens_in":9114,"feed_emoji":"⚛️","tokens_out":12259,"duration_ms":106978,"temperature":0.7,"pith_summary":"This paper claims the first calculation within lattice QCD, with two light and one strange dynamical quark flavor, of the radiative decays $J/\\psi \\to \\gamma \\eta$ and $J/\\psi \\to \\gamma \\eta'$. It reports the transition form factors over a wide range of photon virtuality and determines the real-photon amplitudes at a pion mass of about 391 MeV, finding that $\\eta'$ production is enhanced over $\\eta$ by a factor $3.30(29)$. A sympathetic reader would care because these decay amplitudes are a direct, non-perturbative prediction of QCD for processes that are measured experimentally and are relevant to light-meson and glueball spectroscopy. The paper also shows that the variational and averaging technology makes this noisy 'disconnected' sector tractable, which is the prerequisite for studying radiative production of light-meson resonances in $J/\\psi$ decays.","feed_headline":"Lattice QCD computes J/psi radiative decays to eta, eta'","feed_subtitle":"The first 2+1-flavor lattice QCD calculation of these decays lands below experiment, hinting at quark-mass or vacuum-topology effects.","key_machinery":"The load-bearing machinery is the variational construction of optimized meson operators: in a basis of fermion-bilinear interpolating operators, a matrix of two-point correlation functions is solved variationally at each momentum and each irreducible representation of the (boosted) lattice symmetry group, producing operators with dominant overlap with the $\\eta'$ excited state and cleaner $\\eta$ and $J/\\psi$ signals. On top of this, a two-stage correlator-averaging procedure reduces 1748 non-zero three-point correlators to 70 well-determined values of $F(Q^2)$: first, Wigner–Eckart averaging of correlators related by exact lattice symmetries; second, an over-constrained linear least-squares fit across different irreps assuming approximate Lorentz symmetry via subduction. The electromagnetic current is evaluated in its charm-quark part only, renormalized using the $\\eta_c$ form factor at $Q^2=0$ from the same lattice action, and the real-photon amplitudes are extracted by parameterizing the $Q^2$ dependence with convergent conformal-mapping forms. The single identity carrying the physical interpretation is the ratio $|F_{\\psi\\eta'}(0)|/|F_{\\psi\\eta}(0)|$, which exposes the flavor-singlet content of the $\\eta'$.","core_discovery":"This paper presents the first lattice QCD calculation, with two degenerate light quark flavors and a heavier strange flavor, of the radiative decays $J/\\psi \\to \\gamma \\eta$ and $J/\\psi \\to \\gamma \\eta'$. It computes the transition form factor $F(Q^2)$ defined by the matrix element $\\langle \\eta^{(\\prime)}(p') | j^\\mu_{\\rm em}(0) | J/\\psi(p,\\lambda)\\rangle = \\epsilon^{\\mu\\nu\\rho\\sigma} p'_\\nu p_\\rho \\epsilon_\\sigma(p,\\lambda) F_{\\psi\\eta^{(\\prime)}}(Q^2)$, obtaining it at 70 discrete values of the photon virtuality $Q^2$ from the timelike region (Dalitz decay) to the real-photon point. At $m_\\pi \\simeq 391$ MeV the real-photon amplitudes are $|F_{\\psi\\eta}(0)| = 0.00235(18)\\,\\mathrm{GeV}^{-1}$ and $|F_{\\psi\\eta'}(0)| = 0.00777(37)\\,\\mathrm{GeV}^{-1}$, with ratio $3.30(29)$, where the $\\eta'$ is isolated as the first-excited pseudoscalar isoscalar state using variationally optimized operators. The paper reports that both amplitudes lie below the experimentally measured values and discusses as candidate origins a strong light-quark-mass dependence or an under-realized axial $U(1)$ anomaly on this ensemble.","pith_inferences":["A direct test of the charm-only current approximation is to compute the light-quark part of the electromagnetic current on this same ensemble; if the omitted piece is not negligible, the amplitudes and possibly the $\\eta'/\\eta$ ratio would move toward the experimental values.","The paper's observation that the $\\eta'$ mass, 945(9) MeV, is unexpectedly low at this pion mass suggests a measurable accompanying prediction: the topological-charge distribution on this ensemble should show a suppressed topological susceptibility, which would simultaneously explain the low mass and the low radiative amplitudes.","If the common $Q^2$ shape for $\\eta$ and $\\eta'$ persists for resonant final states, the factorization hypothesis could be used to analyze $J/\\psi \\to \\gamma\\,(\\pi\\pi,\\,K\\bar K)$ data in terms of a single universal charm-quark production amplitude multiplied by a light-meson transition form factor.","A finer lattice spacing at the same quark masses would discriminate whether part of the deficit relative to experiment is a discretization artifact rather than a physical quark-mass or topology effect."],"forward_implications":["The measured ratio $|F_{\\psi\\eta'}(0)|/|F_{\\psi\\eta}(0)| = 3.30(29)$ confirms that the flavor-singlet, gluon-rich component of the $\\eta'$ drives its enhanced production in charmonium radiative decay.","The $Q^2$ dependence of the $\\eta$ and $\\eta'$ form factors is consistent with a common shape, supporting the hypothesis that the production amplitude factorizes from the light-meson final-state dynamics.","The computed amplitudes lie below the experimental central values, with the paper attributing the gap to either strong light-quark-mass dependence or an under-realized axial $U(1)$ anomaly on this lattice ensemble.","The demonstrated signal quality for the disconnected diagram means the same methods can be extended to other charmonium radiative transitions, to $h_c$ and $\\psi(2S)$, and to processes like $J/\\psi \\to \\gamma\\,(\\pi\\pi,\\,K\\bar K)$ where light-meson resonances appear."],"supporting_citations":[{"why":"Supplies the variational basis of fermion-bilinear operators that isolates the eta' as an excited state.","marker":"[11, 12]"},{"why":"Provides the distillation framework that makes the large number of three-point correlators computationally feasible.","marker":"[13]"},{"why":"Sets the multiplicative renormalization of the charm vector current via the eta_c form factor at Q^2=0 on the same lattice action.","marker":"[28]"},{"why":"Provides the AIC-based weighting used to combine timeslice fits into conservative averages.","marker":"[33]"},{"why":"Supplies lattice Clebsch-Gordan coefficients for the Wigner-Eckart averaging of correlators related by exact lattice symmetries.","marker":"[32]"},{"why":"Gives the subduction relations that justify combining different irreps under approximate Lorentz symmetry.","marker":"[34]"},{"why":"Experimental Dalitz-decay measurement whose dipole parameterization of the Q^2 dependence is compared with the current data.","marker":"[7]"},{"why":"Experimental measurement of J/psi -> gamma eta and gamma eta' used for comparison of the real-photon amplitudes.","marker":"[6]"},{"why":"World-average experimental values used for the comparison of the eta'/eta ratio.","marker":"[35]"},{"why":"Previous one- or two-flavor lattice calculation lacking a true eta-eta' distinction, which this work supersedes.","marker":"[9]"}],"fun_headline_variants":["First 2+1-flavor LQCD calc of J/psi to gamma eta, eta'","Lattice QCD computes J/psi radiative decays to eta, eta' with ratio 3.3","J/psi to gamma eta' from LQCD: first excited-state extraction","LQCD J/psi -> gamma eta, gamma eta' below experiment","2+1-flavor LQCD: J/psi radiative decays, eta' from excited state"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes the photon couples only to the charm quark in the J/psi, so only the charm piece of the electromagnetic current is evaluated; if the neglected light-quark current contributes at the few-percent level, the absolute amplitudes and possibly the eta'/eta ratio would shift.","fun_headline_variants_meta":{"raw":{"variants":["First 2+1-flavor LQCD calc of J/psi to gamma eta, eta'","Lattice QCD computes J/psi radiative decays to eta, eta' with ratio 3.3","J/psi to gamma eta' from LQCD: first excited-state extraction","LQCD J/psi -> gamma eta, gamma eta' below experiment","2+1-flavor LQCD: J/psi radiative decays, eta' from excited state"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00068,"raw_usage":{"total_tokens":3180,"prompt_tokens":1123,"completion_tokens":2057,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":739,"completion_tokens_details":{"reasoning_tokens":1938}},"tokens_in":739,"tokens_out":2057,"duration_ms":16088,"temperature":1.0,"reasoning_tokens":1938,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:51:58.609872+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the amplitudes on the same lattice including the full electromagnetic current (light and charm quarks) and compare |F(0)| for both mesons; if the values move toward the experimental ones, the charm-only approximation was responsible, whereas if they do not, a measurement of the topological-charge distribution or a physical-pion-mass ensemble would discriminate the quark-mass and axial-anomaly explanations.","supporting_citations":[{"cited_title":"From the best estimates in the current calculation, the ratio, |FJ/ψ η′(0)| |FJ/ψ η(0)| = 3.30(29), which is somewhat larger than the value extracted from the PDG averages, 2.44(4)","cited_arxiv_id":null,"evidence_quote":"World-average experimental values used for the comparison of the eta'/eta ratio."}],"review_version":1}