{"id":"48acb049-40d8-4b42-bdfe-df4dcd99735e","arxiv_id":"2501.16124","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using a meson-loop model calibrated to psi(3770) to J/psi eta, the paper predicts Gamma(psi2(3823) to J/psi eta) = 29.6 keV and smaller eta_c omega and psi3(3842) rates.","lead":"This paper calculates the hidden charm decay rates of three D-wave charmonium states using meson loops, with one model parameter fixed by the measured psi(3770) to J/psi eta branching fraction. It predicts a roughly 30 keV width for psi2(3823) to J/psi eta, a level that BESIII, Belle II and LHCb can test.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The η-η' mixing angle sign is stated inconsistently (negative range quoted, then θ = 19.1°), and the headline ψ2(3823)→J/ψη width is sensitive to this sign; this is the most load-bearing issue, more so than the transferability of αΛ between D-wave charmonia.","rationale":"The central claim is the ψ2(3823)→J/ψη width of about 30 keV and the ~10% ratio to γχc1. The reader's weakest_assumption is the transferability of αΛ from ψ(3770) to ψ2(3823). I think the more load-bearing issue is the internal sign inconsistency for the η-η' mixing angle, because it directly enters the η coupling and the computed amplitude. While the fit to ψ(3770) can absorb an overall rescaling of α, the ψ2 prediction's dependence on αΛ is not the same as the ψ1 dependence, so the sign choice can change the central number. The manuscript does not explain how 19.1° is compatible with the quoted negative range, and it cites experimental Refs. [48,49] without clarifying the convention. This is not an ad hoc model assumption but a stated, unresolved inconsistency in the input. The proposed recomputation with the negative angle and the endpoints would settle it. Secondary issues—the omitted ψ3 DDbar loop and the model-systematic error bars—are real but do not threaten the ψ2 claim as directly. The reader's CONDITIONAL verdict already captures the need for corrections; my read does not change that verdict.","tokens_in":18912,"tokens_out":10496,"duration_ms":92984,"concrete_test":"Recompute Γ[ψ2(3823)→J/ψη] and the ratio to γχc1 with θ = −19.1°, and also with the stated endpoints θ = −10° and −20°, refitting αΛ each time to the measured Br(ψ(3770)→J/ψη) = (8.7 ± 1.2) × 10⁻⁴. If the resulting central value differs from 29.64 keV by more than the quoted ±4 keV, or if the ratio moves outside the BESIII upper limit (0.14) or the LHCb 1σ interval, the headline prediction is not robust to the sign ambiguity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The manuscript states in Section II (after Eq. (11)) that θ ranges from −10° to −20°, but then sets θ = 19.1°. The η coupling to charm mesons in Eq. (18) is proportional to α(θ) = (cosθ − √2 sinθ)/√6; at θ = +19.1° α ≈ 0.20, whereas at θ = −19.1° α ≈ 0.58. All J/ψη amplitudes (Eqs. (12), (A1), (A3)) are linear in α, so the αΛ fitted to Br(ψ(3770)→J/ψη) shifts with θ. Because the ψ2(3823) loop integrals have a different αΛ dependence than the ψ(3770) loop integrals, the central prediction Γ[ψ2→J/ψη] = 29.64 keV does not simply rescale and could move substantially. The error bar is also quoted inconsistently (+4.01/−4.63 in the abstract, +4.01/−4.43 in Eq. (19), +4.10/−4.43 in the summary), which further obscures the true uncertainty. These internal inconsistencies are more directly load-bearing than the assumption that αΛ transfers between D-wave charmonia, since they affect the computed amplitude itself.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies two-body hidden-charm decays of the D-wave charmonia ψ(3770), ψ2(3823), and ψ3(3842) in a hadronic meson-loop model. The model parameter αΛ is fixed by reproducing the measured branching fraction of ψ(3770)→J/ψη, and the same parameter range is then used to predict the partial widths of ψ(3770)→ηcω, ψ2(3823)→J/ψη/ηcω, and ψ3(3842)→J/ψη/ηcω. The central result is Γ[ψ2(3823)→J/ψη] = (29.64^{+4.01}_{-4.63}) keV, which corresponds to about a 10% ratio of ψ2(3823)→J/ψη to ψ2(3823)→γχc1 and is proposed as a testable observable for BESIII, Belle II, and LHCb.","tokens_in":19232,"tokens_out":3836,"duration_ms":37271,"significance":"If the predictions are reliable, the paper provides a useful quantitative estimate for a channel that is directly accessible to ongoing experiments, particularly the ψ2(3823)→J/ψη width and its ratio to the radiative width. The work is concrete and falsifiable, and the authors are explicit about the model, the amplitudes, and the parameter determination. The main strengths are the complete one-loop expressions and the use of an experimentally determined branching fraction to fix the cutoff parameter. However, the central numerical prediction depends sensitively on an η-η' mixing sign convention that is stated inconsistently, and the ψ3 predictions omit a vertex whose contribution the authors themselves acknowledge can be sizable. These issues must be resolved before the numerical results can be used as quantitative predictions.","major_comments":[{"comment":"The η-η' mixing angle is stated inconsistently. The text says θ ranges from −10° to −20°, citing Refs. [46,47], but then sets θ = 19.1°, citing Refs. [48,49]. Because α(θ) = (cosθ − √2 sinθ)/√6 is linear in the amplitudes, α ≈ 0.58 at θ = −19.1° but α ≈ 0.20 at θ = +19.1°. Since αΛ is fitted to Br(ψ(3770)→J/ψη), a change in the sign convention shifts αΛ and does not simply rescale the predicted ψ2(3823)→J/ψη width, because the loop integrals have an αΛ dependence through the form factor. The authors must specify the mixing convention used for Refs. [48,49], repeat the fit with a consistent sign, and show how the headline value and its uncertainty change.","section":"Section II, after Eq. (11); Section III.B"},{"comment":"The quoted uncertainty of the central prediction is internally inconsistent: the abstract gives Γ[ψ2(3823)→J/ψη] = (29.64^{+4.01}_{-4.63}) keV, Eq. (19) gives (29.64^{+4.01}_{-4.43}) keV, and the summary gives (29.64^{+4.10}_{-4.43}) keV. Since the paper presents the asymmetric error as part of its quantitative claim, the authors should reconcile these numbers and explain how the error is propagated from the αΛ range, including whether the upper/lower asymmetry arises from the non-linear dependence of the loop integrals.","section":"Eq. (19), Abstract, and Section IV"},{"comment":"The ψ3(3842)→J/ψη predictions omit the ψ3(3842)D Dbar vertex because it vanishes at leading order in the heavy-quark expansion, but the authors explicitly acknowledge that 'the meson loops relevant to ψ3(3842)D Dbar may have sizable contributions since the D Dbar in the meson loops could be on-shell.' Given that the predicted ψ3(3842) partial widths are only 7.54 eV and 1.12 eV, an omitted on-shell contribution is not negligible and could change the result by orders of magnitude. The authors should either estimate this contribution, or present the ψ3 predictions with a clear caveat that they are not complete quantitative predictions.","section":"Section III.B, last paragraph; Appendix A, Eqs. (A3)-(A4)"},{"comment":"The extrapolation of αΛ from ψ(3770) to ψ2(3823) and ψ3(3842) is justified only by the statement 'Considering the similarity of the of the D-wave charmonia'. The initial states have different masses, different spin structures, and different allowed charmed-meson channels, so the off-shell form factor and the effective coupling strength need not be identical. Since the central ψ2 prediction depends on this transferability, the authors should provide a quantitative check, for example by showing the sensitivity of Γ[ψ2→J/ψη] to a state-dependent αΛ variation or by comparing the loop integrals for different J states.","section":"Section III.B"}],"minor_comments":[{"comment":"The mixing angle θ appears with two different sign conventions in Refs. [46,47] and [48,49]. Please define the convention explicitly in the text so that the numerical value θ = 19.1° is unambiguous.","section":"Section II, Eq. (11)"},{"comment":"The measured branching fraction of ψ(3770)→J/ψη is quoted as (8.7±1.0±0.8)×10^-4 in the Introduction and as (8.7±1.2)×10^-4 in Section III.B. Please use one consistent experimental value with the full uncertainty breakdown.","section":"Section I and Section III.B"},{"comment":"The caption says 'lift panel' where 'left panel' is intended.","section":"Fig. 4 caption"},{"comment":"The sentence 'Considering the similarity of the of the D-wave charmonia' has a grammatical error and should be rewritten.","section":"Section III.B"},{"comment":"Several terms in the effective Lagrangian have index contractions that are hard to verify, for example the expressions involving pνϵα(p) and terms with pα1νgβμ−pβ2νgμα. Please check that all Lorentz indices are contracted consistently, since the reader needs to reproduce the amplitudes independently.","section":"Eq. (8)"},{"comment":"The phrase 'which are much small comparing to widths' should read 'which are much smaller than the widths'.","section":"Section III.B, ψ3 discussion"}],"recommendation":"major_revision","confidential_remarks":"The manuscript deserves serious consideration after the authors fix the η-η' sign convention and its effect on the fitted αΛ, reconcile the inconsistent error bars, and address the omitted ψ3-DDbar vertex. The central prediction for ψ2(3823)→J/ψη is interesting and testable, but the current internal inconsistencies make the quoted numbers unreliable. The paper fits the journal's scope; no novelty concern from my side."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a competent meson-loop calculation that produces a testable number—Γ(ψ2(3823)→J/ψη) ≈ 30 keV, about 10% of the γχc1 width—and it passes the obvious experimental constraints. The method is standard (the same meson-loop mechanism used for ψ(3770) non-DDbar decays), so the new content is the application to ψ2 and ψ3, the ηcω channels, and the partial widths for states that nobody has calculated before. That is worth having.\n\nThe calculation is carried out carefully: the amplitudes are given explicitly, the couplings come from heavy-quark/chiral Lagrangians, and αΛ is fit to the measured Br(ψ(3770)→J/ψη). The ψ2 result is consistent with BESIII's upper limit and with the Belle/LHCb ratio. Good.\n\nNow the soft spots, in order of size. First, the η-η' mixing angle sign. The text says θ ranges from −10° to −20° and then sets θ = 19.1°. That is an internal contradiction. α(θ) = (cosθ − √2 sinθ)/√6 changes by a factor of about three between +19.1° and −19.1°, and since every J/ψη amplitude is linear in α, the fit to αΛ and the predicted ψ2 width will move significantly. If the calculation actually used −19.1° (likely from the cited Mark III/DM2 values), then the text has a simple sign typo, but as written this is load-bearing and needs to be fixed before the numbers are used. The inconsistent error bars (4.63 vs 4.43 vs 4.10 in different places) don't change the physics but suggest the uncertainty accounting needs another pass.\n\nSecond, the ψ3(3842) results are explicitly incomplete—the authors note that ψ3DDbar loop contributions could be sizable because the DDbar pair can go on-shell, but they don't compute them. That is an honest caveat, and the ψ3 numbers are presented as partial, but it means the eV-level widths in Eq. (21) should not be treated as a final prediction.\n\nThird, the assumption that αΛ transfers from ψ(3770) to ψ2(3823) and ψ3(3842) is plausible but unchecked. The quoted uncertainties only cover the fit range, not this model systematics. For the ψ2 central prediction that's a caveat, not a killer.\n\nBottom line: the paper deserves a serious referee. The sign issue must be resolved, the errors made consistent, and the ψ3 caveat kept front and center, but the ψ2(3823)→J/ψη width is exactly the kind of concrete target BESIII and LHCb can go after. I'd send it to review.","headline":"A competent meson-loop calculation with a testable ψ2(3823)→J/ψη width, but the η-η' mixing angle sign is stated inconsistently and needs fixing.","tokens_in":19826,"tokens_out":3266,"would_cite":false,"duration_ms":29186,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper predicts that psi2(3823) decays to J/psi eta with a partial width near 30 keV, about 10% of its radiative width.","keywords":["D-wave charmonia","hidden charm decay","meson loop mechanism","psi(3770)","psi2(3823)","psi3(3842)","J/psi eta","eta_c omega"],"falsifier":"Measure the ratio $\\mathcal{B}[\\psi_2(3823)\\to J/\\psi\\eta]/\\mathcal{B}[\\psi_2(3823)\\to\\gamma\\chi_{c1}]$ with the next generation of charmonium data; a central value outside roughly $5\\%$–$15\\%$, or an absolute $\\psi_2(3823)\\to J/\\psi\\eta$ width far from $30$ keV, would falsify the $\\alpha_\\Lambda$ transfer assumption.","tokens_in":18666,"feed_emoji":"⚛️","tokens_out":9285,"duration_ms":73100,"temperature":0.7,"pith_summary":"This paper predicts the two-body hidden-charm decay rates of the spin-triplet D-wave charmonia using the meson loop mechanism. A single form-factor parameter $\\alpha_\\Lambda$ is fixed by reproducing the measured branching fraction of $\\psi(3770)\\to J/\\psi\\eta$, and the same parameter then yields $\\Gamma[\\psi_2(3823)\\to J/\\psi\\eta]=(29.64^{+4.01}_{-4.63})$ keV. The corresponding ratio to $\\psi_2(3823)\\to\\gamma\\chi_{c1}$ is about 10%, below the current experimental upper limit and consistent with existing Belle and LHCb data. Because $\\psi_2(3823)$ cannot decay to $D\\bar D$, these hidden-charm channels are among its only strong decay modes, so the prediction gives a concrete target for BESIII, Belle II, and LHCb.","feed_headline":"psi2(3823) hidden-charm width predicted near 30 keV","feed_subtitle":"The ratio to the radiative gamma-chi_c1 mode is about 10 percent, a target current experiments can test.","key_machinery":"The machinery is the meson loop mechanism: the initial charmonium fluctuates into an $S$-wave charmed-meson pair ($D\\bar D$, $D\\bar D^*$, $D^*\\bar D^*$) that rescatters into $J/\\psi\\eta$ or $\\eta_c\\omega$. The amplitudes are built from heavy-quark effective Lagrangians — the superfield $R$ for $S$-wave charmonia, the spin multiplet $J^{\\mu\\lambda}$ for $D$-wave charmonia, and the $H$ superfields for charmed mesons — so all couplings are fixed by symmetry up to the gauge couplings $g_1$ and $g_2$. Loop convergence and off-shell effects are controlled by the monopole form factor $F=(m_q^2-\\Lambda^2)/(q^2-\\Lambda^2)$ with $\\Lambda=m+\\alpha_\\Lambda\\Lambda_{\\mathrm{QCD}}$; the single free parameter $\\alpha_\\Lambda$ is the load-bearing dial.","core_discovery":"The paper's central claim is that one meson-loop amplitude, regulated by a monopole form factor with a single fitted parameter, describes the hidden-charm decays of all three $D$-wave charmonia spin triplets. The fitted range $\\alpha_\\Lambda=(1.11^{+0.04}_{-0.05})$ reproduces $\\mathcal{B}[\\psi(3770)\\to J/\\psi\\eta]=(8.7\\pm1.2)\\times10^{-4}$, and from it the paper obtains $\\mathcal{B}[\\psi(3770)\\to\\eta_c\\omega]=(6.03^{+0.82}_{-0.92})\\times10^{-5}$, $\\Gamma[\\psi_2(3823)\\to J/\\psi\\eta]=(29.64^{+4.01}_{-4.63})$ keV, and $\\Gamma[\\psi_2(3823)\\to\\eta_c\\omega]=(0.38^{+0.05}_{-0.06})$ keV. The ratio $\\Gamma[\\psi_2(3823)\\to\\eta_c\\omega]/\\Gamma[\\psi_2(3823)\\to J/\\psi\\eta]=0.127$ is essentially parameter-independent. For $\\psi_3(3842)$, the widths are only $7.54$ eV and $1.12$ eV because its hidden-charm final states couple through an $F$ wave, so the paper concludes that hidden charm is negligible for that state.","pith_inferences":["If the predicted 30 keV width is correct, the hidden-charm channels exhaust only a small part of $\\psi_2(3823)$'s $<2.9$ MeV width, so its total width should be dominated by radiative transitions; a future width measurement would calibrate the E1-transition scale.","The same fitted parameter predicts $\\psi(3770)\\to\\eta_c\\omega$ at $6\\times10^{-5}$; measuring that mode would provide a direct test of whether $\\alpha_\\Lambda$ truly transfers across spin states.","The framework leaves the $F$-wave coupling $\\psi_3(3842)D\\bar D$ out because it vanishes at leading order, so a sizable $\\psi_3(3842)\\to D\\bar D$ contribution from on-shell loops could be the next place to look.","Extending the same calculation to the spin-singlet $\\eta_{c2}$ partner would fill in the missing piece of the $D$-wave multiplet's hidden-charm decays."],"forward_implications":["The $\\psi_2(3823)\\to J/\\psi\\eta$ partial width is $(29.64^{+4.01}_{-4.63})$ keV, making it the dominant hidden-charm strong decay of $\\psi_2(3823)$.","The ratio of this width to $\\psi_2(3823)\\to\\gamma\\chi_{c1}$ is about 10%, below the BESIII upper limit of 0.14 and consistent with the Belle and LHCb cascade measurements.","The $\\psi_2(3823)\\to\\eta_c\\omega$ mode is predicted at $(0.38^{+0.05}_{-0.06})$ keV, with a parameter-independent ratio of $0.127$ to $J/\\psi\\eta$.","$\\psi(3770)\\to\\eta_c\\omega$ has branching fraction $(6.03^{+0.82}_{-0.92})\\times10^{-5}$, about an order of magnitude below $\\psi(3770)\\to J/\\psi\\eta$.","$\\psi_3(3842)$ hidden-charm widths are only $7.54$ eV and $1.12$ eV, so hidden charm does not contribute meaningfully to its total width."],"supporting_citations":[{"why":"Supplies the measured $\\mathcal{B}[\\psi(3770)\\to J/\\psi\\eta]=(8.7\\pm1.2)\\times10^{-4}$ and the resonance parameters used to fix $\\alpha_\\Lambda$ and evaluate widths.","marker":"[15]"},{"why":"Establishes the meson-loop description of $\\psi(3770)$ non-$D\\bar D$ decays that this paper extends.","marker":"[19]"},{"why":"Provides additional meson-loop calculations for $\\psi(3770)$ hidden-charm decays supporting the mechanism.","marker":"[20]"},{"why":"Gives the heavy-quark superfield multiplets and coupling relations used to build the $D$-wave charmonia amplitudes.","marker":"[36]"},{"why":"Supplies the chiral effective Lagrangians for charmed mesons with light pseudoscalar and vector mesons used at the decay vertices.","marker":"[39]"},{"why":"Gives the $D$-wave charmonia gauge coupling $g_2$ and the charmed-meson couplings used in the loop amplitudes.","marker":"[54]"},{"why":"Reports the BESIII upper limit of 0.14 for the $\\psi_2(3823)\\to\\eta J/\\psi$ to $\\gamma\\chi_{c1}$ branching-fraction ratio, which the prediction must satisfy.","marker":"[55]"},{"why":"Gives the LHCb cascade measurement from which the $(12.9^{+8.3}_{-6.7})\\%$ ratio is derived, the experimental consistency check.","marker":"[56]"}],"fun_headline_variants":["psi2(3823) -> J/psi eta width estimated at 30 keV","Hidden-charm decays of D-wave charmonia computed","Meson loop model fixes psi2(3823) hidden-charm width","psi2(3823) hidden-charm: 30 keV, 10% of radiative mode"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The prediction stands or falls on the assumption that the form-factor parameter $\\alpha_\\Lambda$ fitted to $\\psi(3770)\\to J/\\psi\\eta$ applies unchanged to $\\psi_2(3823)$ and $\\psi_3(3842)$ because the three $D$-wave states are similar; if the dressed meson-loop coupling or off-shell behavior differs with spin, the 30 keV width and the eV-scale $\\psi_3(3842)$ widths would shift.","fun_headline_variants_meta":{"raw":{"variants":["psi2(3823) -> J/psi eta width estimated at 30 keV","Hidden-charm decays of D-wave charmonia computed","Meson loop model fixes psi2(3823) hidden-charm width","psi2(3823) hidden-charm: 30 keV, 10% of radiative mode"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000415,"raw_usage":{"total_tokens":2224,"prompt_tokens":1108,"completion_tokens":1116,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":724,"completion_tokens_details":{"reasoning_tokens":1030}},"tokens_in":724,"tokens_out":1116,"duration_ms":9981,"temperature":1.0,"reasoning_tokens":1030,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:42:48.123385+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the ratio $\\mathcal{B}[\\psi_2(3823)\\to J/\\psi\\eta]/\\mathcal{B}[\\psi_2(3823)\\to\\gamma\\chi_{c1}]$ with the next generation of charmonium data; a central value outside roughly $5\\%$–$15\\%$, or an absolute $\\psi_2(3823)\\to J/\\psi\\eta$ width far from $30$ keV, would falsify the $\\alpha_\\Lambda$ transfer assumption.","supporting_citations":[{"cited_title":"Towards a dynamical understanding of the non-$D \\bar D$ decay of $\\psi(3770)$","cited_arxiv_id":"0902.1300","evidence_quote":"Establishes the meson-loop description of $\\psi(3770)$ non-$D\\bar D$ decays that this paper extends."},{"cited_title":"The puzzle of excessive non-$D\\bar D$ component of the inclusive $\\psi(3770)$ decay and the long-distant contribution","cited_arxiv_id":"0902.0480","evidence_quote":"Provides additional meson-loop calculations for $\\psi(3770)$ hidden-charm decays supporting the mechanism."},{"cited_title":"Colangelo, F","cited_arxiv_id":null,"evidence_quote":"Gives the heavy-quark superfield multiplets and coupling relations used to build the $D$-wave charmonia amplitudes."},{"cited_title":"Pionic transitions from $Z_c(4020)$ to $D$ wave charmonia","cited_arxiv_id":"2302.10050","evidence_quote":"Gives the $D$-wave charmonia gauge coupling $g_2$ and the charmed-meson couplings used in the loop amplitudes."},{"cited_title":"Ablikim et al","cited_arxiv_id":null,"evidence_quote":"Reports the BESIII upper limit of 0.14 for the $\\psi_2(3823)\\to\\eta J/\\psi$ to $\\gamma\\chi_{c1}$ branching-fraction ratio, which the prediction must satisfy."}],"review_version":1}