{"id":"dc46925e-f147-4ffc-bed1-88dc40d4bd5b","arxiv_id":"2608.13537","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The nucleon-triggered V_B model predicts observable events beyond the on-shell kinematic limit in eta to pi0 gamma gamma on nucleon targets.","lead":"A new analysis predicts that a hypothetical nucleon-triggered boson would create rare events outside the normal kinematic limits in eta meson decays on proton targets. If those events appear at JLab or MAMI, they would support a proposed explanation for a 5.5-sigma disagreement between experiments.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Neglected principal-value interference may shift the Rubicon yields by more than the quoted 20% uncertainty.","rationale":"The reader's CONDITIONAL verdict and weakest_assumption match the most load-bearing concern: the PV interference term is neglected under a symmetric-in-Delta assumption, while the actual selection is symmetric in M_X. I read the paper's Eqs. (15)–(17) carefully: the 'Neglected in this work' label is explicit, and the only given justification is 'odd in Delta ... cancels when integrated over a symmetric invariant-mass window in Delta'. The selection window in Eq. (20) is |M_X - m_eta| <= Delta_cut, which is symmetric in M_X, not in Delta. Transforming to Delta = M_X^2 - m_eta^2 gives an interval [-2 m_eta Delta_cut - Delta_cut^2, +2 m_eta Delta_cut + Delta_cut^2], which is asymmetric since the lower endpoint has magnitude smaller by Delta_cut^2. The PV term is odd in Delta, so over this asymmetric interval its integral is not zero even for constant C; the residual is ~ Re C(Delta_+) - Re C(Delta_-) with weights that do not cancel. The paper never numerically estimates this term, and the fit of C_eff to the on-shell MAMI spectrum cannot constrain the off-shell Re C. The central prediction (4–23 Rubicon events) is proportional to the off-shell |M_VB|^2 tail, so an unquantified PV residual of even a few percent of the pole contribution could change the tail fraction significantly, because the pole term dominates the denominator. This is exactly the kind of unquantified approximation that warrants a conditional verdict rather than rejection, since a relatively straightforward numerical evaluation could settle it. The disclosed 10% code bug and the fitted-constant caveat are secondary; my focus is the PV term. I agree with the reader's identification, and I recommend CONDITIONAL as the appropriate verdict: the concern is real but addressable, and the paper otherwise makes a clear, testable prediction.","tokens_in":28515,"tokens_out":2896,"duration_ms":25166,"concrete_test":"Compute the exact contribution of the neglected PV term in Eq. (15) for the eta -> pi0 gamma gamma case, using the same amplitudes and the same M_X window of Eq. (20) for Delta_cut = 50, 75, 100 MeV, without invoking the symmetric-in-Delta approximation. Address the pole singularities by keeping the finite eta width Gamma_eta = 1.31 keV (or by evaluating the PV integral numerically with the principal-value prescription). Then compare the resulting absolute contribution to the tail integrals in Eq. (34) and to the Rubicon fractions in Table I. If the PV contribution is below 0.1% of the denominator, the headline yield stands; if it is above ~1%, the quoted 4–23 events and their uncertainties must be revised.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The headline prediction of 4–23 Rubicon-crossing events rests on the claim in Eq. (15)–(17) that the only off-shell contribution to the squared amplitude is |M_VB|^2, because the principal-value (PV) interference term is odd in Delta = M^2 - m_eta^2 and cancels over a symmetric window. But the experimental selection defined by Eq. (20) is a symmetric window in M_X, i.e. in sqrt(m_eta^2 + Delta), not in Delta. A window symmetric in M_X corresponds to an asymmetric interval in Delta: [(m_eta - Delta_cut)^2 - m_eta^2, (m_eta + Delta_cut)^2 - m_eta^2]. The PV term is odd in Delta, so its integral over this window is not zero at leading order; the residual is proportional to Re C evaluated at the endpoints times ~4 m_eta Delta_cut, while the |C| variation in C is phase space Γ_VB(M_X), which changes by tens of percent over the 50–100 MeV windows (Figs. 3–4). No numerical estimate of this residual is given. The text says 'Neglected in this work' and 'suppressed principal value term', but the only justification is cancellation on a symmetric-in-Delta window, which is not the window imposed. The size of the residual PV term could be comparable to or larger than the quoted ~9% continuum fraction, since Re C involves the resonant SM amplitude and the VB amplitude, both of order the individually large pieces that interfere to produce the 2.6-fold enhancement. Since the Rubicon fraction is defined relative to the denominator which includes the large pole term, even an O(percent) absolute correction to the numerator could change f_R by O(10–100%). The single fitted constant C_eff absorbs the on-shell rate, so the fit in Eq. (57)–(58) cannot constrain this off-shell PV term; the prediction is therefore unvalidated at the level of its headline yield. A second, related issue: the decomposition in Eq.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends a previously proposed nucleon-triggered leptophobic vector-boson scenario, V_B, introduced to explain the discrepancy between the KLOE and MAMI determinations of BR(η→π^0γγ). The central new step is to relax the on-shell condition M_X = m_η(′) for the reconstructed π^0(η)γγ subsystem, retaining the off-shell continuum term |M_VB|^2 while neglecting the principal-value part of the SM–V_B interference. From this setup the author derives several observable signatures: invariant-mass tails beyond the on-shell kinematic endpoints (the 'Rubicon' regions), recoil-proton angular shifts relative to the on-shell hypothesis, an upward shift of the reconstructed mass, and weak dependence of the effective branching fraction on the MAMI- versus JEF-like production energy. The headline numerical result is 4–23 Rubicon-crossing events in a reference sample of 1200 η→π^0γγ events, depending on the selection window, with much smaller yields in η′→π^0γγ. The paper closes with a qualitative suggestion that V_B-mediated two-nucleon diagrams could contribute to the flat deuteron angular distributions in γd→π^0ηd and γd→π^0π^0d.","tokens_in":28895,"tokens_out":10445,"duration_ms":119682,"significance":"If the central derivation were sound, the paper would provide a genuinely falsifiable observable: events populating kinematic regions that are forbidden for an isolated on-shell η decay, with a predicted correlation to the recoil-proton kinematics. The phase-space factorization in Appendix B is a useful technical contribution, and the public code together with the explicit cut and energy scans in Tables I–II are strengths that make the numerical results checkable. However, the quantitative predictions are not parameter-free: the single new coefficient C_eff is fitted to the MAMI differential width, and the headline Rubicon yields rest on an unquantified principal-value approximation. The deuteron discussion is illustrative rather than quantitative. The paper is therefore best viewed as a proposal of a new observable with provisional numerics, not as a closed prediction.","major_comments":[{"comment":"The neglect of the principal-value (PV) interference term is not justified by the cancellation argument given in the text. The experimental selection window is symmetric in M_X, namely M_X^2 ∈ [(m_η−Δcut)^2, (m_η+Δcut)^2], which is not an interval symmetric in Δ = M_X^2 − m_η^2. The PV term 2 PV[Re C/(M^2−m^2)] is odd in Δ, so its integral over this window does not cancel at leading order; the residual is of order Re C evaluated at the endpoints times 4m_η Δcut. Moreover, Re C(M,Ω) is not slowly varying, since it contains the production phase-space factor Ω2 and the continuum width Γ_VB(M), both of which vary appreciably over the 50–100 MeV windows (Figs. 3–4). No numerical estimate of this residual is provided. Because Re C involves the same SM and V_B amplitudes whose interference produces the main 2.6-fold enhancement, the residual PV contribution could be comparable to or larger than the |M_VB|^2 continuum that drives all Rubicon predictions in Tables I–II and Figs. 8–10. This needs to be quantified or removed by a more careful treatment before the headline yields can be considered reliable.","section":"Section III, Eqs. (15), (17), (20)"},{"comment":"The single model parameter C_eff is obtained from a χ^2 fit to the MAMI differential width dΓ(η→π^0γγ)/dm^2_γγ. Consequently, the on-shell branching fractions in Tables I–II are not independent predictions of the model; they are a re-description of the fitted channel. The Rubicon yields are shape predictions conditional on the fitted C_eff and on the assumed functional form of M_VB, rather than parameter-free predictions. This distinction should be stated in the abstract and conclusions, since the quoted '4–23 events' could otherwise be misread as an absolute test of the normalization of the V_B contribution.","section":"Section V, Eqs. (57)–(58)"},{"comment":"The definition of Γ_eff_VB as a production-phase-space average (Ω2-weighted and normalized by ∫Ω2) is not compatible with the definition of Γ_pole as an unweighted Dalitz-integrated decay width, yet Eq. (28) sums them as the total observed width. According to the factorization in Eq. (21), the pole contribution should enter with the factor Ω2(Eγ,m_η), while the continuum contribution should enter as ∫ dM_X^2/(2π) Ω2(Eγ,m_p,M_X) Γ_VB(M_X). Using a normalized average changes the relative weight of pole and continuum, and therefore affects the cut dependence and the MAMI-versus-JEF comparison. Please specify the event-rate normalization explicitly or correct the formula.","section":"Section III, Eqs. (26)–(28)"}],"minor_comments":[{"comment":"The displayed formula for Γ_eff_VB appears as two integrals on the same line without a clear fraction bar; this should be typeset explicitly as a ratio to avoid ambiguity.","section":"Section III, Eq. (26)"},{"comment":"The captions reference 'Fig. (68)' where they presumably mean Eq. (68); please correct the cross-reference.","section":"Captions of Figs. 11 and 12"},{"comment":"The notation is not uniform: the figure labels use 'η0' in some places where 'η′' is intended; please unify the notation throughout.","section":"Fig. 1 and text"},{"comment":"The sentence 'The cleanest discriminator of the model is a kinematically forbidden tail in the γγ and π^0γ spectra, and for η→π^0γγ, and we predict 4–23 events...' has a grammatical break; please rephrase.","section":"Abstract"},{"comment":"The fitted C_eff differs by about 10% from the value reported in the earlier paper [9] because of a numerical bug. Please state explicitly whether the figures and tables of [9] are superseded by the present results, since readers comparing the two papers will otherwise see an unexplained shift.","section":"Section V, after Eq. (58)"},{"comment":"The deuteron diagrams are presented without a quantitative estimate, and the text correctly defers their evaluation to future work; please state even more explicitly that these plots do not yet provide evidence for or against the V_B model.","section":"Section VII"}],"recommendation":"major_revision","confidential_remarks":"The paper's core qualitative idea—a kinematic tail correlated with the recoil nucleon—is interesting and worth pursuing, but the quantitative claims are currently contingent on an unjustified principal-value approximation and on a fitted coefficient. The normalization issue in Eqs. (26)–(28) also needs to be resolved. I would not accept the paper in its present form, but the problems seem fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know: this is not a recycled version of [9]. The off-shell continuum analysis and the Rubicon tail predictions are new, and the recoil-proton angular correlation gives experimentalists something concrete to look for. The code is released, the derivation is transparent, and the author openly discloses the 10% shift in C_eff from a coding bug. Credit where due.\n\nThe model itself remains what it was: one effective coefficient C_eff fit to the MAMI differential width. That means the factor-2.6 enhancement is not an independent prediction. But that is not the real problem. The paper predicts a separate observable—events beyond the on-shell endpoints—using that same C_eff. That is a legitimate use of the parameter.\n\nThe real soft spot is the one the stress-test flags. The interference term in Eq. (15) is dropped because the principal-value part is odd in Delta = M^2 - m_eta^2 and \"cancels over a symmetric window.\" But the experimental window in Eq. (20) is symmetric in M_X, not in Delta. For Delta_cut = 75 MeV the implied Delta interval is [-2md + d^2, 2md + d^2], shifted positive by d^2. The PV integral of 1/Delta over that interval is ln((2md+d^2)/(2md-d^2)), about d/m, roughly 0.14 for the benchmark cut, times ReC. ReC is built from the same amplitudes that interfere to produce the 2.6-fold enhancement, so the residual is not obviously small compared with the ~9% |M_VB|^2 continuum. Since the continuum fraction is defined against the big pole+interference denominator, even a few-percent correction to the numerator can move f_R by tens of percent. No estimate of this residual appears anywhere in the paper. The same point applies to Eq. (17), which assigns all off-shell weight to |M_VB|^2.\n\nThe other caveats are minor: the \"world average\" sentence should have the PDG treatment of KLOE checked, since the paper's motivation leans on it; the deuteron diagrams are explicitly deferred and add nothing yet. Neither undermines the main observable.\n\nOverall: this deserves a serious referee. I would send it back with a request to compute or bound the PV residual, and to show the Rubicon yield with that term included. If the residual changes the yield by a factor of two, the paper still has value; if it changes it by an order of magnitude, the headline should be revised. But the question is quantitative, and the paper is set up to answer it.","headline":"The off-shell Rubicon prediction is genuinely new and worth examining, but the headline yield rests on an unquantified principal-value residual that should be computed before the number is trusted.","tokens_in":29512,"tokens_out":4940,"would_cite":false,"duration_ms":55403,"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 a nucleon-triggered $V_{\\mathcal B}$ leaves 4–23 events beyond the kinematic boundary in $\\eta\\to\\pi^0\\gamma\\gamma$, correlated with the recoil proton.","keywords":["nucleon-triggered vector boson","V_B model","eta to pi0 gamma gamma","kinematic Rubicon","off-shell continuum","production-dependent branching discrepancy","photoproduction","rare meson decays"],"falsifier":"Reanalyze the low-energy photoproduction dataset with the reconstructed mass left free and count events with $m^2_{\\gamma\\gamma}>(m_\\eta-m_{\\pi^0})^2$ or $m^2_{\\pi^0\\gamma}>m_\\eta^2$; the model predicts 4–23 such events per 1200 signal events depending on the window, so a 95% confidence upper limit below 4 events in those tails would falsify the central prediction. A higher-energy photoproduction branching fraction equal to the leptonic $e^+e^-$ value would be an independent falsifier.","tokens_in":28251,"feed_emoji":"🎯","tokens_out":15436,"duration_ms":136322,"temperature":0.7,"pith_summary":"The paper argues that if a recently proposed nucleon-triggered vector boson $V_{\\mathcal B}$ explains the discrepancy between the leptonic $e^+e^-$ measurement and the nucleon-target world average of $\\mathrm{BR}(\\eta\\to\\pi^0\\gamma\\gamma)$, the model leaves a distinctive kinematic fingerprint: events whose reconstructed $\\pi^0\\gamma\\gamma$ mass is off shell populate invariant-mass regions that are forbidden for an isolated on-shell $\\eta$ decay. In a benchmark sample of 1200 reconstructed signal events, the continuum part of the amplitude produces 4–23 such 'Rubicon-crossing' events depending on the selection window, and those events are correlated with the recoil proton's laboratory angle. The same off-shell continuum shifts the mean reconstructed mass upward by 2–7 MeV and makes the low-energy and high-energy photoproduction predictions differ by less than 1% for identical selection windows. The paper positions $\\eta\\to\\pi^0\\gamma\\gamma$ as the decisive discovery channel and lists measurable outcomes that would rule the scenario out or disfavor it.","feed_headline":"Forbidden decay tail: 4-23 events predicted in η→π0γγ","feed_subtitle":"A nucleon-triggered boson would push rare η decays past their kinematical edge, tied to the recoil proton.","key_machinery":"The load-bearing object is the decomposition of the squared nucleon-activated amplitude into a pole piece and a continuum piece, $|M_{\\rm nucleon}|^2 \\simeq W_{\\rm pole} + W_{\\rm cont}$, with $W_{\\rm cont}(M_X,\\Omega)=|M_{V_{\\mathcal B}}(M_X,\\Omega)|^2$. The pole piece is production-independent and confined to the $\\eta$ (or $\\eta'$) resonance; the continuum piece lets the reconstructed invariant mass $M_X\\equiv M_{\\pi^0(\\eta)\\gamma\\gamma}$ float and is the only term that reaches beyond the on-shell endpoints. The 'kinematic Rubicon' is the boundary set by an on-shell decay, $m^2_{\\gamma\\gamma}\\le(m_{\\eta'}-m_f)^2$ and $m^2_{f\\gamma}\\le m^2_{\\eta'}$ with $f=\\pi^0,\\eta$; the paper shows the continuum populates the complementary tails and derives the minimum $M_X$ needed to cross two Rubicons at once ($\\Delta_{\\rm cut}\\ge 146$ MeV for $\\eta\\to\\pi^0\\gamma\\gamma$). The production phase-space factor $\\Omega_2(E_\\gamma,m_p,M_X)$ carries the difference between the near-threshold ($E_\\gamma=1.4$ GeV) and higher-energy ($E_\\gamma=11$ GeV) regimes.","core_discovery":"The central claim is that the $V_{\\mathcal B}$ amplitude contains a piece $|M_{V_{\\mathcal B}}|^2$ that is not anchored to the $\\eta$ pole; through energy–momentum exchange with the recoil nucleon, this continuum extends into regions of the $\\gamma\\gamma$ and $\\pi^0\\gamma$ invariant-mass spectra that a genuinely on-shell $\\eta\\to\\pi^0\\gamma\\gamma$ decay cannot reach. For $\\eta\\to\\pi^0\\gamma\\gamma$ the paper predicts a Rubicon-crossing fraction $f_R = 0.351$–$1.92\\%$ (about 4–23 events in 1200) for window half-widths $\\Delta_{\\rm cut}=50$–$100$ MeV, with the $\\gamma\\gamma$ tail dominant because crossing the $\\pi^0\\gamma$ boundary requires an extremely soft photon. The same calculation yields a positive reconstructed-mass shift $\\langle M_{\\pi^0\\gamma\\gamma}\\rangle - m_\\eta \\simeq 2$–$7$ MeV, a less-than-1\\% difference between the two photoproduction energy regimes, and a recoil-proton angular displacement that reaches about $-5^\\circ$ in the near-threshold regime but only about $-0.2^\\circ$ at the higher energy. For $\\eta'\\to\\pi^0\\gamma\\gamma$ the corresponding tails are roughly two orders of magnitude smaller. The paper also sketches $V_{\\mathcal B}$-mediated two-nucleon topologies that could act as an alternative source for the flat deuteron angular distributions in $\\gamma d\\to\\pi^0\\eta d$ and $\\gamma d\\to\\pi^0\\pi^0 d$, deferring their quantitative evaluation.","pith_inferences":["Because the principal-value interference term is left unquantified, the 4–23 event prediction is conditional on that cancellation; computing the residual would either firm up or shift the central yield.","The same operator implies an $A$-dependent enhancement of the effective $\\eta\\to\\pi^0\\gamma\\gamma$ branching on heavy nuclear targets; a quantitative light-versus-heavy target comparison is a testable extension the paper only sketches qualitatively.","The recoil-proton correlation could be turned into a selection variable: requiring each candidate's measured proton angle to match the predicted $\\theta_p$–$|t|$ relation for its $M_X$ would suppress detector-migration backgrounds beyond what the paper quantifies."],"forward_implications":["If the higher-energy photoproduction experiment measures a branching fraction matching the leptonic $e^+e^-$ value, the $V_{\\mathcal B}$ scenario is ruled out or at least severely constrained.","A future leptonic $J/\\psi\\to\\gamma\\eta$ measurement of $\\eta\\to\\pi^0\\gamma\\gamma$ that agrees with the nucleon-target value rather than the earlier leptonic value would disfavor the environment-dependent mechanism; agreement with the leptonic value would confirm its qualitative pattern.","Reanalyzing existing near-threshold photoproduction data without fixing the on-shell $\\eta$ signal template should reveal roughly 10 Rubicon-crossing events in a 1200-event sample at $\\Delta_{\\rm cut}=75$ MeV, with a recoil-proton angular shift that can exceed $-5^\\circ$.","Widening the reconstructed-mass window from 50 to 100 MeV raises the predicted effective branching fraction by about 3–4% and increases the predicted Rubicon yield from about 4 to about 23 events in $\\eta\\to\\pi^0\\gamma\\gamma$.","For $\\eta'\\to\\pi^0\\gamma\\gamma$ the predicted Rubicon yield is about one event in a 3500-event sample even at $\\Delta_{\\rm cut}=100$ MeV, so that channel is not the discovery channel."],"supporting_citations":[{"why":"Introduces the $V_{\\mathcal B}$ model and its on-shell amplitudes; this paper relaxes that on-shell approximation and uses its fitted coupling $C_{\\rm eff}$.","marker":"[9]"},{"why":"The photoproduction measurement whose branching ratio dominates the nucleon-target world average and defines the on-shell signal template to be relaxed.","marker":"[5]"},{"why":"The leptonic $e^+e^-$ measurement that motivates the discrepancy and that the model must leave unchanged.","marker":"[2]"},{"why":"The VMD+L$\\sigma$M Standard Model benchmark used as the theoretical baseline and in the $\\chi^2$ fit for $C_{\\rm eff}$.","marker":"[15]"},{"why":"The world-average branching ratio that the model aims to reproduce on nucleon targets.","marker":"[4]"},{"why":"Defines the higher-energy photoproduction program whose planned $\\eta\\to\\pi^0\\gamma\\gamma$ measurement would test the prediction.","marker":"[17]"},{"why":"The extended proposal for the same higher-energy experiment, specifying the projected larger signal sample.","marker":"[18]"}],"fun_headline_variants":["Nucleon-triggered boson yields 4–23 events in η→π0γγ tail","Recoil proton angle exposes V_B: -5° at MAMI, -0.2° at JEF","Forbidden tail in η→π0γγ: 4–23 events from nucleon trigger","JEF vs MAMI: recoil angle -0.2° vs -5° constrains V_B","Mass shift up to 7 MeV and forbidden tail: signs of V_B in η decay"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation depends on the unquantified assumption that the principal-value interference term integrates to zero over the experimental window, so that the whole off-shell signal is the $|M_{V_{\\mathcal B}}|^2$ continuum, even though the window is symmetric in $M_X$ rather than in the offset $\\Delta$ where that cancellation is argued.","fun_headline_variants_meta":{"raw":{"variants":["Nucleon-triggered boson yields 4–23 events in η→π0γγ tail","Recoil proton angle exposes V_B: -5° at MAMI, -0.2° at JEF","Forbidden tail in η→π0γγ: 4–23 events from nucleon trigger","JEF vs MAMI: recoil angle -0.2° vs -5° constrains V_B","Mass shift up to 7 MeV and forbidden tail: signs of V_B in η decay"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001304,"raw_usage":{"total_tokens":5522,"prompt_tokens":1352,"completion_tokens":4170,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":968,"completion_tokens_details":{"reasoning_tokens":4040}},"tokens_in":968,"tokens_out":4170,"duration_ms":32070,"temperature":1.0,"reasoning_tokens":4040,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:42:21.272369+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reanalyze the low-energy photoproduction dataset with the reconstructed mass left free and count events with $m^2_{\\gamma\\gamma}>(m_\\eta-m_{\\pi^0})^2$ or $m^2_{\\pi^0\\gamma}>m_\\eta^2$; the model predicts 4–23 such events per 1200 signal events depending on the window, so a 95% confidence upper limit below 4 events in those tails would falsify the central prediction. A higher-energy photoproduction branching fraction equal to the leptonic $e^+e^-$ value would be an independent falsifier.","supporting_citations":[{"cited_title":"Di Miccoet al.(KLOE Collaboration), Acta Phys","cited_arxiv_id":null,"evidence_quote":"Introduces the $V_{\\mathcal B}$ model and its on-shell amplitudes; this paper relaxes that on-shell approximation and uses its fitted coupling $C_{\\rm eff}$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The photoproduction measurement whose branching ratio dominates the nucleon-target world average and defines the on-shell signal template to be relaxed."},{"cited_title":"Babusciet al.(KLOE-2 Collaboration), J","cited_arxiv_id":null,"evidence_quote":"The leptonic $e^+e^-$ measurement that motivates the discrepancy and that the model must leave unchanged."},{"cited_title":"Balytskyi, J","cited_arxiv_id":null,"evidence_quote":"The VMD+L$\\sigma$M Standard Model benchmark used as the theoretical baseline and in the $\\chi^2$ fit for $C_{\\rm eff}$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The world-average branching ratio that the model aims to reproduce on nucleon targets."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the higher-energy photoproduction program whose planned $\\eta\\to\\pi^0\\gamma\\gamma$ measurement would test the prediction."},{"cited_title":"Ablikimet al.(BESIII Collaboration), Phys","cited_arxiv_id":null,"evidence_quote":"The extended proposal for the same higher-energy experiment, specifying the projected larger signal sample."}],"review_version":1}