{"id":"dd843235-6d08-4a8f-b206-2b76ebf0b94b","arxiv_id":"2506.04144","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"The authors propose that an axion-like particle with mass about 2.98 GeV and width about 31 MeV may explain the discrepancy in eta_c to gamma gamma measurements and show it is not yet excluded.","lead":"A new axion-like particle with a mass very close to the charmonium state eta_c could be hiding in a recent BESIII measurement of eta_c decaying to two photons. The paper finds that current data cannot rule this particle out, and lists future searches that could confirm or exclude it.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The required g_acc values (Fig. 3b) induce sizable eta_c-a mixing because m_a is within ~6 MeV of m_eta_c, so the ALP acquires an eta_c component and a non-negligible hadronic width; the 'pure eta_c' assumption behind Eqs. (2.1)-(2.4) is likely inconsistent rather than merely untested.","rationale":"The paper's central claim—that an ALP can hide in eta_c->gamma gamma and that the extracted m_a and Gamma_a are meaningful—rests on subtracting a 'pure eta_c' baseline fixed by the PDG. The reader identified this as the weakest assumption. My stress-test agrees but goes further: the assumption is not merely untested; it is in tension with the paper's own coupling requirements. Eq. (3.1) needs |g_acc| of order 0.03-0.1 GeV^-1 to yield the B(J/psi->gamma a) demanded by Eq. (2.5) once B(a->gamma gamma) < 4.7e-3 from Eq. (3.4). Such a charm coupling, with m_a only about 6 MeV from m_eta_c, produces an eta_c-a mixing amplitude Sigma = g_acc f_eta_c m_eta_c^2 of order 0.1 GeV^2, while the squared-mass splitting is only about 0.04 GeV^2. The mixing angle is therefore large, so the ALP necessarily has a non-negligible eta_c component and decays to hadrons. This would contaminate the very PDG baseline the fit treats as pure eta_c, shifting or destroying the inferred ALP excess. This is an internal-consistency issue, not merely a disagreement with existing constraints. The paper's other arguments—the Belle II recast and the future search prospects—are conditional and do not address this mixing. Because the concern is concrete and testable but not yet settled, the reader's CONDITIONAL verdict is appropriate; if the proposed check confirms a large hadronic width, the verdict should move to REJECT.","tokens_in":9056,"tokens_out":22080,"duration_ms":216213,"concrete_test":"Evaluate the eta_c-a mixing angle using the allowed g_acc from Fig. 3(b): take Sigma = g_acc f_eta_c m_eta_c^2 with f_eta_c about 0.4 GeV and m_eta_c^2 about 8.9 GeV^2, form theta = Sigma/(m_eta_c^2 - m_a^2) for the central m_a of Eq. (2.3), and estimate Gamma(a->hadrons) ~ theta^2 Gamma_eta_c, with Gamma_eta_c about 32 MeV. If theta is not much smaller than 1, or if Gamma(a->hadrons) is a substantial fraction of Gamma_a = 31.3 MeV, then the fixed-PDG subtraction in Eq. (2.1) is invalid and the extracted ALP parameters cannot be interpreted as an ALP. Additionally, recompute Gamma(a->gg) from the charm-quark loop at the same g_acc; if Gamma(a->hadrons) is at least about 0.1 Gamma_a, the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2 fixes the eta_c->gamma gamma contribution to the PDG-derived product B(J/psi->gamma eta_c) B(eta_c->gamma gamma) and fits all remaining BESIII excess to an ALP, explicitly assuming the indirect gamma gamma->eta_c->hadrons measurement is pure eta_c. This assumption is load-bearing because the ALP yield, mass, and width (Eqs. (2.3)-(2.4)) are defined as the difference between the BESIII direct measurement and that fixed eta_c baseline. The paper justifies 'small (or negligible) decay BF into hadrons' by weak light-quark couplings, but the same charm-quark coupling g_acc needed in Eq. (3.1) to produce B(J/psi->gamma a)>5.5e-5 (from Eqs. (2.5) and (3.4)) generates an eta_c-a transition amplitude Sigma ~ g_acc f_eta_c m_eta_c^2. With g_acc about 0.03-0.1 GeV^-1, f_eta_c about 0.4 GeV, m_eta_c^2 about 8.9 GeV^2, and |m_eta_c^2 - m_a^2| about 0.04 GeV^2, the mixing angle is O(1) rather than small. The physical ALP then has an eta_c component, so a->hadrons is not suppressed, and the PDG value used as the 'pure eta_c' baseline is contaminated by the very ALP the paper proposes. This would shift or remove the inferred excess. The paper never computes this mixing or bounds the resulting hadronic width.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes that the recently measured B(eta_c->gamma gamma) from BESIII, which is about a factor of two larger than the PDG world average, is contaminated by an axion-like particle (ALP) decaying to gamma gamma and produced in J/psi->gamma a. The authors refit the BESIII M_gamma gamma distribution with an eta_c-plus-ALP signal, obtaining m_a = (2977.5 +/- 2.6) MeV and Gamma_a = (31.3 +/- 6.7) MeV (Eqs. 2.3 and 2.4), derive a lower bound on B(J/psi->gamma a) B(a->gamma gamma), translate it into coupling ranges for g_a gamma gamma and g_acc (Fig. 3), introduce a dark-sector decay mode to accommodate the large fitted width (Fig. 4), and give predictions for psi(2S)->gamma a and e+e- -> gamma a searches. The paper states its main assumptions explicitly, in particular that the indirect gamma gamma -> eta_c and eta_c -> hadrons measurements are pure eta_c and that the ALP has negligible couplings to light quarks.","tokens_in":9618,"tokens_out":12284,"duration_ms":115351,"significance":"The paper identifies a genuine and interesting experimental discrepancy and proposes a concrete, falsifiable interpretation with quantitative predictions for existing and future experiments. It is transparent about the assumptions underlying the fit and it attempts to confront the scenario with Belle II and other constraints. However, the present version does not establish the central claim that the ALP 'cannot be excluded': there is no statistical comparison with a no-ALP hypothesis, the fitted width is used to relax the very bound that defines the allowed parameter space, and the required charm-quark coupling induces eta_c-a mixing of order one which is not computed and which invalidates the pure-eta_c baseline. If these issues are resolved, the paper could serve as a useful phenomenological benchmark; as it stands, the central conclusion is not yet supported.","major_comments":[{"comment":"The paper never fits a null hypothesis containing only eta_c and reports no goodness-of-fit, chi^2/ndf, or p-value for the eta_c+ALP fit. The statement that the data 'cannot distinguish' different phi values and the conclusion that the ALP 'cannot be excluded' require a quantitative comparison with the no-ALP hypothesis; without such a comparison, the extracted m_a and Gamma_a in Eqs. (2.3)-(2.4) are not statistically established.","section":"Sec. 2, Eq. (2.1)"},{"comment":"The fitted Gamma_a from Eq. (2.4) is inserted into Eq. (3.3) to compute B(a->gamma gamma), and this branching fraction is then used to recast the Belle II limit, yielding B(a->gamma gamma) < 4.7 x 10^-3 in Eq. (3.4). Because Gamma_a is itself extracted under the assumption that the entire BESIII excess is an ALP, the resulting bound on B(a->gamma gamma) and the consequent requirement B(J/psi->gamma a) > 5.5 x 10^-5 (from Eqs. (2.5) and (3.4)) are not independent of the hypothesis being tested. A self-consistent analysis should vary m_a, Gamma_a, and the couplings together and determine the allowed region from a simultaneous treatment of the BESIII and Belle II constraints.","section":"Sec. 3, Eqs. (3.3)-(3.4)"},{"comment":"The parameter space in Fig. 3(b) requires |g_acc| of order 0.03-0.1 GeV^-1 once B(a->gamma gamma) < 4.7 x 10^-3 is combined with Eq. (2.5). Since m_a is only about 6 MeV below m_eta_c, this charm-quark axial coupling induces eta_c-a mixing of order theta ~ g_acc f_eta_c m_eta_c^2 / |m_eta_c^2 - m_a^2|, which is O(1) for the quoted parameters. The paper never computes this mixing; it would give the physical ALP a large eta_c component, invalidating the 'pure eta_c' assumption used in Eqs. (2.1)-(2.4) and making a->hadrons non-negligible. The authors should diagonalize the eta_c-a system and bound the resulting hadronic width, or restrict themselves to parameter choices where the mixing is demonstrably small.","section":"Sec. 3, Eq. (3.1) and Sec. 2 assumption"}],"minor_comments":[{"comment":"'Approximately one times larger' should read 'approximately a factor of 2.2 larger', since 3.71/1.66 is about 2.2.","section":"Sec. 1, second paragraph"},{"comment":"The normalization that converts the fit parameter alpha into the quoted yield N_{a->gamma gamma} is not defined; please state it explicitly and report the correlations among m_a, Gamma_a, and N_{a->gamma gamma}.","section":"Sec. 2, Eq. (2.1)"},{"comment":"The Belle II coupling g'_a gamma gamma is defined only in prose; write the definition as an equation and state explicitly that it is the coupling extracted under the assumption B(a->gamma gamma)=1.","section":"Sec. 3, text near Eq. (3.4)"},{"comment":"The terms 'blue shaded region' and 'allowed region' are used inconsistently between the caption and the text; make the color coding and the region labels uniform across the figure and the discussion.","section":"Fig. 3 caption and Sec. 3 text"},{"comment":"The notation sigma(e+e- -> gamma(gamma gamma) a) is confusing; write the process as e+e- -> gamma a, a -> gamma gamma consistently in the equation and the paragraph.","section":"Sec. 5, Eq. (5.1)"}],"recommendation":"major_revision","confidential_remarks":"For the editor only: This manuscript is below the standard of a full journal article in its present form, mainly because the statistical and mixing issues are central and unresolved. The authors are transparent about their assumptions and the topic is timely; after a substantial revision that adds a null-hypothesis significance statement, a treatment of eta_c-a mixing, and a non-circular recasting of the Belle II limit, the paper could become a useful phenomenological note. I see no indication of misconduct."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nThe paper is the first to apply the standard ALP-in-charmonium framework to the BESIII 2025 measurement of eta_c->gamma gamma, and it maps out testable consequences. The writing is clear, the recasting caveats are honest, and I believe the authors that the ALP they describe is not excluded by present searches. That is the positive side.\n\nThe negative side is that the central extraction rests on an assumption that is likely wrong. The authors fix the eta_c->gamma gamma contribution to the indirect PDG value and assign all extra yield to an ALP, explicitly assuming the indirect measurement is pure eta_c. But the ALP mass is only ~6 MeV below eta_c, and the g_acc values needed in their Fig. 3(b) induce a large eta_c-a mixing. With the small mass splitting, the mixing angle is O(1), meaning the physical state contains a big eta_c component and acquires a sizable hadronic width. That contaminates the indirect measurement they treat as baseline. The paper never estimates this mixing or bounds this width, so the inferred excess, mass, and width are not trustworthy.\n\nThere are statistical gaps too: no fit without the ALP, no significance or p-value, and the interference phase is set to 0 because it maximizes the effect, with the authors conceding the data cannot distinguish phases. Using the fitted width to derive B(a->gamma gamma) and then to recast Belle II adds a circular element. These alone would be fixable; combined with the mixing, they make the specific numbers in Eqs. (2.3)-(2.4) premature.\n\nThe paper is still worth a serious referee, because the idea is falsifiable and the search program (psi(2S)->gamma a, e+e- -> gamma a, dark-sector final states) is sensible. A revised version that computes the mixing and tests the baseline assumption, reports a significance, and scans over phases would be a useful phenomenological note. As it stands, I would recommend major revision rather than acceptance.\n\nSo: send it to a referee, but expect the referee to ask for the mixing calculation.","headline":"A genuinely new application of a known ALP framework to the BESIII diphoton anomaly, but the missing eta_c-ALP mixing calculation undermines the extracted mass and width.","tokens_in":10057,"tokens_out":4292,"would_cite":false,"duration_ms":42520,"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 proposes that an axion-like particle with mass $m_a=(2977.5\\pm2.6)$ MeV/$c^2$ and width $\\Gamma_a=(31.3\\pm6.7)$ MeV hides inside the $\\eta_c\\to\\gamma\\gamma$ signal at BESIII, explaining the gap between the direct and indirect…","keywords":["axion-like particle","eta_c to gamma gamma","charmonium radiative decays","branching fraction anomaly","dark sector portal","BESIII J/psi decays","dark matter"],"falsifier":"Measure the diphoton invariant-mass line shape of $J/\\psi\\to\\gamma\\eta_c$, $\\eta_c\\to\\gamma\\gamma$ using BESIII's $10^{10}$ $J/\\psi$ dataset: if after background subtraction the spectrum near 2.98 GeV is consistent with a single $\\eta_c$ Breit-Wigner and no second resonance at $m_a=(2977.5\\pm2.6)$ MeV appears with a yield at or above the fitted $N_{a\\to\\gamma\\gamma}$, the proposal is falsified.","tokens_in":8880,"feed_emoji":"⚛️","tokens_out":6202,"duration_ms":54888,"temperature":0.7,"pith_summary":"The paper argues that the disagreement between the direct BESIII measurement of $\\eta_c\\to\\gamma\\gamma$ and the world-average value obtained from $\\gamma\\gamma\\to\\eta_c$ plus $\\eta_c\\to$ hadrons can be explained by an axion-like particle (ALP) that is nearly degenerate with the $\\eta_c$ and hides in the same diphoton peak. Refitting the BESIII diphoton mass spectrum with an added ALP resonance yields $m_a=(2977.5\\pm2.6)$ MeV/$c^2$ and $\\Gamma_a=(31.3\\pm6.7)$ MeV, with $\\mathcal{B}(J/\\psi\\to\\gamma a)\\times\\mathcal{B}(a\\to\\gamma\\gamma)>2.6\\times10^{-7}$ at the $2\\sigma$ lower bound. The paper shows that existing constraints from Belle II, the PDG, and earlier searches do not exclude this ALP, provided it decays dominantly to dark-sector states; its visible diphoton branching fraction must be below about $4.7\\times10^{-3}$. If real, such an ALP would both resolve an experimental anomaly and act as a portal to dark matter, with concrete predictions for BESIII, Belle II, and future tau-charm facilities.","feed_headline":"A 2.98 GeV axion-like particle could explain the eta_c diphoton anomaly","feed_subtitle":"Refit of BESIII data finds an ALP at the eta_c mass that is not ruled out and predicts dark-sector decays.","key_machinery":"The mechanism is a second pseudoscalar Breit-Wigner resonance, the ALP, coherently interfering with the $\\eta_c$ Breit-Wigner in the diphoton invariant-mass spectrum of $J/\\psi\\to\\gamma(\\gamma\\gamma)$. The fit PDF combines the fixed $\\eta_c$ shape, a complex amplitude $\\alpha e^{i\\phi}$ for the ALP, and a Gaussian resolution. The production rate is tied to the couplings $g_{a\\gamma\\gamma}$ and $g_{acc}$ through the expression for $\\mathcal{B}(J/\\psi\\to\\gamma a)$, and the Belle II constraint forces the ALP's dominant decay into dark fermions or dark photons, with widths given by the corresponding formulas.","core_discovery":"The central claim is that the $\\eta_c\\to\\gamma\\gamma$ anomaly is not a measurement inconsistency but the superposition of two resonances: the $\\eta_c$ plus an ALP of almost the same mass. In the $\\phi=0$ fit the ALP signal yield is $N_{a\\to\\gamma\\gamma}=73.3^{+9.7}_{-8.4}$ events, or $73.3^{+23.5}_{-19.7}$ when the PDG normalization uncertainty is included. Because the ALP is assumed to couple weakly to light quarks, it contributes negligibly to the indirect $\\gamma\\gamma\\to\\eta_c$ and $\\eta_c\\to$ hadrons measurements, so it can appear strongly in $J/\\psi\\to\\gamma\\eta_c$ and $\\eta_c\\to\\gamma\\gamma$ without conflicting with those data. The paper concludes that such an ALP is not excluded by current experimental constraints and identifies the searches that could confirm or exclude it.","pith_inferences":["If the ALP is real, every charmonium radiative decay that uses an $\\eta_c$ tag is a contaminated measurement until the two nearly degenerate resonances are separated.","The fit fixes $\\phi=0$ to obtain a minimum ALP yield; a general interference phase would shift the extracted mass, width, and yield, so a phase-scan refit with more BESIII statistics is a natural next test.","A high-luminosity photon-photon measurement of the $\\eta_c$ line shape could reveal a second peak or a distorted interference pattern, directly testing whether the ALP contaminates the indirect $\\gamma\\gamma\\to\\eta_c$ channel.","If the ALP decays to a dark photon that subsequently decays to lepton pairs, existing BESIII $J/\\psi$ data may already contain multi-lepton signatures that have not been searched for."],"forward_implications":["The ALP explanation is currently allowed: no existing search covers this mass with sufficient sensitivity to exclude it.","The model predicts $\\mathcal{B}(J/\\psi\\to\\gamma a)\\times\\mathcal{B}(a\\to\\gamma\\gamma)>2.6\\times10^{-7}$ and $\\mathcal{B}(\\psi(2S)\\to\\gamma a)\\times\\mathcal{B}(a\\to\\gamma\\gamma)>2.3\\times10^{-7}$, both accessible to BESIII.","The ALP must decay mostly invisibly or to dark-sector final states; its visible diphoton mode is subdominant.","If the ALP decays to a dark fermion $\\chi$, the allowed parameter space includes a cross section near the thermal relic value, making the ALP a plausible dark-matter portal.","Future searches for $e^+e^-\\to\\gamma a$ with $a\\to\\gamma\\gamma$, $a\\to$ invisible, $a\\to l^+l^-l'^+l'^-$, $a\\to\\gamma\\,\\mathrm{invisible}$, and $a\\to\\gamma l^+l^-$ can confirm or exclude the hypothesis."],"supporting_citations":[{"why":"BESIII's observation of $\\eta_c\\to\\gamma\\gamma$ in $J/\\psi\\to\\gamma\\eta_c$; this is the dataset and fixed $\\eta_c$ shape that the paper refits.","marker":"[30]"},{"why":"PDG world averages giving the indirect $\\eta_c\\to\\gamma\\gamma$ branching fraction and the $J/\\psi$ width and branching-fraction constraints used in the analysis.","marker":"[33]"},{"why":"Belle II's limit on $e^+e^-\\to\\gamma a$, $a\\to\\gamma\\gamma$ is recast into the constraint $\\mathcal{B}(a\\to\\gamma\\gamma)<4.7\\times10^{-3}$.","marker":"[25]"},{"why":"Supplies the formula for $\\mathcal{B}(J/\\psi\\to\\gamma a)$ used in Eq. (3.1).","marker":"[31]"},{"why":"Provides the expression for $\\Gamma(a\\to\\gamma\\gamma)$, the dark-matter annihilation cross section, and the Belle II sensitivity for invisible ALPs.","marker":"[39]"},{"why":"Supports the radiative quarkonia decay formalism for ALPs, including the $g_{acc}$ coupling structure.","marker":"[32]"},{"why":"Provides an alternative OPAL-derived constraint on $g_{a\\gamma\\gamma}$ that the paper considers and sets aside in favor of Belle II.","marker":"[22]"}],"fun_headline_variants":["ALP at 2.98 GeV hides in eta_c diphoton data","Eta_c anomaly may be an axion-like particle","New fit: ALP not ruled out in eta_c to gamma gamma","Axion-like particle could explain eta_c decay","2.98 GeV ALP survives eta_c data test"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the indirect measurements $\\gamma\\gamma\\to\\eta_c$ and $\\eta_c\\to$ hadrons are pure $\\eta_c$; the entire gap between the direct and indirect branching fractions is credited to the ALP, so any ALP contribution to those indirect channels would change the extracted mass, width, and yield.","fun_headline_variants_meta":{"raw":{"variants":["ALP at 2.98 GeV hides in eta_c diphoton data","Eta_c anomaly may be an axion-like particle","New fit: ALP not ruled out in eta_c to gamma gamma","Axion-like particle could explain eta_c decay","2.98 GeV ALP survives eta_c data test"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000439,"raw_usage":{"total_tokens":2158,"prompt_tokens":803,"completion_tokens":1355,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":419,"completion_tokens_details":{"reasoning_tokens":1268}},"tokens_in":419,"tokens_out":1355,"duration_ms":10025,"temperature":1.0,"reasoning_tokens":1268,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:46:18.731601+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the diphoton invariant-mass line shape of $J/\\psi\\to\\gamma\\eta_c$, $\\eta_c\\to\\gamma\\gamma$ using BESIII's $10^{10}$ $J/\\psi$ dataset: if after background subtraction the spectrum near 2.98 GeV is consistent with a single $\\eta_c$ Breit-Wigner and no second resonance at $m_a=(2977.5\\pm2.6)$ MeV appears with a yield at or above the fitted $N_{a\\to\\gamma\\gamma}$, the proposal is falsified.","supporting_citations":[],"review_version":1}