Could an axion-like particle be hidden in $\eta_c\to\gamma\gamma$?

Xiao-Rui Lyu; Zheng-Yun You; Zhi-Jun Li

REVIEW 3 major objections 5 minor 29 references

Could an axion-like particle be hidden in $\eta_c\to\gamma\gamma$?

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2506.04144 v1 pith:EZUU6HWB submitted 2025-06-04 hep-ph

Zhi-Jun Li , Zheng-Yun You , Xiao-Rui Lyu This is my paper

classification hep-ph

keywords axion-likeparticleeta_ctogammacharmoniumradiativedecaysbranchingfractionanomalydarksectorportalBESIIIJ/psimatter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear [Colleague],

The 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.

The 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.

There 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.

The 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.

So: send it to a referee, but expect the referee to ask for the mixing calculation.

Referee Report

3 major / 5 minor

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.

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 (3)

[Sec. 2, Eq. (2.1)] 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.
[Sec. 3, Eqs. (3.3)-(3.4)] 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.
[Sec. 3, Eq. (3.1) and Sec. 2 assumption] 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.

minor comments (5)

[Sec. 1, second paragraph] 'Approximately one times larger' should read 'approximately a factor of 2.2 larger', since 3.71/1.66 is about 2.2.
[Sec. 2, Eq. (2.1)] 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}.
[Sec. 3, text near Eq. (3.4)] 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.
[Fig. 3 caption and Sec. 3 text] 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.
[Sec. 5, Eq. (5.1)] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ALP parameters are extracted from the BESIII Mγγ fit, and the ψ(2S) and e+e− rates are genuinely external predictions.

full rationale

The derivation chain is self-contained. Section 2 explicitly states the load-bearing model assumption—'we assume that the measurements from γγ→η_c and η_c→hadrons are based on a pure η_c state, fixing the contribution of η_c→γγ using the world-average value ... in the current PDG'—and then performs a two-resonance fit to the BESIII Mγγ distribution, extracting m_a and Γ_a from the data. The resulting N_{a→γγ} is a fit output, and the inequality B(J/ψ→γa)×B(a→γγ)>2.6×10^-7 is a lower bound derived from that output, not an independent prediction of the same data. Eq. (3.3) legitimately relates the partial width to the fitted total width Γ_a and the coupling g_aγγ; using this relation to recast the Belle II limit is a standard constraint procedure. The parameter space in Fig. 3(b) is a constraint region, not a result claimed as a test of the model. The genuinely new observables in Sec. 5—B(ψ(2S)→γa)×B(a→γγ) and σ(e+e−→γ(γγ)a)—are computed from the fitted couplings for channels not used in the fit, so they are falsifiable predictions. The pure-η_c assumption and the assumed negligible light-quark coupling are explicit inputs; the paper does not use the fit to prove them, so they are a robustness/self-consistency concern (e.g., possible η_c–a mixing is not evaluated) rather than a circular step. No load-bearing self-citations or uniqueness imports are present.

Assumptions & free parameters 7 free parameters · 6 assumptions · 3 invented entities

The central claim rests on several fitted parameters (m_a, Gamma_a, signal yield) and on ad hoc assumptions about negligible light-quark couplings and a dark sector that dominates the ALP width. The dark sector entities and their couplings are introduced specifically to make the fitted width consistent with constraints, which increases the circularity burden.

free parameters (7)

ALP mass m_a = 2977.5 +/- 2.6 MeV/c^2
Fitted to the M_gamma gamma distribution from BESIII in Section 2.
ALP width Gamma_a = 31.3 +/- 6.7 MeV
Fitted to the M_gamma gamma distribution in Section 2; used in Eq (3.3) to derive B(a to gamma gamma).
ALP signal yield N_{a to gamma gamma} = 73.3^{+23.5}_{-19.7}
Fitted amplitude alpha squared, normalized to events in Section 2.
Interference phase phi = 0 (fixed)
Chosen to maximize constructive interference in Section 2; other values give similar fit quality.
Dark sector coupling g_{a chi chi} or g_{a gamma' gamma'} = Range shown in Figure 4
Chosen so that B(a to dark sector) = 1 to reproduce the fitted Gamma_a; not independently measured.
Dark particle mass m_chi or m_{gamma'} = Less than m_a/2; example m_chi = 0.4 GeV
Assumed to open dark decay channels; only constrained to be below threshold.
Couplings g_{a gamma gamma} and g_{a c c} = Allowed regions in Figure 3(b)
Derived from B(J/psi to gamma a) and B(a to gamma gamma) constraints; free couplings of the EFT, not directly fitted.

assumptions (6)

domain assumption ALP effective Lagrangian Eq (1.1) correctly describes ALP-photon and ALP-fermion interactions.
Invoked in Section 1; no UV completion is needed for the analysis.
domain assumption The BESIII data after background subtraction are reproduced by the fixed eta_c lineshape, efficiency, and resolution functions from Ref [30].
Used in Section 2; the paper does not reproduce these functions.
ad hoc to paper The indirect measurements gamma gamma to eta_c and eta_c to hadrons receive no ALP contribution.
Stated in Section 2; this defines the anomaly and is essential for attributing the full gap to the ALP.
ad hoc to paper ALP couplings to light quarks and hadrons are negligible.
Assumed in Section 1 to avoid constraints from hadronic decays.
ad hoc to paper A dark sector containing a fermion chi or dark photon gamma' with mass less than m_a/2 exists and dominates the ALP width.
Introduced in Section 4 to accommodate the large fitted width.
domain assumption The tree-level formula Eq (3.1) is adequate for J/psi to gamma a.
Used in Section 3; authors cite lattice results saying corrections are small at m_a around 2.98 GeV.

invented entities (3)

ALP state with m_a around 2.98 GeV, Gamma_a around 31 MeV
purpose: Fit the BESIII eta_c to gamma gamma excess
No external signal; parameters come from the fit that assumes it. Falsifiable via proposed searches.
Dark fermion chi
purpose: Provide invisible decays to explain the large ALP width and possibly dark matter
Postulated in Section 4 with assumed coupling; no direct detection.
Dark photon gamma'
purpose: Alternative dark decay channel to explain the ALP width
Postulated in Section 4; with kinetic mixing it would give visible decays, but no evidence is provided.

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Cite this review

Pith. "Pith review of Could an axion-like particle be hidden in $\eta_c\to\gamma\gamma$?." pith.science (2026). https://pith.science/paper/EZUU6HWB

@misc{pith2026250604144,
  author       = {Pith},
  title        = {Pith review of: Could an axion-like particle be hidden in $\eta_c\to\gamma\gamma$?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EZUU6HWB}},
  note         = {Machine review of arXiv:2506.04144}
}

abstract

We discuss the possibility of an axion-like particle being merged in the recent observation of $\eta_c \to \gamma\gamma$ at BESIII and find that it cannot be excluded in the current experimental data. The mass, width, and coupling strengths of the axion-like particle are extracted, and several other channels to confirm or exclude the existence of such an axion-like particle are also discussed.

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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Peccei and H.R

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[2] [2]

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