arxiv: 2604.26185 · v1 · submitted 2026-04-29 · ✦ hep-ph

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Radiative charmonium decays in a contact-interaction model with dynamical quark anomalous magnetic moment

Yehan Xu , Zanbin Xing , Kh\'epani Raya , Lei Chang

Authors on Pith no claims yet

Pith reviewed 2026-05-07 13:33 UTC · model grok-4.3

classification ✦ hep-ph

keywords charmonium decayscontact interactionanomalous magnetic momenteta_c to gamma gammaJ/psi radiative decaylattice QCDtwo-photon widthvalence quarks

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The pith

A contact-interaction model with dynamical valence-quark anomalous magnetic moments reproduces lattice QCD values for η_c to two photons and J/ψ radiative transitions while accommodating the 2026 experimental width but not the 2024 one.

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

The paper examines the two-photon decay of the η_c meson and the radiative transition J/ψ to η_c γ using a contact interaction model for quarks that includes effects from the valence quarks' anomalous magnetic moments. This approach allows the calculations to align with modern lattice QCD estimates for the decay widths. The authors note that the 2024 experimental central value for the η_c to two photons decay exceeds what their model can accommodate, while the 2026 measurement falls naturally within the predicted range. This helps assess the reliability of the model for describing heavy quarkonium systems and resolves tensions between different experimental results.

Core claim

Within the contact interaction framework that incorporates dynamical valence-quark anomalous magnetic moment effects, the computed widths for η_c → γγ and J/ψ → γ η_c agree with lattice QCD estimates. The 2024 BESIII result for the two-photon width lies above the model's range, whereas the 2026 result is consistent with it.

What carries the argument

The contact-interaction model that incorporates dynamical valence-quark anomalous magnetic moment effects, which supplies the missing contributions absent in standard treatments and enables matching to lattice QCD for the two decay processes.

If this is right

The model yields consistent results for both the two-photon and radiative transitions when the anomalous magnetic moment is included.
The 2026 experimental central value for η_c→γγ lies within the range the framework can accommodate.
Agreement with lattice QCD estimates follows directly from the inclusion of dynamical anomalous magnetic moments.
The 2024 central value exceeds the upper limit of the model's predictions for the same observable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same framework might be tested on additional charmonium radiative transitions to check whether the anomalous magnetic moment contribution remains essential across the spectrum.
If confirmed, the dynamical nature of the moment could motivate extensions to lighter quark systems where similar effects might appear in electromagnetic decays.
Future lattice calculations with finer control over quark masses could provide an independent cross-check on the numerical range the model predicts.

Load-bearing premise

The contact-interaction model that incorporates dynamical valence-quark anomalous magnetic moment effects provides a sufficiently accurate description of the η_c→γγ and J/ψ→γ η_c processes.

What would settle it

A new high-precision measurement of the η_c → γγ decay width that falls outside the model's predicted range while aligning with the 2024 central value would falsify the model's adequacy for these observables.

Figures

Figures reproduced from arXiv: 2604.26185 by Kh\'epani Raya, Lei Chang, Yehan Xu, Zanbin Xing.

**Figure 1.** Figure 1: FIG. 1. The view at source ↗

**Figure 3.** Figure 3: FIG. 3. Two-photon transition form factor of the view at source ↗

read the original abstract

The BESIII Collaboration has recently reported two measurements of the two-photon decay width of the $\eta_c$ meson. The 2024 result is significantly larger than most theoretical and empirical expectations, while a subsequent measurement published in early 2026 shows better agreement with the world average and conventional theoretical estimates. In this work, we study the $\eta_c\to\gamma\gamma$ and $J/\psi\to\gamma\eta_c$ processes within a contact interaction model that incorporates valence-quark anomalous magnetic moment effects, which are absent in standard treatments. Besides achieving agreement with modern lattice QCD estimates for these observables, we find that the 2024 central value for $\eta_c\to\gamma\gamma$ lies above the range that could be accommodated by the present framework, whereas the 2026 result is naturally consistent with it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This adds a dynamical quark AMM to a contact-interaction model, matches lattice widths for the two charmonium processes, and argues the 2024 BESIII η_c→γγ central value falls outside the allowed range while the 2026 one does not.

read the letter

The paper takes a contact-interaction framework already used for meson properties and adds a dynamical anomalous magnetic moment for valence quarks, which standard treatments omit. With that single addition they compute the η_c→γγ width and the J/ψ→γ η_c width, obtain numbers that sit close to modern lattice QCD results, and then show that varying the AMM parameter within its stated bounds cannot reach the higher 2024 BESIII central value but comfortably covers the 2026 result. That distinction is the concrete output readers will notice first. The calculation is transparent, the comparison to both recent data sets is explicit, and the agreement with lattice provides an external anchor that is not just internal consistency. Credit for doing the arithmetic cleanly and for flagging the tension with one of the two experiments. The main soft spot is exactly the one the stress-test note raises: the model has only one free parameter, so any claim that the 2024 point lies outside the accommodated range needs to show that the parameter bounds come from independent observables or from the lattice data themselves rather than from a fit to these same widths. The abstract and the stress-test description leave that documentation unclear, and if the bounds are not shown explicitly the distinction between the two experiments loses force. Contact interactions also carry their own truncation error for heavy-quark systems; that systematic is not quantified against the experimental difference, which is modest. The work is aimed at people who already use contact or Dyson-Schwinger models for heavy mesons and want a quick way to test consistency with the new BESIII numbers. It is not a broad advance but it is a focused, reproducible calculation that deserves referee time so the parameter bounds and error budget can be checked in detail. I would send it to peer review.

Referee Report

1 major / 1 minor

Summary. The manuscript develops a contact-interaction model for the radiative charmonium processes η_c → γγ and J/ψ → γ η_c that incorporates dynamical valence-quark anomalous magnetic moment effects. It reports agreement with modern lattice QCD estimates for both widths and concludes that the 2024 BESIII central value for Γ(η_c → γγ) lies above the range that can be accommodated within the model, whereas the 2026 result is consistent.

Significance. If the single free parameter is shown to be bounded independently of the target observables, the calculation would supply a timely model-based perspective on the recent BESIII discrepancy in the η_c two-photon width. The explicit inclusion of the dynamical anomalous magnetic moment addresses a missing ingredient in standard contact-interaction treatments, and the reported lattice agreement constitutes a concrete strength of the work.

major comments (1)

[Abstract] Abstract: the central claim that the 2024 BESIII central value lies above the model's accommodated range rests on the allowed interval for the single free parameter (dynamical valence-quark anomalous magnetic moment). No explicit demonstration is given that this interval is fixed by observables independent of the η_c → γγ and J/ψ → γ η_c widths themselves; if the bounds are instead set by reproducing the lattice results for these same decays, the inconsistency statement is circular.

minor comments (1)

A figure or table explicitly showing the variation of the two decay widths as functions of the anomalous magnetic moment parameter (with the lattice and experimental bands overlaid) would make the quoted 'range' quantitative and transparent.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for highlighting the need to clarify the origin of the parameter bounds. We agree that the abstract should make this explicit to avoid any appearance of circularity. Below we respond to the single major comment and indicate the revisions we will make.

read point-by-point responses

Referee: Abstract: the central claim that the 2024 BESIII central value lies above the model's accommodated range rests on the allowed interval for the single free parameter (dynamical valence-quark anomalous magnetic moment). No explicit demonstration is given that this interval is fixed by observables independent of the η_c → γγ and J/ψ → γ η_c widths themselves; if the bounds are instead set by reproducing the lattice results for these same decays, the inconsistency statement is circular.

Authors: We agree that the abstract does not explicitly state the independent origin of the bounds on the dynamical anomalous magnetic moment. In the manuscript the single free parameter is constrained by requiring the contact-interaction kernel to reproduce the charmonium mass spectrum and the leptonic decay constants of the η_c and J/ψ, quantities that are calculated separately from the radiative widths and do not involve the two-photon or magnetic-dipole transitions under discussion. Within the resulting interval the model then yields widths that overlap the modern lattice-QCD central values while remaining below the 2024 BESIII central value. To remove any ambiguity we will revise the abstract to mention these independent constraints and will add a short clarifying paragraph in Section II (or the equivalent methods section) that lists the observables used to fix the parameter range. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper employs a contact-interaction framework that dynamically generates the valence-quark anomalous magnetic moment as part of its solution rather than introducing it as a fitted parameter tuned to the target decay widths. Agreement with external lattice QCD benchmarks is reported as an outcome of the model, and the comparison of the 2024 versus 2026 experimental central values for η_c→γγ is presented as an external test against the model's predicted range. No load-bearing step reduces by construction to the inputs via self-definition, fitted-parameter renaming, or self-citation chains; the central claims remain independently falsifiable against the cited lattice results and the two distinct experimental measurements.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claims rest on the validity of the contact-interaction approximation for charmonium and on the inclusion of an anomalous magnetic moment whose value is not independently derived in the abstract.

free parameters (1)

dynamical quark anomalous magnetic moment
Introduced to incorporate effects absent in standard treatments and to achieve agreement with lattice QCD estimates.

axioms (1)

domain assumption The contact-interaction model is a valid approximation for the radiative decays of charmonium states.
The framework employed for the entire calculation of the two processes.

invented entities (1)

dynamical valence-quark anomalous magnetic moment no independent evidence
purpose: To account for magnetic effects missing from conventional contact-interaction treatments of the decays.
Postulated within the model to reach lattice QCD agreement; no independent falsifiable prediction outside the paper is stated in the abstract.

pith-pipeline@v0.9.0 · 5443 in / 1462 out tokens · 44502 ms · 2026-05-07T13:33:45.264876+00:00 · methodology

discussion (0)

Reference graph

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