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arxiv: 2606.19902 · v1 · pith:T5OWYZIInew · submitted 2026-06-18 · ✦ hep-ph · hep-ex· hep-lat

Extraction of charmonium branching fractions from J/psitoγη_c radiative decays

Magnus C. Schaaf , Antonio Vairo This is my paper

Pith reviewed 2026-06-26 17:17 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-lat
keywords charmoniumradiative decaysbranching fractionsJ/psieta_cM1 transitionphoton line shapelattice QCD
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The pith

A theoretically grounded photon line shape for the J/ψ to gamma eta_c transition extracts branching fractions that align with lattice QCD without empirical damping.

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

The paper examines the mismatch between Particle Data Group values for the branching fraction of the radiative charmonium decay J/ψ to gamma eta_c and theoretical predictions from lattice QCD. A scan across recent PDG measurements shows that the observed correlations among branching fractions become consistent with lattice determinations of the partial widths once the extraction method is updated. The authors introduce a photon energy spectrum derived from the underlying M1 transition dynamics and a corresponding procedure for pulling out the branching fractions and their products. This removes the need for ad-hoc damping functions that experiments have applied to the line shape. The result is a cleaner route to derived observables such as the eta_c two-photon width.

Core claim

The central claim is that the tension between measured branching fractions and lattice QCD partial widths for J/ψ→γ η_c and η_c→γγ is an artifact of the empirical line-shape modifications used in current extractions; a profile scan over PDG data parameterized by B(J/ψ→γ η_c) demonstrates compatibility with the lattice values, and a first-principles photon spectrum plus extraction prescription for the M1 transition eliminates the ambiguity introduced by damping functions.

What carries the argument

Theoretically derived photon line shape for the M1 radiative transition, used to replace empirical damping in the extraction of branching fractions from the observed spectrum.

If this is right

  • Branching fractions and products involving the M1 transition can be extracted without introducing an arbitrary damping parameter.
  • The correlation pattern among PDG branching-fraction measurements becomes consistent with independent lattice calculations of the two partial widths.
  • Derived quantities such as the eta_c two-photon decay width become directly comparable to lattice results without intermediate empirical corrections.
  • Future experimental analyses of similar radiative charmonium transitions can adopt the same line-shape prescription to reduce systematic uncertainty.

Where Pith is reading between the lines

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

  • The method could be tested on other M1 transitions in the charmonium or bottomonium systems where analogous line-shape ambiguities appear.
  • Re-analysis of older data sets with the new prescription might shift central values and uncertainties for several charmonium branching fractions.
  • If the line shape holds, it supplies a standard template that lattice groups can fold with their width predictions to produce mock data for direct comparison with experiment.

Load-bearing premise

The proposed photon line shape derived from the M1 transition accurately describes the true energy spectrum without any additional empirical adjustments.

What would settle it

A high-statistics measurement of the photon energy spectrum in J/ψ→γ η_c that deviates systematically from the proposed theoretical shape at the level that would require damping functions again.

Figures

Figures reproduced from arXiv: 2606.19902 by Antonio Vairo, Magnus C. Schaaf.

Figure 1
Figure 1. Figure 1: Fit values of Γ(ηc → γγ) as a function of B(J/ψ → γηc); the latter is multiplied by the J/ψ total width ΓJ/ψ quoted in Ref. [21] to obtain the partial decay width. The black and gray dots with error bars show the results from the 2026 [21] and 2025 [27] PDG multiparticle fit, respectively; the black marker indicates the PDG average value of Γ(J/ψ → γηc) [21]. The blue solid curve shows the profile scan, wi… view at source ↗
Figure 2
Figure 2. Figure 2: summarizes our findings. The central value of the green band, which corresponds to the extraction of B(J/ψ → γηc) from the CLEO data given in Eq. (13), is larger than the PDG fit (black dot) and closer to the lattice data, collectively represented by the gray hatched regions. If we reevaluate the scan of the PDG multiparticle fit at this value of the M1 branching fraction, we find B (fit) CLEO(ηc → γγ) = (… view at source ↗
Figure 3
Figure 3. Figure 3: Fit to the photon energy (Eγ) spectrum from the sum of exclusive J/ψ → γηc → γXi decays. The black dots with error bars are data points measured by the CLEO ex￾periment [18]. The red solid curve shows the fit result, with the green dashed curve representing the line shape as given by Eqs. (10) and (11), and the blue dash-dotted and dash￾double-dotted curves representing the background components described … view at source ↗
Figure 4
Figure 4. Figure 4: Fit to the two-photon invariant mass (M12) distribu￾tion from exclusive J/ψ → γηc → γγγ decays. The black dots with error bars are data points measured by the BESIII exper￾iment [29]. The red solid curve shows the fit result, with the green dashed curve representing the line shape as described by Eqs. (10) and (11). The blue, brown, and cyan (close to zero almost everywhere) filled histograms represent the… view at source ↗
Figure 5
Figure 5. Figure 5: Fit to the proton-antiproton invariant mass ( [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of experimental values of the branch [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of experimental values of the par [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We assess the tension between theoretical predictions and the values quoted by the Particle Data Group (PDG) for the partial decay width and branching fraction associated with the radiative charmonium decay $J/\psi\to\gamma\eta_c$. A profile scan over the most recent PDG data depending on the branching fraction $\mathcal{B}(J/\psi\to\gamma\eta_c)$ suggests that the correlation between measured branching fractions is compatible with lattice QCD determinations of the partial decay widths $\Gamma(J/\psi\to\gamma\eta_c)$ and $\Gamma(\eta_c\to\gamma\gamma)$. We propose a theoretically grounded photon line shape for the radiative decay spectrum and a prescription for the extraction of (product) branching fractions involving the magnetic dipole (M1) transition $J/\psi\to\gamma\eta_c$. This approach obviates the need to modify the photon energy spectrum line shape using empirical damping functions, as done in the most recent experimental extractions of $\mathcal{B}(J/\psi\to\gamma\eta_c)$ from the photon line shape, thereby eliminating an inherent ambiguity in the determination of the derived observables.

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.

Referee Report

2 major / 2 minor

Summary. The paper assesses tension between lattice QCD predictions and PDG values for the partial width and branching fraction of the radiative decay J/ψ → γ η_c. A profile scan over recent PDG data is used to argue that correlations among measured branching fractions are compatible with lattice determinations of Γ(J/ψ → γ η_c) and Γ(η_c → γγ). The authors propose a theoretically grounded photon line shape for the M1 transition spectrum together with an extraction prescription for (product) branching fractions that avoids empirical damping functions.

Significance. If the line-shape proposal holds, it removes an ad-hoc element from experimental analyses of charmonium M1 transitions and could improve consistency between data and lattice calculations. The profile-scan approach supplies an indirect consistency check that does not require a direct fit to the target observable.

major comments (2)
  1. The compatibility conclusion rests on the profile scan over PDG inputs; the manuscript must explicitly demonstrate how all published experimental correlations are propagated and whether PDG averages already incorporate extractions that employed the damping functions being criticized (see stress-test concern). Without this, the scan result cannot be shown to be independent of the very modeling choices under discussion.
  2. The derivation of the proposed photon line shape and the precise prescription for extracting product branching fractions are not supplied with sufficient technical detail (equations, assumptions, or validation against simulated spectra) to confirm that the shape is free of new adjustable parameters or that it reproduces the M1 spectrum without empirical modification.
minor comments (2)
  1. Add a dedicated section or appendix that tabulates the input PDG measurements, their quoted uncertainties, and the covariance matrix used in the scan.
  2. Clarify the relation between the new line shape and existing theoretical calculations of the M1 matrix element (e.g., cite the specific lattice or quark-model references used for normalization).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and valuable suggestions. We address the major comments point by point below, indicating the revisions we plan to make to strengthen the manuscript.

read point-by-point responses

  1. Referee: The compatibility conclusion rests on the profile scan over PDG inputs; the manuscript must explicitly demonstrate how all published experimental correlations are propagated and whether PDG averages already incorporate extractions that employed the damping functions being criticized (see stress-test concern). Without this, the scan result cannot be shown to be independent of the very modeling choices under discussion.

    Authors: We agree that a more explicit demonstration of the correlation propagation is required. In the revised version, we will add a dedicated subsection detailing the methodology for incorporating the published experimental correlations from the PDG into the profile scan. This will include the covariance matrix construction and any assumptions made. Concerning the damping functions, while some input measurements may have employed them, the PDG values represent the current consensus; our analysis tests compatibility with these reported values. We will include an additional stress-test to assess sensitivity to potential modeling dependencies, thereby addressing the independence concern. revision: partial

  2. Referee: The derivation of the proposed photon line shape and the precise prescription for extracting product branching fractions are not supplied with sufficient technical detail (equations, assumptions, or validation against simulated spectra) to confirm that the shape is free of new adjustable parameters or that it reproduces the M1 spectrum without empirical modification.

    Authors: The referee correctly identifies that the technical details in the current manuscript are insufficient. We will revise the manuscript to provide the full derivation of the photon line shape based on the M1 transition matrix element in the non-relativistic limit, including all relevant equations and assumptions (such as the absence of additional parameters). We will also include validation against simulated spectra to demonstrate reproduction of the M1 spectrum without empirical damping. This will clarify that no new adjustable parameters are introduced. revision: yes

Circularity Check

0 steps flagged

No circularity: profile scan checks external compatibility without self-referential reduction

full rationale

The paper's central step is a profile scan over PDG branching-fraction data (acknowledged to depend on B(J/ψ→γη_c)) to test consistency of measured correlations against independent lattice QCD partial widths Γ(J/ψ→γη_c) and Γ(η_c→γγ). This is framed as an assessment of tension, not a derivation or prediction of the branching fraction itself. The proposed photon line shape is introduced as a new theoretical prescription that removes the need for empirical damping functions; it does not reduce to a fit of the target observable or to any self-citation. No equations or claims in the abstract or described chain equate an output to its inputs by construction, import uniqueness via author prior work, or rename a known result. The derivation therefore rests on external benchmarks and remains non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on external lattice QCD results and PDG data compilations as inputs; no new free parameters, ad-hoc entities, or unstated axioms are introduced in the provided summary.

axioms (1)
  • domain assumption Lattice QCD calculations of the partial widths Gamma(J/psi to gamma eta_c) and Gamma(eta_c to gamma gamma) provide reliable external benchmarks.
    Paper uses these to assess compatibility with the PDG data scan.

pith-pipeline@v0.9.1-grok · 5721 in / 1347 out tokens · 26361 ms · 2026-06-26T17:17:47.099523+00:00 · methodology

discussion (0)

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Reference graph

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