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The branching fraction measurements of $J/\psi$ decay into $\rho \eta$ and $\phi \eta$ final states

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Pith's one-line read Using 4.93 million J/ψ events, the authors measure B(J/ψ→ρη) = (2.04 ± 0.58 ± 0.39) × 10⁻⁴ and B(J/ψ→φη) = (7.82 ± 1.17 ± 0.58) × 10⁻⁴, and find hints of ρ(1450)η and a₂±π∓ contributions in the π⁺π⁻η Dalitz plot.

desk verdict A competent, transparent KEDR measurement that independently confirms the ρη and φη branching fractions and adds weak dynamical hints; the main risk is model-dependence of the ρη extraction, plus a small internal inconsistency in Eq. 13. read the letter →

arxiv 2506.08453 v2 pith:P4SE7ERP submitted 2025-06-10 hep-ex

KEDR Collaboration , V. V. Anashin , O. V. Anchugov , K. V. Astrelina , V. M. Aulchenko , V. V. Balakin , E. M. Baldin , G. N. Baranov
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A. K. Barladyan A. Yu. Barnyakov M. Yu. Barnyakov I. Yu. Basok E. A. Bekhtenev O. V. Belikov D. E. Berkaev A. E. Blinov V. E. Blinov A. V. Bobrov V. S. Bobrovnikov A. V. Bogomyagkov D. Yu. Bolkhovityanov A. E. Bondar V. M. Borin A. R. Buzykaev V. L. Dorokhov D. V. Dorokhova F. A. Emanov D. N. Grigoriev V. V. Kaminskiy S. E. Karnaev G. V. Karpov K. Yu. Karukina P. V. Kasyanenko A. A. Katcin T. A. Kharlamova V. A. Kiselev A. A. Kovalenko E. V. Kozyrev A. A. Krasnov E. A. Kravchenko V. N. Kudryavtsev V. F. Kulikov G. Ya. Kurkin I. A. Kuyanov D. A. Kyshtymov N. N. Lebedev E. B. Levichev P. V. Logachev D. A. Maksimov T. V. Maltsev V. M. Malyshev R. Z. Mamutov A. L. Maslennikov O. I. Meshkov I. I. Morozov I. A. Morozov A. A. Murasev S. A. Nikitin I. B. Nikolaev I. N. Okunev S. B. Oreshkin A. A. Osipov I. V. Ovtin A. V. Pavlenko S. V. Peleganchuk K. G. Petrukhin P. A. Piminov S. G. Pivovarov A. V. Polyanskiy V. G. Prisekin O. L. Rezanova A. A. Ruban G. A. Savinov D. V. Senkov A. G. Shamov L. I. Shekhtman D. A. Shvedov B. A. Shwartz E. A. Simonov S. V. Sinyatkin M. A. Skamarokha A. N. Skrinsky A. V. Sokolov E. V. Starostina D. P. Sukhanov A. M. Sukharev A. A. Talyshev V. A. Tayursky V. I. Telnov Yu. A. Tikhonov K. Yu. Todyshev Yu. V. Usov A. I. Vorobiov V. N. Zhilich A. A. Zhukov V. V. Zhulanov A. N. Zhuravlev D. A. Zubkov
This is my paper · ORCID
classification hep-ex PACS 13.25.Gv
keywords J/ψdecaysbranchingfractionρηfinalstateφDalitzplotanalysischarmoniume+e−experimentsintermediatestates
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 reports new measurements of the branching fractions of the J/ψ meson into ρη and φη final states, based on 4.93 million J/ψ events collected with the KEDR detector. The results—B(J/ψ→ρη)=(2.04±0.58±0.39)×10⁻⁴ and B(J/ψ→φη)=(7.82±1.17±0.58)×10⁻⁴—agree with earlier experiments, providing an independent check of the world-average values. For the ρη channel, a fit to the π⁺π⁻η Dalitz plot finds hints of contributions from ρ(1450)η and a₂±π∓ intermediate states, with a 90% confidence upper limit on the ρ(1450)η contribution. If correct, the measurements confirm the standard picture of these charmonium decays while suggesting that the π⁺π⁻η final state contains more dynamics than a simple ρη plus ωη description.

What carries the argument

The central object is the Dalitz plot of J/ψ→π⁺π⁻η, modeled as the coherent sum of vector–pseudoscalar amplitudes (ρη, ωη, ρ(1450)η) with energy-dependent line shapes and relative phases, plus an incoherent tensor–pseudoscalar a₂±π∓ term. Each resonance amplitude uses a Breit–Wigner form with an energy-dependent width (Eqs. 2–3), and the interference terms are included in cosine and sine parts with Monte Carlo templates. The fit minimizes a binned Baker–Cousins likelihood (Eq. 9). For φη, the machinery reduces to a one-dimensional fit of the K⁺K⁻ invariant mass with a ϕ line shape plus a non-resonant contribution. The same generator (from the earlier KEDR analysis) provides the efficiency corrections and background templates.

What would settle it

A model-independent partial-wave analysis of J/ψ→π⁺π⁻η on a high-statistics sample would settle the issue: if it does not reproduce the ρη yield of 67 events and the ρ(1450)η upper limit of 1.51×10⁻⁴, the central branching fraction would need to be revised.

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Extended reading notes

Core claim

The central claim is that B(J/ψ→ρη)=(2.04±0.58±0.39)×10⁻⁴ and B(J/ψ→φη)=(7.82±1.17±0.58)×10⁻⁴, extracted from 4.93 million J/ψ decays recorded at the KEDR detector. The ρη value comes from a fit to the π⁺π⁻η Dalitz plot that models the final state as coherent ρη, ωη, and ρ(1450)η amplitudes plus an incoherent a₂±π∓ term; the fit yields 67 ρη events out of 134 total and the additional branching fractions B(J/ψ→π⁺π⁻η)=(4.73±0.49±1.17)×10⁻⁴, B(J/ψ→a₂±π∓)=(1.05±0.37±0.34)×10⁻³, and B(J/ψ→ρ(1450)η→π⁺π⁻η)<1.51×10⁻⁴ at 90% CL. The φη result is obtained from a fit to the K⁺K⁻ invariant mass with a ϕ resonance and a non-resonant term. The paper reports that all results are consistent with previous experiments and provides interference phases between ρ–ω and ρ–ρ(1450) as model inputs.

Load-bearing premise

The load-bearing premise is the assumed interference model for the π⁺π⁻η Dalitz plot—coherent ρη, ωη, ρ(1450)η plus incoherent a₂±π∓ with the specified line shapes; if additional interference structure exists, the ρη yield and the 17% efficiency correction could shift beyond the quoted uncertainties.

Editorial extensions

If this is right

  • The measured branching fractions independently confirm the world-average values for J/ψ→ρη and J/ψ→φη, strengthening the empirical basis for these decay rates.
  • The Dalitz fit implies that J/ψ→π⁺π⁻η is not fully described by ρη and ωη alone; the contributions from ρ(1450)η and a₂±π∓ found in the model should be included in future amplitude analyses.
  • The interference phases between ρ–ω and ρ–ρ(1450) provide new constraints on the relative strong and electromagnetic amplitudes in J/ψ decays into vector–pseudoscalar pairs.
  • The 90% CL upper limit on ρ(1450)η→π⁺π⁻η bounds the excited-vector contribution, complementing studies of the analogous π⁺π⁻π⁰ channel.

Reading between the lines

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

  • If the a₂±π∓ hint is real, its branching fraction of about 1.05×10⁻³ falls well below the theoretical estimate of 3.8×10⁻³ cited in the paper, suggesting the production mechanism may suppress this mode or the estimate is too high.
  • A high-statistics sample from a future experiment could turn the ρ(1450)η hint into a signal or push the upper limit below 1.51×10⁻⁴, directly testing the model used here.
  • The dominant 10.7% systematic from unaccounted interference is a model-comparison estimate; a data-driven extraction of the interference phases from angular distributions would reduce this uncertainty.
  • The 17% efficiency for ρη is computed with the same generator model used in the fit; an independent efficiency calibration would verify the absolute branching-fraction scale.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper reports measurements of the branching fractions B(J/ψ→ρη) and B(J/ψ→φη) using 4.93 million J/ψ events collected with the KEDR detector. The ρη result is obtained from a binned Dalitz-plot fit to J/ψ→π+π−η, where the signal is modeled as a coherent sum of ρη, ωη, and ρ(1450)η amplitudes with an incoherent a2±π∓ term and fixed continuum and background contributions. The φη result is obtained from a one-dimensional fit to the K+K− invariant mass in J/ψ→K+K−η. The paper also reports B(J/ψ→π+π−η), B(J/ψ→a2±π∓), an upper limit on B(J/ψ→ρ(1450)η→π+π−η), and the ρ−ω and ρ−ρ(1450) interference phases. All quoted numerical results are internally arithmetically consistent: the 2.2% correction reconciles the Section 6.1 values with the Section 7 values, and the systematic tables add in quadrature to the stated totals.

Significance. If the results hold, the paper provides an independent KEDR confirmation of the world-average values for B(J/ψ→ρη) and B(J/ψ→φη) from a dataset that is modest in size but complementary to BES/BaBar. The dynamic analysis of π+π−η adds useful, albeit low-significance, information on possible ρ(1450)η and a2±π∓ contributions. The paper is careful to quote separate statistical and systematic uncertainties, uses external normalization anchors (PDG branching fractions, BES-II B(J/ψ→ωη), BaBar continuum cross-section), and the internal arithmetic is sound. The main limitation is that the largest systematic uncertainty in the ρη measurement, the 10.7% assigned to unaccounted interference effects, is estimated from a two-model comparison rather than from a data-driven or closure-test constraint, and the same model enters the efficiency calculation. This prevents the central ρη result from being as robust as the quoted uncertainty suggests.

major comments (3)
  1. [Section 6.2 and Eq. (8)] The largest systematic uncertainty in the ρη measurement, 10.7% from 'unaccounted interference effects between tensor mesons and between V+P and T+P processes,' is estimated by comparing two fit variants: one in which interference with a2±π∓ is included at zero phase and one in which it is excluded. This comparison does not scan the interference phase or its magnitude. Given that the fitted a2±π∓ yield is 23 events out of 134 and that p1 (the ρη strength) is determined in the same fit, an a2π–ρη interference term at an arbitrary phase and with a magnitude comparable to the fitted a2π yield could shift p1 by more than this estimate. In addition, the 17% selection efficiency for ρη (Section 5.1) is computed with the same generator model, so an incorrect interference model enters both the fitted yield and the efficiency. A closure test with pseudo-experiments generated from a model with a2π–ρη interference at several phases and magnitudes, then fitted with the nominal model, should be performed (or a data-driven constraint on this interference should be provided) before the 10.7% systematic can be considered to cover the dominant model uncertainty.
  2. [Section 5.1, Eqs. (8) and (13)] There is an internal inconsistency in the definition of the π+π−π0γγ background subtraction. Equation (8) uses p5 as the strength of the Hπ+π−π0γγ histogram, while Eq. (13) defines Nπ+π−π0γγ = p4 Iπ+π−π0γγ, where p4 is the a2±π∓ strength in Eq. (8). If taken literally, the subtraction used to obtain Nπ+π−η in Eq. (13) uses the wrong fit parameter, which directly affects the derived B(J/ψ→π+π−η) in Eq. (10). The authors should correct this notation and verify explicitly that the quoted B(J/ψ→π+π−η) value is unaffected.
  3. [Section 6.1 and Section 7] The paper reports 'hints' of ρ(1450)η and a2±π∓ contributions, but no statistical significance is given for the improvement of the fit when these components are added. The statement that the fit without these intermediate states gives 'worse likelihood function values' should be quantified with Δ(-2lnL) or a p-value, and the procedure used to set the 90% confidence-level upper limit on ρ(1450)η should be described (e.g., profile likelihood or Feldman-Cousins). This is needed to support the secondary dynamical claims, especially because the extracted a2±π∓ branching fraction has a central value only about two standard deviations from zero.
minor comments (5)
  1. [Section 7 and Fig. 5] The text refers to 'Belle-II' in the list of experiments with consistent results, but reference [7] and the figure label are for Belle. Please correct this inconsistency.
  2. [Section 2.1, Eq. (2)] The resonance amplitude in Eq. (2) is written with an explicit B(J/ψ→ρη)B(ρ→ππ) factor, but the relation between the fit parameter p1 and this branching fraction is not shown explicitly. It would improve clarity to state the proportionality constant and how it is absorbed into Eq. (10).
  3. [Section 3] The Monte Carlo generators from references [13] and [14] are internal to the KEDR collaboration. Please provide a brief description of the assumed production angular distributions and any version/parameter choices, so that the interference-term histograms Hc± and Hs± are reproducible from the text.
  4. [Section 6.2] The 2.2% upward correction from track inefficiency and photon loss is applied to all branching fractions, but this correction is not listed in Tables 3 or 5. Please state clearly in the table captions or text that the quoted central values include this correction, and list the 2.2% as a separate item for transparency.
  5. [Section 6.4] The non-resonant K+K−η contribution is simulated with an 'infinite decay width' of the vector particle (Section 3). This is a potentially ambiguous line shape; please specify the functional form used and how the 4.3% systematic was obtained from the alternative phase-space simulation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central branching-fraction results are fit to KEDR data with external normalization anchors and independent benchmark agreement.

full rationale

The paper's derivation chain for B(J/ψ → ρη) starts from the binned Dalitz fit of Eq. 8, where the yield parameter p1 multiplies the MC template H_ρη. The template is generated from an external line-shape prescription (Eqs. 2–3, same as used by SND [11]), and p1 is determined by maximizing the likelihood in Eq. 9 against the observed Dalitz distribution. The conversion to a branching fraction in Eq. 10 uses external inputs: PDG values for B(η → γγ), B(ρ → ππ), and B(a2 → πη); the B(J/ψ → ωη) constraint from BES-II [21]; and the continuum contribution fixed to the BaBar cross-section [3]. Similarly, B(J/ψ → φη) is obtained from the one-dimensional fit in Eq. 14 with a free φη yield p6, normalized by the PDG values B(η → γγ) and B(φ → K+K−). The self-citations to [13], [14], and [20] provide the Monte Carlo event generators, the track and photon-loss correction of 2.2%, and the number of J/ψ events; these are calibration and simulation inputs, not fitted parameters that encode the target branching fractions. No equation defines a fitted yield as the normalization of the same quantity, and no prediction is obtained from a parameter that was itself fit to that prediction. The main risk identified in the paper is model dependence of the ρη extraction, quantified by the 10.7% systematic from comparing interference models in Section 6.2; this is a correctness and robustness concern, not a circularity, because the systematic is estimated by varying the model and does not reduce the measurement to its own input. The apparent p4/p5 inconsistency between Eq. 8 and Eq. 13 is a labeling typo in the paper text and does not constitute a circular step. Overall, the central results are anchored to external measurements and to the KEDR data themselves, with no circular reduction identified.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

About nine fitted parameters are extracted from 134 π⁺π⁻η events and 64 φη events; the absolute normalization rests on external anchors (PDG, BES-II, BaBar). No new entities are postulated; ρ(1450) and a₂ are established resonances. The main risks are the assumed interference structure and the data-tuned background weights.

free parameters (9)
  • p1 (J/ψ → ρη normalization) = B = 2.04 x 10^-4, 67 of 134 events
    Signal strength fitted to the π⁺π⁻η Dalitz histogram (Eq. 8, Section 5.1); the central claim depends on it.
  • p3 (J/ψ → ρ(1450)η normalization) = B = (6.23 ± 4.70) x 10^-5, consistent with zero; 90% CL upper limit 1.51 x 10^-4
    Fitted Dalitz component (Section 6.1); included though consistent with zero, which feeds the ρη yield via interference terms.
  • p4 (J/ψ → a₂±π∓ normalization) = B = (1.05 ± 0.37 ± 0.34) x 10^-3, 23 of 134 events
    Fitted incoherent tensor-pseudoscalar component (Section 6.1); combined significance about 2σ.
  • φ(ρ-ω) interference phase = (88.4 ± 2.5 ± 3.1) degrees
    Free phase in Eq. 8 fitted to the Dalitz distribution.
  • φ(ρ-ρ(1450)) interference phase = (148.6 ± 44.3 ± 41.0) degrees
    Free phase in Eq. 8; barely constrained by the data.
  • φ(ρ-continuum) interference phase = (47.0 ± 161.7) degrees
    Free phase in Hcont.+interf. (Section 5.1); effectively unconstrained by 4 continuum events.
  • p6/p7 (φη and non-resonant K+K-η normalizations) = 64 φη events; B(φη) = 7.82 x 10^-4
    Fitted to the M(K+K-) distribution (Eq. 14, Section 5.2).
  • φ(φη, non-resonant) phase = (-6.0 ± 9.1) degrees
    Free phase in Eq. 14.
  • J/ψ → π+π-π0γγ MC component weights = tuned to data
    Weights of ωη, φη, a₂ρ, and non-resonant contributions tuned to the observed M(π+π-π0) distribution near the η mass (Section 3), then used as background model in Eq. 8 with a 2.7% systematic.
assumptions (5)
  • domain assumption The V+P amplitude has the relativistic Breit-Wigner form of Eq. 2 with the energy-dependent width of Eq. 3, with the matrix element taken from SND [11].
    Adopted from prior literature without independent derivation or data validation in this paper; the ρη efficiency is computed with this same model.
  • domain assumption The a₂π tensor-pseudoscalar term and the V+P terms do not interfere with each other (Eq. 5).
    Load-bearing for the fit decomposition in Eq. 8; the paper estimates the violation of this assumption only as a 10.7% systematic (Section 6.2).
  • domain assumption B(J/ψ → ωη) from BES-II [21] is fixed in the fit, fixing the ωη contribution to 12 events; B(ω → π+π-) is likewise fixed.
    External input; varied by its uncertainty for a 2.6% systematic (Section 6.2).
  • domain assumption The continuum e+e- → π+π-η background is fixed from the BaBar cross-section [3] scaled by KEDR luminosity; only 2 events were seen outside the J/ψ peak.
    Small-statistics anchor for the continuum subtraction (Section 4 and Section 5.1); the continuum phase is left free.
  • domain assumption The detector simulation with the GHEISHA nuclear-interaction model and the BES/JETSET generators reproduces background and acceptance.
    GHEISHA was chosen over FLUKA for kaons because it 'provided a more accurate representation of the experimental data' (Section 6.4), a data-informed model choice; the resulting uncertainty is estimated by raising the nuclear cross-section by 20%.

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Pith. "Pith review of The branching fraction measurements of $J/\psi$ decay into $\rho \eta$ and $\phi \eta$ final states." pith.science (2026). https://pith.science/paper/P4SE7ERP

@misc{pith2026250608453,
  author       = {Pith},
  title        = {Pith review of: The branching fraction measurements of $J/\psi$ decay into $\rho \eta$ and $\phi \eta$ final states},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P4SE7ERP}},
  note         = {Machine review of arXiv:2506.08453}
}
abstract

We present measurements of the branching fractions for the $J/\psi$ meson decays into the $\rho\eta$ and $\phi\eta$ final states, based on data collected with the KEDR detector at the VEPP-4M collider. The data set consisted of 4.93 million $J/\psi$ events. The resulting branching fractions are: - $\mathcal{B}(J/\psi \to \rho\eta) = (2.04 \pm 0.58 \pm 0.39)\times 10^{-4}$, - $\mathcal{B}(J/\psi \to \phi\eta) = (7.82 \pm 1.17 \pm 0.58) \times 10^{-4}$, where the first uncertainty is statistical and the second one is systematic. In the study of the $\rho\eta$ decay, the dynamics of $J/\psi\to\pi^+\pi^-\eta$ is analyzed. The hints from contributions of $\rho(1450)\eta$ and $a^{\pm}_2\pi^{\mp}$ intermediate states are observed. Additional measured branching fractions in the model that includes $\rho(1450)\eta$ and $a^{\pm}_2\pi^{\mp}$ are: - $\mathcal{B}(J/\psi \to \pi^+\pi^-\eta) = (4.73 \pm 0.49 \pm 1.17)\times10^{-4}$, - $\mathcal{B}(J/\psi \to (a_2^+\pi^- + a_2^- \pi^+)) = (1.05\pm 0.37 \pm 0.34)\times 10^{-3}$, - $\mathcal{B}(J/\psi \to \rho(1450)\eta \to \pi^+\pi^-\eta) < 1.51 \times 10^{-4}$, at a confidence level of 90\%. All results are consistent with previous studies.

Figures

Figures reproduced from arXiv: 2506.08453 by the authors.

Figure 1
Figure 1. The (a) Mπ+π− and (b) Mπ+η distributions. The Kolmogorov probability of agreement for Mπ+π− is 0.43 and for Mπ+η is ∼1. Here, the black dots are observed events in the experiment. The result distribution is shown as a brown line, that includes all in￾terference effects between ρη, ωη and ρ(1450)η processes. Others individual contributions without interferences are: red histogram is the ρη process, blue — ωη, green —… view at source ↗
Figure 2
Figure 2. The variations of selection criteria for (a) [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. The data fit result for the MK+K− invariant mass obtained by maximizing the likelihood function LK+K−η. The Kolmogorov probability of agreement for this distribu￾tion is ∼1. The observed events from the experiment are shown as black dots in the figure. The resulting distribution is presented as a brown line. The black histogram represents the contribution from the ϕη channel, while the blue one — the non resonant J/… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The variations of selection criteria for (a) [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: The comparison of the branching fraction measurements among other experi [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]

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Pith tools

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