arxiv: 2603.23081 · v2 · submitted 2026-03-24 · ✦ hep-ex

Recognition: 1 theorem link

· Lean Theorem

Amplitude Analysis of the Isospin-Violating Decay J/psirightarrowγηπ⁰

BESIII Collaboration: M. Ablikim , M. N. Achasov , P. Adlarson , X. C. Ai , C. S. Akondi , R. Aliberti , A. Amoroso , Q. An

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Y. H. An Y. Bai O. Bakina H.-R. Bao X. L. Bao M. Barbagiovanni V. Batozskaya K. Begzsuren N. Berger M. Berlowski M. B. Bertani D. Bettoni F. Bianchi E. Bianco A. Bortone I. Boyko R. A. Briere A. Brueggemann D. Cabiati H. Cai M. H. Cai X. Cai A. Calcaterra G. F. Cao N. Cao S. A. Cetin X. Y. Chai J. F. Chang T. T. Chang G. R. Che Y. Z. Che C. H. Chen Chao Chen G. Chen H. S. Chen H. Y. Chen M. L. Chen S. J. Chen S. M. Chen T. Chen W. Chen X. R. Chen X. T. Chen X. Y. Chen Y. B. Chen Y. Q. Chen Z. K. Chen J. Cheng L. N. Cheng S. K. Choi X. Chu G. Cibinetto F. Cossio J. Cottee-Meldrum H. L. Dai J. P. Dai X. C. Dai A. Dbeyssi R. E. de Boer D. Dedovich C. Q. Deng Z. Y. Deng A. Denig I. Denisenko M. Destefanis F. De Mori E. Di Fiore X. X. Ding Y. Ding Y. X. Ding Yi. Ding J. Dong L. Y. Dong M. Y. Dong X. Dong M. C. Du S. X. Du Shaoxu Du X. L. Du Y. Q. Du Y. Y. Duan Z. H. Duan P. Egorov G. F. Fan J. J. Fan Y. H. Fan J. Fang Jin Fang S. S. Fang W. X. Fang Y. Q. Fang L. Fava F. Feldbauer G. 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Peters K. Petridis J. L. Ping R. G. Ping S. Plura V. Prasad L. P\"opping F. Z. Qi H. R. Qi M. Qi S. Qian W. B. Qian C. F. Qiao J. H. Qiao J. J. Qin J. L. Qin L. Q. Qin L. Y. Qin P. B. Qin X. P. Qin X. S. Qin Z. H. Qin J. F. Qiu Z. H. Qu J. Rademacker C. F. Redmer A. Rivetti M. Rolo G. Rong S. S. Rong F. Rosini Ch. Rosner M. Q. Ruan N. Salone A. Sarantsev Y. Schelhaas M. Schernau K. Schoenning M. Scodeggio W. Shan X. Y. Shan Z. J. Shang J. F. Shangguan L. G. Shao M. Shao C. P. Shen H. F. Shen W. H. Shen X. Y. Shen B. A. Shi Ch. Y. Shi H. Shi J. L. Shi J. Y. Shi M. H. Shi S. Y. Shi X. Shi H. L. Song J. J. Song M. H. Song T. Z. Song W. M. Song Y. X. Song Zirong Song S. Sosio S. Spataro S. Stansilaus F. Stieler M. Stolte S. S Su G. B. Sun G. X. Sun H. Sun H. K. Sun J. F. Sun K. Sun L. Sun R. Sun S. S. Sun T. Sun W. Y. Sun Y. C. Sun Y. H. Sun Y. J. Sun Y. Z. Sun Z. Q. Sun Z. T. Sun H. Tabaharizato C. J. Tang G. Y. Tang J. Tang J. J. Tang L. F. Tang Y. A. Tang Z. H. Tang L. Y. Tao M. Tat J. X. Teng J. Y. Tian W. H. Tian Y. Tian Z. F. Tian I. Uman E. van der Smagt B. Wang Bin Wang Bo Wang C. Wang Chao Wang Cong Wang D. Y. Wang H. J. Wang H. R. Wang J. Wang J. J. Wang J. P. Wang K. Wang L. L. Wang L. W. Wang M. Wang Mi Wang N. Y. Wang S. Wang Shun Wang T. Wang T. J. Wang W. Wang W. P. Wang X. F. Wang X. L. Wang X. N. Wang Xin Wang Y. Wang Y. D. Wang Y. F. Wang Y. H. Wang Y. J. Wang Y. L. Wang Y. N. Wang Yanning Wang Yaqian Wang Yi Wang Yuan Wang Z. Wang Z. L. Wang Z. Q. Wang Z. Y. Wang Zhi Wang Ziyi Wang D. Wei D. H. Wei D. J. Wei H. R. Wei F. Weidner H. R. Wen S. P. Wen U. Wiedner G. Wilkinson M. Wolke J. F. Wu L. H. Wu L. J. Wu Lianjie Wu S. G. Wu S. M. Wu X. W. Wu Z. Wu H. L. Xia L. Xia B. H. Xiang D. Xiao G. Y. Xiao H. Xiao Y. L. Xiao Z. J. Xiao C. Xie K. J. Xie Y. Xie Y. G. Xie Y. H. Xie Z. P. Xie T. Y. Xing D. B. Xiong C. J. Xu G. F. Xu H. Y. Xu Q. J. Xu Q. N. Xu T. D. Xu X. P. Xu Y. Xu Y. C. Xu Z. S. Xu F. Yan L. Yan W. B. Yan W. C. Yan W. H. Yan W. P. Yan X. Q. 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X. Zhang Z. Y. Zhang Zh. Zh. Zhang Zhilong Zhang Ziyang Zhang Ziyu Zhang G. Zhao J.-P. Zhao J. Y. Zhao J. Z. Zhao L. Zhao Lei Zhao M. G. Zhao R. P. Zhao S. J. Zhao Y. B. Zhao Y. L. Zhao Y. P. Zhao Y. X. Zhao Z. G. Zhao A. Zhemchugov B. Zheng B. M. Zheng J. P. Zheng W. J. Zheng W. Q. Zheng X. R. Zheng Y. H. Zheng B. Zhong C. Zhong H. Zhou J. Q. Zhou S. Zhou X. Zhou X. K. Zhou X. R. Zhou X. Y. Zhou Y. X. Zhou Y. Z. Zhou A. N. Zhu J. Zhu K. Zhu K. J. Zhu K. S. Zhu L. X. Zhu Lin Zhu S. H. Zhu T. J. Zhu W. D. Zhu W. J. Zhu W. Z. Zhu Y. C. Zhu Z. A. Zhu X. Y. Zhuang M. Zhuge J. H. Zou J. Zu

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Pith reviewed 2026-05-15 00:35 UTC · model grok-4.3

classification ✦ hep-ex

keywords amplitude analysisJ/psi decaysisospin violationeta pi0a0(980)branching fractionradiative decaysscalar mesons

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The pith

The first amplitude analysis of J/ψ → γ η π⁰ observes radiative transitions to isospin-triplet scalar mesons with over 5σ significance.

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

Using more than ten billion J/ψ events, the analysis examines the isospin-violating decay into a photon, eta, and neutral pion. Dominant pathways involve intermediate resonances b1(1235), ρ(1450), and h1(1170). Signals from a0(980), a2(1320), and a2(1700) stand out above 5σ, providing the first clear evidence for J/ψ radiative decays to these isospin-triplet states. The total branching fraction is measured with twice the previous precision.

Core claim

The decay J/ψ → γ η π⁰ is dominated by J/ψ → π⁰ b₁(1235)⁰ → γ η π⁰, J/ψ → π⁰ ρ(1450)⁰ → γ η π⁰, and J/ψ → η h₁(1170) → γ η π⁰. Contributions from J/ψ → γ a₀(980)⁰, J/ψ → γ a₂(1320)⁰, and J/ψ → γ a₂(1700)⁰ are observed with statistical significance exceeding 5σ, marking the first observation of radiative transitions of J/ψ to isospin-triplet scalar mesons.

What carries the argument

Amplitude analysis fitting the decay distribution with a coherent sum of intermediate resonance amplitudes including a0(980), a2(1320), a2(1700), b1(1235), ρ(1450), and h1(1170) plus background terms.

Load-bearing premise

The fit model includes only the listed resonances and assumes interference patterns and background shapes are correctly parameterized without significant missing contributions.

What would settle it

An independent analysis with substantially larger statistics that measures the significance of the a0(980) contribution below 5σ would falsify the observation.

Figures

Figures reproduced from arXiv: 2603.23081 by A. Amoroso, A. A. Zafar, A. Bortone, A. Brueggemann, A. Calcaterra, A. Dbeyssi, A. Denig, A. Gilman, A. Guskov, A. Khoukaz, A. Kupsc, A. Limphirat, A. Marshall, A. N. Zhu, A. Pathak, A. Q. Guo, A. Rivetti, A. Sarantsev, A. Zhemchugov, B. A. Shi, B. C. Ke, BESIII Collaboration: M. Ablikim, B. H. Xiang, Bin Wang, B. J. Liu, B. Kopf, B. L. Zhang, B. Moses, B. M. Zheng, Bo Wang, B. Wang, B. X. Liu, B. X. Yu, B. X. Zhang, B. Zheng, B. Zhong, C. C. Lin, C. D. Fu, C. F. Qiao, C. F. Redmer, C. Geng, Chao Chen, Chao Wang, C. H. Chen, C. Herold, C. H. Heinz, C. H. Li, Ch. Rosner, Chunkai Li, Ch. Y. Shi, C. J. Tang, C. J. Xu, C. K. Li, C. Li, C. Liang, C. Liu, C. L. Luo, C. Normand, Cong Li, Cong Wang, C. P. Shen, C. Q. Deng, C. Q. Feng, C. S. Akondi, C. Wang, C. Xie, C. X. Lin, C. X. Liu, C. X. Yu, C. X. Yue, C. Y. Guan, C. Z. He, C. Zhong, C. Z. Yuan, D. Bettoni, D. B. Xiong, D. Cabiati, D. Dedovich, D. H. Wei, D. H. Zhang, D. Jiang, D. J. Wei, D. 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**Figure 2.** Figure 2: FIG. 2. Projections of the nominal results on the (a) [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

read the original abstract

Using $(10\,087 \pm 44) \times 10^6$ $J/\psi$ events collected with the BESIII detector, we perform the first amplitude analysis of the process $J/\psi\to\gamma\eta\pi^0$. The decay is dominated by the intermediate processes $J/\psi\to\pi^0 b_1(1235)^0 \to\gamma\eta\pi^0$, $J/\psi\to\pi^{0}\rho(1450)^0 \to\gamma\eta \pi^0$ and $J/\psi\to\eta h_1(1170) \to\gamma\eta\pi^0$. Contributions from $J/\psi\to\gamma a_0(980)^0\to\gamma\eta\pi^0$, $J/\psi\to\gamma a_2(1320)^0\to\gamma\eta\pi^0$ and $J/\psi\to\gamma a_2(1700)^0\to\gamma\eta\pi^0$ are observed with a statistical significance exceeding $5\sigma$, constituting the first observation of radiative transitions of $J/\psi$ to isospin-triplet scalar mesons. The total branching fraction of $J/\psi\to\gamma \eta \pi^0$ is measured to be $(25.7\pm0.3\pm1.5)\times 10^{-6}$, where the first uncertainty is statistical and the second systematic. This result is consistent with the previous measurement, with the precision improved by more than a factor of two.

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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.

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BESIII gives the first amplitude analysis of J/ψ → γ η π⁰, with >5σ signals for three new radiative transitions to isospin-triplet states and a factor-of-two tighter branching fraction.

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This paper reports the first amplitude analysis of J/ψ → γ η π⁰ using 10 billion events. It claims first observations of the radiative transitions J/ψ → γ a₀(980)⁰, γ a₂(1320)⁰, and γ a₂(1700)⁰ at >5σ each, plus a total branching fraction of (25.7 ± 0.3 ± 1.5) × 10^{-6} that matches the prior result but with more than twice the precision. The dominant intermediates are the usual ones: π⁰ b₁(1235)⁰, π⁰ ρ(1450)⁰, and η h₁(1170).

Referee Report

0 major / 1 minor

Summary. The manuscript reports the first amplitude analysis of the decay J/ψ → γ η π⁰ using (10,087 ± 44) × 10^6 J/ψ events from BESIII. It identifies dominant intermediate states including π⁰ b₁(1235)⁰, π⁰ ρ(1450)⁰, and η h₁(1170), and observes contributions from J/ψ → γ a₀(980)⁰, J/ψ → γ a₂(1320)⁰, and J/ψ → γ a₂(1700)⁰ with significances exceeding 5σ. The total branching fraction is measured as (25.7 ± 0.3 ± 1.5) × 10^{-6}, consistent with prior results but with improved precision.

Significance. If the amplitude analysis holds, this constitutes the first observation of radiative J/ψ decays to isovector mesons a₀(980), a₂(1320), and a₂(1700), advancing the understanding of isospin violation and light meson spectroscopy in charmonium decays. The large dataset supports high statistical significance, and the results align with previous branching fraction measurements.

minor comments (1)

[Abstract] The description 'first observation of radiative transitions of J/ψ to isospin-triplet scalar mesons' is imprecise because a₂(1320)⁰ and a₂(1700)⁰ are tensor mesons with J^P=2^+, whereas scalar mesons have J^P=0^+. The statement should be revised to refer to isovector mesons or explicitly list the quantum numbers.

Simulated Author's Rebuttal

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We thank the referee for the positive assessment of our manuscript and the recommendation to accept it for publication.

Circularity Check

0 steps flagged

Minor self-citations to prior BESIII results; central amplitude fit is data-driven

full rationale

The paper reports a data-driven amplitude analysis of collected J/ψ events, extracting resonance contributions and branching fractions via fits to the observed ηπ⁰ mass and angular distributions. No central result is obtained by defining a quantity in terms of a fitted parameter that is then relabeled as a prediction, nor does any load-bearing step reduce to a self-citation chain whose validity depends on the present work. Self-citations are limited to earlier BESIII measurements of the same final state and serve only as consistency checks. The derivation therefore remains self-contained against external data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard resonance parameters taken from the PDG, on the assumption that the selected set of intermediate states is complete, and on conventional isospin and angular-momentum conservation rules. No new particles or forces are postulated.

free parameters (1)

resonance amplitudes and phases
Fitted to data in the amplitude analysis; values not reported in abstract but central to extracting branching fractions and significances.

axioms (2)

domain assumption Standard quantum numbers and decay widths of listed resonances (b1(1235), rho(1450), h1(1170), a0(980), a2(1320), a2(1700)) are taken from PDG.
Invoked when constructing the amplitude model for the fit.
domain assumption Isospin violation is small and can be accommodated by including both isovector and isoscalar intermediates.
Underlying motivation for studying this decay channel.

pith-pipeline@v0.9.0 · 9703 in / 1669 out tokens · 34655 ms · 2026-05-15T00:35:45.329024+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

first amplitude analysis of J/ψ→γηπ⁰ … contributions … observed with statistical significance exceeding 5σ

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matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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