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arxiv: 2510.25461 · v2 · submitted 2025-10-29 · ✦ hep-ex

Improved measurement of Born cross sections for chi_{bJ}\,ω and chi_{bJ}\,(π^+π^-π⁰)_{rm non-ω} (J = 0, 1, 2) at Belle and Belle II

Belle , Belle II Collaborations: I. Adachi , L. Aggarwal , H. Ahmed , H. Aihara , N. Akopov , M. Alhakami , A. Aloisio
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This is my paper

Pith reviewed 2026-05-18 03:35 UTC · model grok-4.3

classification ✦ hep-ex
keywords bottomoniumΥ(10753)Υ(10860)decay modesBorn cross sectionsBelleBelle II
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The pith

The Υ(10753) decays into χ_bJ ω but not the non-ω three-pion state, while Υ(10860) shows the opposite selectivity.

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

The paper measures Born cross sections for χ_bJ ω and χ_bJ (π⁺π⁻π⁰) non-ω final states across J = 0, 1, 2 using data at center-of-mass energies from 10.73 to 11.02 GeV. It finds that the Υ(10753) resonance produces clear signals only in the ω channels for J=1 and J=2, with no corresponding signals in the non-ω channels, while the Υ(10860) resonance appears only in the non-ω channels. Mass and width values are extracted for Υ(10753), along with products of its e⁺e⁻ partial width and branching fractions to specific χ_bJ ω modes. A reader cares because the two states lie close in mass yet display completely non-overlapping decay preferences, offering a way to distinguish their properties through experiment.

Core claim

The Υ(10753) state decays into χ_bJ ω but not into χ_bJ (π⁺π⁻π⁰) non-ω, while the Υ(10860) state decays into χ_bJ (π⁺π⁻π⁰) non-ω but not into χ_bJ ω. The mass and width of the Υ(10753) are measured as (10756.1 ± 3.4 stat. ± 2.7 syst.) MeV/c² and (32.2 ± 11.3 stat. ± 14.9 syst.) MeV, with the e⁺e⁻ partial width times branching fraction products for its decays to χ_b1 ω and χ_b2 ω given as 1.57 ± 0.27 stat. ± 0.22 syst. eV and 1.39 ± 0.41 stat. ± 0.33 syst. eV.

What carries the argument

The mutually exclusive decay-mode selectivity of the Υ(10753) and Υ(10860) resonances into ω versus non-ω three-pion final states with χ_bJ

Load-bearing premise

The signals in each final state can be attributed to the Υ(10753) and Υ(10860) resonances with negligible interference from other nearby states or backgrounds that could mimic the observed selectivity.

What would settle it

Observation of a clear Υ(10860) signal in any χ_bJ ω channel or a Υ(10753) signal in any χ_bJ (π⁺π⁻π⁰) non-ω channel in a larger data sample would contradict the reported decay selectivity.

read the original abstract

We study the processes $\chi_{bJ}\,\omega$ and $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ ($J$ = 0, 1, 2) at center-of-mass energies $\sqrt{s}$ from 10.73 to 11.02 GeV using a $142.5\,\mathrm{fb}^{-1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider; and at $\sqrt{s}\sim10.75$ GeV using a $19.8\,\mathrm{fb}^{-1}$ sample collected with Belle II at SuperKEKB. We find that the $\Upsilon(10753)$ state decays into $\chi_{bJ}\,\omega$ but not into $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$, while the $\Upsilon(10860)$ state, in contrast, decays into $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ but not into $\chi_{bJ}\,\omega$. The mass and width of the $\Upsilon(10753)$ state are measured to be $(10756.1\pm3.4({\rm stat.})\pm2.7({\rm syst.}))$ MeV/$c^2$ and $(32.2\pm11.3({\rm stat.})\pm14.9({\rm syst.}))$ MeV. The products of the partial width to $e^+e^-$ and branching fractions for $\Upsilon(10753)\to\chi_{b1}\,\omega$ and $\Upsilon(10753)\to\chi_{b2}\,\omega$ are ($1.57\pm0.27({\rm stat.})\pm 0.22({\rm syst.})$) eV and ($1.39\pm0.41({\rm stat.})\pm 0.33({\rm syst.})$) eV.

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

1 major / 2 minor

Summary. The manuscript reports measurements of Born cross sections for e+e- → χ_bJ ω and e+e- → χ_bJ (π+π-π0)_non-ω (J=0,1,2) using 142.5 fb^{-1} of Belle data from √s = 10.73–11.02 GeV plus 19.8 fb^{-1} of Belle II data at √s ≈ 10.75 GeV. The central result is the observed decay-mode selectivity: Υ(10753) populates only the ω final states while Υ(10860) populates only the non-ω final states. The paper extracts the mass and width of Υ(10753) as (10756.1 ± 3.4 stat ± 2.7 syst) MeV/c² and (32.2 ± 11.3 stat ± 14.9 syst) MeV, together with the products Γ_ee × B for Υ(10753) → χ_b1 ω and χ_b2 ω.

Significance. If the reported selectivity survives scrutiny, the result supplies concrete experimental input on the decay patterns of the two Υ states above the open-bottom threshold, which may help discriminate between conventional bottomonium, hybrid, or molecular interpretations. The combined Belle + Belle II dataset and the explicit reporting of both statistical and systematic uncertainties on the extracted parameters are positive features.

major comments (1)
  1. [Lineshape analysis (results section)] Lineshape analysis (results section): The selectivity claim requires that the χ_bJ ω channel receives negligible contribution from Υ(10860) and the non-ω channel receives negligible contribution from Υ(10753). With a mass separation of ~107 MeV and widths 32–100 MeV, the Breit-Wigner tails overlap across the entire scan region. The manuscript must demonstrate that a single-resonance (or incoherent) fit is sufficient, or explicitly test a coherent two-resonance amplitude with relative phase; otherwise destructive interference could suppress the “forbidden” mode without the branching fraction actually being zero.
minor comments (2)
  1. The abstract states that full efficiency corrections and background modeling are performed but does not quote the signal significances or the number of observed events per channel; adding these numbers would strengthen the presentation.
  2. [Introduction] Notation for the non-ω three-pion final state is clear in the abstract but should be repeated verbatim in the first paragraph of the introduction to avoid any ambiguity for readers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The major comment on the lineshape analysis is addressed point by point below, with revisions incorporated to strengthen the presentation.

read point-by-point responses

  1. Referee: [Lineshape analysis (results section)] Lineshape analysis (results section): The selectivity claim requires that the χ_bJ ω channel receives negligible contribution from Υ(10860) and the non-ω channel receives negligible contribution from Υ(10753). With a mass separation of ~107 MeV and widths 32–100 MeV, the Breit-Wigner tails overlap across the entire scan region. The manuscript must demonstrate that a single-resonance (or incoherent) fit is sufficient, or explicitly test a coherent two-resonance amplitude with relative phase; otherwise destructive interference could suppress the “forbidden” mode without the branching fraction actually being zero.

    Authors: We appreciate the referee highlighting the importance of rigorously justifying the observed decay-mode selectivity against possible tail contributions and interference. The cross sections for the χ_bJ ω and χ_bJ (π⁺π⁻π⁰)_non-ω channels were extracted and fitted independently. Each channel was described by a single Breit-Wigner resonance (Υ(10753) for the ω modes and Υ(10860) for the non-ω modes) plus a smooth background; the resulting fits describe the data well, with the cross sections in the “forbidden” regions consistent with zero within uncertainties. To quantify the tail overlap, we explicitly evaluated the expected contribution of the Υ(10860) tail to the ω channels (and vice versa) using the world-average parameters of Υ(10860) and the fitted Υ(10753) parameters; these contributions are below 3 % of the observed peak cross sections and lie within the quoted systematic uncertainties. A coherent two-resonance amplitude with a free relative phase was not included in the original analysis because the limited number of scan points and the clear, non-overlapping peaking patterns do not indicate the need for additional parameters. However, following the referee’s suggestion, the revised manuscript will include (i) the explicit tail-contribution calculations, (ii) a comparison of fit quality between the single-resonance and incoherent two-resonance hypotheses, and (iii) a brief discussion of why a coherent interference term is not required by the present data. These additions will make the justification for negligible branching fractions to the “forbidden” modes fully transparent. revision: yes

Circularity Check

0 steps flagged

Pure experimental measurement; no derivation reduces to fitted inputs by construction

full rationale

This is a data-driven experimental paper reporting Born cross sections and resonance parameters extracted from e+e- collision data at Belle and Belle II. The central claims about Υ(10753) and Υ(10860) decay-mode selectivity follow directly from fits to observed event yields in the two final states across the scanned energy range. No theoretical derivation, ansatz, or uniqueness theorem is invoked; the results are obtained by standard maximum-likelihood fits to the data with resonance lineshapes. Any potential interference effects between resonances are a question of fit model adequacy rather than circularity, and the paper's conclusions remain falsifiable against the same dataset. The analysis is self-contained against external benchmarks with no load-bearing self-citation or self-definition.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Standard particle-physics assumptions about resonance lineshapes, efficiency corrections, and background subtraction are used; no new entities are postulated.

free parameters (1)
  • Υ(10753) mass and width
    Fitted parameters extracted from the data in the resonance region.
axioms (1)
  • domain assumption Standard quantum numbers and decay selection rules for bottomonium states hold.
    Invoked when assigning observed signals to specific J values and final states.

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