REVIEW 2 major objections 5 minor 82 references
First evidence for the Υ1(1D) and Υ3(1D) bottomonium states, with measured masses and energy-dependent production cross sections.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · grok-4.5
2026-07-11 19:42 UTC pith:4K2PX62Z
load-bearing objection First evidence for Υ1(1D) and Υ3(1D) with usable mass splittings from a clean on-peak 3D fit; energy dependence is secondary and thinner. the 2 major comments →
First measurement of the masses of the Upsilon₁(1D) and Upsilon₃(1D) states and the energy dependence of the cross sections for e^+e^-toUpsilon_J(1D)η and e^+e^-toUpsilon_J(1D)π^+π^-
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The collaboration finds first evidence for the Υ1(1D) and Υ3(1D) states in exclusive e+e− o ΥJ(1D)η and e+e− o ΥJ(1D)π+π− channels, measures the Υ2(1D) mass as (10167.0 ± 1.0 ± 0.2) MeV/c^{2}, and reports the mass splittings Δm12 = (11.8 ± 1.5 ± 0.4) MeV/c^{2} and Δm23 = (7.6 ± 2.4 ± 0.6) MeV/c^{2}, together with the energy dependence of the combined production cross sections from 10.73 to 11.02 GeV.
What carries the argument
A simultaneous three-dimensional unbinned extended maximum-likelihood fit to the χb mass, the ΥJ(1D)–χb mass difference, and the η or π+π− recoil mass, performed after a five-constraint kinematic fit that enforces four-momentum conservation and the Υ(1S) mass.
Load-bearing premise
Outside the main peak sample the three ΥJ(1D) states are merged into one yield because of cross-feed, and the background at every energy is scaled from a single global fit under the assumption that it is purely non-resonant and proportional only to luminosity.
What would settle it
A higher-statistics scan that resolves the three J states separately at several energies away from the Υ(10860) peak and finds either a different mass ordering or a background shape that does not scale with luminosity would overturn the reported mass splittings and energy-dependent cross sections.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports a Belle analysis of e+e-→ΥJ(1D)η and e+e-→ΥJ(1D)π+π- using 142.5 fb-1 (122 fb-1 on the Υ(10860) peak). Exclusive reconstruction of the cascade ΥJ(1D)→χb1,2γ, χb1,2→Υ(1S)γ, Υ(1S)→ℓ+ℓ- with a 5C kinematic fit and a simultaneous 3D unbinned fit to M'(ℓ+ℓ-γH), ΔM and recoil mass yields first evidence for Υ1(1D) (4.8σ) and Υ3(1D) (3.0σ) including systematics, a precise Υ2(1D) mass of (10167.0±1.0±0.2) MeV/c2, and mass splittings Δm12=(11.8±1.5±0.4) MeV/c2 and Δm23=(7.6±2.4±0.6) MeV/c2. Products of Born cross sections and radiative branching fractions, corresponding Υ(10860) branching fractions, and the energy dependence of the combined ΥJ(1D) cross sections (fitted with coherent Υ(10860)/Υ(11020) Breit-Wigners plus phase space) are also presented.
Significance. Observation of the remaining 1D bottomonium multiplet members and a first measurement of their mass splittings constitute a clear advance for heavy-quarkonium spectroscopy. The results directly confront relativized, non-relativistic and screened-potential models (Fig. 3) and supply the first energy-dependent cross-section data near the Υ(11020). The analysis is data-driven, employs a standard 5C fit plus 3D likelihood, folds additive systematics into the quoted significances, and provides HEPData numerical results; these strengths make the central claims robust and of lasting reference value.
major comments (2)
- Text after Eq. (2) and Supplemental Material: for the energy-scan points the three ΥJ(1D) states are combined and Nbg is scaled from a global 3D fit under the assumption of purely non-resonant background proportional to luminosity. While this does not affect the on-peak mass and significance results, it is load-bearing for the energy-dependence fit of Fig. 2 and Table III. A quantitative check (e.g., allowing a resonant component or energy-dependent background shape, or quoting the change in ΓeeB when Nbg is varied by its full uncertainty) should be added so that residual bias can be assessed.
- Table III and Eq. (3): the fitted ΓeeB products for both Υ(10860) and Υ(11020) are all <3σ and the paper already quotes 90% C.L. upper limits. The text should state more explicitly that the energy-dependence results are upper limits rather than measurements, and that the coherent-sum fit is used only to parameterize the radiative-correction factors.
minor comments (5)
- Fig. 1 caption and body: the label “Preliminary” appears on all panels; it should be removed for the journal version.
- Eq. (1) and surrounding text: the vacuum-polarization factor |1-Π|2=0.93 is stated without a reference or energy dependence; a short citation or note that it is taken constant would help.
- Table I vs. Supplemental Tables IV–V: the notation σ(1)Born/σ(2)Born (resolved J) versus σ(3)Born/σ(4)Born (combined) is easy to confuse; a single consistent superscript scheme would improve readability.
- Fig. 3: the correlation coefficient ρ(Δm12,Δm23)=-0.06 is given only in the caption; it would be useful to quote it also in the text when the splittings are compared with theory.
- Supplemental Material: the profile-likelihood parameterizations (Eqs. (4)–(5)) and the GitHub link for fitted coefficients are valuable but should be archived with the paper (e.g., HEPData or journal supplemental) rather than left solely on an external repository.
Circularity Check
No circularity: purely data-driven extraction of masses, yields and cross sections from fits and counting; theory used only for post-hoc comparison.
full rationale
The central results (Υ1(1D)/Υ3(1D) evidence, Υ2(1D) mass, mass splittings, and Born cross-section products) are obtained from a simultaneous 3D unbinned extended maximum-likelihood fit to the on-peak data (M'(ℓ+ℓ−γH), ΔM, M'rec(η)/Mrec(π+π−)) with free ΥJ(1D) masses and free yields; all other shape parameters are fixed from MC and additive systematics are taken as the envelope of peak-position/resolution/background-order/fit-range variations. Off-peak points use simple event counting with luminosity-scaled non-resonant background estimated from a global fit; the subsequent energy-dependence fit floats only ΓeeB and relative phases while fixing PDG masses/widths of Υ(10860)/Υ(11020). The sole mild self-consistency (radiative-correction factors evaluated with the measured energy dependence itself) is the standard iterative procedure of e+e− analyses and is quantified as a multiplicative systematic by varying the fitted parameters by ±1σ. No quantity is defined in terms of itself, no fitted parameter is re-labeled a prediction, and no load-bearing uniqueness claim or ansatz is imported via self-citation. Theoretical mass-splitting predictions appear only in a comparison figure after the measurements are complete. The derivation chain is therefore self-contained against external data and does not reduce to its inputs by construction.
Axiom & Free-Parameter Ledger
free parameters (4)
- ΥJ(1D) masses and mass splittings =
m(Υ2)=10167.0±1.0±0.2 MeV/c²; Δm12=11.8±1.5±0.4; Δm23=7.6±2.4±0.6 MeV/c²
- Signal yields Nsig for each J and decay mode =
see Table I / Table IV
- Γee B(Υ(10860/11020)→ΥJ(1D)η/ππ) Bf =
0.091±0.039±0.016 eV (η, 10860); others consistent with zero or upper limits
- Non-resonant coefficient cNR and relative phase ϕ
axioms (4)
- domain assumption Reconstruction efficiencies and signal shapes are correctly given by GEANT3-simulated Monte Carlo (including NLO ISR via PHOKHARA).
- domain assumption PDG values for intermediate branching fractions B(η→γγ), B(χbJ→Υ(1S)γ), B(Υ(1S)→ℓℓ), vacuum-polarization factor |1−Π|²=0.93, and Υ(10860/11020) masses and widths.
- domain assumption Combinatorial background in the three fit observables is adequately described by a first-order polynomial (validated on control channels Υ(2S)η/ππ).
- ad hoc to paper Off-peak background is non-resonant and scales strictly with luminosity from the global fit.
read the original abstract
We study the processes $e^+e^-\to\Upsilon_J(1D)\eta$ and $e^+e^-\to\Upsilon_J(1D)\pi^+\pi^-$ at center-of-mass energies $\sqrt{s}$=(10.73 -- 11.02) GeV using a $142.5\,\mathrm{fb}^{-1}$ data sample, including 122~fb$^{-1}$ near the $\Upsilon$(10860) peak ($\sqrt{s}$ = 10.866 GeV), collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. From the peak sample, the products of Born cross section times branching fraction are obtained for $\sigma_{\rm Born}(e^+e^-\to\Upsilon_J(1D)\eta)$ or $\sigma_{\rm Born}(e^+e^-\to\Upsilon_J(1D)\pi^+\pi^-)$ and ${\cal B}(\Upsilon_J(1D)\to\chi_{b1}\gamma)$ or ${\cal B}(\Upsilon_J(1D)\to\chi_{b2}\gamma)$ for each $\Upsilon_J(1D)$ state. The corresponding branching fractions for $\Upsilon(10860)$ decays are also obtained. The significances of the $\Upsilon_1(1D)$, $\Upsilon_2(1D)$, and $\Upsilon_3(1D)$ signals are 4.8$\sigma$, ${>}10\sigma$, and 3.0$\sigma$, respectively, including systematic uncertainties. The mass for $\Upsilon_2(1D)$ is measured to be $(10167.0\pm 1.0\pm 0.2)$ MeV/$c^2$, where the first and second uncertainties are statistical and systematic. The mass splittings $\Delta m_{12}=m(\Upsilon_2(1D))-m(\Upsilon_1(1D))$ and $\Delta m_{23}=m(\Upsilon_3(1D))-m(\Upsilon_2(1D))$ are $(11.8\pm1.5\pm0.4)$ MeV/$c^2$ and $(7.6\pm2.4\pm0.6)$ MeV/$c^2$, respectively.~We determine the energy dependence of the cross sections for $e^+e^-\to\Upsilon_J(1D)\eta$ and $e^+e^-\to\Upsilon_J(1D)\pi^+\pi^-$ for the $\Upsilon_1(1D)$, $\Upsilon_2(1D)$, and $\Upsilon_3(1D)$ states, combined.
Figures
Reference graph
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[GeV/cHγ- l+M'(l9.75 9.8 9.85 9.9 9.95 10 ) 2 Events / (10 MeV/c 0 10 20 Data Total fit Background γ b1 χ→(1D)1ϒγ b1 χ→(1D)2ϒγ b2 χ→(1D)2ϒγ b2 χ→(1D)3ϒ-1 Belle, 122 fb = 10.8658 GeV s (a) Preliminary ] 2M [GeV/cΔ0.15 0.2 0.25 0.3 0.35 ) 2 Events / (10 MeV/c 0 5 10 15 20 -1 Belle, 122 fb = 10.8658 GeV s (b) Preliminary ]
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[GeV/cHγ- l+M'(l9.75 9.8 9.85 9.9 9.95 10 ) 2 Events / (10 MeV/c 0 10 20 30 -1 Belle, 122 fb = 10.8658 GeV s (d) Preliminary ] 2M [GeV/cΔ0.15 0.2 0.25 0.3 0.35 ) 2 Events / (10 MeV/c 0 10 20 -1 Belle, 122 fb = 10.8658 GeV s (e) Preliminary ]
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4: TheM ′ rec(η) distributions in data at each energy point at Belle
[GeV/cη(recM'10.1 10.15 10.2 ) 2 Events / (4 MeV/c 1 2 3 4 5 -1 Belle, 1.0 fb = 11.0208 GeV s FIG. 4: TheM ′ rec(η) distributions in data at each energy point at Belle. The vertical dashed lines show the Υ J(1D) signal region. ]
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5: TheM rec(π+π−) distributions in data at each energy point at Belle
[GeV/c-π+π(recM10.1 10.15 10.2 ) 2 Events / (4 MeV/c 1 2 3 4 5 -1 Belle, 1.0 fb = 11.0208 GeV s FIG. 5: TheM rec(π+π−) distributions in data at each energy point at Belle. The vertical dashed lines show the Υ J(1D) signal region. 10 •The signal yields, Born cross sections, and upper limits on the Born cross sections fore +e− →Υ J(1D)ηat Belle are listed i...
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[80]
7: The distribution ofM(π +π−) ine +e− →Υ J(1D)π+π− in data at √s= 10.8658 GeV
[GeV/c-π+πM(0.3 0.4 0.5 0.6 0.7 ) 2 Events / (10 MeV/c 0 5 10 -1 Belle, 122 fb = 10.8658 GeV s Preliminary FIG. 7: The distribution ofM(π +π−) ine +e− →Υ J(1D)π+π− in data at √s= 10.8658 GeV
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Abumusabhet al.(Belle II Collaboration), JHEP06(2026) 278
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discussion (0)
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