Recognition: unknown
Measurement of inclusive production of charmonium states in b-hadron decays via their decay into φ φ
Pith reviewed 2026-05-10 16:05 UTC · model grok-4.3
The pith
Inclusive branching fractions for χ_c states in b-hadron decays are measured via φφ decays, with an updated η_c(1S) mass.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The central claim is that the inclusive branching fractions for b-hadron decays into χ_c states via the φφ channel are B(b→χ_c0 X)=(1.34±0.13±0.06±0.37)×10^{-3}, B(b→χ_c1 X)=(1.58±0.12±0.09±0.44)×10^{-3}, B(b→χ_c2 X)=(0.55±0.08±0.05±0.15)×10^{-3}, with the η_c(2S) product branching fraction B(b→η_c(2S) X)×B(η_c(2S)→φφ)=(4.0±0.6±0.6±1.1)×10^{-7}, and the η_c(1S) mass measured as 2984.1±0.5±0.5 MeV with the highest precision to date.
What carries the argument
The φφ decay channel serving as the common signature for detecting and normalizing the production of different charmonium states in b-hadron decays.
Load-bearing premise
The reported absolute branching fractions scale directly with the value of the reference branching fraction B(η_c(1S) → φφ), which is taken from prior measurements.
What would settle it
An independent determination of B(η_c(1S) → φφ) that deviates from the assumed value by more than the quoted uncertainty would invalidate the absolute scales of the reported branching fractions.
Figures
read the original abstract
The inclusive production of the $\eta_c(1S)$, $\eta_c(2S)$ and $\chi_{c}$ charmonium states in $b$-hadron decays is studied with LHCb Run~2 data, corresponding to an integrated luminosity of $5.9~\text{fb}^{-1}$, using charmonia decays to $\phi\phi$ pairs. The production branching fractions of the $\chi_{c}(1P)$ states in $b$-hadron decays are measured, using $b \to \eta_c(1S) (\to \phi \phi) X$ as a normalisation channel, with $X$ indicating any additional particles. The results are \begin{align*} &{\cal{B}} (b \to \chi_{c0} X) = (1.34 \pm 0.13 \pm 0.06 \pm 0.37) \times 10^{-3}, &{\cal{B}} (b \to \chi_{c1} X) = (1.58 \pm 0.12 \pm 0.09 \pm 0.44) \times 10^{-3}, &{\cal{B}} (b \to \chi_{c2} X) = (0.55 \pm 0.08 \pm 0.05 \pm 0.15) \times 10^{-3}, \end{align*} where the first uncertainty is statistical, the second systematic and the last is due to the limited knowledge of externally measured branching fractions. The production branching fraction of $\eta_c(2S)$ times the branching fraction of its decay into $\phi \phi$ is measured as ${\cal{B}} (b \to \eta_c(2S) X) \times {\cal{B}} (\eta_c(2S) \to \phi \phi) = (4.0 \pm 0.6 \pm 0.6 \pm 1.1) \times 10^{-7}$. Furthermore, the mass of the $\eta_c(1S)$ state is measured to be $M_{\eta_c(1S)} = 2984.1 \pm 0.5 \pm 0.5$ MeV with the best precision to date.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports measurements of inclusive branching fractions for b-hadron decays to the χ_c0, χ_c1, χ_c2 and η_c(2S) charmonium states via their decays to φφ pairs, using 5.9 fb^{-1} of LHCb Run 2 data. The χ_c results are normalized to the b → η_c(1S)(→φφ)X reference channel and converted to absolute branching fractions using external inputs; the η_c(2S) result is reported as a product branching fraction. The paper also presents a high-precision measurement of the η_c(1S) mass.
Significance. These results provide updated experimental inputs on charmonium production in b decays that can test heavy-quark fragmentation models and serve as references for other analyses. The separation of statistical, systematic and external uncertainties is a clear strength, as is the use of an independent normalization channel. The dominant external uncertainties correctly flag the dependence on reference branching fractions such as B(η_c(1S)→φφ).
major comments (1)
- Abstract and Results: the absolute branching fractions for the χ_c states scale directly with the external B(η_c(1S)→φφ) (and related inputs), as indicated by the third uncertainty term. The manuscript should explicitly quote the numerical value adopted for this external branching fraction, state its source, and quantify the sensitivity of the final results to plausible variations in that input.
minor comments (2)
- Abstract: the branching-fraction results are presented inside a LaTeX align* environment that does not render cleanly in plain text or some journal formats; a bulleted list or compact table would improve readability.
- Abstract: the claim that the η_c(1S) mass has 'the best precision to date' should be supported by a brief comparison to the current PDG average or previous measurements.
Simulated Author's Rebuttal
We thank the referee for the careful reading of the manuscript, the positive assessment, and the constructive suggestion. We address the comment below.
read point-by-point responses
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Referee: Abstract and Results: the absolute branching fractions for the χ_c states scale directly with the external B(η_c(1S)→φφ) (and related inputs), as indicated by the third uncertainty term. The manuscript should explicitly quote the numerical value adopted for this external branching fraction, state its source, and quantify the sensitivity of the final results to plausible variations in that input.
Authors: We agree that explicitly quoting the adopted value of the external branching fraction improves clarity for the reader. In the revised manuscript we will state the numerical value of B(η_c(1S) → φφ) used in the analysis, cite its source (the PDG average employed for the external inputs), and add a short sentence noting that the third uncertainty term already quantifies the propagation of the uncertainty on this input; any plausible variation within the quoted external uncertainty is therefore directly reflected in the reported third uncertainty on the χ_c branching fractions. revision: yes
Circularity Check
No significant circularity; direct experimental measurements normalized to independent external references
full rationale
The paper performs a standard LHCb branching-fraction measurement that normalizes the χ_c and η_c(2S) yields to the b→η_c(1S)(→φφ)X reference channel, extracts relative efficiencies from simulation and data-driven methods, and converts the ratio to absolute B(b→χ_c X) by multiplying by the external B(η_c(1S)→φφ) taken from the PDG or prior experiments. The third uncertainty term is explicitly attributed to that external input. No equation, fit, or ansatz inside the paper reduces to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The mass measurement is likewise a direct fit to the invariant-mass distribution. The derivation chain is therefore self-contained against external benchmarks and receives the default non-circularity finding.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Standard assumptions in particle-physics data analysis such as accurate detector simulation and background modeling hold.
Reference graph
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