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REVIEW 3 major objections 5 minor 51 references

Measurement of the W boson decay branching fraction ratio $\mathcal{B}$(W $\to$ cq) / $\mathcal{B}$(W $\to$ $\mathrm{q\bar{q}'}$) in proton-proton collisions at $\sqrt{s}$ = 13 TeV

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The W boson's charm branching fraction ratio is measured to 0.489 ± 0.020, a 4% precision that agrees with the Standard Model.

desk verdict Most precise R_c^W to date, with a reasonable but under-validated OS=SS background subtraction; deserves refereeing and likely publication after adding a control-region check. read the letter →

arxiv 2412.16296 v2 pith:BRFFSUXF submitted 2024-12-20 hep-ex

CMS Collaboration This is my paper · ORCID
classification hep-ex
keywords WbosoncharmquarkbranchingfractionCKMmatrixtoppairmuontaggingproton-protoncollisionsunitaritytest
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

This paper reports the most precise measurement yet of the ratio R_c^W = B(W → cq)/B(W → qq'), the fraction of hadronic W boson decays that produce a charm quark, using 138 $fb^{-1}$ of proton-proton collision data at a center-of-mass energy of 13 TeV. The measurement exploits the large sample of top-quark-pair events in which one W boson decays leptonically and the other hadronically; charm jets are tagged by requiring a muon inside the jet. The result, R_c^W = 0.489 ± 0.020, is consistent with the Standard Model expectation of 1/2 under CKM unitarity and is twice as precise as the previous world average. If the result is right, it strengthens the evidence that the weak interaction couples to all quark generations with the same strength and provides an independent route to the CKM matrix element |Vcs|.

What carries the argument

The central quantity is R_c^W, which by Eq. (1) equals (|Vcd|^2 + |Vcs|^2 + |Vcb|^2) divided by the sum of the squared magnitudes of all CKM elements in the first two rows; under unitarity this ratio is 1/2. The analysis is carried by the muon-based charm tag, selecting a non-isolated muon with 5 < pT < 25 GeV inside one of the two jets from the hadronically decaying W boson, which exploits the roughly 9% semileptonic branching fraction of charm hadrons. The dominant charge-symmetric background is estimated from data using the assumption that opposite-sign (OS) and same-sign (SS) event rates are equal for backgrounds, so the observed SS sample directly models the OS background; simulation then contributes only about 3% of the charm-tagged background prediction. A counting fit to four event categories (prompt electron or muon, charm-tagged or not) extracts R_c^W with the signal and background yields modeled by the combination of OS−SS subtracted simulation and SS data.

What would settle it

In a control sample enriched in the charge-symmetric backgrounds, such as dileptonic top-quark-pair events with one muon inside a jet, count opposite-sign and same-sign events after the same jet and lepton requirements; if the measured OS/SS ratio differs from unity by more than about 1.6%, the OS=SS assumption fails and the reported background subtraction would be biased at the level of the total uncertainty.

Watch

Extended reading notes

Core claim

The central claim is that R_c^W = 0.489 ± 0.005 (stat) ± 0.019 (syst) in proton-proton collisions at √s = 13 TeV, making it the most precise determination of this quantity to date and twice as precise as the previous world average of 0.49 ± 0.04. Assuming CKM unitarity, the expected value is 0.5, and the measurement agrees with it within the total uncertainty of 0.020. Combining R_c^W with a measured value of the sum of the squared CKM elements in the first two rows (1.984 ± 0.021) gives a second-row sum of 0.970 ± 0.041, and using world-average values of |Vcd| and |Vcb| gives |Vcs| = 0.959 ± 0.021. The paper concludes that the measurement is limited by systematic uncertainty in the charm-tagging efficiency and that it provides a consistency test of CKM unitarity from hadronic W decays.

Load-bearing premise

The entire background-subtraction strategy assumes that the number of background events with a muon in the tagged jet having opposite charge to the prompt lepton equals the number with the same charge; if this OS=SS symmetry is violated, the data-driven background estimate is biased and R_c^W shifts by an amount that could exceed the quoted systematic uncertainty.

Editorial extensions

If this is right

  • The measured value 0.489 ± 0.020 is consistent with the Standard Model prediction of 1/2, so the weak interaction's universality in the quark sector holds at the 4% precision level.
  • Combined with the independently measured leptonic W branching fractions, the paper derives a sum of squared CKM elements in the second row of 0.970 ± 0.041, an additional consistency check of CKM unitarity.
  • The derived |Vcs| = 0.959 ± 0.021 is an independent determination from hadronic W decays that does not rely on charm-meson decay measurements.
  • The charm-tagged sample has 97% purity, demonstrating that muon-in-jet tagging is a viable percent-level tool for charm measurements in hadron-collider final states.
  • The dominant systematic is the charm-tagging calibration, so better external measurements of charm fragmentation fractions and semileptonic branching fractions would reduce the uncertainty in future determinations.

Reading between the lines

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

  • If this level of precision is combined with future data from the same collisions, the second-row CKM sum could be pushed below 2%, at which point it would become one of the sharper probes of deviations from the Standard Model.
  • A direct experimental test of the OS=SS symmetry in a dedicated control region, for example using dileptonic top-pair events, would validate the dominant systematic from first principles rather than relying on the physics argument given in the paper.
  • Applying the same muon-tag method but using electrons inside jets could roughly double the charm-tagged sample; the gain in statistics would only matter once the electron-related backgrounds are brought under control, and it could test the charm-tagging systematics independently.
  • Because the ratio is sensitive to the charm-quark couplings of the W boson, a future measurement that diverges from 1/2 would be hard to explain by QCD effects and would point toward non-unitarity or new physics in the W-c vertex.
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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 manuscript reports a measurement of R_c^W = B(W→cq)/B(W→qq') using 138 fb^-1 of 13 TeV CMS pp collision data. Events are selected with one isolated lepton, at least four jets, two b-tagged jets, and a charm tag defined by a nonisolated muon within one of the two W-candidate jets. The dominant backgrounds are estimated with a data-driven opposite-sign/same-sign (OS/SS) subtraction, in which the SS data sample is used to model charge-symmetric backgrounds in the OS sample. A counting fit to four categories (lepton flavor × charm tag) yields R_c^W = 0.489 ± 0.005 (stat) ± 0.019 (syst), with a total uncertainty of ±0.020, consistent with the standard model prediction of 1/2 and with previous LEP measurements. From this result the authors derive a value of the second-row CKM sum, 0.970 ± 0.041, and |Vcs| = 0.959 ± 0.021.

Significance. If the result holds, this is the most precise measurement of R_c^W to date, with a 4% relative uncertainty that is twice as good as the current world average. It provides an independent test of CKM unitarity and an independent determination of |Vcs| from hadronic W decays. The paper is careful in several respects: the systematic uncertainty table is detailed, the four-category counting fit is clearly described, the muon-in-jet charm tagging efficiency is calibrated using b-jet data, and the post-fit control distributions are shown. The main unresolved issue is the validation of the OS=SS symmetry assumption that underlies the background subtraction; because this assumption is load-bearing for the central value, the paper should be revised to address it explicitly before acceptance.

major comments (3)
  1. [§4.1 and §5, Table 1] The OS=SS symmetry assumption is not validated, and it is load-bearing for the central result. The SS data sample contains 4097 events and is used as the prediction for the dominant backgrounds in the 17,973-event OS charm-tagged sample. If the true OS/SS ratio for the summed backgrounds is r rather than 1, the inferred W→cq signal yield changes by approximately (r-1)×4097/13165 ≈ 0.31×(r-1), and R_c^W shifts by a comparable relative amount. A 10% violation of the symmetry would therefore produce a bias comparable to the quoted total uncertainty of 0.020. The only quantitative check reported, that “SS data and MC yields differ by approximately 10%,” concerns the absolute normalization of the SS prediction, not the OS/SS ratio. The 1.6% “SS data statistical uncertainty” in Table 1 is the Poisson uncertainty of the 4097-event sample and does not cover a systematic violation of the symmetry. Please provide a control-region validation of OS=SS, for example using a b-jet-enriched sample with the same muon-in-jet tag, or explicitly assign a systematic uncertainty for possible OS=SS breaking.
  2. [§4.1, paragraph on charge-symmetric backgrounds] The statement that “in most of the backgrounds, the number of OS events is the same as the number of events for which the charges . . . are the same” should be made quantitative. Which backgrounds are treated as charge-symmetric, and what fraction of the charm-tagged background do they constitute after the full selection? Without this information, a reader cannot judge how large a violation of the symmetry would be needed to affect the result, nor whether the backgrounds that are omitted from the symmetry assumption are indeed negligible.
  3. [§6, fit description] The description of the fit would benefit from a more explicit statement of how R_c^W is identified. As written, the global normalization of the combined W→cq + W→uq contribution is a free parameter, and the W→cq and W→uq predictions are varied anticorrelatedly. It would be helpful to state that R_c^W is determined by the ratio of c-tagged to untagged W→qq' yields after the fit, and that the global normalization cancels to first order in that ratio. This is likely implicit, but making it explicit would strengthen the paper and rule out any impression that the result is an absolute cross-section measurement.
minor comments (5)
  1. [§4.1 and Figures 1, 3, 4] The ratio panels in the figures show data-to-prediction agreement visually, but no quantitative goodness-of-fit values are given. Adding chi-square per number of bins (or a similar summary) would help the reader assess the agreement.
  2. [§5, Table 1] The row labeled “SS data statistical uncertainty” is listed as a systematic uncertainty. Consider renaming it to make clear that it is the statistical uncertainty of the SS data sample propagated as a systematic, and note that it does not cover a possible OS=SS asymmetry.
  3. [§4.1, paragraph beginning “In most of the backgrounds”] The phrase “in most of the backgrounds” is vague. Specify the relevant background processes and, if possible, give the fraction of the charm-tagged OS sample that is estimated from SS data after all selection criteria.
  4. [§6, sentence beginning “The observed data yields entering the fit”] This sentence is slightly confusing because the SS data enter the fit as part of the prediction as well. Rewording to distinguish the observed OS event counts from the SS-data component of the prediction would improve clarity.
  5. [Various] There are minor typographical and formatting issues, such as inconsistent spacing in “p_T^miss” and the reference formatting for Ref. [46]. These do not affect the physics content.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: R_c^W is extracted from observed event counts in four categories with independently calibrated efficiencies and external CKM inputs; no fitted parameter is renamed as a prediction.

full rationale

The central quantity R_c^W is obtained from a counting fit to four exclusive categories (prompt muon/electron by charm-tag presence) using observed OS data and predictions built from OS-SS-subtracted simulation plus SS data for charge-symmetric backgrounds. The SS data are an independent same-sign control sample; they do not encode the fitted R_c^W value, so the background estimate is data-driven rather than self-referential. The charm-tagging efficiency is calibrated using muons in b jets from the same l+jets selection, but this calibrates an auxiliary muon-identification correction factor and is not tuned to the target ratio or to the SM prediction. The muon-rate correction in c-hadron decays is fixed to external fragmentation-fraction and branching-fraction measurements, not to the final result. The CKM interpretation uses Eq. (1) with world-average |Vcd|, |Vcb| and the CMS leptonic W branching-fraction measurement as inputs; these are external to the fitted value. Self-citations to previous CMS publications (e.g., refs. [6-9], [51]) concern detector performance, method development, or independent W/BF measurements; none is used as an unverified uniqueness theorem or as a forbidden-alternative argument. The OS=SS assumption used for the dominant charm-tag background is an experimental approximation and, if broken, would contribute a systematic bias, but it is not circular: it does not make the prediction equal to the input by construction. No step in the derivation reduces to its own inputs, so the paper is self-contained against external benchmarks for the purpose of circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The measurement is an experimental counting experiment with no invented physical entities. The free parameter is a statistical nuisance, not an ad hoc physical constant. The main assumptions are domain-specific modeling and symmetry assumptions common to collider analyses.

free parameters (1)
  • Global normalization of semileptonic tt (W to cq + W to uq) signal
    The combine fit in Section 6 determines this normalization jointly with R_c^W. It is a nuisance parameter that does not set the ratio of interest, since the ratio is fixed by the relative yields in charm-tagged versus untagged categories.
assumptions (4)
  • domain assumption OS=SS charge symmetry for background processes
    Section 4.1 uses the equality of opposite-sign and same-sign yields to predict the dominant charm-tag background from the SS data sample. Any violation directly biases the extracted R_c^W.
  • domain assumption Muon-in-jet identification scale factor measured in b jets is applicable to c jets
    Section 4.1.1 calibrates the muon efficiency using b jets and transfers the correction to c jets. The 2.7% systematic accounts for residual differences, but the transfer itself is assumed.
  • domain assumption POWHEG + PYTHIA simulation correctly models ttbar and single-top kinematics after reweighting
    The fit relies on simulated yields for the tagged and untagged categories, including generator, parton shower, and hadronization models. Control distributions in Figures 1, 3, and 4 support this but do not prove it.
  • domain assumption External charm fragmentation fractions and semileptonic branching fractions are accurate
    Corrections to the simulated muon rate from c hadron decays use values from Refs. [33] and [3]. Their uncertainties are propagated, but the input values are taken as reliable.

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Cite this review

Pith. "Pith review of Measurement of the W boson decay branching fraction ratio $\mathcal{B}$(W $\to$ cq) / $\mathcal{B}$(W $\to$ $\mathrm{q\bar{q}'}$) in proton-proton collisions at $\sqrt{s}$ = 13 TeV." pith.science (2026). https://pith.science/paper/BRFFSUXF

@misc{pith2026241216296,
  author       = {Pith},
  title        = {Pith review of: Measurement of the W boson decay branching fraction ratio $\mathcalB$(W $\to$ cq) / $\mathcalB$(W $\to$ $\mathrmq\barq'$) in proton-proton collisions at $\sqrts$ = 13 TeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BRFFSUXF}},
  note         = {Machine review of arXiv:2412.16296}
}
abstract

The most precise measurement to date of the W boson hadronic decay branching fraction ratio $R_\mathrm{c}^\mathrm{W}$ = $\mathcal{B}$(W $\to$ cq) / $\mathcal{B}$(W $\to$ $\mathrm{q\bar{q}'}$) is presented. The measurement is based on a sample of proton-proton collision data from the CERN LHC collected by the CMS experiment at a center-of-mass energy of 13 TeV in 2016-2018 with an integrated luminosity of 138 fb$^{-1}$. The large cross section of top quark-antiquark production at the LHC offers a sizable high-purity sample of W bosons suitable for this measurement. Events with one charged lepton (electron or muon) and at least four jets, two tagged as bottom quark jets, are analyzed. Charm jets are tagged using the presence of a muon inside the jet. The result, $R_\mathrm{c}^\mathrm{W}$ = 0.489 $\pm$ 0.020, is consistent with the standard model prediction and is twice as precise as the current world-average value.

Figures

Figures reproduced from arXiv: 2412.16296 by the authors.

Figure 1
Figure 1. Kinematic distributions of the muon inside the c-tagged jets: transverse momentum [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Comparison of the measured value of R W c with previous LEP2 measurements [4, 5], and the world-average value [3]. Horizontal bars represent the total uncertainty of the measurements. Kobayashi–Maskawa (CKM) matrix, 0.970±0.041, and the CKM matrix element |Vcs | = 0.959± 0.021 are derived. These results provide a consistency test of the CKM unitarity and a measure￾ment of |Vcs | from hadronic W boson decays. Acknowl… view at source ↗
Figure 3
Figure 3. Invariant mass of the two jets associated with the W boson, for the four event cate [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Invariant mass of the three jets associated with the top quark, for the four event cat [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

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