REVIEW
Simultaneous production of a $W$ boson and a charmed hadron at the LHC in general-mass variable-flavour-number scheme
High Energy Physics - Phenomenology · Submitted 14 Aug 2026 · 83 references
Pith's verdict: A solid, genuinely new NLO GM-VFNS study of W+charmed-hadron production whose main claim (CT18A wins on the charge ratio) is well-supported at NLO but needs a sharper NNLO caveat before being sold as settled.
T0 · AI review
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Referee report
The paper
The paper claims
This paper argues that the charge ratio of W boson plus charmed meson production at the LHC is a clean probe of the proton's strange-sea asymmetry, with 13 TeV data favoring a symmetric strange sea.
The reading
What carries the argument
The central object is the charge ratio $R^\pm_c$ of Eq. (3.1), defined as the ratio of the sums of cross sections for $W^+$ with $D^-$ or $D^{*-}$ to $W^-$ with $D^+$ or $D^{*+}$. In this ratio the fragmentation-function uncertainties and the residual scale dependence cancel almost completely, as do several experimental systematics, leaving the PDFs as the dominant uncertainty. The load-bearing identity is Eq. (3.2), which shows that the ratio is controlled by the PDF combination $(|V_{cd}|^2 \bar{d} + |V_{cs}|^2 \bar{s})/(|V_{cd}|^2 d + |V_{cs}|^2 s)$, approximately $1 - 2(\epsilon d^- + s^-)/s^+$ with $s^- = s - \bar{s}$, $s^+ = s + \bar{s}$, $d^- = d - \bar{d}$, and $\epsilon = |V_{cd}|^2/|V_{cs}|^2 \approx 0.05$. This identity is what converts the measured ratio into a direct test of whether the strange sea is asymmetric.
Extended reading notes
Core claim
On the paper's own terms, the central discovery is that the charge ratio $R^\pm_c$, the ratio of $W^+ + D^-$ (and $D^{*-}$) to $W^- + D^+$ (and $D^{*+}$) cross sections after subtracting same-sign events, cancels essentially all non-PDF uncertainties and is controlled by a single combination of parton distributions, approximately $1 - 2(\epsilon d^- + s^-)/(s^+)$, where $s^- = s - \bar{s}$ is the strange sea asymmetry, $s^+ = s + \bar{s}$, $d^- = d - \bar{d}$, and $\epsilon = |V_{cd}|^2/|V_{cs}|^2 \approx 0.05$. Applied to the ATLAS 13 TeV data, the ratio prefers CT18A, which sets $s^- = 0$, over MSHT20 and NNPDF4.0, which fit a non-zero $s^-$. Reweighting the PDFs to the ratio data pulls MSHT20 and NNPDF4.0 toward smaller $s^-$ and larger $s^+$, and for NNPDF4.0 the required shift is large enough that a simple reweighting may lose accuracy. The authors therefore conclude that $W$+charmed-hadron production provides a new constraint on the strangeness asymmetry and should be included in future PDF analyses.
Load-bearing premise
The entire comparison rests on the assumption that charm quarks fragment into $D^+$ and $D^-$ (and $D^{*+}$ and $D^{*-}$) with the same probability, so the fragmentation uncertainties cancel in the charge ratio; if that charge symmetry does not hold, the ratio would no longer cleanly measure the proton's strange-quark content.
Editorial extensions
If this is right
- Future global PDF fits should add the $W+D$ charge ratio as a data constraint, since it breaks the degeneracy between the total strange momentum $s^+$ and the asymmetry $s^-$.
- The ranking of the three PDF sets implies that a large strangeness asymmetry of the size fitted by MSHT20 or NNPDF4.0 is disfavored by the 13 TeV data, favoring the CT18A assumption of $s=\bar{s}$.
- The ratio's sensitivity grows with meson transverse momentum and lepton pseudorapidity, so higher-luminosity LHC runs should sharpen the PDF discrimination in the same kinematic corners.
- The ratio also offers a way to test the modeling of charm fragmentation: comparing the $D^\pm$ and $D^{*\pm}$ channels separately could help resolve discrepancies between fragmentation measured in $e^+e^-$ and $pp$ collisions.
Reading between the lines
- A full NNLO calculation of the charge ratio in the same scheme would test whether the roughly +15% shift seen in zero-mass absolute cross sections cancels in the ratio; if it does not, the PDF ranking could change.
- The same charge-ratio strategy could be applied to other charmed hadrons, such as $\Lambda_c^+$, or to bottom-hadron final states, providing independent cross-checks of the strange-sea asymmetry.
- The observation that the ratio's PDF sensitivity grows toward larger $x$ suggests that dedicated $W+$charm measurements at higher rapidity or with a lower $p_T$ cut could map the $x$-dependence of $s^-$ rather than only its integrated sign.
Original abstract
The simultaneous production of a $W^\pm$ boson and a charmed hadron in proton-proton collisions offers a potential probe for constraining the strange quark parton distribution functions (PDFs). We study these processes at next-to-leading order in perturbative Quantum Chromodynamics within the general-mass variable-flavor-number scheme. By considering ratios of cross-section between oppositely charged mesons, uncertainties associated with unphysical scale choices and fragmentation functions are shown to effectively cancel out, leaving the uncertainty originating from the PDFs as the dominant one. By comparing our calculations with CT18A, MSHT20 and NNPDF4.0 PDFs with the recent ATLAS measurement at $\sqrt{s} = 13\,{\rm TeV}$ we find that CT18A, which imposes zero strangeness asymmetry, agrees best with the data, while MSHT20 and NNPDF4.0, both of which allow for a non-zero strangeness asymmetry, exhibit greater tension with the ATLAS data. The sensitivity to the strangeness asymmetry is further confirmed by the PDF reweighting methods. We also study the impact of possible intrinsic charm content of the proton finding no significant sensitivity. Finally, we explore the possibility of measuring these processes in proton-lead collisions. With the estimated detector efficiencies and projected luminositites at the high-luminosity LHC, these processes should be visible, yet with a rather limited constraining power for nuclear PDFs.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The simultaneous production of a $W^\pm$ boson and a charmed hadron in proton-proton collisions offers a potential probe for constraining the strange quark parton distribution functions (PDFs). We study these processes at next-to-leading order in perturbative Quantum Chromodynamics within the general-mass variable-flavor-number scheme. By considering ratios of cross-section between oppositely charged mesons, uncertainties associated with unphysical scale choices and fragmentation functions are shown to effectively cancel out, leaving the uncertainty originating from the PDFs as the dominant one. By comparing our calculations with CT18A, MSHT20 and NNPDF4.0 PDFs with the recent ATLAS measurement at $\sqrt{s} = 13\,{\rm TeV}$ we find that CT18A, which imposes zero strangeness asymmetry, agrees best with the data, while MSHT20 and NNPDF4.0, both of which allow for a non-zero strangeness asymmetry, exhibit greater tension with the ATLAS data. The sensitivity to the strangeness asymmetry is further confirmed by the PDF reweighting methods. We also study the impact of possible intrinsic charm content of the proton finding no significant sensitivity. Finally, we explore the possibility of measuring these processes in proton-lead collisions. With the estimated detector efficiencies and projected luminositites at the high-luminosity LHC, these processes should be visible, yet with a rather limited constraining power for nuclear PDFs.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The simultaneous production of a $W^\pm$ boson and a charmed hadron in proton-proton collisions offers a potential probe for constraining the strange quark parton distribution functions (PDFs). | background 0.99 | 0.08 | 0.07 | hedged possibility 0.98 |
| s1 | We study these processes at next-to-leading order in perturbative Quantum Chromodynamics within the general-mass variable-flavor-number scheme. | method 0.63 | 0.93 | 0.02 | asserted 0.94 |
| s2 | By considering ratios of cross-section between oppositely charged mesons, uncertainties associated with unphysical scale choices and fragmentation functions are shown to effectively cancel out, leaving the uncertainty originating from the PDFs as the dominant one. | result 0.62 | 0.90 | 0.10 | asserted 1.00 |
| s3 | By comparing our calculations with CT18A, MSHT20 and NNPDF4.0 PDFs with the recent ATLAS measurement at $\sqrt{s} = 13\,{\rm TeV}$ we find that CT18A, which imposes zero strangeness asymmetry, agrees best with the data, while MSHT20 and NNPDF4.0, both of which allow for a non-zero strangeness asymmetry, exhibit greater tension with the ATLAS data. | result 0.99 | 0.95 | 0.78 | asserted 1.00 |
| s4 | The sensitivity to the strangeness asymmetry is further confirmed by the PDF reweighting methods. | result 0.85 | 0.88 | 0.11 | asserted 1.00 |
| s5 | We also study the impact of possible intrinsic charm content of the proton finding no significant sensitivity. | result 0.96 | 0.96 | 0.04 | asserted 0.99 |
| s6 | Finally, we explore the possibility of measuring these processes in proton-lead collisions. | contribution 0.89 | 0.86 | 0.03 | hedged possibility 0.68 |
| s7 | With the estimated detector efficiencies and projected luminositites at the high-luminosity LHC, these processes should be visible, yet with a rather limited constraining power for nuclear PDFs. | result 0.46 | 0.80 | 0.09 | hedged possibility 0.74 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
References
How the literature uses it
What this paper does with the arXiv papers it cites
Papers whose main result relates to this one's
States the same result 1 paper
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An approximate PDF-level analysis of the production ratio indicates that this tension could be attributed to a too large strangeness asymmetry.
Associated $W$ + charm production: indications for PDF analysis · 0.99
What it cites · 62 sentences without a confident label
Uses the method or tool of 7 papers
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In the case of CT18A and MSHT20 we use linear Hessian reweighting [ref] and for NNPDF4.0 the bayesian reweighting [ref] .
Reweighting NNPDFs: the W lepton asymmetry · Proton-proton collisions · 1.00
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In the case of CT18A and MSHT20 we use linear Hessian reweighting [ref] and for NNPDF4.0 the bayesian reweighting [ref] .
Reweighting and Unweighting of Parton Distributions and the LHC W lepton asymmetry data · Proton-proton collisions · 1.00
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In the case of CT18A and MSHT20 we use linear Hessian reweighting [ref] and for NNPDF4.0 the bayesian reweighting [ref] .
Non-quadratic improved Hessian PDF reweighting and application to CMS dijet measurements at 5.02 TeV · Proton-proton collisions · 1.00
Uses data or values from 3 papers
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The ATLAS experiment [ref] tagged these mesons, i.e. measured the processes in Eq. [ref].
Measurement of the production of a $W$ boson in association with a charmed hadron in $pp$ collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with the ATLAS detector · Theoretical framework · 0.89
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We note that these observables were not explicitly considered in the original ATLAS publication [ref] but we have formed the experimental values from the measured cross sections propagating the correlated systematic uncertainties in a standard way as done e.g. in Ref. [ref] .
Proton-PDF uncertainties in extracting nuclear PDFs from $W^\pm$ production in p+Pb collisions · Proton-proton collisions · 0.81
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We take as the integrated luminosity of the $p$Pb experiment $L_int (pPb) = 1.2pb^-1$, which has been suggested as a reasonable goal for ATLAS [ref] .
Future physics opportunities for high-density QCD at the LHC with heavy-ion and proton beams · Proton-lead collisions · 0.86
Compares with 5 papers
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In the case of $pp$ collisions we compare our predictions with the experimental data from ATLAS [ref] , and then use the PDF reweighting techniques to study the implications of the ATLAS data on PDFs.
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These results are roughly compatible with the zero-mass results of Ref. [ref] which indicates that within the considered kinematic regime the residual charm-mass effects are rather weak.
2510.24525 · Proton-proton collisions · 0.98
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We also note that the measured relative abundances of $D^±$ and $D^*±$ here do not seem to follow the trend seen in the inclusive charm production in $pp$ collisions where it has been observed that the production of $D^±$ becomes actually more likely than that of $D^*±$ along with an increased rate of baryon production [ref] , although within the systematic uncertainties shown in Figure [ref] the evidence is not conclusive.
Charm-quark fragmentation fractions and production cross section at midrapidity in pp collisions at the LHC · Proton-proton collisions · 0.96
Cites as background 22 papers
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The assumption that the cross section organizes in this way into parts encoding the long-distance physics (PDFs and FFs) and the short-distance physics (partonic cross section) is called collinear factorization [ref] .
Comments on collinear factorization · Introduction · 0.93
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The assumption that the cross section organizes in this way into parts encoding the long-distance physics (PDFs and FFs) and the short-distance physics (partonic cross section) is called collinear factorization [ref] .
Factorization of Hard Processes in QCD · Introduction · 0.93
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The idea of using $W^± +$ charm production in hadronic collisions to constrain the strange-quark content of nucleons was originally proposed in Ref. [ref] leading to the first experimental studies at Tevatron [ref] and to more recent studies at the LHC [ref] .
The Charm Content of W+1 Jet Events as a Probe of the Strange Quark Distribution Function · Introduction · 0.89
Discussion
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