Recent QCD results from the xFitter project: Probing the strange content of the proton with charm production in charged current at LHeC

Achim Geiser; Agnieszka Luszczak; Alexander Glazov; Amanda Cooper-Sarkar; Andrey Sapronov; Daniel Britzger; Francesco Giuli; Fred Olness; Ivan Novikov; Oleksandr Zenaiev

REVIEW 3 major objections 6 minor 14 references

Recent QCD results from the xFitter project: Probing the strange content of the proton with charm production in charged current at LHeC

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper projects that LHeC charged-current charm data would dramatically shrink the strange-quark PDF uncertainty, independent of heavy-flavor scheme.

desk verdict A clear proceedings summary of the companion paper; the LHeC projection is a closure test and the 'scheme independent' phrasing overstates the evidence. read the letter →

arxiv 1909.00451 v1 pith:4NWSXOYH submitted 2019-09-01 hep-ph

xFitter Developers Team: Hamed Abdolmaleki , Valerio Bertone , Daniel Britzger , Stefano Camarda , Amanda Cooper-Sarkar , Achim Geiser , Francesco Giuli , Alexander Glazov

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Agnieszka Luszczak Ivan Novikov Fred Olness Andrey Sapronov Oleksandr Zenaiev

This is my paper · ORCID

classification hep-ph

keywords strangequarkPDFcharged-currentdeep-inelasticscatteringcharmproductionLHeCxFitterprofilingvariableflavornumberschemefixed

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

Charm production in charged-current deep-inelastic scattering—where a $W$ boson turns a strange quark inside the proton into a charm quark—is a direct window onto the strange-quark parton distribution function ($s(x)$, the probability density of finding a strange quark carrying momentum fraction $x$). This paper uses the xFitter QCD analysis framework to compare two theoretical treatments of this process—one where charm appears only through gluon splitting (fixed flavor number scheme) and one where charm has its own parton distribution (variable flavor number scheme)—and to show where in the kinematic plane they differ. It then simulates LHeC measurements of this observable and 'profiles' an existing PDF set against those pseudodata, concluding that the LHeC would dramatically reduce the strange-quark PDF uncertainty in the intermediate-to-low $x$ region. The authors also argue that this projected improvement is essentially independent of the heavy-flavor scheme choice, because restricting the data to the region where the two schemes agree leaves the profiled uncertainty almost unchanged. The net takeaway is a quantitative case that one LHeC measurement could serve as a strangeness probe.

What carries the argument

The load-bearing mechanism is xFitter's profiling procedure: given pseudodata (or real data) and a starting PDF set, xFitter recomputes the PDF uncertainty band by spanning the parameter space of the PDF eigenvectors (or replicas) weighted by the $\chi^2$ of the new data, effectively reweighting the original set to the new measurements. The heavy-flavor comparison is carried by two concrete calculations, FONLL-B for the variable flavor number scheme and FFNS-A for the fixed flavor number scheme, together with the generalized matching conditions from APFEL that let the matching scale $\mu_m$ interpolate continuously between the two schemes. The argument also rests on the profiling of a restricted data set—points where $\Delta_{\rm scheme} < \Delta_{\rm PDF}$—to isolate the scheme dependence from the projected PDF constraint.

What would settle it

Generate the LHeC pseudodata not from the PDF set used for profiling but from an independent PDF prior whose strange-quark distribution differs by more than the current uncertainty in the intermediate-$x$ region; if the profiled $s(x)$ central value shifts by more than the shrunk uncertainty, or if the uncertainty reduction largely disappears, then the reported dramatic improvement is a closure artifact rather than a genuine LHeC measurement forecast.

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Extended reading notes

Core claim

The paper's central discovery is a projection: precision measurements of charged-current charm production at the proposed Large Hadron Electron Collider (LHeC) would dramatically reduce the uncertainty on the strange-quark PDF, and this reduction is independent of the heavy-flavor scheme choice. Concretely, the authors generate LHeC pseudodata for the differential CC charm cross section at 100 fb$^{-1}$ with electron polarization $P = -0.8$, using the NNPDF3.1 NLO PDF set as the theory input, and then use xFitter's profiling capability to update the PDF uncertainties. In the intermediate-to-low $x$ region the $s(x)$ uncertainty shrinks substantially. When the pseudodata are restricted to the kinematic points where the fixed-flavor and variable-flavor number schemes differ by less than the PDF uncertainty ($\Delta_{\rm scheme} < \Delta_{\rm PDF}$), the profiled uncertainty is nearly the same as with the full data set, which is the evidence for scheme independence. The scheme comparison itself shows that VFNS and FFNS agree at low $Q^2$, where charm quark degrees of freedom are absent, and diverge at high $Q^2$, where the VFNS resums $\alpha_s \ln(Q^2/m_c^2)$ terms through DGLAP evolution; the residual $x$-dependence of the difference is traced to the balance between those resummed logarithms and NLO counter-terms.

Load-bearing premise

The projected uncertainty reduction assumes that the simulated LHeC data, generated from the same PDF set that is then profiled against them, faithfully represent what a real experiment would measure and how uncertain that measurement would be.

Editorial extensions

If this is right

A 100 fb$^{-1}$ LHeC run with $P=-0.8$ would sharpen the strange-quark PDF in the intermediate-to-low $x$ region, complementing existing constraints from fixed-target neutrino data and LHC $W$+charm measurements.
The projected improvement in $s(x)$ does not depend on choosing a fixed or variable flavor number scheme, provided the analysis restricts to the region where the two schemes agree within the PDF uncertainty.
At large $Q^2$, PDF extractions using CC charm production must treat the VFNS resummation of $\alpha_s \ln(Q^2/m_c^2)$ terms carefully, because that is where scheme differences grow.
Because xFitter's matching scale $\mu_m$ can vary continuously, the same infrastructure can test scheme dependence in other multi-scale observables and propagate scheme choice into PDF uncertainties.

Reading between the lines

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

Editor's inference: The reported dramatic improvement is a closure test—the pseudodata are generated from one PDF set and then profiled against that same set—so repeating the exercise with pseudodata generated from an independent PDF prior would tell whether the projected tightening is a genuine property of the LHeC measurement or an artifact of fitting a set to its own predictions.
Editor's inference: The scheme-independence claim would be stronger if it compared the profiled central values of $s(x)$ from the full and restricted data sets, not just the uncertainty bands; a central-value shift larger than the shrunk uncertainty would still matter for physics even if the PDF error is reduced.
Editor's inference: The restricted-data set removes points where $\Delta_{\rm scheme} > \Delta_{\rm PDF}$; if those points are the ones most sensitive to $s(x)$, the conservative cut could be removing exactly the constraining power, so the near-identical result between full and restricted sets deserves a kinematic breakdown to verify it is not accidental.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read this as a conference summary of arXiv:1907.01014, not a standalone analysis. Every quantitative figure is cited to the companion paper, so the contribution is narrative plus a showcase of xFitter, not new results. That is fine for a proceedings, and the paper is honest about the dependency.

It does a good job explaining why the VFNS and FFNS predictions diverge at large Q^2 and large x: the VFNS resums alpha_s ln(Q^2/m_c^2) and the charm PDF contribution mirrors the gluon contribution in the FFNS. The observation about the scale 'shuffling' between the charm PDF and the hard cross section is a useful pedagogical point, and the text is candid that the two PDF sets carry different uncertainties that cannot be directly compared.

The main soft spot is the conclusion. The LHeC pseudodata are generated with NNPDF3.1 and the same PDF set is profiled against them, so the dramatic reduction of the strange PDF uncertainty is a closure test, not a prediction about real data. The scheme-independence statement is supported by a restricted data set that removes exactly the points where VFNS and FFNS differ most. Finding similar results with the full set does not establish independence, because the pseudodata are generated from a single scheme; the exercise never generates data under the alternative scheme and asks whether the profiling result changes. That missing control is the real test. The assumed systematic uncertainties are also taken as realistic without a sensitivity scan.

None of this is an internal error, and the central projection is plausible. But the wording 'independent of the underlying heavy flavor scheme' goes beyond the evidence. The paper would be stronger with one sentence flagging the closure-test nature and a minor revision to the conclusion. As a proceedings contribution, it deserves a normal peer review and would be acceptable after that tempering. The companion paper remains the citable reference; this one is a quick, clear illustration of how pseudodata projections can overstate their scope.

Referee Report

3 major / 6 minor

Summary. This DIS2019 proceedings paper from the xFitter developers studies charged-current charm production in deep-inelastic scattering as a probe of the strange-quark PDF. After a brief overview of the xFitter framework, the paper compares NLO predictions computed in the Variable Flavor Number Scheme (FONLL-B with NNPDF3.1) and the Fixed Flavor Number Scheme (FFNS A with ABMP16), and attributes the growing differences at large Q^2 and large x to DGLAP resummation and its balance with NLO counter-terms. It then decomposes the cross section into flavor-initiated components, noting that the VFNS charm contribution closely tracks the FFNS gluon contribution. Using LHeC pseudodata at 100 fb^-1 and polarization P = -0.8, the authors profile NNPDF3.1 against the full and a restricted dataset, where the latter is defined by requiring the VFNS/FFNS central-value difference to be smaller than the PDF uncertainty (Fig. 3a). They find a dramatic reduction of the s(x) uncertainty at intermediate-to-low x (Fig. 3b) and conclude in Sec. 6 that the improvement is independent of the heavy-flavor scheme. All quantitative details are deferred to the companion paper Ref. [2].

Significance. The projection, if robust, is valuable for LHeC planning and for PDF fits: a substantial reduction of the strange-quark PDF uncertainty at intermediate-to-low x from charged-current charm data is a concrete and testable physics payoff, and the paper usefully demonstrates xFitter's profiling and heavy-flavor-scheme capabilities in an open-source, reproducible framework. The qualitative account of the scheme differences (Secs. 3-4) is grounded in known QCD and consistent with Ref. [14], and the flavor-decomposition observation that the VFNS charm PDF plays the role of the FFNS gluon contribution is pedagogically instructive. The main caveats are that the headline improvement is obtained in a closure test (pseudodata generated from and profiled against the same PDF set) and that the scheme-independence test excludes the kinematic region where the schemes differ most, so the conclusion is somewhat stronger than the evidence presented in this manuscript.

major comments (3)

[Sec. 5 (Fig. 3b); Sec. 6] The central projection is a closure test rather than an independent prediction: the LHeC pseudodata are generated from theoretical predictions that use the NNPDF3.1 PDF set, and the same NNPDF3.1 set is then profiled against them, so the dramatic reduction of the s(x) uncertainty shown in Fig. 3b is built into the input by construction. This demonstrates the self-consistency of the xFitter profiling machinery, but it cannot by itself predict the improvement that real LHeC data would produce if the true PDF differs from NNPDF3.1. The Sec. 6 conclusion that the LHeC 'can dramatically improve the PDF uncertainty' should therefore be qualified as a demonstration under the closure assumption; the authors could strengthen it by generating pseudodata from an alternative PDF set or by presenting a sensitivity scan over the assumed systematic uncertainties, which are currently taken to be realistic without further study.
[Sec. 5 (Fig. 3a); Sec. 3; footnote 2] The scheme-independence claim is tested only after removing the region where the schemes actually disagree. The restricted dataset is defined by Delta_scheme < Delta_PDF (Fig. 3a), which removes precisely the kinematic points where the VFNS and FFNS predictions differ most, so the agreement between the full and restricted profilings in Fig. 3b shows only that those excluded points do not drive the profiling outcome; it does not establish that the improvement is independent of the heavy-flavor scheme in the regions where the schemes differ. In addition, Delta_scheme is computed between predictions that use different underlying PDF sets (NNPDF3.1 for the VFNS and ABMP16 for the FFNS, as stated in Sec. 3), and footnote 2 itself acknowledges that the uncertainties of these two sets cannot be directly compared; the cut therefore conflates scheme dependence with PDF-set dependence. The conclusion in Sec. 6 should be rephrased to state that the result is insensitive to the scheme choice within the region where the scheme difference is smaller than the PDF uncertainty, or the analysis should be redone with the same PDF set in both schemes.
[Sec. 5] All quantitative details of the pseudodata generation, the profiling chi^2, and the resulting uncertainty bands are deferred to Ref. [2]; the manuscript presents only figures and qualitative statements, so the central quantitative claim cannot be independently checked from this paper alone. This is understandable for a proceedings contribution, but the abstract and Sec. 6 should state explicitly that the quantitative result, including the assumed detector/systematic uncertainties of the pseudodata, is established in Ref. [2] and only illustrated here. As it stands, the abstract presents the dramatic improvement without this qualification.

minor comments (6)

[Sec. 3] 'NPDF3.1' is a typo for 'NNPDF3.1'.
[Fig. 3b caption] 'Q2=100 GeV2' should read 'Q^2 = 100 GeV^2'.
[Sec. 6] 'constraint the PDF uncertainty' should be 'constrain the PDF uncertainty'.
[Sec. 4] The sentence 'the strange fraction increases for xBj and decreases for Q2 and y' should specify that this refers to the fractional contribution of the strange-initiated subprocess to the total cross section, and should state in which scheme the statement applies.
[Sec. 4] 'This is a triumph of the QCD theory' is too informal for a journal report; a neutral formulation would be more appropriate.
[Intro] The paper cites Ref. [2] for all numerical details; it would help the reader if the introduction noted explicitly that this is a summary of Ref. [2] and that the figures in this paper are reproduced from that analysis.

Circularity Check

2 steps flagged · score 6.0 of 10

Projected LHeC strange-PDF improvement is a closure test on NNPDF3.1, and the scheme-independence claim is defined by the cut that removes scheme-sensitive points.

fitted input called prediction [Section 5, Fig. 3b and Section 6 (Conclusion)]
"We use pseudodata for differential CC charm production cross sections in Q2 and xBj corresponding to an integrated luminosity of 100 fb−1 and polarization P =−0.8. ... Details are provided in Ref. [2]. ... In Fig. 3b we display the strange PDF uncertainty for the the original PDF set, the proﬁled PDF set with the all data, and with the PDF with the restricted data set with cuts. (Fig. 3b caption: "The relative strange quark PDF uncertainties at Q2=100 GeV2 of the original and proﬁled NNPDF3.1 PDF set.")"

The pseudodata central values are generated from a theory calculation using the same NNPDF3.1 set that is subsequently profiled: the VFNS curve in Fig. 1 is "computed ... with the NPDF3.1 NLO PDF set," and Fig. 3b profiles the "NNPDF3.1 PDF set," with generation details deferred to the authors' companion Ref. [2]. Thus the profiled PDF is tested against data that are, by construction, its own predictions. The "dramatic improvement" in uncertainty is a closure-test result: it shows the xFitter machinery returns the input model with reduced errors under assumed LHeC systematics, not that independent data from an unknown underlying PDF would produce that reduction. Presenting this as "infer how these might improve" turns a built-in consistency condition into a quantitative projection.
self definitional [Section 5, Fig. 3a and Section 6 (Conclusion)]
"we will therefore perform the proﬁling study of the PDFs with i) the full set of LHeC pseudodata, and ii) the restricted set (with cuts) where the difference between the VFNS and FFNS is smaller than the PDF uncertainty, ∆scheme < ∆PDF (solid data points.). This latter proﬁled PDF will provide a conservative estimate that is independent of the particular VFNS or FFNS,"

The condition ∆scheme < ∆PDF is precisely the statement that the two schemes agree within the current PDF uncertainty. Selecting only such points and then labeling the result "independent of the particular VFNS or FFNS" builds the conclusion into the selection: the kinematic regions that could discriminate the schemes are removed before the profiling. The later claim that "any uncertainty arising from the VFNS/FFNS choice has a negligible impact" is therefore a restatement of the cut, not a test of it. The full-data comparison does not break the circularity, because both full and restricted sets use the same VFNS/NNPDF3.1-based pseudodata; no profiling is performed with an alternative scheme on the discriminating points.

full rationale

The paper has genuinely independent components: the VFNS/FFNS flavor decomposition and the Q2/x dependence of scheme differences are anchored to known QCD arguments and to external references such as [14]; these parts are not circular. However, the headline quantitative claim—the projected "dramatic" improvement of the strange PDF uncertainty at the LHeC, independent of the heavy-flavor scheme—is partially constructed from its own inputs. The improvement is obtained by profiling NNPDF3.1 against pseudodata whose central values are generated from the same NNPDF3.1/FONLL-B model (a closure test), and the scheme-independence is asserted on a restricted set defined by ∆scheme < ∆PDF, which removes the discriminating points. The paper also defers the defining details of the pseudodata to the authors' own companion Ref. [2], so the central projection rests on a self-citation rather than on an external benchmark. These features warrant a partial-circularity score of 6: the central claim is not fully independent, though it is not a pure tautology and the qualitative QCD discussion has external substance.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities or free parameters fitted here; the listed free parameters are chosen inputs for the pseudodata projection. All physical content rests on standard QCD and on the reliability of the cited PDF sets and future collider assumptions.

free parameters (3)

integrated_luminosity = 100 fb^-1
Chosen for the LHeC pseudodata; directly sets statistical precision and therefore the size of the projected uncertainty reduction.
beam_polarization = -0.8
Chosen for the LHeC pseudodata; enters the cross-section normalization and kinematic acceptance.
scale_choice = mu_r^2 = mu_f^2 = Q^2
Renormalization and factorization scale choice; affects the cross-section values and the FFNS/VFNS comparison. Not varied.

assumptions (5)

domain assumption NLO QCD factorization and DGLAP evolution are valid for CC charm production in DIS.
Invoked throughout Sections 2 and 3 when computing cross sections and evolving PDFs.
domain assumption FONLL-B (VFNS) and FFNS A (FFNS) are correct NLO implementations for this process.
Section 3 compares these schemes and attributes differences to resummation; the claim depends on both being correct.
domain assumption The NNPDF3.1 and ABMP16 PDF sets are reliable inputs for the comparison and profiling.
Used in Sections 3 and 5; no independent validation is given in this paper.
domain assumption LHeC pseudodata uncertainties realistically represent future measurements.
Section 5; this is the key assumption for the central projection.
ad hoc to paper The restricted dataset (delta_scheme < delta_PDF) is sufficient to conclude scheme independence.
Section 5; the cut is introduced specifically for this conclusion.

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Cite this review

Pith. "Pith review of Recent QCD results from the xFitter project: Probing the strange content of the proton with charm production in charged current at LHeC." pith.science (2026). https://pith.science/paper/4NWSXOYH

@misc{pith2026190900451,
  author       = {Pith},
  title        = {Pith review of: Recent QCD results from the xFitter project: Probing the strange content of the proton with charm production in charged current at LHeC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4NWSXOYH}},
  note         = {Machine review of arXiv:1909.00451}
}

read the original abstract

We investigate charm production in charged-current deep-inelastic scattering (DIS) using the xFitter program. xFitter is an open-source software framework for the determination of PDFs and the analysis of QCD physics, and has been used for a variety of LHC studies. The study of charged current DIS charm production provides an important perspective on the strange quark PDF, s(x). We make use of the xFitter tools to study the present s(x) constraints, and then use LHeC pseudodata to infer how these might improve. Furthermore, as xFitter implements both Fixed Flavor and Variable Flavor number schemes, we can examine the impact of these different theoretical choices; this highlights some interesting aspects of multi-scale calculations. This study provides a practical illustration of the many features of xFitter.

Figures

Figures reproduced from arXiv: 1909.00451 by the authors.

**Figure 2.** The partonic subprocesses for charm CC production cross sections for FFNS (FFNS A) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** LHeC Constraints on the Strange PDF, c.f., Ref. [2]. 5. LHeC Constraints on the Strange PDF Having outlined the theoretical ingredients we now assess the ability of the LHeC to constrain the PDFs. We use pseudodata for differential CC charm production cross sections in Q 2 and xBj corresponding to an integrated luminosity of 100 fb−1 and polarization P = −0.8. The charm-mass reference value in the MS scheme is set t… view at source ↗

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Works this paper leans on

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [2]

Probing the strange content of the proton with charm production in charged current at LHeC

Hamed Abdolmaleki et al. “Probing the strange content of the proton with charm production in charged current at LHeC”. In: (2019). arXiv: 1907.01014 [hep-ph]

work page Pith review arXiv 2019

[2] [14]

Hybrid scheme for heavy ﬂavors: Merging the ﬁxed ﬂavor number scheme and variable ﬂavor number scheme

A. Kusina et al. “Hybrid scheme for heavy ﬂavors: Merging the ﬁxed ﬂavor number scheme and variable ﬂavor number scheme”. In: Phys. Rev. D88.7 (2013), p. 074032. arXiv: 1306. 6553 [hep-ph]. 6

work page 2013

[3] [1]

HERAFitter

S. Alekhin et al. “HERAFitter”. In: Eur. Phys. J.C75.7 (2015), p. 304. arXiv: 1410.4412 [hep-ph]

arXiv 2015

[4] [3]

Probing Proton Structure at the Large Hadron electron Collider

Rabah Abdul Khalek et al. “Probing Proton Structure at the Large Hadron electron Collider”. In: (2019). arXiv: 1906.10127 [hep-ph]

work page Pith review arXiv 2019

[5] [4]

QCDNUM: Fast QCD Evolution and Convolution

M. Botje. “QCDNUM: Fast QCD Evolution and Convolution”. In:Comput. Phys. Commun. 182 (2011), pp. 490–532. arXiv: 1005.1481 [hep-ph]

arXiv 2011

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APFEL: A PDF Evolution Library with QED corrections

Valerio Bertone, Stefano Carrazza, and Juan Rojo. “APFEL: A PDF Evolution Library with QED corrections”. In: Comput. Phys. Commun. 185 (2014), pp. 1647–1668. arXiv: 1310.1394 [hep-ph]

arXiv 2014

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arXiv 2015

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Tancredi Carli et al. “A posteriori inclusion of parton density functions in NLO QCD ﬁnal- state calculations at hadron colliders: The APPLGRID Project”. In: Eur. Phys. J. C66 (2010), pp. 503–524. arXiv: 0911.2985 [hep-ph]

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