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REVIEW 3 major objections 6 minor 37 references

This paper demonstrates that a single NNLO QCD fit to HERA and LHC data can simultaneously determine the proton PDFs, the strong coupling, the top quark pole mass, and the effective weak mixing angle with precision competitive with dedicate

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2026-08-01 04:53 UTC pith:BASSDSR7

load-bearing objection Genuinely first simultaneous fit of PDFs, alpha_s, m_t, and sin^2theta_eff, worth reading; the top-mass shift rests on an unmatched NRQCD correction that needs a real uncertainty. the 3 major comments →

arxiv 2607.22390 v1 pith:BASSDSR7 submitted 2026-07-24 hep-ph

Simultaneous extraction of top quark mass, strong coupling, effective mixing angle, and proton PDFs using inclusive DIS and proton-proton collision data

Mikel Mendizabal Morentin , Katerina Lipka , Giovanni Limatola , Efstathios Agrafiotis , Oleksandr Zenaiev , XiaoMin Shen , Sven Olaf Moch This is my paper
classification hep-ph
keywords parton distribution functionstop quark pole massstrong couplingeffective weak mixing angleNRQCD threshold correctionssoft-gluon resummationglobal QCD analysisSMEFT
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents the first global QCD analysis that determines the proton's parton distribution functions at the same time as three Standard Model parameters: the strong coupling, the top quark pole mass, and the effective weak mixing angle. Using inclusive deep-inelastic scattering data from HERA together with LHC jet, Drell-Yan, and top-pair measurements, the authors fit everything simultaneously at next-to-next-to-leading order and show the results are as precise as dedicated single-parameter extractions. The central innovation is a threshold correction for top-pair production near the 2m_t invariant-mass boundary, computed in non-relativistic QCD plus soft-gluon resummation, which shifts the extracted top mass upward by about half a gigaelectronvolt. Why this matters: the correlations among these parameters and the PDFs are shown to be significant (for instance, the strong coupling and the weak mixing angle are anti-correlated with correlation -0.59), so fitting them separately can bias the results.

Core claim

The authors claim the first-ever simultaneous extraction of the proton PDFs, the strong coupling alpha_s at the Z mass, the top quark pole mass, and the effective leptonic weak mixing angle from a single NNLO QCD fit. The central results are m_t^pole = 172.59 +0.51/-0.49 GeV, alpha_s(mZ)=0.1179 +0.0030/-0.0016, and sin^2 theta_eff^l = 0.23142 +0.00032/-0.00029, with parameter correlations of rho=0.26 between m_t and alpha_s and rho=-0.59 between alpha_s and sin^2 theta. The top mass value includes a +0.45 GeV shift from including NLO non-relativistic QCD threshold effects and an additional +0.11 GeV from NLL soft-gluon resummation, both implemented as a fixed additive correction to the first

What carries the argument

The load-bearing piece is the additive threshold correction: an excess cross-section of 7.31 pb (with +1.93/-0.91 pb scale uncertainty) added to the fixed-order NNLO prediction for the first top-pair invariant-mass bin (340 to 355 GeV), computed as the difference between NLO non-relativistic QCD plus NLL resummation and NLO fixed-order predictions, and treated as independent of the top mass because the residual mass dependence lies within the scale band. This correction is combined with the authors' global QCD fit framework (using a linear interpolation of the cross-section in m_t and a profiled nuisance parameter for sin^2 theta) to perform the simultaneous fit.

Load-bearing premise

The entire extraction rests on treating the non-relativistic QCD threshold excess as a fixed, top-mass-independent 7.31 pb add-on to a single invariant-mass bin, justified by the overlap of the NLO scale bands; if that correspondence fails, the central top-mass shift and all derived correlations change.

What would settle it

Recompute the first top-pair invariant-mass bin (340-355 GeV) cross-section with a fully matched NNLO+NRQCD prediction and compare with the LHC data used in the fit; if the data prefer the fixed-order-only prediction (no 7.31 pb excess), the central m_t shift of +0.45 GeV is not supported.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Quantified correlations (rho=-0.59 between alpha_s and sin^2 theta) show how much single-parameter fits can misestimate uncertainties when PDFs are held fixed.
  • The +0.45 GeV upward shift of the top pole mass from threshold effects suggests earlier extractions that ignored these effects may be systematically low by about half a gigaelectronvolt.
  • The simultaneous fit reaches precision competitive with dedicated extractions, establishing a template for future global interpretations of LHC data that include Standard Model effective field theory alongside SM parameters.
  • The method also constrains two top-quark SMEFT operators together with PDFs, yielding values consistent with the Standard Model within uncertainties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A sharper test would replace the fixed additive correction with a mass-dependent matching between NRQCD and fixed-order predictions; the current choice confines the correction to one bin and may miss shape information in M_ttbar.
  • The dominant uncertainty for all three parameters is missing higher-order QCD scale variation, driven largely by the low-energy inclusive jet data; adding more sea-quark-sensitive measurements could shrink that envelope.
  • If the observed alpha_s--sin^2 theta anti-correlation persists in future data, combined fits will be needed to exploit the precision of forthcoming Drell-Yan measurements.
  • The additive-correction approach could be transferred to other heavy-flavour thresholds (such as bottom quarks), but the overlap-validity assumption would need revalidation there.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper presents a simultaneous NNLO QCD fit of proton PDFs, alpha_s(mZ), the top-quark pole mass, and sin^2(theta_eff^l), using HERA inclusive DIS, CMS inclusive jets, Drell-Yan, and t-tbar production data within the xFitter framework. Non-relativistic QCD (NRQCD) threshold corrections and NLL soft-gluon resummation are included as an additive correction to the fixed-order t-tbar prediction in the first M_ttbar bin. The fit also explores two SMEFT operators. The central results are m_t^pole = 172.59^{+0.51}_{-0.49} GeV, alpha_s(mZ) = 0.1179^{+0.0030}_{-0.0016}, and sin^2(theta_eff^l) = 0.23142^{+0.00032}_{-0.00029}, with a significant alpha_s--sin^2 correlation rho=-0.59.

Significance. If the central claim holds, this is a useful proof-of-principle demonstration that PDFs and multiple SM parameters can be extracted simultaneously with correlations accounted for, and that NRQCD threshold effects materially shift the extracted top mass. The use of public experimental data, the xFitter framework, and interpolation grids is a strength, and the chi^2/N_dof = 1.05 indicates a good global fit quality. However, the load-bearing NRQCD matching assumption is not sufficiently scrutinized; the central m_t shift and the reported correlations depend on an additive correction whose relation to the NNLO baseline is not quantified. The paper is therefore not yet suitable for publication without a major revision of the treatment and validation of that correction.

major comments (3)
  1. [Sec. 3, Eqs. (3.1)-(3.2)] The additive correction Delta_sigma_NRQCD is defined by Eq. (3.1) as sigma_NRQCD - sigma_NLO, i.e., the excess over NLO fixed order, but it is then added to the NNLO MATRIX prediction in the first M_ttbar bin. The paper acknowledges the absence of a formal matching prescription but does not estimate the NLO-to-NNLO difference in that bin. If the NNLO and NLO fixed-order predictions in the 340-355 GeV bin differ by an amount comparable to 7.31 pb, the additive correction is mis-specified, and the central m_t shift (+0.45 GeV) as well as the correlations in Tables 3-4 would change. This is the only bin where NRQCD is active, so the issue is load-bearing. A concrete test would be to quote the NNLO vs NLO fixed-order difference in this bin and to repeat the fit with the additive factor shifted by that difference (or by half of it) as an additional uncertainty.
  2. [Sec. 3, validity region vs. integration range] The text states that the validity region of the NRQCD approximation is |M_ttbar - 2 m_t| <= 5 GeV. For m_t = 172.5 GeV this corresponds to [340, 350] GeV, but Eq. (3.1) integrates the excess over M_ttbar in [340, 355] GeV. Figure 1 shows overlap beginning near 355 GeV, so the integration extends 5 GeV beyond the stated validity region. The sensitivity of the extracted parameters to this upper bin edge is not given. I request a variation of the integration range, e.g., [340, 350] GeV, and an assessment of how Delta_sigma and the fitted m_t change.
  3. [Sec. 3, Fig. 2] The paper claims that the m_t dependence of Delta_sigma is 'well within the scale uncertainty' and therefore treats Delta_sigma as independent of m_t. However, Fig. 2 shows a fitted slope of 0.18 GeV^-1, which across the considered range m_t = 169-176 GeV changes Delta_sigma by about 1.26 pb. The quoted scale uncertainty is +1.93/-0.91 pb, so the mass variation exceeds the lower uncertainty by about 40%. Since m_t is a free parameter in the fit, this omitted dependence can bias the extracted m_t. Please propagate the full m_t dependence of Delta_sigma in the fit, or alternatively add the observed variation as a theory uncertainty in quadrature.
minor comments (6)
  1. [Sec. 5] Typo: 'reults' should be 'results'.
  2. [Table 3 caption] Typo: 'summatized' should be 'summarized'.
  3. [Table 4] The row 'FO NNLO + NLO NRQCD + NLL + EFT' reports central values without uncertainties, while the text says the changes are within experimental uncertainties. Please either provide uncertainties for this row or explicitly state that they are omitted for brevity.
  4. [Sec. 4.2, Eq. (4.8)] The notation sigma_{delta m_t} for the linear coefficient is ambiguous. Define it as d sigma / d m_t or use a clearer subscript.
  5. [Sec. 3, Fig. 1 caption] The caption says the validity region is defined by the intersection of central values and scale-uncertainty bands; the text says the curves 'begin to overlap' near 355 GeV. Please clarify whether the criterion is central-value overlap or band overlap.
  6. [Table 3] The NRQCD scale uncertainty for sin^2(theta_eff^l) is listed as '>0.00000'; this should be quantified as '< 0.00001' or with an explicit upper bound.

Circularity Check

0 steps flagged

No significant circularity: the NRQCD correction is an external fixed input, not a fitted prediction, and the central QCD+SMEFT fit is self-contained.

full rationale

The paper's central derivation is a conventional simultaneous QCD+SMEFT fit of PDFs, alpha_s(mZ), m_t^pole, and sin^2(theta_eff) to inclusive HERA DIS, jet, Drell-Yan, and ttbar data. The NRQCD correction entering m_t extraction is defined in Eqs. (3.1)-(3.2) as an external, fixed additive factor Delta_sigma_NRQCD = sigma_NRQCD - sigma_NLO, taken from refs. [9,37,38] and not fitted to the data of this analysis. The resulting m_t shift (+0.45 GeV from NRQCD, +0.11 GeV from NLL) is a consequence of this fixed input, not a re-encoding of a fitted parameter, and the paper explicitly acknowledges the absence of a formal matching prescription when adding the NLO-level NRQCD excess to the NNLO fixed-order baseline. That is a stated modeling limitation and a potential correctness risk, but it does not reduce an output to an input by construction. The extraction of sin^2(theta_eff) is profiled directly from the CMS A4 measurement, while alpha_s is constrained by jet and DIS data; none of these steps are self-referential in the fit. The self-citations for the NRQCD correction involve overlapping authors, but the cited results are independently published calculations that are externally falsifiable and are cross-checked against the independent NNPDF result [7], so per the rules this does not raise the circularity score. No equation or fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is smuggled in via citation. Overall, the derivation chain is not circular; the unquantified matching ambiguity belongs in correctness risk, not circularity.

Axiom & Free-Parameter Ledger

9 free parameters · 10 axioms · 0 invented entities

The extraction is a fit: the SM parameters and PDF shape parameters are free parameters constrained by data. The theory model includes fixed heavy-quark masses, a fixed strangeness fraction, a chosen charm threshold, and an additive NRQCD correction from prior work by overlapping authors. These choices are varied as model/MHOU uncertainties but are not derived in this paper.

free parameters (9)
  • alpha_s(mZ) = 0.1179 +0.0030/-0.0016
    SM parameter extracted simultaneously with PDFs; free parameter of the fit (Table 3).
  • m_t^pole = 172.59 +0.51/-0.49 GeV
    Top quark pole mass extracted via EFTREACTION linear interpolation (Eq. 4.8).
  • sin^2 theta_eff^l = 0.23142 +0.00032/-0.00029
    Effective leptonic weak mixing angle profiled as nuisance parameter for the DY A4 data.
  • PDF shape parameters = set of 19 parameters (Eqs. 4.2-4.7) subject to sum rules
    Basis function parameters fitted to the global dataset; central PDF parametrization chosen by chi2 scan.
  • m_c = 1.47 GeV
    Charm quark mass fixed by hand, varied in model uncertainty band (1.4-1.54 GeV).
  • m_b = 4.5 GeV
    Bottom quark mass fixed by hand, varied in model uncertainty (4.25-4.75 GeV).
  • f_s = 0.4
    Strangeness fraction fixed from HERAPDF2.0, varied in model uncertainty (0.3-0.5).
  • k_mc = 2.16
    Charm threshold factor chosen so charm threshold coincides with starting scale, effectively excluding intrinsic charm.
  • Delta_sigma_NRQCD+NLL = 7.31 +1.93/-0.91 pb
    Additive factor for the first M_ttbar bin (340-355 GeV) computed from NLO NRQCD+NLL; treated as mt-independent and applied to NNLO FO predictions.
axioms (10)
  • standard math QCD factorization and NNLO DGLAP evolution relate PDFs to observables.
    Used throughout; basis of the global fit.
  • domain assumption FONLL general-mass variable-flavour-number scheme is valid for HERA DIS at Q^2>10 GeV^2.
    Section 2; low-Q resummation and higher-twist neglected.
  • domain assumption Leading-colour approximation for NNLOJET inclusive jet predictions is accurate enough.
    Section 2; full color NNLO not used.
  • ad hoc to paper NRQCD factorization and the identification of validity region |M_ttbar-2mt|<=5 GeV from overlap of NLO scale bands.
    Section 3 and Fig. 1; defines where NRQCD correction is applied.
  • ad hoc to paper The additive combination of NRQCD correction with NNLO FO cross section is valid in the threshold bin.
    Section 3: 'In the absence of a formal matching prescription... we incorporate the NRQCD effects as an additive correction.'
  • ad hoc to paper The NRQCD additive correction is independent of m_t within uncertainty.
    Fig. 2 shows linear mt dependence but treated as negligible vs scale uncertainty.
  • domain assumption Linear interpolation of ttbar cross section in m_t is sufficient (Eq. 4.8).
    From EFTREACTION module [22].
  • ad hoc to paper Quadratic SMEFT parametrization in Wilson coefficients and neglect of ctG*c_tq mixing (Eq. 4.9).
    Section 4.3; mixing term neglected.
  • domain assumption Bonvini-Giuli PDF parametrization with no intrinsic charm and f_s=0.4.
    Section 4.1; chosen by chi2 scan, but absence of intrinsic charm is an input.
  • domain assumption PDF replicas (37) are sufficient for sin^2 theta_eff uncertainty propagation.
    Section 4.4; 36 shifts summed in quadrature.

pith-pipeline@v1.3.0-alltime-deepseek · 13027 in / 17297 out tokens · 179344 ms · 2026-08-01T04:53:54.696169+00:00 · methodology

0 comments
read the original abstract

We present the first simultaneous determination of the proton parton distribution functions (PDFs) together with the strong coupling, the top quark pole mass, and the effective weak mixing angle. The analysis is performed at next-to-next-to-leading order in QCD using the xFitter framework, based on inclusive deep-inelastic scattering measurements at HERA and precise measurements of jet, electroweak boson, and top quark-antiquark pair production in proton-proton collisions at the LHC. Non-relativistic QCD effects in top quark-antiquark pair production are considered at next-to-leading order, and combined with next-to-leading logarithmic soft-gluon resummation. Simultaneously with PDFs and Standard Model (SM) parameters, relevant top quark SM effective-field-theory (SMEFT) operators are constrained. The precision of the obtained SM parameters is competitive with the state-of-the art individual extractions and accounts for the correlations among those parameters and PDFs. This work paves the way for future global interpretation of the LHC data in terms of QCD, SM and SMEFT.

discussion (0)

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Reference graph

Works this paper leans on

37 extracted references · 31 linked inside Pith

  1. [7]

    R. Ball, J. ter Hoeve and R. Stegeman,A Determination of the Top Mass from a Global PDF Analysis,2603.28865

    Pith/arXiv arXiv

  2. [8]

    B. Fuks, K. Hagiwara, K. Ma and Y.-J. Zheng,Simulating toponium formation signals at the LHC,Eur. Phys. J. C85(2025) 157 [2411.18962]

    Pith/arXiv arXiv 2025

  3. [9]

    Garzelli, G

    M.V. Garzelli, G. Limatola, S.O. Moch, M. Steinhauser and O. Zenaiev,Updated predictions for toponium production at the LHC,Phys. Lett. B866(2025) 139532 [2412.16685]

    Pith/arXiv arXiv 2025

  4. [10]

    Hou et al.,New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC,Phys

    T.-J. Hou et al.,New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC,Phys. Rev. D103(2021) 014013 [1912.10053]

    Pith/arXiv arXiv 2021

  5. [11]

    Alekhin, M.V

    S. Alekhin, M.V. Garzelli, S. Moch and O. Zenaiev,Determination of the strong coupling from high-energy data,Eur. Phys. J. C86(2026) 161 [2510.21435]. [12]CMScollaboration,Measurement oft ¯tnormalised multi-differential cross sections in pp collisions at √s= 13TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and pa...

    arXiv 2026

  6. [22]

    X. Shen, S. Amoroso, J. Gao, K. Lipka and O. Zenaiev,A framework for simultaneous fit of QCD and BSM parameters with xFitter,Eur. Phys. J. C84(2024) 1235 [2407.16061]

    Pith/arXiv arXiv 2024

  7. [23]

    Forte, E

    S. Forte, E. Laenen, P. Nason and J. Rojo,Heavy quarks in deep-inelastic scattering,Nucl. Phys. B834(2010) 116 [1001.2312]

    Pith/arXiv arXiv 2010

  8. [24]

    Bertone, G

    V. Bertone, G. Bozzi and F. Hautmann,Perturbative hysteresis and emergent resummation scales,Phys. Rev. D105(2022) 096003 [2202.03380]

    Pith/arXiv arXiv 2022

  9. [25]

    Bertone, G

    V. Bertone, G. Bozzi and F. Hautmann,Perturbative RGE systematics in precision observables,Phys. Rev. D111(2025) 074005 [2407.20842]

    Pith/arXiv arXiv 2025

  10. [26]

    Resummation-scale uncertainties in deep-inelastic scattering fits with xFitter

    xFitter Developers’ Team, “Resummation-scale uncertainties in deep-inelastic scattering fits with xFitter.” to appear in 2026. [27]CMScollaboration,Measurements of Differential Jet Cross Sections in Proton-Proton Collisions at √s= 7TeV with the CMS Detector,Phys. Rev. D87(2013) 112002 [1212.6660]

    Pith/arXiv arXiv 2026

  11. [28]

    Currie, E.W.N

    J. Currie, E.W.N. Glover and J. Pires,Next-to-Next-to Leading Order QCD Predictions for Single Jet Inclusive Production at the LHC,Phys. Rev. Lett.118(2017) 072002 [1611.01460]

    Pith/arXiv arXiv 2017

  12. [29]

    Britzger et al.,NNLO interpolation grids for jet production at the LHC,Eur

    D. Britzger et al.,NNLO interpolation grids for jet production at the LHC,Eur. Phys. J. C 82(2022) 930 [2207.13735]

    Pith/arXiv arXiv 2022

  13. [30]

    Grazzini, S

    M. Grazzini, S. Kallweit and M. Wiesemann,Fully differential NNLO computations with MATRIX,Eur. Phys. J. C78(2018) 537 [1711.06631]

    Pith/arXiv arXiv 2018

  14. [31]

    Catani, S

    S. Catani, S. Devoto, M. Grazzini, S. Kallweit and J. Mazzitelli,Top-quark pair production at the LHC: Fully differential QCD predictions at NNLO,JHEP07(2019) 100 [1906.06535]. – 14 –

    Pith/arXiv arXiv 2019

  15. [32]

    Carrazza, E.R

    S. Carrazza, E.R. Nocera, C. Schwan and M. Zaro,PineAPPL: combining EW and QCD corrections for fast evaluation of LHC processes,JHEP12(2020) 108 [2008.12789]

    Pith/arXiv arXiv 2020

  16. [33]

    Jeˇ zo, E.R

    T. Jeˇ zo, E.R. Nocera, T.R. Rabemananjara, C. Schwan, T. Sharma and J. Wissmann, PineAPPLv1: fast and flexible theory predictions for present and future colliders, 2606.17134. [34]ATLAScollaboration,Measurements of top-quark pair differential and double-differential cross-sections in theℓ+jets channel withppcollisions at √s= 13TeV using the ATLAS detecto...

    Pith/arXiv arXiv 2019

  17. [35]

    Catani, S

    S. Catani, S. Devoto, M. Grazzini, S. Kallweit, J. Mazzitelli and H. Sargsyan,Top-quark pair hadroproduction at next-to-next-to-leading order in QCD,Phys. Rev. D99(2019) 051501 [1901.04005]

    Pith/arXiv arXiv 2019

  18. [36]

    Garzelli, J

    M.V. Garzelli, J. Mazzitelli, S.O. Moch and O. Zenaiev,Top-quark pole mass extraction at NNLO accuracy, from total, single- and double-differential cross sections fort t+ X production at the LHC,JHEP05(2024) 321 [2311.05509]

    Pith/arXiv arXiv 2024

  19. [37]

    Kiyo, J.H

    Y. Kiyo, J.H. Kuhn, S. Moch, M. Steinhauser and P. Uwer,Top-quark pair production near threshold at LHC,Eur. Phys. J. C60(2009) 375 [0812.0919]

    Pith/arXiv arXiv 2009

  20. [38]

    Garzelli, G

    M.V. Garzelli, G. Limatola, S.-O. Moch, M. Steinhauser and O. Zenaiev,Threshold Top-Quark Pair-Production: Cross Sections and Key Uncertainties,2604.09485

    Pith/arXiv arXiv

  21. [39]

    Lepage, L

    G.P. Lepage, L. Magnea, C. Nakhleh, U. Magnea and K. Hornbostel,Improved nonrelativistic QCD for heavy quark physics,Phys. Rev. D46(1992) 4052 [hep-lat/9205007]

    Pith/arXiv arXiv 1992

  22. [40]

    Pineda and J

    A. Pineda and J. Soto,Effective field theory for ultrasoft momenta in NRQCD and NRQED, Nucl. Phys. B Proc. Suppl.64(1998) 428 [hep-ph/9707481]

    Pith/arXiv arXiv 1998

  23. [41]

    Bigi, Y.L

    I.I.Y. Bigi, Y.L. Dokshitzer, V.A. Khoze, J.H. Kuhn and P.M. Zerwas,Production and Decay Properties of Ultraheavy Quarks,Phys. Lett. B181(1986) 157

    1986

  24. [42]

    Fadin and V.A

    V.S. Fadin and V.A. Khoze,Threshold Behavior of Heavy Top Production in e+ e- Collisions,JETP Lett.46(1987) 525

    1987

  25. [43]

    Fadin, V.A

    V.S. Fadin, V.A. Khoze and T. Sjostrand,On the Threshold Behavior of Heavy Top Production,Z. Phys. C48(1990) 613

    1990

  26. [44]

    Hagiwara, Y

    K. Hagiwara, Y. Sumino and H. Yokoya,Bound-state Effects on Top Quark Production at Hadron Colliders,Phys. Lett. B666(2008) 71 [0804.1014]

    Pith/arXiv arXiv 2008

  27. [45]

    W.-L. Ju, G. Wang, X. Wang, X. Xu, Y. Xu and L.L. Yang,Top quark pair production near threshold: single/double distributions and mass determination,JHEP06(2020) 158 [2004.03088]

    Pith/arXiv arXiv 2020

  28. [46]

    Alekhin et al.,HERAFitter,Eur

    S. Alekhin et al.,HERAFitter,Eur. Phys. J. C75(2015) 304 [1410.4412]. [47]xFitter Developers’ Teamcollaboration,xFitter 2.0.0: An open source QCD fit framework,PoSDIS2017(2018) 203 [1709.01151]

    Pith/arXiv arXiv 2015

  29. [48]

    Agarwal, K

    S. Agarwal, K. Mierle and T.C.S. Team,Ceres Solver, 10, 2023

    2023

  30. [49]

    Bonvini and F

    M. Bonvini and F. Giuli,A new simple PDF parametrization: improved description of the HERA data,Eur. Phys. J. Plus134(2019) 531 [1902.11125]

    Pith/arXiv arXiv 2019

  31. [50]

    Grzadkowski, M

    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek,Dimension-Six Terms in the Standard Model Lagrangian,JHEP10(2010) 085 [1008.4884]. – 15 –

    Pith/arXiv arXiv 2010

  32. [51]

    Alwall, R

    J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer et al.,The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,JHEP07(2014) 079 [1405.0301]

    Pith/arXiv arXiv 2014

  33. [52]

    James and M

    F. James and M. Roos,Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations,Comput. Phys. Commun.10(1975) 343

    1975

  34. [53]

    Pumplin, D.R

    J. Pumplin, D.R. Stump and W.K. Tung,Multivariate fitting and the error matrix in global analysis of data,Phys. Rev. D65(2001) 014011 [hep-ph/0008191]

    Pith/arXiv arXiv 2001

  35. [54]

    Pumplin, D.R

    J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P.M. Nadolsky and W.K. Tung,New generation of parton distributions with uncertainties from global QCD analysis,JHEP07 (2002) 012 [hep-ph/0201195]

    Pith/arXiv arXiv 2002

  36. [55]

    Alekhin, J

    S. Alekhin, J. Bl¨ umlein, S. Moch and R. Placakyte,Parton distribution functions,α s, and heavy-quark masses for LHC Run II,Phys. Rev. D96(2017) 014011 [1701.05838]. [56]xFitter Developers’ Teamcollaboration,Impact of low-xresummation on QCD analysis of HERA data,Eur. Phys. J. C78(2018) 621 [1802.00064]

    Pith/arXiv arXiv 2017

  37. [57]

    Tackmann,Beyond scale variations: perturbative theory uncertainties from nuisance parameters,JHEP08(2025) 098 [2411.18606]

    F.J. Tackmann,Beyond scale variations: perturbative theory uncertainties from nuisance parameters,JHEP08(2025) 098 [2411.18606]. [58]NNPDFcollaboration,Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy,Eur. Phys. J. C84(2024) 517 [2401.10319]. – 16 –

    Pith/arXiv arXiv 2025