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How to include exclusive $J/\psi$ production data in global PDF analyses

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Pith's one-line read The paper shows that exclusive J/psi photoproduction, calculated at NLO in collinear QCD with an optimal scale plus a double-counting subtraction, is consistent with HERA data and can let LHCb data directly determine the gluon PDF at very…

desk verdict Plausible NLO collinear description of HERA exclusive J/ψ data with global PDFs, but the load-bearing Q0 subtraction is borrowed from the authors' earlier paper and left unspecified here — worth engaging, needs a closer look at the bookkeeping. read the letter →

arxiv 1908.08398 v2 pith:5ODW6DAG submitted 2019-08-22 hep-ph

Chris A. Flett , Stephen P. Jones , Alan D. Martin , Misha G. Ryskin , Thomas Teubner This is my paper · ORCID
classification hep-ph
keywords exclusiveJ/psiphotoproductiongluonPDFatsmallxNLOcollinearfactorizationdoublecountingQ0subtractionoptimalscalegeneralisedpartondistributionsLHCbultraperipheralcollisions
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

The paper tries to remove the obstacles that kept exclusive $J/\psi$ photoproduction out of global fits of proton parton distributions. It argues that the large, sign-changing NLO corrections seen in earlier collinear-factorization calculations are largely artifacts of two mishandled pieces: unresummed double logarithmic terms and double counting between the NLO coefficient function and the input PDFs. Choosing the factorization scale $\mu_F = M_\psi/2$ in the leading-order term resums the double logs, and subtracting the $k_t

What carries the argument

The mechanism is a two-part prescription applied to the collinear factorization formula for $\gamma p\to J/\psi p$. The first part is the optimum-scale choice $\mu_F=M_\psi/2$ in the leading-order term, which moves the $(\alpha_s \ln\mu_F^2 \ln(1/x))^n$ double logarithms into the incoming PDFs and resums them. The second part is the $Q_0$ subtraction: the NLO coefficient function is computed with the low-transverse-momentum region $k_t<Q_0$ removed, because that region is already present in the PDFs at the input scale $Q_0$. The Shuvaev transform, which reconstructs generalized parton distributions from integrated PDFs at small skewness, supplies the bridge from the exclusive amplitude to the usual gluon PDF.

What would settle it

Apply the same optimum-scale plus $Q_0$-subtraction prescription to exclusive $\Upsilon$ photoproduction, where the ratio $Q_0^2/M_\Upsilon^2$ is much smaller than for $J/\psi$; if the advertised scale stability and agreement with data do not survive, the success for $J/\psi$ is tied to the charm-mass scale rather than to the general formalism.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the previous failure of NLO collinear QCD to describe exclusive $J/\psi$ photoproduction at HERA was not a sign that the process needs an intrinsically different formalism. The apparent instability came from double logarithms of $x$ and from double counting between the NLO coefficient functions and the DGLAP-evolved input PDFs. Fixing the factorization scale in the LO term to $\mu_F=M_\psi/2$ resums the double logarithms, while removing the $k_t<Q_0$ contribution from the NLO coefficient functions compensates for what the PDF input already contains. After both corrections, the LO plus NLO amplitude is stable under scale variation, the quark NLO term becomes negligible, and the gluon GPD extracted from ordinary PDFs describes the HERA data and gives definite predictions for LHCb. The paper states this is the first successful description of the HERA $J/\psi$ data within NLO collinear factorization using global PDFs.

Load-bearing premise

The construction stands or falls on the claim that the low-transverse-momentum part of the NLO correction is already present in the input PDFs, so subtracting it removes double counting rather than discarding real physics.

Editorial extensions

If this is right

  • HERA exclusive $J/\psi$ data can be included in future global PDF analyses without invoking a special non-collinear treatment.
  • LHCb ultraperipheral $J/\psi$ data probe the gluon PDF in the interval $10^{-6}<x<10^{-2}$ at the low scale $\mu_F=M_\psi/2$, a kinematic region no current global fit constrains directly.
  • Because the LHCb data are more precise than the current gluon uncertainty at low $x$, including them should sharply reduce the low-$x$ gluon PDF uncertainty.
  • After the $Q_0$ subtraction the NLO quark contribution is practically negligible, making the observable an essentially pure gluon probe.

Reading between the lines

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

  • One implication the authors do not pursue explicitly: the same two-step prescription should serve as a template for other exclusive vector-meson observables, with the size of the power correction set by $Q_0^2/M_V^2$.
  • A natural next test is an actual global fit that includes the HERA and LHCb $J/\psi$ data under this prescription; the paper demonstrates consistency but does not perform such a fit.
  • If the extracted low-$x$ gluon at $\mu_F\simeq 1.5$ GeV were to disagree with extrapolations from DGLAP evolution, that would be evidence for saturation or higher-twist effects that the paper treats as absorbed into the input PDFs.
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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 / 4 minor

Summary. The paper argues that exclusive J/ψ photoproduction, measured at HERA and by LHCb in ultraperipheral pp collisions, can be described in NLO collinear factorization using the PDFs from existing global analyses, provided two ingredients are added: (i) the Shuvaev transform to convert conventional PDFs into the relevant GPDs, and (ii) an 'optimal scale' µF = Mψ/2 that resums double-logarithmic terms, together with a subtraction of the kt < Q0 part of the NLO coefficient function to avoid double counting with the DGLAP-evolved input PDFs. The authors show that after these ingredients the prediction becomes more stable under scale variations and that three global PDF sets (NNPDF3.0, MMHT2014, CT14) reproduce the HERA data reasonably well, while the much larger spread at LHCb energies reflects the poorly known low-x gluon. They conclude that exclusive J/ψ LHCb data can directly constrain the gluon PDF over 10^-6 < x < 10^-2 at a fixed low scale.

Significance. If the central claim is correct, this is a useful step toward including exclusive J/ψ data in global PDF fits: it would open a genuinely new low-x, low-scale kinematic window and would resolve the long-standing scale-instability problem of NLO exclusive vector-meson production. The use of external HERA and LHCb data makes the test non-circular, and the comparison across three independent PDF sets is a strength. However, the decisive technical ingredient, the subtracted NLO coefficient function C_NLO_rem, is not specified in this paper but is imported from a self-cited reference, and the paper's own footnote 5 concedes that the central global PDFs fail to describe the HERA data at the lowest x values. The evidence for 'consistency within uncertainties' is therefore not as complete as the abstract suggests.

major comments (3)
  1. [§4.2 and Eq. (4)] The central object C_NLO_rem, defined by subtracting the kt < Q0 contribution from the NLO coefficient function, is never explicitly given in this paper. Section 4.2 states only that 'we use the NLO correction C_NLO_rem for J/ψ photoproduction excluding the contribution coming from the low virtuality domain', citing reference [29]. Because the subtraction is numerically large — the left panel of Fig. 2 shows the unsubtracted NLO term comparable in size to the LO term and even changing sign with µf — the agreement with HERA in Fig. 4 and the apparent scale stability in the right panel of Fig. 2 rest entirely on this unstated expression. The paper is not self-contained at a load-bearing point, and the reader cannot check whether the subtraction removes a genuine DGLAP-generated contribution or simply cancels a large negative NLO term. A derivation, or at least an explicit formula for C_NLO_rem, must be included.
  2. [§4.2, Eq. (9), and footnote 4] The physical justification of the Q0 subtraction is scheme-dependent in a way the paper does not address. The argument that the |l^2| < Q0^2 part of Fig. 1(b) is 'already included in the input gluon GPD at Q0' presumes that Q0 is the parametrization scale of the input PDFs. But with Q0 = µF = mc = Mψ/2 (Eq. (9)), this is not true for the sets used: NNPDF3.0 starts at Q0 = 1 GeV, CT14 at 1.3 GeV, and MMHT2014 fits at Q^2 > 2 GeV^2 (footnote 4). At Q0 ≈ 1.55 GeV the 'input' is itself already partly a product of DGLAP evolution from a lower scale, so the double-counting subtraction is not uniquely defined. The paper should explain how C_NLO_rem is defined when Q0 differs from the fit's true input scale, and should test the sensitivity of the HERA conclusions to this choice.
  3. [§5.1, Fig. 4, Fig. 6, and footnote 5] The abstract and Section 5.1 claim that the existing global PDFs are 'consistent with the data within their uncertainties', but the quantitative evidence is incomplete. Fig. 4 shows only central predictions for MMHT2014 and CT14, with no uncertainty bands, and Fig. 6 provides a 1σ band only for NNPDF3.0. Moreover footnote 5 concedes that 'when x <~ few x 10^-4 the central global partons fail to describe the HERA data.' Since the conclusion is that the data are consistent within PDF uncertainties, the paper should provide a quantitative comparison — e.g., χ² values or uncertainty bands for all three PDF sets over the HERA x range — rather than relying on visual inspection of central curves.
minor comments (4)
  1. [Figure 2 caption] The caption says 'with µF = mc before (left panel) and after (right panel) the double counting correction', but the text and Eq. (4) distinguish the fixed resummation scale µF = mc from the varying factorization scale µf. It would be clearer to state explicitly which scale is varied in each panel and which term is plotted.
  2. [Notation in Eq. (4) and surrounding text] The symbols µF, µf, µ0 and mc are used interchangeably at several points (e.g., Section 4.1 says 'µF = µ0 = Mψ/2' while Eq. (9) sets 'Q0 = µF = mc'). A consistent notation, with a single symbol for the optimal scale, would prevent confusion.
  3. [Section 5.1] The text says 'the above choice of Q0 and µF give a stable theoretical prediction also when the scales µf and µR are varied', but only µf variations are shown in Figs. 3 and 4; the dependence on µR is not displayed separately.
  4. [References] Reference [34] appears in the text as 'Hoodhboy' but the correct name is Hoodbhoy; please correct the typo.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the consistency claim is tested against external HERA and LHCb data, and the theoretical inputs are prior-work prescriptions rather than fits to the target data.

full rationale

The paper's central result is a comparison of NLO collinear-factorization predictions with HERA and LHCb exclusive J/psi data, using existing global PDFs. The data are external and are not used to determine the PDFs or the coefficient functions. The Shuvaev transform, the optimal-scale choice mu_F = M_psi/2, and the Q0 subtraction are adopted from earlier work (some of it self-cited), but these are parameter-free theoretical prescriptions with stated physical motivations and are not fitted to the J/psi data displayed here. The paper explicitly acknowledges that the Q0 subtraction is a large power correction and that the input scale Q0 differs across PDF sets, which is a legitimate theoretical-robustness concern, but this does not amount to circularity because the comparison to HERA and LHCb data remains an independent test. No equation in the paper reduces by construction to a fitted parameter, a renamed known result, or a self-citation whose content is the claimed prediction itself; therefore no circular step is identified.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central prediction rests mainly on the standard collinear factorization framework plus two input choices: setting the factorization scale to M_psi/2 and subtracting the k_t < Q0 region from the NLO coefficient function. Both are motivated by resummation and double-counting arguments from earlier papers by the same group, and they are large enough to be numerically decisive.

free parameters (3)
  • Q0 subtraction scale = Q0 = m_c = M_psi/2 = 1.55 GeV
    Controls the size of the double-counting subtraction in Section 4.2; the choice Q0 = m_c is made by hand and is numerically important because the subtracted power correction is O(Q0^2/m_c^2).
  • t-slope parameters B(W) = 4.9 + 4 alpha'_P ln(W/W0) = B0 = 4.9 GeV^-2, alpha'_P = 0.06 GeV^-2, W0 = 90 GeV
    Determines the extrapolation from t = 0 to the integrated cross section; taken from Model 4 of ref. [36]. Different choices shift the predicted normalization.
  • NRQCD matrix element <O1>_{J/psi} = not quoted numerically; from nonrelativistic wave function
    Normalizes the amplitude in Eq. (1); a nonperturbative input taken from NRQCD and potential-model literature, not computed in this paper.
assumptions (6)
  • domain assumption Collinear factorization for exclusive J/psi photoproduction, including NRQCD for the meson wave function and the NLO coefficient functions of ref. [19].
    Invoked in Eq. (1); the entire calculation lives inside this factorization scheme, which is standard but not derived here.
  • domain assumption The Shuvaev transform relates the low-x GPDs to ordinary integrated PDFs with O(x) accuracy.
    Used in Section 3 to turn GPDs into PDFs; relies on the assumption of no additional singularities in the j > 1 plane, which the authors state but do not prove.
  • domain assumption The factorization scale mu_F = M_psi/2 resums all double logarithmic (alpha_s ln(1/xi) ln(mu_F^2))^n terms.
    Taken from the authors' previous analysis [25]; it is the optimal scale prescription that removes the large double logarithms from the NLO coefficient functions.
  • domain assumption The low k_t < Q0 contribution of the NLO coefficient function is already contained in the input PDFs and must be subtracted.
    Section 4.2; central to the method, but argued rather than proven from factorization theorems.
  • domain assumption Soft survival probability S2(W) from the eikonal model of ref. [37] describes the probability of no extra soft interactions.
    Used in Section 5.2 when converting LHC pp measurements into photon-proton cross sections; the model is cited, not derived.
  • standard math The real part of the amplitude is obtained from the imaginary part by the local-slope dispersion relation of Eq. (7).
    High-energy even-signature approximation, cited to ref. [33]; standard but an approximation.

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Pith. "Pith review of How to include exclusive $J/\psi$ production data in global PDF analyses." pith.science (2026). https://pith.science/paper/5ODW6DAG

@misc{pith2026190808398,
  author       = {Pith},
  title        = {Pith review of: How to include exclusive $J/\psi$ production data in global PDF analyses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5ODW6DAG}},
  note         = {Machine review of arXiv:1908.08398}
}
abstract

We compare the cross section for exclusive $J/\psi$ photoproduction calculated at NLO in the collinear factorization approach with HERA and LHCb data. Using the optimum scale formalism together with the subtraction of the low $k_t<Q_0$ contribution from the NLO coefficient function to avoid double counting we show that the existing global parton distribution functions (PDFs) are consistent with the data within their uncertainties. However, at low $x$ the uncertainties of the present global PDFs are large. On the other hand, the accuracy of the LHCb data are rather good. Therefore, these data provide the possibility to directly measure the gluon PDF over the very large interval of $x$, $10^{-6}<x<10^{-2}$, at a fixed low scale.

Figures

Figures reproduced from arXiv: 1908.08398 by the authors.

Figure 1
Figure 1. (a) LO contribution to γp → V + p. (b) NLO quark contribution. For these graphs all permutations of the parton lines and couplings of the gluon lines to the heavy-quark pair are to be understood. Here the momentum P ≡ (p + p 0 )/2 and l is the loop momentum. Note that the momentum fractions of the left and right partons are x = X + ξ and x 0 = X − ξ respectively; for the upper gluons we have x 0 x and so x ' 2ξ. fro… view at source ↗
Figure 2
Figure 2. LO and LO+NLO contributions to the imaginary part of the γp → V + p amplitude as a function of the γp centre-of-mass energy, W, with µF = mc before (left panel) and after (right panel) the double counting correction has been implemented, as explained in the text. The dashed, continuous and dot-dashed (red) curves correspond to three choices of the factorization scale µf : namely µ 2 f = 2m2 c , m2 c , Q2 0 , respect… view at source ↗
Figure 3
Figure 3. The gluon LO+NLO and quark NLO contributions to the imaginary part of the γp → J/ψ + p amplitude for two different choices of the factorization scale µ 2 f = µ 2 R = m2 c , 2m2 c shown by the continuous and dashed curves respectively. CT14 global PDFs [3] are used and the ‘optimal’ scale µF = mc is chosen. evolution, while the part with scales µ > µR accounts for the running αs behaviour obtained after the regulariz… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The γp → J/ψ + p data obtained at HERA [18] and LHCb [8] compared with the predictions obtained using the PDFs taken from three different sets of global partons [1, 2, 3] with µf = mc (solid lines). The dashed line for the CT14 prediction, corresponding to µ 2 f = 2m2 …
Figure 5
Figure 5. Figure 5: The two diagrams describing exclusive J/ψ production at the LHC. The vertical lines represent two-gluon exchange. Diagram (a), the W+ component, is the major contribution to the pp → p+J/ψ+p cross section for a J/ψ produced at large rapidity Y . Thus such data allow a …
Figure 6
Figure 6. Figure 6: The central scale prediction σ for a given global input set of partons, here NNPDF3.0 [1], together with its 1σ (shaded) error band show that the current PDF uncertainties are much greater than the experimental uncertainty and the scale variations of the theoretical re…

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Gluon Saturation Effects in Exclusive Heavy Vector Meson Photoproduction

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    Exclusive J/psi photoproduction off Pb targets prefers BK evolution with gluon saturation over linear BFKL evolution, and Upsilon production is predicted to distinguish them only at higher energies.

  2. Relativistic corrections and high-energy resummation for exclusive heavy quarkonium photoproduction

    hep-ph 2026-07 accept novelty 5.0 of 10

    The O(v²) correction to the high-energy-resummed coefficient function for exclusive heavy-quarkonium photoproduction is derived and shown to be small but useful for stabilizing μ_F dependence.

Reference graph

Works this paper leans on

38 extracted references · 17 canonical work pages · cited by 2 Pith papers

  1. [29]

    The exclusive $J/\psi$ process at the LHC tamed to probe the low $x$ gluon

    S.P. Jones, A.D. Martin, M.G. Ryskin, T. Teubner, Eur. Phys. J. C76 (2016) 633 [arXiv:1610.02272]

    work page Pith review arXiv 2016

  2. [1]

    Ball et al

    R.D. Ball et al. [NNPDF Collaboration], JHEP 1504 (2015) 040 [arXiv:1410.8849]

    arXiv 2015

  3. [2]

    Harland-Lang, A.D

    L.A. Harland-Lang, A.D. Martin, P. Motylinski, R.S. Thorne, Eur. Phys. J. C75 (2015) 204 [arXiv:1412.3989]

    arXiv 2015

  4. [3]

    Dulat et al

    S. Dulat et al. , Phys. Rev. D93 (2016) 033006 [arXiv:1506.07443]

    arXiv 2016

  5. [4]

    The Green Function for the BFKL Pomeron and the Transition to DGLAP Evolution

    H. Kowalski, L.N. Lipatov, D.A Ross, Eur. Phys. J. C74 (2014) 2919 [arXiv:1401.6298]; Eur. Phys. J. C76 (2016) 23 [arXiv:1508.05744]

    work page Pith review arXiv 2014

  6. [5]

    Decoupling of the leading contribution in the discrete BFKL Analysis of High-Precision HERA Data

    H. Kowalski, L. N. Lipatov, D. A. Ross and O. Schulz, Eur. Phys. J. C77 (2017) [arXiv:1707.01460]

    work page Pith review arXiv 2017

  7. [6]

    Aaij et al., Nucl

    LHCb Collaboration: R. Aaij et al., Nucl. Phys. B871 (2013) 1; JHEP 1603 (2016) 159, erratum: JHEP 1609 (2016) 013; JHEP 1705 (2017) 074; JHEP 1706 (2017) 147

    work page 2013

  8. [7]

    Measurement of B meson production cross-sections in proton-proton collisions at sqrt(s)= 7 TeV

    LHCb Collaboration: R. Aaij et al., JHEP 1308 (2013) 117 [arXiv:1306.3663]; Phys. Rev. Lett. 118 (2017) 052002 [arXiv:1612.05140]

    work page Pith review arXiv 2013

Show all 38 references
  1. [8]

    Aaij et al., J

    LHCb Collaboration: R. Aaij et al., J. Phys. G41 (2014) 055002 [arXiv:1401.3288]; JHEP 1810 (2018) 167 [arXiv:1806.04079]

    2014 arXiv

  2. [9]

    Zenaiev et al

    O. Zenaiev et al. [PROSA Collaboration], Eur. Phys. J. C75 (2015) 396 [arXiv:1503.04581]

    2015 arXiv

  3. [10]

    Gauld, J

    R. Gauld, J. Rojo, L. Rottoli and J. Talbert, JHEP 1511 (2015) 009 [arXiv:1506.0802]

    2015

  4. [11]

    Cacciari, M

    M. Cacciari, M. L. Mangano and P. Nason, Eur. Phys. J. C75 (2015) 610 [arXiv:1507.06197]

    2015 arXiv

  5. [12]

    Gauld and J

    R. Gauld and J. Rojo, Phys. Rev. Lett. 118 (2017) 072001 [arXiv:1610.09373]

    2017 arXiv

  6. [13]

    Gauld, JHEP 05 (2017) 084 [arXiv:1703.03636]

    R. Gauld, JHEP 05 (2017) 084 [arXiv:1703.03636]

    2017 arXiv

  7. [14]

    de Oliveira, A.D

    E.G. de Oliveira, A.D. Martin and M.G. Ryskin, Phys. Rev. D97 (2018) 074021 [arXiv:1712.06834]

    2018 arXiv

  8. [15]

    Diehl, Phys

    M. Diehl, Phys. Rept. 388 (2003) 41 [hep-ph/0307382]

    2003 arXiv

  9. [16]

    Shuvaev, K.J

    A.G. Shuvaev, K.J. Golec-Biernat, A.D. Martin, M.G. Ryskin, Phys. Rev. D60 (1999) 014015 [hep-ph/9902410]; A.G. Shuvaev, Phys. Rev. D60 (1999) 116005. 14

    1999 arXiv

  10. [17]

    Jones, A.D

    S.P. Jones, A.D. Martin, M.G. Ryskin, T. Teubner, J. Phys. G44 (2017) [arXiv:1611.03711]

    2017 arXiv

  11. [18]

    Chekanov et al.) Eur

    ZEUS Collaboration (S. Chekanov et al.) Eur. Phys. J. C24 (2002) 345 [hep-ex/0201043]; Nucl. Phys. B695 (2004) 3 [hep-ex/0404008]; H1 Collaboration (A. Aktas et al.), Eur. Phys. J. C46 (2006) 585 [hep-ex/0510016]; (C. Alexa et al.) Eur. Phys. J. C73 (2013) 2466 [arXiv:1304.5162]

    2002 arXiv

  12. [19]

    Ivanov, A

    D.Yu. Ivanov, A. Schafer, L. Szymanowski, G. Krasnikov, Eur. Phys. J. C34 (2004) 297, Erratum: Eur. Phys. J. C75 (2015) 75 [hep-ph/0401131]

    2004 arXiv

  13. [20]

    Ohrndorf, Nucl

    T. Ohrndorf, Nucl. Phys. B198 (1982) 26

    1982

  14. [21]

    X. Ji, J. Phys. G24 (1998) 1181 [hep-ph/9807358]

    1998 arXiv

  15. [22]

    Buckley, J

    A. Buckley, J. Ferrando, S. Lloyd, K. Nordstr¨ om, B. Page, M. R¨ ufenacht, M. Sch¨ onherr, G. Watt, Eur. Phys. J. C75 (2015) 132 [arXiv:1412.7420]

    2015 arXiv

  16. [23]

    Martin, C

    A.D. Martin, C. Nockles, M.G. Ryskin, A.G. Shuvaev, T. Teubner, Eur. Phys. J. C63 (2009) 57 [arXiv:0812.3558]

    2009 arXiv

  17. [24]

    Kumericki, D

    K. Kumericki, D. Mueller, Nucl. Phys. B841 (2010) 1 [arXiv:0904.0458]

    2010 arXiv

  18. [25]

    Jones, A.D

    S.P. Jones, A.D. Martin, M.G. Ryskin, T. Teubner, J. Phys. G43 (2016) 035002 [arXiv:1507.06942]

    2016 arXiv

  19. [26]

    Zi-Qiang Chen, Cong-Feng Qiao, Phys. Lett. B797 (2019) 134816 [arXiv:1903.00171]

    2019 arXiv

  20. [27]

    de Oliveira, A.D

    E.G. de Oliveira, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C72 (2012) 2069 [arXiv:1205.6108]

    2012 arXiv

  21. [28]

    Ivanov, B

    D.Yu. Ivanov, B. Pire, L. Szymanowski, J. Wagner, arXiv:1510.06710

    arXiv

  22. [30]

    Nadolsky, H-L

    P.M. Nadolsky, H-L. Lai, T. Hua, Q-H Cao, J. Huston, J. Pumplin, D. Stump, Wu-Ki Tung, C.-P. Yuan, Phys. Rev. D78 (2008) 013004 [arXiv:0802.0007]

    2008 arXiv

  23. [31]

    Brodsky, G.P

    S.J. Brodsky, G.P. Lepage, P.B. Mackenzie, Phys. Rev. D28 (1983) 228

    1983

  24. [32]

    Harland-Lang, V.A

    L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, Phys. Lett. B761 (2016) 20 [arXiv:1605.04935]

    2016 arXiv

  25. [33]

    M. G. Ryskin, R. G. Roberts, A. D. Martin and E. M. Levin, Z. Phys. C 76 (1997) 231 [hep-ph/9511228]

    1997 arXiv

  26. [34]

    Hoodbhoy, Phys

    P. Hoodbhoy, Phys. Rev. D56 (1997) 388 [hep-ph/9611207]. 15

    1997 arXiv

  27. [35]

    Alexa et al

    C. Alexa et al. [H1 Collaboration], Eur. Phys. J. C73 (2013) 2466 [arXiv:1304.5162]

    2013 arXiv

  28. [36]

    Khoze, A.D

    V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C73 (2013) 2503 [arXiv:1306.2149]

    2013 arXiv

  29. [37]

    Khoze, A.D

    V.A. Khoze, A.D. Martin, M.G. Ryskin, Eur. Phys. J. C74 (2014) 2756 [arXiv:1312.3851]

    2014 arXiv

  30. [38]

    Ball et al

    R.D. Ball et al. [NNPDF Collaboration], Eur. Phys. J. C77 (2017) 663 [arXiv:1706.00428]. 16

    2017 arXiv

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