Pith. sign in

REVIEW 4 major objections 4 minor 65 references

Role of higher twist effects in diffractive DIS and determination of diffractive parton distribution functions

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Including a fitted higher-twist term proportional to $1/Q^2$ in the diffractive structure function $F_2$ improves the NLO QCD description of HERA diffractive deep-inelastic scattering data and changes the extracted gluon density.

desk verdict A competent NLO diffractive-PDF fit with a fitted higher-twist term, but the 'first-time' novelty is overstated and the twist-4 neglect needs quantitative support. read the letter →

arxiv 1908.10154 v2 pith:T4SQEMOI submitted 2019-08-27 hep-ph hep-ex

Atefeh Maktoubian , Hossein Mehraban , Hamzeh Khanpour , Muhammad Goharipour This is my paper · ORCID
classification hep-phhep-ex
keywords diffractivedeepinelasticscatteringhighertwisteffectspartondistributionfunctionsNLOQCDanalysisHessianuncertaintiesHERAPomeronfluxvariable-flavor-numberscheme
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper sets out to establish that nonperturbative higher-twist (HT) effects are visible in diffractive deep inelastic scattering and should be included when extracting diffractive parton distribution functions (PDFs). The authors perform an NLO QCD fit to all available HERA diffractive datasets with a fitted correction of the form $F_2 = F_2^{\rm LT}\,(1 + C_{\rm HT}(x)/Q^2)$, where $C_{\rm HT}(x)=h_0 x^{h_1}(1+h_2 x)$; the fit quality improves from $\chi^2/{\rm dof}=1.052$ to $1.013$, and the data can be described down to $Q^2=6.5$ GeV$^2$ rather than the usual $8.5$ GeV$^2$ cut. Including the HT term changes the extracted gluon density, suppressing it at medium and large momentum fraction $z$ while slightly enhancing it at small $z$. A sympathetic reader would take the conclusion to be that leading-twist-only analyses of low-$Q^2$ diffractive data have been missing a power correction that matters for the shape of the gluon.

What carries the argument

The load-bearing object is the phenomenological higher-twist factor applied to the diffractive $F_2$: $F_2(x,Q^2) = F_2^{\rm LT}(x,Q^2)\,(1 + C_{\rm HT}(x)/Q^2)$, with $C_{\rm HT}(x)=h_0 x^{h_1}(1+h_2 x)$. This is a $1/Q^2$ power correction whose three parameters are fitted simultaneously with the diffractive PDFs; the $x^{h_1}$ factor makes the correction grow at large $x$, and the $h_2$ term allows behavior at small $x$. The argument also relies on the $\beta\le 0.80$ cut to justify ignoring twist-4 contributions from longitudinal virtual photons, which would otherwise dominate the large-$\beta$ region.

What would settle it

Use the published PDF sets to predict the diffractive reduced cross sections at $Q^2=2.5$ and $5.09$ GeV$^2$ shown in the theory-to-data comparisons; those points were excluded from the fit, so the HT model either reproduces them better than the leading-twist model or it does not.

Watch

Extended reading notes

Core claim

The central claim is that a simple power-suppressed correction to the diffractive structure function $F_2$ is required to describe HERA diffractive DIS data at NLO accuracy. The paper shows that the diffractive reduced cross section is better reproduced when the leading-twist structure function is multiplied by $(1 + C_{\rm HT}(x)/Q^2)$ with $C_{\rm HT}(x)=h_0 x^{h_1}(1+h_2 x)$, and the three HT parameters are fitted together with the diffractive PDFs, giving $h_0=-25.798$, $h_1=2.536$, and $h_2=-1.381$. With a $\beta\le 0.80$ cut and $Q^2_{\rm min}=6.5$ GeV$^2$, the fit keeps 499 of 526 data points; the same fit without the HT term gives $\chi^2/{\rm dof}=1.052$, while with the HT term it gives $1.013$. The largest improvement comes from the largest rapidity-gap dataset, and the extracted gluon density at the input scale $Q_0^2=1.8$ GeV$^2$ is reduced at medium and large $z$. The authors conclude that HT effects are sizable at large $x$ and low $Q^2$ and that they should be included in diffractive PDF determinations.

Load-bearing premise

The whole fit improvement rests on the assumption that the higher-twist correction takes exactly the factorized form $F_2 = F_2^{\rm LT}\,(1 + h_0 x^{h_1}(1+h_2 x)/Q^2)$, acts only on $F_2$, and that target-mass and twist-4 effects are negligible after the $\beta\le 0.80$ and $Q^2\ge 6.5$ GeV$^2$ cuts.

Editorial extensions

If this is right

  • Diffractive PDF fits can safely include data with $Q^2$ down to $6.5$ GeV$^2$ instead of $8.5$ GeV$^2$, adding more data points without degrading the fit quality.
  • The extracted diffractive gluon density at the input scale is suppressed at medium and large $z$ when HT effects are included, so predictions for diffractive dijet and charm production built from this PDF set will differ from leading-twist-based sets.
  • The combined HERA data improve from $\chi^2/{\rm dof}=1.052$ to $1.013$ when the HT term is added, with the largest single reduction coming from the largest rapidity-gap sample.
  • The HT correction affects theoretical predictions most at low $Q^2$ and at medium $\beta$ values, gradually shifting to larger $\beta$ as $Q^2$ increases.
  • Accounting for HT effects changes the shape and size of the extracted diffractive quark and gluon densities while leaving the size of their uncertainty bands largely unchanged.

Reading between the lines

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

  • A direct extension would apply the same $C_{\rm HT}(x)/Q^2$ form to the longitudinal diffractive structure function $F_L^D$, not only to $F_2$; high-$y$ data could then discriminate between a genuine power correction and an effective rescaling of $F_2$.
  • If the gluon suppression at medium and large $z$ is real, diffractive dijet rates at moderate $Q^2$ should fall below current NLO predictions based on leading-twist-only fits, a cross-check that existing HERA dijet samples could perform.
  • The fitted $C_{\rm HT}(x)$ has a negative overall scale and an $x$-dependent shape; testing alternative forms such as $a(1-x)^p/Q^2$ or a twist-4-motivated term would show whether the improvement is robust or an artifact of the chosen parametrization.
  • Releasing the $\beta\le 0.80$ cut and allowing an explicit twist-4 contribution would reveal whether the fitted higher-twist term is the standard $1/Q^2$ correction or a stand-in for missing large-$\beta$ physics.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. This paper presents an NLO QCD fit to HERA diffractive DIS data (H1 LRG-2011, H1 LRG-2012, and the H1/ZEUS combined dataset) using Regge factorization for the Pomeron and Reggeon contributions, the FONLL general-mass variable-flavor-number scheme for heavy quarks, and the APFEL/MINUIT toolchain. The claimed novelty is the inclusion of a phenomenological higher-twist (HT) correction to the diffractive structure function F2 of the form F2 = F2_LT (1 + C_HT(x)/Q^2) with C_HT(x) = h0 x^h1 (1 + h2 x), applied only to F2. The authors report that including this term improves the global chi^2 from 390.46 to 376.08 for the same 371 degrees of freedom, motivates lowering Q^2_min from 8.5 to 6.5 GeV^2 on the basis of a chi^2 scan, and leads to a gluon density that is suppressed at medium and large z while the quark density is enhanced at small z.

Significance. If the central claim is correct, the paper would justify extending diffractive PDF fits to lower Q^2 and would alter the extracted diffractive gluon at medium and large z, which is relevant for diffractive phenomenology at HERA and the LHC. The fit strategy is standard and the paper is transparent about datasets, parameterizations, and numerical tools, which is a strength. However, the evidence for the HT contribution is entirely in-sample: the three HT parameters are fitted to the same data used to claim the effect, the Q^2_min cut is chosen from the same chi^2 scan, the HT parameters are quoted without uncertainties, and the neglect of the twist-4 contribution to F_L is asserted rather than demonstrated. These issues are load-bearing for the abstract's claim of 'first evidence' for HT effects in diffractive DIS, so the manuscript requires substantial revision before that claim can be accepted.

major comments (4)
  1. [Sec. II.D, Eqs. (7)–(8) and Table II] The three higher-twist parameters h0, h1, and h2 are fitted to the data, yet Table II quotes them without uncertainties: h0 = -25.798, h1 = 2.536, h2 = -1.381. Since the paper's central claim is that these parameters are determined by the diffractive DIS data and improve the fit, the absence of uncertainties and of correlations with the PDF parameters makes it impossible to judge whether the HT term is statistically meaningful. The authors should provide Hessian uncertainties for h0, h1, h2, and ideally a correlation matrix with the other fitted parameters.
  2. [Sec. II.D and Sec. III.B] The statement that the twist-4 contribution to F_L from longitudinally polarized photons 'can be strongly reduced and safely ignored' after the beta <= 0.80 cut is an assertion, not a quantitative estimate. The reduced cross section in Eq. (1) depends on F_L through a y-dependent coefficient, while the fitted HT correction in Eq. (7) multiplies only F2. A residual twist-4 F_L term would therefore be partially absorbed by h0, h1, h2, biasing the extracted gluon. Since Ref. [47] found that including twist-4 changes the diffractive gluon, the authors should quantify the residual twist-4 contribution at the fitted beta <= 0.80 and Q^2 >= 6.5 GeV^2 points, or perform a robustness fit that includes a twist-4 F_L term.
  3. [Sec. III.B, Fig. 3] The choice Q^2_min = 6.5 GeV^2 is selected from a chi^2 scan performed on the same data that are then used to claim that HT effects improve the description. This data-driven cut selection makes the reported chi^2 improvement an in-sample statistic and can bias the apparent gain. The authors should provide an out-of-sample test, for example fitting at Q^2_min = 8.5 GeV^2 and then predicting the data below that cut, or using a hold-out subset of the combined dataset, and should separately show the stability of the HT parameters under this procedure.
  4. [Sec. IV, Table III] The improvement in global chi^2 from 390.46 to 376.08 for the same 371 dof is modest, especially given that it is achieved by adding three free parameters. The authors should report a significance test (e.g., an F-test or likelihood-ratio test) and should show that the improvement is not driven by a small number of data points; the largest per-dataset gain appears in H1-LRG-12, so pull distributions for that dataset would be informative. Without such a test, the abstract's wording that HT effects 'can improve the description of the data' overstates the strength of the evidence.
minor comments (4)
  1. [Global] The text contains several typographical issues: 'Difrractive' in the Section III title, 'heay quark' in Section II.C, 'This analysis are enriched' in the abstract, and 'HK19-DDPF' instead of 'HK19-DPDF' in the introduction.
  2. [Sec. II.D] The sentence 'hi should be determined along with the fit parameters and then keep fixed' is ambiguous; the authors should clarify whether the HT parameters are profiled, marginalized, or simply frozen at their best-fit values when the PDF uncertainties are computed.
  3. [Figs. 13–15] Several theory-to-data comparisons show data with Q^2 = 2.5 and 5.09 GeV^2, which lie below the chosen Q^2_min = 6.5 GeV^2 and are excluded from the fit. The text should state explicitly whether these low-Q^2 panels are genuine predictions of the fitted model or are included only as a qualitative illustration of the HT extrapolation.
  4. [Table I] The table lists 526 data points before cuts, and the text later says 499 points are included after cuts, implying 27 points excluded; this arithmetic is consistent, but the breakdown of how many points are removed by the beta, M_X, and Q^2 cuts separately would be helpful.

Circularity Check

1 steps flagged · score 6.0 of 10

Central evidence for HT effects is an in-sample fit: the HT parameters are fitted to the same data whose improved description is presented as the main result.

  1. fitted input called prediction [Sec. II.D (Eqs. 7-8), Sec. III.B (Fig. 3), Sec. IV (Table III)]
    "F2(x,Q^2) = F^LT_2(x,Q^2)(1 + C_HT(x)/Q^2); C_HT(x) = h0 x^h1 (1 + h2 x); In Eq. (8), hi{i = 0, 1, 2} should be determined along with the fit parameters and then keep fixed. ... χ2/dof 390.46/371 = 1.052 376.079/371 = 1.013"

    The paper's headline claim is that including HT effects improves the data description, but the HT parameters h0,h1,h2 are free parameters fitted to exactly the same datasets whose improved χ2 is then quoted. The no-HT model is the special case h0=0 of Eq. (7), so the HT fit is a nested model and its minimized χ2 cannot be worse than the no-HT χ2 on the same data; the decrease from 390.46 to 376.08 is thus guaranteed by construction, not an independent empirical discovery. The paper then presents the resulting curves as 'NLO theory predictions' for the fitted data, so the in-sample agreement is a fit rather than a prediction. The Q2_min=6.5 cut is also chosen from the same in-sample χ2 scan (Fig. 3), further optimizing the apparent improvement.

full rationale

The paper is a standard NLO QCD fit to HERA diffractive DIS data, and the extraction of diffractive PDFs from those data is not itself circular. The problematic step is the evidential use of the HT fit: the three parameters of the phenomenological HT term, Eq. (8), are determined by minimizing χ2 on the same datasets whose 'improved description' is presented in Table III and the abstract. Because h0=0 recovers the no-HT model, the HT fit is nested, so the raw χ2 decrease is mathematically forced; it cannot by itself establish that HT effects are required. The paper does include some genuinely out-of-sample comparisons, in Figs. 13-14, to data below Q2_min=6.5 that are excluded from the fit, and there the HT curves reduce data-theory differences qualitatively; this provides independent content but is not the basis of the headline claim. The assertion that the twist-4 contribution to F_L is 'strongly reduced and safely ignored' after the β≤0.80 cut (Sec. II.D) is an unquantified assumption and a correctness risk, but not circularity. Self-citations to GKG18 [13] and HK19 [18] are present but not load-bearing: the analysis uses standard parameterization forms and compares with those works rather than deriving its central result from them. Overall, one central evidential step is circular in the fitted-input sense, while the rest of the analysis is self-contained.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a fitted 3-parameter HT function and a data-chosen Q^2 cut, plus standard Regge/DGLAP machinery. No new physical entities are introduced. The main unstated assumption is that the 1/Q^2 correction applies to F2 only and that TMC/twist-4 are negligible.

free parameters (9)
  • h0 (HT scale) = -25.798
    Fitted to diffractive DIS data in Model (inc. HT), Table II, with no uncertainty quoted. Controls overall normalization of the 1/Q^2 correction.
  • h1 (HT slope) = 2.536
    Fitted to data in Table II, no uncertainty quoted. Governs large-x enhancement of C_HT(x).
  • h2 (HT curvature) = -1.381
    Fitted to data in Table II, no uncertainty quoted. Allows HT contribution at small x.
  • alpha_IP(0) (Pomeron intercept) = 1.091 (Model), 1.090 (HT)
    Fitted parameter in the flux factor, Eq. (6), Table II.
  • alpha_IR(0) (Reggeon intercept) = 0.436 (Model), 0.437 (HT)
    Fitted parameter in the flux factor, Eq. (6), Table II.
  • A_IR (Reggeon normalization) = 6.279
    Fitted parameter in the flux factor, Eq. (6), Table II.
  • a_q, b_q, c_q (quark PDF shape) = 0.376/0.436, 1.699/1.541, 0.607/0.723
    Fitted parameters in Eq. (4), Table II, for the two models.
  • a_g, b_g, c_g (gluon PDF shape) = 2.166/6.244, 0.545/0.831, 0.741/2.400
    Fitted parameters in Eq. (5), Table II. The gluon parameters shift strongly with HT and are poorly constrained (a_g has 36% uncertainty in the HT model).
  • Q^2_min kinematic cut = 6.5 GeV^2
    Chosen from the chi2/dof scan in Fig. 3, i.e., data-driven rather than fixed a priori, and lower than the 8.5 GeV^2 used in previous analyses.
assumptions (5)
  • domain assumption Regge factorization: diffractive PDFs factor into x_IP-dependent fluxes and beta-dependent parton densities (Eq. 3).
    Standard assumption for diffractive PDFs, taken from H1/ZEUS analyses; not re-derived here.
  • standard math NLO QCD factorization for diffractive structure functions, Eq. (2), with DGLAP evolution of diffractive PDFs.
    Assumed validity of collinear factorization for diffractive DIS at NLO.
  • ad hoc to paper The higher-twist correction has the multiplicative form F2 = F2_LT (1 + C_HT(x)/Q^2) with C_HT(x)=h0 x^h1 (1+h2 x), applied only to F2 (Eqs. 7-8).
    Phenomenological ansatz imported from inclusive DIS fits (Ref [46]); applied to diffractive DIS without independent justification. FL is not corrected.
  • domain assumption Twist-4 and target mass corrections are negligible for beta <= 0.80 and Q^2 >= 6.5 GeV^2.
    The paper cuts at beta <= 0.80 to suppress twist-4 (Sec. II.D) and mentions TMC (Ref [45]) but does not include them, implicitly assuming they are small.
  • domain assumption Experimental systematic uncertainties can be treated by adding statistical and systematic errors in quadrature.
    Figures show errors added in quadrature; no correlated covariance treatment is described for the fit chi2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Role of higher twist effects in diffractive DIS and determination of diffractive parton distribution functions." pith.science (2026). https://pith.science/paper/T4SQEMOI

@misc{pith2026190810154,
  author       = {Pith},
  title        = {Pith review of: Role of higher twist effects in diffractive DIS and determination of diffractive parton distribution functions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T4SQEMOI}},
  note         = {Machine review of arXiv:1908.10154}
}
abstract

The current analysis aims to present the results of a QCD analysis of diffractive parton distribution functions (diffractive PDFs) at next-to-leading order (NLO) accuracy in perturbative QCD. In this new determination of diffractive PDFs, we use all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) datasets from H1 and ZEUS Collaborations at HERA including the most recent H1/ZEUS combined measurements. In this analysis, we consider the heavy quark contributions to the diffractive DIS in the so-called framework of {\tt FONLL} general mass variable flavor number scheme (GM-VFNS). The uncertainties on the diffractive PDFs are calculated using the standard "Hessian error propagation" which served to provide a more realistic estimate of the uncertainties. This analysis are enriched, for the first time, by including the nonperturbative higher twist (HT) effects in the calculation of diffractive DIS cross sections which are particularly important at large-$x$ and low $Q^{2}$ regions. Then, the stability and reliability of the extracted diffractive PDFs are investigated upon inclusion of HT effects. We discuss the novel aspects of the approach used in this QCD fit, namely, optimized and flexible parameterizations of diffractive PDFs, the inclusion of HT effects, and considering the recent H1/ZEUS combined dataset. Finally, we present the extracted diffractive PDFs with and without the presence of HT effects, and discuss the fit quality and the stability upon variations of the kinematic cuts and the fitted datasets. We show that the inclusion of HT effects in diffractive DIS can improve the description of the data which leads, in general, to a very good agreement between data and theory predictions.

Figures

Figures reproduced from arXiv: 1908.10154 by the authors.

Figure 1
Figure 1. A schematic parton model diagram of inclusive diffractive DIS ep → epX. Four-momenta are indicated in parentheses as well. The variable β is the momentum fraction of the struck quark. the outgoing and incoming protons, P and P 0 , respec￾tively. The fraction of the momentum of proton carried by the diffractive exchange, which is denoted by xIP , is related to x and β variables through xIP = x/β. The only available d… view at source ↗
Figure 2
Figure 2. Different experiments of diffractive DIS datasets in the β and Q 2 plane. The dashed lines represent the kinematic cuts applied on Q 2 and β in this analysis. The data points lying outside these lines shown in the figure are only excluded in the present QCD fits. side these lines shown in the figure are only excluded in the present QCD fits. For our analysis, in particular, we use LRG data from the H1 Collaboration … view at source ↗
Figure 3
Figure 3. The value of the total χ 2 /dof vs the minimum GeV2 of data, Q2 min, for all datasets entering in this study which represents our specific choice of the kinematical cuts on the Q2 min. However the kinematical cut on the Q2 needs some more discussions. To this end, the dependence of the χ 2 on the Q2 cut applied to the analyzed datasets is investi￾gated in our analysis, and the results are shown in [PITH_FULL_IMAGE:… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: The diffractive PDFs as a function of momentum fraction z obtained at the input scale of Q 2 0 = 1.8 GeV2 for both of our analyses with and without the HT corrections. The error bands represent the uncertainty estimation coming from the experimental errors. Table III: …
Figure 5
Figure 5. Figure 5: The extracted diffractive PDFs for gluon and quark densities in three photon virtuality of Q 2 = 6 , 20 and 200 GeV2 compared to the results of H1-2006 Fit B [16] and ZEUS-2010 Fit SJ [17]. analysis. GKG18 used the same datasets in their analysis with different and big…
Figure 6
Figure 6. Figure 6: The extracted diffractive PDFs for gluon and quark densities at Q 2 = 6 GeV2 compared to the most recent analysis by GKG18 [13]. almost all analyzed datasets in other to judge the fit quality, and then, to see the effect arising from the HT correction in some certain k…
Figure 7
Figure 7. Figure 7: Comparison between the experimental data on the diffractive reduced cross sections xIP σ D(3) r (β, Q2 ; xIP ) from the recent H1 and ZEUS combined dataset [15] and the corresponding NLO theoretical predictions from our NLO QCD fits without (solid curves) and with (das…
Figure 8
Figure 8. Figure 8: Comparison between the experimental data on the diffractive reduced cross sections xIP σ D(3) r (β, Q2 ; xIP ) from the H1-LRG-2012 datasets [25] and the corresponding NLO theoretical predictions from our NLO QCD fits without (solid curves) and with (dashed curves) con…
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13 [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]
Figure 14
Figure 14. Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 32 canonical work pages

  1. [47]

    Precision de- termination of the strong coupling constant within a global PDF analysis,

    R. D. Ballet al. [NNPDF Collaboration], “Precision de- termination of the strong coupling constant within a global PDF analysis,” Eur. Phys. J. C78, no. 5, 408 (2018), [arXiv:1802.03398 [hep-ph]]

    arXiv 2018

  2. [1]

    Since the HERA diffractive DIS datasets could only constrain the sum of diffractive PDFs, and on the other hand, the avail- able data are not sufficient enough to constrain all shape parameters of the separate flavors, diffractive PDFs are usually parameterized as simple functional forms at the initial scale in terms of quark zfq(z,Q 2

    work page

  3. [2]

    and gluon 4 zfg(z,Q 2

    work page

  4. [3]

    The quark and antiquark dis- tributions are assumed to be equal,fu =fd =fs =f¯u = f ¯d =f¯s

    distributions. The quark and antiquark dis- tributions are assumed to be equal,fu =fd =fs =f¯u = f ¯d =f¯s. It should be also noted that,z is the longitudinal mo- mentum fraction of the struck parton with respect to the diffractive exchange that differs toβ when the higher- order processes are also included. In the present work, the Pomeron partonic densiti...

    work page

  5. [4]

    =αqzβq(1−z)γq(1 +ηq √z), (4) zfg(z,Q 2

    work page

  6. [5]

    (5) One should notice here that an extra factor exp[−0.001/(1−z)] is simply multiplied to the above pa- rameterizations, in order to ensure that they go to zero forz→ 1

    =αgzβg(1−z)γg(1 +ηg √z). (5) One should notice here that an extra factor exp[−0.001/(1−z)] is simply multiplied to the above pa- rameterizations, in order to ensure that they go to zero forz→ 1. Considering the above parameterizations, the parameters γq, γg, ηq and ηg have the freedom in our analysis to extract from the QCD fit, so that can get negative or...

    work page 2010

  7. [6]

    The Structure of the Proton in the LHC Precision Era,

    J. Gao, L. Harland-Lang and J. Rojo, “The Structure of the Proton in the LHC Precision Era,” Phys. Rept.742, 1 (2018), [arXiv:1709.04922 [hep-ph]]

    arXiv 2018

  8. [7]

    A First Determination of Parton Distributions with Theoretical Uncertainties,

    R. Abdul Khalek et al. , “A First Determination of Parton Distributions with Theoretical Uncertainties,” arXiv:1905.04311 [hep-ph]

    arXiv 1905

Show all 65 references
  1. [8]

    Towards Ultimate Parton Distributions at the High-Luminosity LHC,

    R. Abdul Khalek, S. Bailey, J. Gao, L. Harland-Lang and J. Rojo, “Towards Ultimate Parton Distributions at the High-Luminosity LHC,” Eur. Phys. J. C78, no. 11, 962 (2018), [arXiv:1810.03639 [hep-ph]]

    2018 arXiv

  2. [9]

    Precision QCD at the LHC: from the structure of the proton to all-order resummations,

    L. Rottoli, “Precision QCD at the LHC: from the structure of the proton to all-order resummations,” arXiv:1810.08257 [hep-ph]

    arXiv

  3. [10]

    Parton distributions and lattice QCD calculations: a community white paper,

    H. W. Linet al., “Parton distributions and lattice QCD calculations: a community white paper,” Prog. Part. Nucl.Phys. 100, 107(2018), [arXiv:1711.07916[hep-ph]]

    2018 arXiv

  4. [11]

    Modified structure of protons and neutrons in correlated pairs,

    B. Schmookler et al. [CLAS Collaboration], “Modified structure of protons and neutrons in correlated pairs,” Nature 566, no. 7744, 354 (2019),

    2019

  5. [12]

    Models for total, elastic and diffractive cross sections,

    C. O. Rasmussen and T. Sjöstrand, “Models for total, elastic and diffractive cross sections,” Eur. Phys. J. C 78, no. 6, 461 (2018), [arXiv:1804.10373 [hep-ph]]

    2018 arXiv

  6. [13]

    Hard diffraction in photoproduction with Pythia 8,

    I. Helenius and C. O. Rasmussen, “Hard diffraction in photoproduction with Pythia 8,” Eur. Phys. J. C79, no. 5, 413 (2019), [arXiv:1901.05261 [hep-ph]]

    2019 arXiv

  7. [14]

    Dijet production in diffrac- tive deep-inelastic scattering in next-to-next-to-leading order QCD,

    D. Britzger, J. Currie, T. Gehrmann, A. Huss, J. Niehues and R. Žlebík, “Dijet production in diffrac- tive deep-inelastic scattering in next-to-next-to-leading order QCD,” Eur. Phys. J. C78, no. 7, 538 (2018), [arXiv:1804.05663 [hep-ph]]

    2018 arXiv

  8. [15]

    Factor- ization for hard exclusive electroproduction of mesons in QCD,

    J. C. Collins, L. Frankfurt and M. Strikman, “Factor- ization for hard exclusive electroproduction of mesons in QCD,” Phys. Rev. D56, 2982 (1997), [hep-ph/9611433]

    1997 arXiv

  9. [16]

    Factorization in hard diffraction,

    J. C. Collins, “Factorization in hard diffraction,” J. Phys. G 28, 1069 (2002), [hep-ph/0107252]

    2002 arXiv

  10. [17]

    Proof of factorization for diffractive hard scattering,

    J. C. Collins, “Proof of factorization for diffractive hard scattering,” Phys. Rev. D57, 3051 (1998), Erratum: [Phys. Rev. D61, 019902 (2000)], [hep-ph/9709499]

    1998 arXiv

  11. [18]

    First global next-to-leading order determination of diffractive parton distribution functions and their uncertainties within the Fitter framework,

    M. Goharipour, H. Khanpour and V. Guzey, “First global next-to-leading order determination of diffractive parton distribution functions and their uncertainties within the Fitter framework,” Eur. Phys. J. C78, no. 4, 309 (2018), [arXiv:1802.01363 [hep-ph]]

    2018 arXiv

  12. [19]

    HERAFitter,

    S. Alekhinet al., “HERAFitter,” Eur. Phys. J. C75, no. 7, 304 (2015). [arXiv:1410.4412 [hep-ph]]

    2015 arXiv

  13. [20]

    Com- bined inclusive diffractive cross sections measured with forward proton spectrometers in deep inelasticep scat- tering at HERA,

    F. D. Aaronet al. [H1 and ZEUS Collaborations], “Com- bined inclusive diffractive cross sections measured with forward proton spectrometers in deep inelasticep scat- tering at HERA,” Eur. Phys. J. C 72, 2175 (2012), [arXiv:1207.4864 [hep-ex]]

    2012 arXiv

  14. [21]

    Measurement and QCD analysis of the diffractive deep-inelastic scattering cross-section at HERA,

    A. Aktas et al. [H1 Collaboration], “Measurement and QCD analysis of the diffractive deep-inelastic scattering cross-section at HERA,” Eur. Phys. J. C48, 715 (2006), [hep-ex/0606004]

    2006 arXiv

  15. [22]

    A QCD anal- ysis of ZEUS diffractive data,

    S. Chekanovet al. [ZEUS Collaboration], “A QCD anal- ysis of ZEUS diffractive data,” Nucl. Phys. B831, 1 (2010), [arXiv:0911.4119 [hep-ex]]

    2010 arXiv

  16. [23]

    Phenomenology of diffractive DIS in the framework of fracture functions and determination of diffractive parton distribution functions,

    H. Khanpour, “Phenomenology of diffractive DIS in the framework of fracture functions and determination of diffractive parton distribution functions,” Phys. Rev. D 99, no. 5, 054007 (2019), [arXiv:1902.10734 [hep-ph]]

    2019 arXiv

  17. [24]

    Parton distributions in the LHC era: MMHT 2014 PDFs,

    L. A. Harland-Lang, A. D. Martin, P. Motylinski and R. S. Thorne, “Parton distributions in the LHC era: MMHT 2014 PDFs,” Eur. Phys. J. C75, no. 5, 204 (2015), [arXiv:1412.3989 [hep-ph]]

    2015 arXiv

  18. [25]

    An Ordered analysis of heavy flavor production in deep inelastic scattering,

    R. S. Thorne and R. G. Roberts, “An Ordered analysis of heavy flavor production in deep inelastic scattering,” Phys. Rev. D57, 6871 (1998), [hep-ph/9709442]

    1998 arXiv

  19. [26]

    A Variable-flavor number scheme for NNLO,

    R. S. Thorne, “A Variable-flavor number scheme for NNLO,” Phys. Rev. D 73, 054019 (2006), [hep- ph/0601245]

    2006

  20. [27]

    AGlobalanalysisofinclusivediffractivecross sections at HERA,

    C. Royon, L. Schoeffel, S. Sapeta, R. B. Peschanski and E.Sauvan, “AGlobalanalysisofinclusivediffractivecross sections at HERA,” Nucl. Phys. B781, 1 (2007), [hep- ph/0609291]

    2007

  21. [28]

    Deep inelastic scattering with leading protons or large rapidity gaps at HERA,

    S. Chekanovet al. [ZEUS Collaboration], “Deep inelastic scattering with leading protons or large rapidity gaps at HERA,” Nucl. Phys. B816, 1 (2009), [arXiv:0812.2003 [hep-ex]]

    2009 arXiv

  22. [29]

    Measurement of the Diffractive Longitudinal Structure FunctionF D L at HERA,

    F. D. Aaron et al. [H1 Collaboration], “Measurement of the Diffractive Longitudinal Structure FunctionF D L at HERA,”? Eur. Phys. J. C 71, 1836 (2011), [arXiv:1107.3420 [hep-ex]]

    2011 arXiv

  23. [30]

    InclusiveMeasure- ment of Diffractive Deep-Inelastic Scattering at HERA,

    F.D.Aaron et al. [H1Collaboration], “InclusiveMeasure- ment of Diffractive Deep-Inelastic Scattering at HERA,” Eur. Phys. J. C72, 2074 (2012), [arXiv:1203.4495 [hep- ex]]

    2012 arXiv

  24. [31]

    Diffractive open charm production in deep-inelastic scattering and pho- toproduction at HERA,

    A. Aktas et al. [H1 Collaboration], “Diffractive open charm production in deep-inelastic scattering and pho- toproduction at HERA,” Eur. Phys. J. C50, 1 (2007), [hep-ex/0610076]

    2007 arXiv

  25. [32]

    Measurement of Beauty and Charm Photoproduction using Semi-muonic Decays in Dijet Events at HERA,

    F. D. Aaronet al. [H1 Collaboration], “Measurement of Beauty and Charm Photoproduction using Semi-muonic Decays in Dijet Events at HERA,” Eur. Phys. J. C72, 2047 (2012), [arXiv:1205.2495 [hep-ex]]

    2012 arXiv

  26. [33]

    Tests of QCD fac- torisation in the diffractive production of dijets in deep- inelastic scattering and photoproduction at HERA,

    A. Aktas et al. [H1 Collaboration], “Tests of QCD fac- torisation in the diffractive production of dijets in deep- inelastic scattering and photoproduction at HERA,” Eur. Phys. J. C51, 549 (2007), [hep-ex/0703022]

    2007 arXiv

  27. [34]

    Deep inelastic inclusive and diffractive scattering atQ2 values from 25 to 320 GeV2 with the ZEUS forward plug calorimeter,

    S. Chekanovet al. [ZEUS Collaboration], “Deep inelastic inclusive and diffractive scattering atQ2 values from 25 to 320 GeV2 with the ZEUS forward plug calorimeter,” Nucl. Phys. B800, 1 (2008), [arXiv:0802.3017 [hep-ex]]

    2008 arXiv

  28. [35]

    Study of deep inelastic inclusive and diffractive scattering with the ZEUS forward plug calorimeter,

    S. Chekanovet al. [ZEUS Collaboration], “Study of deep inelastic inclusive and diffractive scattering with the ZEUS forward plug calorimeter,” Nucl. Phys. B713, 3 (2005), [hep-ex/0501060]

    2005 arXiv

  29. [36]

    Dissociation of virtual photons in events with a leading proton at HERA,

    S. Chekanov et al. [ZEUS Collaboration], “Dissociation of virtual photons in events with a leading proton at HERA,” Eur. Phys. J. C38, 43 (2004), [hep-ex/0408009]

    2004 arXiv

  30. [37]

    Behaviorofdiffractiveparton distribution functions,

    A.BereraandD.E.Soper, “Behaviorofdiffractiveparton distribution functions,” Phys. Rev. D53, 6162 (1996), [hep-ph/9509239]

    1996 arXiv

  31. [38]

    Diffractive parton distributions from H1 data,

    A. D. Martin, M. G. Ryskin and G. Watt, “Diffractive parton distributions from H1 data,” Phys. Lett. B644, 131 (2007), [hep-ph/0609273]

    2007 arXiv

  32. [39]

    Hard diffractive scattering: Partons and QCD,

    Z. Kunszt and W. J. Stirling, “Hard diffractive scattering: Partons and QCD,” hep-ph/9609245

    arXiv

  33. [40]

    The Third- order QCD corrections to deep-inelastic scattering by photon exchange,

    J. A. M. Vermaseren, A. Vogt and S. Moch, “The Third- order QCD corrections to deep-inelastic scattering by photon exchange,” Nucl. Phys. B724, 3 (2005), [hep- ph/0504242]. 19

    2005

  34. [41]

    Parton distributions for high-energy collisions,

    M. Gluck, E. Reya and A. Vogt, “Parton distributions for high-energy collisions,” Z. Phys. C53, 127 (1992),

    1992

  35. [42]

    APFEL: A PDF Evolution Library with QED corrections,

    V. Bertone, S. Carrazza and J. Rojo, “APFEL: A PDF Evolution Library with QED corrections,” Com- put. Phys. Commun.185, 1647 (2014), [arXiv:1310.1394 [hep-ph]]

    2014 arXiv

  36. [43]

    Heavy quarks in deep-inelastic scattering,

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

    2010 arXiv

  37. [44]

    Review of Particle Physics,

    M. Tanabashi et al. [Particle Data Group], “Review of Particle Physics,” Phys. Rev. D98, no. 3, 030001 (2018),

    2018

  38. [45]

    QCD Coupling from a Nonperturbative Determination of the Three- Flavor Λ Parameter,

    M. Brunoet al. [ALPHA Collaboration], “QCD Coupling from a Nonperturbative Determination of the Three- Flavor Λ Parameter,” Phys. Rev. Lett.119, no. 10, 102001 (2017), [arXiv:1706.03821 [hep-lat]]

    2017 arXiv

  39. [46]

    High precision determination ofαs fromaglobalfitofjetrates,

    A. Verbytskyiet al., “High precision determination ofαs fromaglobalfitofjetrates,” [arXiv:1902.08158[hep-ph]]

    1902 arXiv

  40. [48]

    Strong Running Coupling from the Gauge Sector of Domain Wall Lattice QCD with Physical Quark Masses,

    S. Zafeiropoulos, P. Boucaud, F. De Soto, J. Rodríguez- Quintero and J. Segovia, “Strong Running Coupling from the Gauge Sector of Domain Wall Lattice QCD with Physical Quark Masses,” Phys. Rev. Lett.122, no. 16, 162002 (2019), [arXiv:1902.08148 [hep-ph]]

    2019 arXiv

  41. [49]

    Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations,

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

    1975

  42. [50]

    A Review of Target Mass Correc- tions,

    I. Schienbein et al., “A Review of Target Mass Correc- tions,” J. Phys. G35, 053101 (2008), [arXiv:0709.1775 [hep-ph]]

    2008 arXiv

  43. [51]

    Constraints on large-x parton distributions from new weak boson production and deep-inelastic scat- tering data,

    A. Accardi, L. T. Brady, W. Melnitchouk, J. F. Owens and N. Sato, “Constraints on large-x parton distributions from new weak boson production and deep-inelastic scat- tering data,” Phys. Rev. D93, no. 11, 114017 (2016), [arXiv:1602.03154 [hep-ph]]

    2016 arXiv

  44. [52]

    Diffractive parton distributions from the analysis with higher twist,

    K. J. Golec-Biernat and A. Luszczak, “Diffractive parton distributions from the analysis with higher twist,” Phys. Rev. D76, no. 11, 114014 (2007), [arXiv:0704.1608 [hep- ph]]

    2007 arXiv

  45. [53]

    Diffractive parton distributions from the analysis with higher twist,

    K. Golec-Biernat, “Diffractive parton distributions from the analysis with higher twist,” AIP Conf. Proc.1105, no. 1, 205 (2009),

    2009

  46. [54]

    Diffractive parton distributions from the saturation model,

    K. J. Golec-Biernat and M. Wusthoff, “Diffractive parton distributions from the saturation model,” Eur. Phys. J. C 20, 313 (2001), [hep-ph/0102093]

    2001 arXiv

  47. [55]

    Single-diffractive Drell?Yan pair pro- ductionattheLHC,

    F. A. Ceccopieri, “Single-diffractive Drell?Yan pair pro- ductionattheLHC,” Eur.Phys.J.C 77, no.1, 56(2017), [arXiv:1606.06134 [hep-ph]]

    2017 arXiv

  48. [56]

    Uncertainties of predictions from parton distributions. 2. Theoretical errors,

    A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, “Uncertainties of predictions from parton distributions. 2. Theoretical errors,” Eur. Phys. J. C35, 325 (2004), [hep-ph/0308087]

    2004 arXiv

  49. [57]

    Uncertainties of predictions from parton distribution functions. 2. The Hessian method,

    J. Pumplin, D. Stump, R. Brock, D. Casey, J. Huston, J. Kalk, H. L. Lai and W. K. Tung, “Uncertainties of predictions from parton distribution functions. 2. The Hessian method,” Phys. Rev. D65, 014013 (2001), [hep- ph/0101032]

    2001

  50. [58]

    Parton distributions for the LHC,

    A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt, “Parton distributions for the LHC,” Eur. Phys. J. C63, 189 (2009), [arXiv:0901.0002 [hep-ph]]

    2009 arXiv

  51. [59]

    Global Analysis of Nuclear Parton Distributions,

    D. de Florian, R. Sassot, P. Zurita and M. Stratmann, “Global Analysis of Nuclear Parton Distributions,” Phys. Rev. D85, 074028 (2012), [arXiv:1112.6324 [hep-ph]]

    2012 arXiv

  52. [60]

    Up- dating and optimizing error parton distribution function sets in the Hessian approach,

    C. Schmidt, J. Pumplin, C. P. Yuan and P. Yuan, “Up- dating and optimizing error parton distribution function sets in the Hessian approach,” Phys. Rev. D98, no. 9, 094005 (2018), [arXiv:1806.07950 [hep-ph]]

    2018 arXiv

  53. [61]

    EPS09: A New Generation of NLO and LO Nuclear Par- ton Distribution Functions,

    K. J. Eskola, H. Paukkunen and C. A. Salgado, “EPS09: A New Generation of NLO and LO Nuclear Par- ton Distribution Functions,” JHEP0904, 065 (2009), [arXiv:0902.4154 [hep-ph]]

    2009 arXiv

  54. [62]

    Measure- ment of dijet photoproduction for events with a lead- ing neutron at HERA,

    S. Chekanov et al. [ZEUS Collaboration], “Measure- ment of dijet photoproduction for events with a lead- ing neutron at HERA,” Nucl. Phys. B827, 1 (2010), [arXiv:0909.3032 [hep-ex]]

    2010 arXiv

  55. [63]

    Diffractive Di- jet Production with a Leading Proton inep Collisions at HERA,

    V. Andreev et al. [H1 Collaboration], “Diffractive Di- jet Production with a Leading Proton inep Collisions at HERA,” JHEP1505, 056 (2015), [arXiv:1502.01683 [hep-ex]]

    2015 arXiv

  56. [64]

    Measurement of Dijet Production in Diffractive Deep-Inelastic ep Scatter- ing at HERA,

    V. Andreev et al. [H1 Collaboration], “Measurement of Dijet Production in Diffractive Deep-Inelastic ep Scatter- ing at HERA,” JHEP1503, 092 (2015), [arXiv:1412.0928 [hep-ex]]

    2015 arXiv

  57. [65]

    Diffractive excitation inpp and pA collisions at high energies,

    V. P. Gonçalves, R. P. da Silva and P. V. R. G. Silva, “Diffractive excitation inpp and pA collisions at high energies,” Phys. Rev. D 100, no. 1, 014019 (2019), [arXiv:1905.00806 [hep-ph]]

    2019 arXiv

Pith tools

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