Parton distributions incorporating QED contributions

A.D. Martin; R.G. Roberts; R.S. Thorne; W.J. Stirling

REVIEW

Parton distributions incorporating QED contributions

A.D. Martin, R.G. Roberts, W.J. Stirling, R.S. Thorne

High Energy Physics - Phenomenology · Submitted 2 Nov 2004 · 19 references

Pith's verdict: A careful, honest first global fit with QED-corrected DGLAP; the NuTeV shift and the photon PDF both hold up, though the isospin asymmetry is more input-model than the abstract lets on.

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arXiv IDhep-ph/0411040 (version 1)

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CitationA.D. Martin, R.G. Roberts, R.S. Thorne, W.J. Stirling. "Parton distributions incorporating QED contributions." arXiv:hep-ph/0411040 (2004). https://pith.science/paper/XIISK4OR

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Bottom line: this is the paper that put photon PDFs on the map, and it earns that place. It is the first fit that determines a QED-corrected PDF set from data rather than bolting QED evolution onto an existing QCD set, and it does so at both NLO and NNLO with the exact NNLO splitting functions. The ZEUS ep -> e gamma X comparison (6.2 +/- 1.2 pb against 5.64 pb measured) is a real check with only scale variation in the error band, and it discriminates current from constituent quark masses in the input model. That is evidence, not decoration. The NuTeV piece is sound in direction: radiation off high-x up quarks more than down quarks gives [delta Uv] < 0, [delta Dv] > 0, and a shift of about -0.002 in sin^2 theta_W, growing to -0.0029 at high Q^2. The authors are candid that the NLO chi^2 rises by about 15 and why, and that the NNLO chi^2 falls by 3. Where I would push back on the stress-test: it is numerically right that the input asymmetry at Q0^2 (-0.0024) is slightly larger than the evolved value at 2 GeV^2 (-0.00227), so the low-scale evolution dilutes rather than generates. But the input itself is leading-log QED emission from m_q to Q0, with log(Q0^2/m_q^2) around 10. That is a QED evolution effect, just done analytically in the model rather than numerically. So abstract:s2 is loose, not misleading. The real soft spot is the one the authors already flag: the size scales with that log, so it is sensitive to both the quark-mass choice (up to a factor of four) and Q0^2. The direction is robust; the magnitude is model-dependent, and the paper says so in Section 3 and again in Section 4. Two smaller things: the ZEUS comparison is a post-diction, and the NuTeV electroweak corrections they cite use mass regularisation that likely understates the effect. The authors note both. For anyone working on precision PDFs, electroweak corrections at hadron colliders, or the NuTeV anomaly, this is worth the time. Send it to referees.

Referee report

Significance

This is one of the first global PDF fits in which QED corrections are included consistently in the evolution and the input distributions are re-determined, rather than evolving a fixed QCD-only set upwards. The paper earns credit for two things in particular. First, the e p -> e gamma X prediction of Eq. (21) is a genuinely falsifiable, essentially parameter-free consequence of the fitted photon distribution, and it agrees with an independent ZEUS measurement; the comparison between the current-mass prediction (6.2 pb) and the constituent-mass prediction (3.6 pb) is a concrete, testable discriminator. Second, the quark-mass sensitivity of the isospin asymmetry is studied explicitly rather than hidden, and the resulting NuTeV shift is compared with the independent Lagrange-multiplier analysis of Ref. [8]. If the result holds, it is a useful input to the ongoing discussion of the NuTeV anomaly and a necessary ingredient for future electroweak precision calculations at hadron colliders.

Major objections (3)

[Abstract, sentence s2; Sections 3 and 4] The abstract attributes the isospin violation to 'the different DGLAP evolution of u and d type quarks', but the paper's own numbers indicate that the effect is dominated by the input condition rather than by evolution. From Eq. (8), upV - dnV = -epsilon(upV - 2dpV), so the input asymmetry is -epsilon times the denominator of Eq. (10), i.e. -0.0325 x 0.0746 = -0.0024 at Q0^2 = 1 GeV^2. The evolved value quoted in Section 4 is [delta Uv] = -0.002271 at Q^2 = 2 GeV^2, slightly smaller in magnitude. Evolution between 1 and 2 GeV^2 therefore dilutes the asymmetry by roughly 6% rather than generating it. The reason is structural: the input model of Eq. (5) carries log(Q0^2/m_q^2) of about 10.3 for m_u = 6 MeV, whereas evolution from Q0^2 to 2 GeV^2 contributes only log 2. This does not invalidate the physics conclusion, since the input model is itself a QED effect, but it does mean that the robustness of the central quantitative claim rests on the model of Eq. (5) and on the choice Q0^2 = 1 GeV^2, not on the evolution equations. I recommend rewording the abstract and introduction to distinguish the input-model contribution from the evolution contribution, and adding an explicit numerical decomposition of [delta Uv] and [delta Dv] into input and evolved pieces at, for example, Q^2 = 2 and 20 GeV^2, together with a statement of the Q0^2 dependence of the result.
[Section 4, Eqs. (15)-(16)] The NuTeV shift is the paper's headline number and needs two points tightened. First, on double counting: the paper correctly notes that the NuTeV electroweak corrections of Ref. [17] regularize the collinear singularities with a quark mass of order x m_p, whereas the calculations of Ref. [16] factor out the collinear singularities and are designed for QED-corrected partons. The manuscript states that 'there is certainly minimal double counting' but does not bound the residual ambiguity. Since the shift is only about 1 sigma of the anomaly, a quantitative estimate or bound on the double-counting uncertainty, for example by evaluating the shift with the two regularization schemes or by quoting the size of the large logarithm that is being counted twice, would materially strengthen the claim. Second, on arithmetic: evaluating Eq. (15) with the quoted moments at Q^2 = 2 GeV^2, [delta Uv] = -0.002271, [delta Dv] = 0.001124 and [V^-] = 0.4428, gives [(1 - (7/3) sin^2 theta_W)(-0.002271) - 0.001124] / (2 x 0.4428) = -0.0025, not the quoted -0.0018; at Q^2 = 20 GeV^2 the same evaluation gives about -0.0029 rather than -0.0021. The ratio of the two evaluations is stable at about 1.4, which suggests a convention or normalization difference rather than a random slip. Please reconcile the quoted shifts with Eq. (15) and the tabulated moments, or state explicitly what additional factor enters.
[Section 4, fit quality discussion] The NLO fit with QED corrections has chi^2 about 15 higher than the standard NLO fit, and the paper attributes this to the photon taking 'the very small amount of momentum' from the gluon, together with a shape effect from preferential radiation off high-x up quarks. These two explanations pull in different directions, and the manuscript does not give the numbers needed to apportion them. Please quote the momentum fraction carried by the photon, integral dx x gamma_p(x, Q^2), at Q0^2 = 1 GeV^2 and at Q^2 = 20 GeV^2, and state how much of the 15-unit increase comes from the momentum shift (through the gluon normalization and the small change in alpha_S) and how much from the altered high-x shape that affects the BCDMS proton fit. Relatedly, the abstract's phrase 'the quality of the fit is essentially unchanged' sits uneasily with a 15-unit increase at NLO; the text is candid about this, but the abstract should reflect it.

Minor objections (10)

[Section 3, Eqs. (9)-(10)] The sign of the photon-difference term in Eqs. (9) and (10) appears inconsistent with momentum conservation, Eq. (4), and with the quoted positive value epsilon = 0.0325. Subtracting the two relations in Eq. (4) gives integral dx x(upV + dpV - dnV - unV) = integral dx x(gamma_n - gamma_p), whereas Eq. (9) is printed with gamma_p - gamma_n; with Eq. (8) the left-hand side equals -(1/2) epsilon integral dx x(upV - 2dpV), so the printed Eq. (10) would give a negative epsilon. Since the quoted value is positive and the physics requires it to be, this looks like a typographical sign flip in both equations; please check and correct.
[Section 4, Eq. (15)] The typesetting of Eq. (15) is ambiguous: the string '[delta Dv]2[V^-]' could be read as a denominator or as a product. Please set the whole correction as a single fraction with an explicit denominator, and use consistent notation for the valence distributions (upv, dnv in Eq. (16) versus upV, dpV elsewhere).
[Section 4 and the MRSTQED04 sets] No table of the fitted input parameters at Q0^2 is given; the reader is referred to the Durham web address. For a global-fit paper a table of the input coefficients, or at least the values of the parameters that differ from the standard MRST fit, would make the result reproducible independently of the website.
[Section 4] The QED-corrected sets are quoted without PDF uncertainty estimates. The NuTeV shift and the ZEUS prediction of Eq. (21) would be more useful with an uncertainty band; the paper already quotes a scale variation for the latter, and a comparison with the eigenvector-based limits of Ref. [8] would be natural.
[Section 4] The actual values of alpha_S(M_Z^2) obtained in the NLO and NNLO QED fits are not stated; only the change relative to the standard fits ('about 0.0002') is given. Please quote the numbers.
[Section 5, Eq. (18)] Please state the frame and the approximations used in deriving Eq. (18) for x_gamma, since the expression mixes the electron and proton beam energies in a way that is not transparent from the text.
[Section 5] The statement that the ZEUS agreement lends 'strong support' to the choice of current quark masses is somewhat stronger than the numbers support: with the quoted scale uncertainty the current-mass prediction is 6.2 +/- 1.2 pb against 3.6 pb for constituent masses, a separation of roughly 2 sigma. 'Supportive' or 'consistent with a preference for' would be more proportionate.
[References] Reference [6] is printed as Phys. Lett. B90 (2004) 190; the journal volume should presumably be B590.
[Figures 2 and 3] The photon curve is difficult to distinguish from the sea-quark curves at small x in Figs. 2 and 3. A distinct line style, or an inset showing x gamma separately, would make the comparison with the sea quarks at high x, which is one of the paper's qualitative points, easier to read.
[Text] A few typographical errors should be corrected: 'emmit ted' in the Introduction, 'signﬁcant' in Section 2, and 'mases' in Section 4.

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The paper

The paper claims

Including QED in a global parton fit produces isospin violation that shifts the NuTeV weak mixing angle by about 0.002 and generates a measurable photon distribution in the proton.

The reading

The paper asks whether QED radiation can be folded consistently into a global determination of parton distributions, rather than added afterward to a QCD-only fit. The authors extend the standard DGLAP evolution equations with photon emission from quarks and a photon parton distribution, then refit deep-inelastic and related hard-scattering data at NLO and NNLO. The fit quality barely changes, but the QED evolution treats up and down quarks differently, so the proton and neutron are no longer exact isospin mirrors. The authors argue that this isospin violation goes in the direction needed to reduce the NuTeV $�sin^2�theta_W$ anomaly by roughly $0.002$, about one standard deviation of the discrepancy, and that the same evolution predicts a photon distribution whose $ep�to e�gamma X$ rate agrees with the ZEUS measurement.

What carries the argument

The machinery is the QED-extended DGLAP system in Eq. (1): quark evolution gains $�tilde P_{qq}$ and $P_{q�gamma}$ terms, gluon evolution is unchanged at this order, and a new photon distribution evolves through $P_{�gamma q}$ and $P_{�gamma�gamma}$. The initial photon distribution is modelled by one-photon emission off valence-like constituent quarks, Eq. (5), and the isospin-violating input is parametrised by $�epsilon$ in Eq. (8), fixed by momentum conservation through Eq. (10). That $�epsilon$ is what translates the QED splitting into a definite valence-quark asymmetry and hence into the NuTeV shift.

Extended reading notes

Core claim

The central claim is that a global parton fit with $�mathcal{O}(�alpha_{�mathrm{QED}})$ DGLAP evolution yields two concrete consequences without spoiling the fit. First, because photons couple to quark charge squared, up-type and down-type quarks evolve differently, producing $u^p�neq d^n$; the induced valence asymmetry shifts the value of $�sin^2�theta_W$ extracted from NuTeV by $-0.0018$ at $Q^2=2$ GeV$^2$, $-0.0021$ at $20$ GeV$^2$, and $-0.0029$ at $20000$ GeV$^2$, in the direction that reduces the anomaly. Second, the evolution generates photon parton distributions $�gamma^{p,n}(x,Q^2)$; convoluting $�gamma^p$ with QED Compton scattering predicts $�sigma(ep�to e�gamma X)=6.2�pm1.2$ pb for the ZEUS cuts, compared with the measured $5.64$ pb. The authors present these as the physical payoff of treating QED collinear logarithms as part of the parton distribution rather than as an ad hoc correction.

Load-bearing premise

The size of the isospin violation, and therefore the NuTeV shift, depends on the model for the initial photon distribution and on using current quark masses ($m_u=6$ MeV, $m_d=10$ MeV) in that model; the paper itself notes that constituent masses of $300$ MeV give $�epsilon=0.0074$ instead of $0.0325$ and can reduce the effect by up to a factor of about four.

Editorial extensions

If this is right

If the QED-corrected fit is right, about $0.002$ of the $0.005$ NuTeV discrepancy comes from isospin violation generated by QED evolution, leaving less room for new physics.
The proton and neutron photon distributions become measurable targets at HERA through $eN�to e�gamma X$, giving a direct handle on the QED sector of the parton model.
Electroweak corrections to hadron-collider cross sections can consistently absorb collinear photon logarithms into QED-corrected parton distributions, avoiding double counting with explicit photon radiation.
The valence asymmetry is scale-dependent, so the extracted $�sin^2�theta_W$ shift grows with $Q^2$ from $-0.0018$ at $2$ GeV$^2$ to $-0.0029$ at $20000$ GeV$^2$.

Reading between the lines

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

A useful cross-check would be to repeat the fit with the photon input from the alternative evolution estimate in Eq. (12) rather than the valence-like model in Eq. (5); the paper says the results are similar, but a full fit would quantify how much of the NuTeV shift is model-independent.
Because the shift grows with $Q^2$, comparing low-$Q^2$ and high-$Q^2$ extractions of the same weak angle could in principle separate a QED-isospin contribution from a genuine contact interaction.
The ZEUS agreement is currently a one-bin comparison; extending it to a differential $�gamma^p(x_�gamma,Q^2)$ measurement would turn the photon parton distribution from a prediction into a constrained quantity.
If constituent quark masses were the right scale for photon radiation, both the photon distribution and the isospin asymmetry would shrink, so the same data that discriminate between $3.6$ pb and $6.2$ pb also bear on the mass-scale choice.

Original abstract

We perform a global parton analysis of deep inelastic and related hard-scattering data, including ${\cal O}(\alpha_{\rm QED})$ corrections to the parton evolution. Although the quality of the fit is essentially unchanged, there are two important physical consequences. First, the different DGLAP evolution of u and d type quarks introduces isospin violation, i.e. $u^p \neq d^n$, which is found to be unambiguously in the direction to reduce the NuTeV $\sin^2\theta_W$ anomaly. A second consequence is the appearance of photon parton distributions $\gamma(x,Q^2)$ of the proton and the neutron. In principle these can be measured at HERA via the deep inelastic scattering processes $e N \to e\gamma X$; our predictions are in agreement with the present data.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,354 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.54 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We perform a global parton analysis of deep inelastic and related hard-scattering data, including ${\cal O}(\alpha_{\rm QED})$ corrections to the parton evolution. Although the quality of the fit is essentially unchanged, there are two important physical consequences. First, the different DGLAP evolution of u and d type quarks introduces isospin violation, i.e. $u^p \neq d^n$, which is found to be unambiguously in the direction to reduce the NuTeV $\sin^2\theta_W$ anomaly. A second consequence is the appearance of photon parton distributions $\gamma(x,Q^2)$ of the proton and the neutron. In principle these can be measured at HERA via the deep inelastic scattering processes $e N \to e\gamma X$; our predictions are in agreement with the present data.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We perform a global parton analysis of deep inelastic and related hard-scattering data, including ${\cal O}(\alpha_{\rm QED})$ corrections to the parton evolution.	contribution 0.59	0.96	0.07	asserted 0.98
s1	Although the quality of the fit is essentially unchanged, there are two important physical consequences.	result 0.53	0.67	0.10	asserted 1.00
s2	First, the different DGLAP evolution of u and d type quarks introduces isospin violation, i.e. $u^p \neq d^n$, which is found to be unambiguously in the direction to reduce the NuTeV $\sin^2\theta_W$ anomaly.	result 0.71	0.92	0.43	asserted 1.00
s3	A second consequence is the appearance of photon parton distributions $\gamma(x,Q^2)$ of the proton and the neutron.	result 0.99	0.79	0.12	asserted 1.00
s4	In principle these can be measured at HERA via the deep inelastic scattering processes $e N \to e\gamma X$; our predictions are in agreement with the present data.	result 0.61	0.75	0.08	hedged possibility 0.60

What kind of paper the classifier reports this is: theoretical result 0.57 · evidence from analysis of existing data 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The ratio of valence quarks in the neutron and proton at t

**Figure 2.** The parton distributions in the proton at

**Figure 3.** The parton distributions in the neutron at

**Figure 4.** The difference between the isospin exchanged valence qua

**Figure 5.** Schematic diagram for the deep inelastic scattering proce

Figures reproduced from arXiv:hep-ph/0411040 by the authors.

References

Works cited (19)

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A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Eur. Phys . J. C35 (2004) 325

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D.Yu. Bardin and V.A. Dokuchaeva, JINR E2-86-260 (1986)

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K.-P.O. Diener, S. Dittmaier and W. Hollik, Phys. Rev. D69 (2004) 073005; A.B. Arbuzov, D.Yu. Bardin and L.V. Kalinovskaya, hep-ph/0407203

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U. Baur, S. Keller and D. Wackeroth, Phys. Rev. D59 (1999) 013002; S. Dittmaier and M. Kr¨ amer, Phys. Rev. D65 (2002) 073007; U. Baur and D. Wackeroth, hep-ph/0405191

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U. Baur, O. Brein, W. Hollik, C. Schappacher and D. Wackeroth, P hys. Rev. D65 (2002) 033007

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M. L. Ciccolini, S. Dittmaier and M. Kramer, Phys. Rev. D68 (2003) 073003

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A. De Rujula, R. Petronzio and A. Savoy-Navarro, Nucl. Phys. B154 (1979) 394; J. Kripfganz and H. Perlt, Zeit. Phys. C41 (1988) 319; J. Bl¨ umlein, Zeit. Phys.C47 (1990) 89

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G.P. Zeller et al. , Phys. Rev. Lett. 88 (2002) 091802

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A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, presente d at the 12th Inter- national Workshop on Deep Inelastic Scattering (DIS 2004), hep- ph/0407311

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[10]

S. Moch, J.A.M. Vermaseren and A. Vogt, Nucl. Phys. B688 (2004) 101. 13

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A. Vogt, S. Moch and J.A.M. Vermaseren, Nucl. Phys. B691 (2004) 129

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A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, hep-ph/ 0410230

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See all 61 Pith citations

How later papers used it

107 later papers cite it

Evidence: substantial. 101 of the citing papers share no author with it, and 31 of those carry a confident label from Pith's citation classifier.

Pith read 27 of the 162 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

11 later papers by other authors are listed below: 2 used its method or tool, 8 used its data or values and 1 compared its own results with it.

Uses its method or tool 2 of 10 papers with this label

Used a collinear approach with this paper's photon PDFs to calculate inelastic contributions.

Can the diphoton enhancement at 750 GeV be due to a neutral technipion? (2016) · 0.99 · paraphrased: the licence does not allow quoting
Followed this paper for MRST and used the envelope spanned by assuming current quark masses and constituent quark masses.

Doubly Charged Higgs Boson Production at Hadron Colliders (2019) · 0.88 · paraphrased: the licence does not allow quoting

Uses its data or values 8 of 13 papers with this label

Used this paper's MRST2004QED set of parton density functions to compute all the hadron-level cross sections.

Precision electroweak calculation of the production of a high transverse-momentum lepton pair at hadron colliders (2007) · 0.85 · paraphrased: the licence does not allow quoting
Used this paper's standard parameterization of the parton distribution functions as an input.

Parton distribution functions and quark orbital motion (2007) · 0.94 · paraphrased: the licence does not allow quoting
Used this paper's MRST2004 parton distribution functions in its calculations.

Charged current reactions in the NuSOnG and a test of neutrino-W couplings (2008) · 0.83 · paraphrased: the licence does not allow quoting
Used this paper's MRST set, along with other sets, for the photon PDF inside the proton.

NNLO QCD$\oplus$QED corrections to Higgs production in bottom quark annihilation (2019) · 0.82 · paraphrased: the licence does not allow quoting
Used this paper's standard PDF parameterization as the unpolarized input.

Images of Quark Intrinsic Motion in Covariant Parton Model (2010) · 0.81 · paraphrased: the licence does not allow quoting
Used this paper's MRST2004 parton distribution functions in its calculations.

Probe of anomalous neutrino couplings to W and Z in medium energy setup of a beta-beam facility (2008) · 0.86 · paraphrased: the licence does not allow quoting
Reported a luminosity ratio for this paper's MRST2004 among other sets.

Constraints on 750 GeV colorless Q-onia from running couplings (2016) · 0.91 · paraphrased: the licence does not allow quoting
Used this paper's standard PDF parameterization as the input.

Quark intrinsic motion and the link between TMDs and PDFs in covariant approach (2009) · 0.92 · paraphrased: the licence does not allow quoting

Compares with it 1 of 9 papers with this label

Compared its own result with the QED evolution used in this paper's determination of the MRST2004QED parton distributions.

Parton distribution functions with QED corrections (2015) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

91 arXiv papers cite this in 141 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 79 sentences without a confident label

Builds on it 1 paper

Similar to the DGLAP evolution equation for PDFs in QCD [ref] [equation] with $i,j=q,q̅,g$, DGLAP-type evolution equations for PDFs in the joint QED and QCD factorization approach have the same form as that in Eq. ([ref]), but, the parton indices $i,j$ need to be extended to include leptons, $l,l̅,γ$, with $l=e,μ,τ$ to include the evolution in both QCD and QED, as well as the mixing evolution from QCD to QED or vise versa [ref] .

Factorized QED and QCD Contribution to Deeply Inelastic Scattering · Numerical Results and Impacts · 0.88

Uses its method or tool 9 papers

In this work, we adopt the isospin symmetric approximation (ISA) to relate the proton and neutron quark PDFs, [equation] Due to the QED evolution effect, a small isospin violation will be generated through the $γ→qq̅$ splitting [ref] , which will be properly addressed later with the CT18qed approach [ref] .

The Photon Content of the Neutron · The inelastic photon PDF with the LUXqed approach: CT18lux · 0.81
In particular, DY processes were analyzed using NNLOjet [ref] , Pythia [ref] , Herwig [ref] , DYNNLO [ref] , FEWZ [ref] .

Angular coefficients of the Drell-Yan process across different rapidity and kinematical ranges · Introduction · 0.91
To calculate inelastic contributions we use collinear approach with photon PDFs [ref] .

Can the diphoton enhancement at 750 GeV be due to a neutral technipion? · $2 →1$ subprocess · 0.99

Uses its data or values 12 papers

The set of parton density functions used to compute all the hadron-level cross sections is $MRST2004QED$ [ref] .

Precision electroweak calculation of the production of a high transverse-momentum lepton pair at hadron colliders · Numerical results · 0.85
The relation ([ref]) can be written as [equation] where [equation] At the same time Eq.([ref]) can be replaced by [equation] which after inserting from Eq. ([ref]) gives [equation] This equality together with the relation ([ref]) give [equation] or equivalently [equation] Now, using the input on the $q(x)$ [ref] and $Δq(x)$ [ref] (LO at the scale $4GeV^2$) one can calculate the distributions $ΔP_q,P_q,P_q^±$ and related structure functions $Δf_q,f_q$ and $f_q^±$.

Parton distribution functions and quark orbital motion · Momentum distribution from structure function $g_1$ · 0.95
In our calculations parton distribution functions of Martin, Roberts, Stirling and Thorne (MRST2004) [ref] have been used.

Charged current reactions in the NuSOnG and a test of neutrino-W couplings · cross sections and numerical analysis · 0.83

Compares with it 7 papers

We also compare our PDFs with the first generation QED PDFs, i.e., MRST2004qed [ref] , CT14qed [ref] , and NNPDF2.3qed [ref] in Fig. [ref], which shows a significant improvement in precision, thanks to the LUXqed formalism.

The Photon Content of the Neutron · Conclusions · 1.00
This reduced the uncertainty by a factor of about forty compared to previous photon PDF determinations, such as MRST2004qed [ref] and NNPDF23_qed [ref] , which relied on fits to LHC data and/or modelling.

The photon parton distribution function: updates and applications · Introduction · 1.00
At this point we compare to the QED evolution used in the determination of the MRST2004QED parton distributions [ref] .

Parton distribution functions with QED corrections · Comparison with MRST2004QED · 1.00

Cites it as support 1 paper

Therefore, off-peak Drell-Yan production provides important constraints on the photon PDF [ref] for PDF fits which account for QED corrections [ref] .

The PDF4LHC report on PDFs and LHC data: Results from Run I and preparation for Run II · High and low mass Drell-Yan production · 0.96

Cites it as background 26 papers

Currently, from literature we observe that only the photon content of the proton has been determined based either on model assumptions [ref] , the MRST2004QED set, or on a fit to data [ref] , the NNPDF2.3QED, but no attempt to estimated the lepton PDFs has ever been tried.

Parton distribution functions with QED corrections · Lepton PDFs · 0.87
While weak [ref] , QED [ref] and EW (weak+QED) [ref] corrections to $$ production at hadron colliders have been known for quite some time and the effect of Sudakov logarithms has been quantified and studied, the impact of photon-induced subprocesses has been addressed only in [ref] for only the $gγ$ channel at LO and using the only PDF set with the photon distribution available at that time, i.e., MRST2004QED [ref] .

The impact of the photon PDF and electroweak corrections on $t \bar t$ distributions · Introduction · 0.93
Solutions to the evolution equations including corrections at LO in QED were presented in [ref] and different fits of the parton distributions including these corrections were performed in [ref] .

QED corrections to parton distributions and Altarelli-Parisi splitting functions in the polarized case · Introduction · 0.95

Discussion

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