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The Longitudinal Structure Function at the Third Order

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S. Moch (DESY, Zeuthen), J.A.M. Vermaseren (NIKHEF, Amsterdam), A. Vogt (Durham Univ., IPPP)

High Energy Physics - Phenomenology · Submitted 8 Nov 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We compute the complete third-order contributions to the coefficient functions for the longitudinal structure function F_L, thus completing the next-to-next-to-leading order (NNLO) description of unpolarized electromagnetic deep-inelastic scattering in massless perturbative QCD.

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arXiv IDhep-ph/0411112 (version 2)
Pith IDOR4RD552, Pith's permanent record of this paper and its review
CitationAmsterdam), A. Vogt (Durham Univ., Ippp), J.A.M. Vermaseren (NIKHEF, S. Moch (DESY, Zeuthen). "The Longitudinal Structure Function at the Third Order." arXiv:hep-ph/0411112 (2004). https://pith.science/paper/OR4RD552
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,989 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.92 · mentions code or data availability 0.04.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We compute the complete third-order contributions to the coefficient functions for the longitudinal structure function F_L, thus completing the next-to-next-to-leading order (NNLO) description of unpolarized electromagnetic deep-inelastic scattering in massless perturbative QCD. Our exact results agree with determinations of low even-integer Mellin moments and of the leading small-x terms in the flavour-singlet sector. In this letter we present compact and accurate parametrizations of the results and illustrate the numerical impact of the NNLO corrections.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We compute the complete third-order contributions to the coefficient functions for the longitudinal structure function F_L, thus completing the next-to-next-to-leading order (NNLO) description of unpolarized electromagnetic deep-inelastic scattering in massless perturbative QCD. contribution 0.95 0.96 0.82 asserted 1.00
s1 Our exact results agree with determinations of low even-integer Mellin moments and of the leading small-x terms in the flavour-singlet sector. result 0.95 0.79 0.15 asserted 1.00
s2 In this letter we present compact and accurate parametrizations of the results and illustrate the numerical impact of the NNLO corrections. contribution 0.98 0.93 0.14 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.62.

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The paper
Original abstract

We compute the complete third-order contributions to the coefficient functions for the longitudinal structure function F_L, thus completing the next-to-next-to-leading order (NNLO) description of unpolarized electromagnetic deep-inelastic scattering in massless perturbative QCD. Our exact results agree with determinations of low even-integer Mellin moments and of the leading small-x terms in the flavour-singlet sector. In this letter we present compact and accurate parametrizations of the results and illustrate the numerical impact of the NNLO corrections.

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References
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35 arXiv papers cite this in 48 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 · 33 sentences without a confident label

Uses its method or tool 5 papers
  • The inclusive predictions provided in Table [ref] are at N$^3$LO QCD+NLO EW accuracy and were obtained with proVBFHH v2.1.0 [ref] and Recola+MoCaNLO [ref] , respectively. proVBFHH is based on Hoppet [ref] and makes use of the parametrised two- and three-loop deep inelastic scattering coefficient functions from [ref] for the cross sections presented here.

    Electroweak Higgs boson pair production: Updated inclusive cross sections · Updated cross section values for VBF $hh$ production · 0.97

  • We compute all QCD corrections within the framework [ref] which is based on results presented in Refs. [ref] .

    On the impact of non-factorisable corrections in VBF single and double Higgs production · Setup · 0.99

  • The last of these uses the splitting functions calculated in Refs. [ref] and the (massless) coefficient functions for structure functions calculated in Refs. [ref] together with the massive coefficient functions described in Section [ref].

    Parton distributions for the LHC · Overview of theoretical framework · 0.97

Uses its data or values 2 papers
Compares with it 1 paper
Cites it as background 6 papers
  • Recently there has been a lot of progress in three-loop QCD calculations of the moments (and the corresponding anomalous dimensions) of deep inelastic structure functions [ref] ).

    Massless Propagators, $R(s)$ and Multiloop QCD · Anomalous Dimensions of twist 2 operators · 0.85

  • Exact N$^3$LO massless DIS coefficient functions have been known for several years [ref] , while massive coefficient functions are only available in various approximations [ref] .

    The Path to N$^3$LO Parton Distributions · N$^3$LO partonic cross-sections · 0.96

  • It is one of few processes for which there exists an exact factorisation theorem [ref] , and the massless unpolarised hard perturbative coefficients have been computed through an impressive three loops [ref] with progress on the four loop results presented recently in Ref. [ref] .

    disorder: Deep inelastic scattering at high orders · Introduction · 0.89

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