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Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution

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Aude Gehrmann-De Ridder, Thomas Gehrmann, E. W. N. Glover, Joao Pires

High Energy Physics - Phenomenology · Submitted 30 Jan 2013 · 46 references

Pith's verdict: A genuine first — NNLO jet production at a hadron collider — but the finite numbers rest on an unpublished companion and no validation of the finite remainder.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

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arXiv ID1301.7310 (version 1)
Pith IDT7Z4YPUJ, Pith's permanent record of this paper and its review
CitationAude Gehrmann-De Ridder, E. W. N. Glover, Joao Pires, Thomas Gehrmann. "Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution." arXiv:1301.7310 (2013). https://pith.science/paper/T7Z4YPUJ
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The paper

The paper claims

The paper reports the first next-to-next-to-leading-order QCD calculation of a jet observable at a hadron collider, carried out in the purely gluonic channel with antenna subtraction, and shows the residual scale uncertainty shrinking by a

The reading

The paper sets out to compute the next-to-next-to-leading order (NNLO) correction in QCD to jet production at a proton-proton collider, restricted for now to the purely gluonic channel at leading colour. Jets are the workhorse observable of the LHC: they constrain the gluon content of the proton and give one of the cleanest handles on the strong coupling $a_s$, yet the theory error from missing higher orders has been larger than the experimental error, which is what has kept jet data out of NNLO fits. The authors implement the calculation in a parton-level event generator, NNLOJET, whose three integration channels each pair a double-real, real-virtual or two-loop virtual matrix element with a matching antenna subtraction term, so that each bracket in Eq. (1) is finite. They then present the inclusive jet $p_T$ spectrum, its scale dependence, a double-differential $p_T$ and rapidity spectrum, and the dijet invariant mass at $/sqrt{s}=8$ TeV. If the cancellation holds, this is the first demonstration that a jet-defined observable at a hadron collider can be computed at NNLO.

What carries the argument

Antenna subtraction. An antenna function is a compact analytic object that captures all the unresolved radiation emitted between a pair of hard radiator partons, so that subtracting it from the corresponding matrix element leaves a finite remainder that can be integrated numerically, while the subtraction term itself can be integrated analytically and added back to the virtual contributions to cancel the explicit infrared poles. At NNLO the scheme needs antenna functions with up to two unresolved partons at tree level and one unresolved parton at one loop, and for hadron collider observables one or both radiators may sit in the initial state. The practical carrier is the phase-space decomposition: the three-parton channel is split into 6 wedges and the four-parton channel into 30, each wedge containing only a subset of the infrared singular regions, with several configurations generated inside each wedge by rotating unresolved pairs about their common axis so that the subtraction term converges locally to the matrix element. Symmetry of the all-gluon final state makes many wedges identical and speeds up the evaluation.

Extended reading notes

Core claim

The claim is that a massless jet observable at a hadron collider has now been computed at NNLO in QCD, in the all-gluon channel. Combining the two-loop virtual $2/rightarrow 2$ corrections, the one-loop virtual $2/rightarrow 3$ corrections and the tree-level $2/rightarrow 4$ corrections with their respective antenna subtraction terms, the authors obtain finite distributions for proton-proton collisions at $/sqrt{s}=8$ TeV with the anti-$k_T$ algorithm at $R=0.7$, $|y|<4.4$ and $p_{T1}>80$ GeV, using the MSTW08NNLO gluon distribution. For the central scale $/mu=p_{T1}$ they find the NNLO/NLO $k$-factor to be roughly flat in $p_T$, a 15-25% increase over NLO, and 15-20% for the dijet invariant mass at $/mu=2p_{T1}$; the double-differential $k$-factors run from about 25% at low $p_T$ to 12% at high $p_T$ across the three central rapidity slices shown. The scale dependence of the inclusive cross section is reported as vastly reduced. The authors state plainly that the all-gluon channel alone cannot be compared with experimental data, and that its purpose is to establish the method and gauge the potential size of NNLO effects.

Load-bearing premise

The load-bearing premise is that the antenna subtraction terms built in the authors' earlier papers cancel every infrared pole for these jet-defined observables, which is asserted by citation rather than re-derived or checked against an independent calculation, and no comparison of the generator's NLO limit with the published all-gluon NLO jet results is shown.

Editorial extensions

If this is right

  • The authors state that the same techniques can be applied to the quark contributions, which would turn the all-gluon demonstration into a full NNLO description of dijet production.
  • With the scale band collapsing as shown, jet data become usable in global parton-distribution fits at NNLO rather than only at NLO, and the theory error on $a_s$ extracted from jet cross sections stops being dominated by scale variation.
  • Because the correction is presented differentially in $p_T$ and rapidity, the size of the NNLO shift can be tracked from central to forward jets, which is where the gluon density is least constrained.
  • The exclusive dijet invariant mass distribution, the observable most directly tied to PDF fits, now has an NNLO prediction in this channel, with a $k$-factor flat in $m_{jj}$.
  • The wedge decomposition and local convergence strategy established here is a reusable template for other hadron-collider observables computed with initial-state radiators.

Reading between the lines

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

  • The quoted 15-25% $k$-factor is not the full NNLO correction to dijet production: it is the gluonic channel only, and quark-initiated subprocesses dominate at high $p_T$ and at large rapidity, so the true shift may differ in both normalisation and shape from what is shown here.
  • If the scale band genuinely shrinks as far as the figures indicate, the binding constraint on jet-based determinations of $a_s$ would move from scale variation to parton distributions and non-perturbative corrections, which changes what the next round of measurements should target.
  • An independent implementation of the same all-gluon channel by a different subtraction method would be a cheap and decisive cross-check, and would also test whether the wedge-based local convergence is doing any hidden work.
  • A natural next test is whether the generator, run in its NLO limit, reproduces the published all-gluon NLO jet results; agreement there would isolate any residual issue to the genuinely new two-loop and double-real pieces.
Original abstract

We report the calculation of next-to-next-to-leading order (NNLO) QCD corrections in the purely gluonic channel to dijet production and related observables at hadron colliders. Our result represents the first NNLO calculation of a massless jet observable at hadron colliders, and opens the path towards precision QCD phenomenology with the LHC.

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, 2,314 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.96 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.36 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We report the calculation of next-to-next-to-leading order (NNLO) QCD corrections in the purely gluonic channel to dijet production and related observables at hadron colliders. Our result represents the first NNLO calculation of a massless jet observable at hadron colliders, and opens the path towards precision QCD phenomenology with the LHC.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We report the calculation of next-to-next-to-leading order (NNLO) QCD corrections in the purely gluonic channel to dijet production and related observables at hadron colliders. contribution 0.99 0.96 0.41 asserted 1.00
s1 Our result represents the first NNLO calculation of a massless jet observable at hadron colliders, and opens the path towards precision QCD phenomenology with the LHC. interpretation 0.91 0.86 0.64 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.54.

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
  • C citations
  • R cross-paper relations

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. FIG. 1: Inclusive jet transverse energy distribution,
Figure 2. FIG. 2: Scale dependence of the inclusive jet cross section fo
Figure 3. FIG. 3: The doubly differential inclusive jet transverse ene
Figure 4. shows the double-differential k-factors for the distribution in
Figure 5. FIG. 5: Exclusive dijet invariant mass distribution,

Figures reproduced from arXiv:1301.7310 by the authors.

References
How later papers used it

70 later papers cite it

Evidence: substantial. 59 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 90 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

Uses its method or tool 2 of 9 papers with this label · 2 by the same authors

By the same authors

How the literature uses it

70 arXiv papers cite this in 90 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 · 55 sentences without a confident label

Uses its method or tool 9 papers
  • Jet data is included in the NNLO fits using the improved threshold approximation [ref] , validated with the exact NNLO calculation of the gluon-gluon channel [ref] , which allows to carefully select only those data points with kinematics for which the threshold approximation is close enough to the exact calculation [ref] .

    Parton distributions based on a maximally consistent dataset · The NNPDF3.0 sets · 0.98

  • We would like to thank Joao Pires for many useful and stimulating discussions, Roberto Bonciani for providing us with the numerical code to evaluate the virtual contributions [ref] , and Thomas Gehrmann for adapting the phase space generator used in the di-jet calculation of [ref] to top pair production.

    Light fermionic NNLO QCD corrections to top-antitop production in the quark-antiquark channel · Conclusions · 0.99

  • [Recent progress making use of new unitarity-based techniques will probably allow for complete NNLO results in a near future [ref] .] NLO QCD corrections are implemented in [ref] , that allows to evaluate the 3- and 2-jets cross sections at the parton-level within the Standard Model.

    Constraining new coloured matter from the ratio of 3- to 2-jets cross sections at the LHC · The 32 observable · 0.86

Uses its data or values 1 paper
Cites it as support 2 papers
Cites it as background 21 papers

Discussion

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