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Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit

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Vittorio Del Duca, Alberto Frizzo, Fabio Maltoni

High Energy Physics - Phenomenology · Submitted 21 Sep 1999

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

The authors' main claim Finally, motivated by the reorganization of the color in the high-energy limit, we introduce a color decomposition of the purely gluonic tree amplitudes in terms of the linearly independent subamplitudes only.

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arXiv IDhep-ph/9909464 (version 2)
Pith ID6TAHX2OA, Pith's permanent record of this paper and its review
CitationAlberto Frizzo, Fabio Maltoni, Vittorio Del Duca. "Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit." arXiv:hep-ph/9909464 (1999). https://pith.science/paper/6TAHX2OA
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,114 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In the high-energy limit, we compute the gauge-invariant three-parton forward clusters, which in the BFKL theory constitute the tree parts of the NNLO impact factors. In the triple collinear limit, we obtain the polarized double-splitting functions. For the unpolarized and the spin-correlated double-splitting functions, our results agree with the ones obtained by Campbell-Glover and Catani-Grazzini, respectively. In addition, we compute the four-gluon forward cluster, which in the BFKL theory forms the tree part of the NNNLO gluonic impact factor. In the quadruple collinear limit we obtain the unpolarized triple-splitting functions, while in the limit of a three-parton central cluster we derive the Lipatov vertex for the production of three gluons, relevant for the calculation of a BFKL ladder at NNLL accuracy. Finally, motivated by the reorganization of the color in the high-energy limit, we introduce a color decomposition of the purely gluonic tree amplitudes in terms of the linearly independent subamplitudes only.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In the high-energy limit, we compute the gauge-invariant three-parton forward clusters, which in the BFKL theory constitute the tree parts of the NNLO impact factors. contribution 0.64 0.93 0.15 asserted 1.00
s1 In the triple collinear limit, we obtain the polarized double-splitting functions. result 0.91 0.96 0.09 asserted 1.00
s2 For the unpolarized and the spin-correlated double-splitting functions, our results agree with the ones obtained by Campbell-Glover and Catani-Grazzini, respectively. result 0.92 0.77 0.12 asserted 1.00
s3 In addition, we compute the four-gluon forward cluster, which in the BFKL theory forms the tree part of the NNNLO gluonic impact factor. result 0.50 0.95 0.10 asserted 1.00
s4 In the quadruple collinear limit we obtain the unpolarized triple-splitting functions, while in the limit of a three-parton central cluster we derive the Lipatov vertex for the production of three gluons, relevant for the calculation of a BFKL ladder at NNLL accuracy. result 0.94 0.96 0.11 asserted 1.00
s5 Finally, motivated by the reorganization of the color in the high-energy limit, we introduce a color decomposition of the purely gluonic tree amplitudes in terms of the linearly independent subamplitudes only. contribution 0.97 0.94 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.88.

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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

The paper
Original abstract

In the high-energy limit, we compute the gauge-invariant three-parton forward clusters, which in the BFKL theory constitute the tree parts of the NNLO impact factors. In the triple collinear limit, we obtain the polarized double-splitting functions. For the unpolarized and the spin-correlated double-splitting functions, our results agree with the ones obtained by Campbell-Glover and Catani-Grazzini, respectively. In addition, we compute the four-gluon forward cluster, which in the BFKL theory forms the tree part of the NNNLO gluonic impact factor. In the quadruple collinear limit we obtain the unpolarized triple-splitting functions, while in the limit of a three-parton central cluster we derive the Lipatov vertex for the production of three gluons, relevant for the calculation of a BFKL ladder at NNLL accuracy. Finally, motivated by the reorganization of the color in the high-energy limit, we introduce a color decomposition of the purely gluonic tree amplitudes in terms of the linearly independent subamplitudes only.

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References
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53 arXiv papers cite this in 103 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 · 73 sentences without a confident label

Builds on it 1 paper
Uses its method or tool 5 papers
  • These numerous double and single unresolved limits can be disentangled very elegantly by repeatedly exploiting the $N =1$ supersymmetry relation [ref] among the different triple collinear splitting functions [ref] .

    Antenna subtraction for gluon scattering at NNLO · Final-Final emitters · 0.97

  • It can be written in the most compact form by using an adjoin basis of SU$(N_c)$ generators [ref] .

    Collinear anatomy · One-loop integrand · 0.87

  • We find it convenient to use the DDM form [ref] for the tree amplitudes: [equation] where $^ abc = i√(2)f^abc$ are proportional to the standard structure constants in $SU(N_c)$, the gauge group of our Yang-Mills theory.

    A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory · Multi-peripheral colour decomposition · 0.99

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