High Energy Physics - Phenomenology · arXiv:1007.0213 v1 · submitted 1 Jul 2010
Towards a Loop-Tree Duality at Two Loops and Beyond
The paper says
“We present an extension of the duality theorem, previously defined by S.”
from the abstract · picked out as the main claim by a classifier
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The paper
Abstract
We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here, the one-loop relation is rederived in a way which is more suitable for its extension to higher loop orders. This is shown in detail by considering the two-loop N-leg master diagram and by a short discussion of the four master diagrams at three loops, in this sketching the general structure of the duality theorem at even higher loop orders.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.96
What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.60 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We present an extension of the duality theorem, previously defined by S. | contribution 1.00 | 0.85 | 0.17 | asserted 0.96 |
| Catani et al. on the one-loop level, to higher loop orders. | contribution 0.75 | 0.37 | 0.23 | asserted 0.68 |
| The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. | background 1.00 | 0.09 | 0.09 | asserted 1.00 |
| Here, the one-loop relation is rederived in a way which is more suitable for its extension to higher loop orders. | method 0.62 | 0.93 | 0.10 | asserted 0.98 |
| This is shown in detail by considering the two-loop N-leg master diagram and by a short discussion of the four master diagrams at three loops, in this sketching the general structure of the duality theorem at even higher loop orders. | contribution 0.53 | 0.90 | 0.30 | asserted 0.98 |
What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 1.00
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
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- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,175 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 4 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Loops and trees hep-ph · Jul 2010
- Tree-Loop Duality Relation beyond simple poles hep-ph · Nov 2012
- A Tree-Loop Duality Relation at Two Loops and Beyond hep-ph · Jul 2010
- Theoretical foundations and applications of the Loop-Tree Duality in Quantum Field Theories hep-ph · Sep 2015
How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops.
Papers citing it · 2 sentences without a confident label
Cites it as background 2 papers
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The extension of the Duality Theorem to two loops has been discussed in detail in [ref] .
Tree-Loop Duality Relation beyond simple poles · Duality relation at one– and two–loops · 0.90
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Note: While this paper was being completed, works [ref] appeared in which $iϵ$ prescriptions are discussed in the context of cutting open higher-loop graphs.
Loops and trees · Summary and outlook · 0.88
What it cites · 6 sentences without a confident label
Builds on 1 paper
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In this talk, the extension of the loop–tree duality theorem derived in Ref. [ref] to higher loop orders is described, with the aim of extending the duality method to the computation of cross sections at NNLO or even higher orders.
From loops to trees by-passing Feynman's theorem · INTRODUCTION · 1.00
Cites as background 2 papers
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The question of the occurrence of real and complex masses in the propagators and their effect on the derivation of the duality theorem, has been discussed in [ref] .
From loops to trees by-passing Feynman's theorem · THE DUAL PROPAGATOR $G_D$ · 0.80
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In recent years, important efforts have been devoted to developing efficient methods for the calculation of multi–leg and multi–loop diagrams, realized, e.g., by unitarity–based methods or by traditional Feynman diagram approaches, [ref] .
The SM and NLO multileg working group: Summary report · INTRODUCTION · 0.95
Challenges and discussion
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