High Energy Physics - Phenomenology · arXiv:hep-ph/0408068 v1 · submitted 4 Aug 2004
An algorithm for the high-energy expansion of multi-loop diagrams to next-to-leading logarithmic accuracy
The paper says
“We present an algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrts is much larger than the typical mass scale M, i.e. s>>M^2, while various different energy and mass parameters may be present.”
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Abstract
We present an algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrts is much larger than the typical mass scale M, i.e. s>>M^2, while various different energy and mass parameters may be present. In this region we perform an asymptotic expansion and, using sector decomposition, we extract the leading contributions resulting from ultraviolet and mass singularities, which consist of large logarithms log(s/M^2) and 1/\epsilon poles in D=4-2\epsilon dimensions. To next-to-leading accuracy, at L loops all terms of the form \alpha^L \epsilon^-k log^j(s/M^2) with j+k=2L and j+k=2L-1 are taken into account. This algorithm permits, in particular, to compute higher-order next-to-leading logarithmic electroweak corrections for processes involving various kinematical invariants of the order of hundreds of GeV and masses M_W \sim M_Z \sim M_H \sim M_t of the order of the electroweak scale, in the approximation where the masses of the light fermions are neglected.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.84 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.04 · 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 algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrt{s} is much larger than the typical mass scale M, i.e. s>>M^2, while various different energy and mass parameters may be present. | contribution 0.99 | 0.90 | 0.44 | asserted 1.00 |
| In this region we perform an asymptotic expansion and, using sector decomposition, we extract the leading contributions resulting from ultraviolet and mass singularities, which consist of large logarithms log(s/M^2) and 1/\epsilon poles in D=4-2\epsilon dimensions. | method 0.99 | 0.91 | 0.10 | asserted 1.00 |
| To next-to-leading accuracy, at L loops all terms of the form \alpha^L \epsilon^{-k} log^j(s/M^2) with j+k=2L and j+k=2L-1 are taken into account. | method 0.68 | 0.82 | 0.23 | asserted 1.00 |
| This algorithm permits, in particular, to compute higher-order next-to-leading logarithmic electroweak corrections for processes involving various kinematical invariants of the order of hundreds of GeV and masses M_W \sim M_Z \sim M_H \sim M_t of the order of the electroweak scale, in the approximation where the masses of the light fermions are neglected. | contribution 0.47 | 0.63 | 0.24 | asserted 0.58 |
What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.97
What was examined, and what was not
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,972 input tokens, $0.0002 reported.
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Cited by 4 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- SecDec: A general program for sector decomposition hep-ph · Nov 2010
- Electroweak Evolution Equations hep-ph · May 2005
- Analytic two-loop electroweak corrections at high energies hep-ph · Jun 2026
- Sector Decomposition hep-ph · Mar 2008
How the literature uses it
9 arXiv papers cite this in 10 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 5 papers
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The structure of such logarithmic contributions, referred to as Sudakov logarithms [ref] , and their factorisation properties were derived in full generality by Denner and Pozzorini [ref] at leading and next-to-leading logarithmic accuracy at both one- and two-loop order in the EW coupling expansion.
Automated evaluation of electroweak Sudakov logarithms in Sherpa · Introduction · 0.95
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Especially, general algorithms for the calculation at one and two-loop accuracy were derived in Refs. [ref] and [ref] , respectively.
One-loop electroweak Sudakov logarithms: a revisitation and automation · Introduction · 0.96
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In the literature, logarithmic electroweak corrections at the leading power have been intensively studied [ref] , and have been recently implemented in [ref] .
Analytic two-loop electroweak corrections at high energies · Introduction · 0.95
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