The diamond rule for multi-loop Feynman diagrams
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce...
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2015-06-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269315003524 |
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doaj-715718d97362445cac7e41f9283f5dd32020-11-25T01:56:12ZengElsevierPhysics Letters B0370-26932015-06-01746347350The diamond rule for multi-loop Feynman diagramsB. Ruijl0T. Ueda1J.A.M. Vermaseren2Nikhef Theory Group, Science Park 105, 1098 XG Amsterdam, The Netherlands; Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands; Corresponding author.Nikhef Theory Group, Science Park 105, 1098 XG Amsterdam, The NetherlandsNikhef Theory Group, Science Park 105, 1098 XG Amsterdam, The NetherlandsAn important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed. Keywords: Feynman integrals, Integration by parts identitieshttp://www.sciencedirect.com/science/article/pii/S0370269315003524 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
B. Ruijl T. Ueda J.A.M. Vermaseren |
| spellingShingle |
B. Ruijl T. Ueda J.A.M. Vermaseren The diamond rule for multi-loop Feynman diagrams Physics Letters B |
| author_facet |
B. Ruijl T. Ueda J.A.M. Vermaseren |
| author_sort |
B. Ruijl |
| title |
The diamond rule for multi-loop Feynman diagrams |
| title_short |
The diamond rule for multi-loop Feynman diagrams |
| title_full |
The diamond rule for multi-loop Feynman diagrams |
| title_fullStr |
The diamond rule for multi-loop Feynman diagrams |
| title_full_unstemmed |
The diamond rule for multi-loop Feynman diagrams |
| title_sort |
diamond rule for multi-loop feynman diagrams |
| publisher |
Elsevier |
| series |
Physics Letters B |
| issn |
0370-2693 |
| publishDate |
2015-06-01 |
| description |
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed. Keywords: Feynman integrals, Integration by parts identities |
| url |
http://www.sciencedirect.com/science/article/pii/S0370269315003524 |
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