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Azurite: An algebraic geometry based package for finding bases of loop integrals

Azurite: An algebraic geometry based package for finding bases of loop integrals
Azurite: An algebraic geometry based package for finding bases of loop integrals
For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. We introduce the package Azurite (A ZUR ich-bred method for finding master I nTE grals), which efficiently finds a basis of this vector space. It constructs the needed integration-by-parts (IBP) identities on a set of generalized-unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems Singular and Mathematica. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts. In some cases, the basis obtained by Azurite may be slightly overcomplete.
Computational Physics
Mendeley
Georgoudis, Alessandro
8df046a2-987e-4b85-a5ed-e1db0e66c4fa
Larsen, Kasper
49008353-d8ca-4de6-a377-e34ba737a3e7
Zhang, Yang
b165d56f-015b-4295-bbf4-72438baec173
Georgoudis, Alessandro
8df046a2-987e-4b85-a5ed-e1db0e66c4fa
Larsen, Kasper
49008353-d8ca-4de6-a377-e34ba737a3e7
Zhang, Yang
b165d56f-015b-4295-bbf4-72438baec173

Georgoudis, Alessandro (2017) Azurite: An algebraic geometry based package for finding bases of loop integrals. Mendeley doi:10.17632/G7P7Z3W9DJ.1 [Dataset]

Record type: Dataset

Abstract

For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. We introduce the package Azurite (A ZUR ich-bred method for finding master I nTE grals), which efficiently finds a basis of this vector space. It constructs the needed integration-by-parts (IBP) identities on a set of generalized-unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems Singular and Mathematica. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts. In some cases, the basis obtained by Azurite may be slightly overcomplete.

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More information

Published date: 2017
Keywords: Computational Physics

Identifiers

Local EPrints ID: 436619
URI: http://eprints.soton.ac.uk/id/eprint/436619
PURE UUID: 1fdf08c7-75a7-4e9b-8f27-30ceb6fa7b4b

Catalogue record

Date deposited: 18 Dec 2019 17:31
Last modified: 18 Dec 2019 17:31

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Contributors

Creator: Alessandro Georgoudis
Other: Kasper Larsen
Other: Yang Zhang

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