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
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]
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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Published date: 2017
Keywords:
Computational Physics
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Local EPrints ID: 436619
URI: http://eprints.soton.ac.uk/id/eprint/436619
PURE UUID: 1fdf08c7-75a7-4e9b-8f27-30ceb6fa7b4b
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Date deposited: 18 Dec 2019 17:31
Last modified: 05 May 2023 15:39
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Contributors
Creator:
Alessandro Georgoudis
Other:
Kasper Larsen
Other:
Yang Zhang
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