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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.
0010-4655
203-215
Georgoudis, Alessandro
8df046a2-987e-4b85-a5ed-e1db0e66c4fa
Larsen, Kasper J.
49008353-d8ca-4de6-a377-e34ba737a3e7
Zhang, Yang
b165d56f-015b-4295-bbf4-72438baec173
Georgoudis, Alessandro
8df046a2-987e-4b85-a5ed-e1db0e66c4fa
Larsen, Kasper J.
49008353-d8ca-4de6-a377-e34ba737a3e7
Zhang, Yang
b165d56f-015b-4295-bbf4-72438baec173

Georgoudis, Alessandro, Larsen, Kasper J. and Zhang, Yang (2017) AZURITE: An algebraic geometry based package for finding bases of loop integrals. Computer Physics Communications, 221, 203-215. (doi:10.1016/j.cpc.2017.08.013).

Record type: Article

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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AZURITE: An algebraic geometry based package for finding bases of loop integrals - Accepted Manuscript
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Accepted/In Press date: 14 August 2017
e-pub ahead of print date: 23 August 2017
Published date: December 2017

Identifiers

Local EPrints ID: 416086
URI: http://eprints.soton.ac.uk/id/eprint/416086
ISSN: 0010-4655
PURE UUID: 7eeb6968-aa0d-4ef9-971c-0216d8fb2486

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Date deposited: 01 Dec 2017 17:30
Last modified: 22 Nov 2021 05:57

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Contributors

Author: Alessandro Georgoudis
Author: Kasper J. Larsen
Author: Yang Zhang

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