English

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

High Energy Physics - Theory 2018-08-02 v2 High Energy Physics - Phenomenology

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 {\sc Azurite} ({\bf A ZUR}ich-bred method for finding master {\bf I}n{\bf TE}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 {\sc Singular} and {\sc Mathematica}. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts.

Cite

@article{arxiv.1612.04252,
  title  = {Azurite: An algebraic geometry based package for finding bases of loop integrals},
  author = {Alessandro Georgoudis and Kasper J. Larsen and Yang Zhang},
  journal= {arXiv preprint arXiv:1612.04252},
  year   = {2018}
}

Comments

Version 1.1.0 of the package Azurite, with parallel computations. It can be downloaded from https://bitbucket.org/yzhphy/azurite/raw/master/release/Azurite_1.1.0.tar.gz

R2 v1 2026-06-22T17:22:28.707Z