English

Multi-loop Integrand Reduction with Computational Algebraic Geometry

High Energy Physics - Phenomenology 2015-06-17 v1

Abstract

We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Gr\"obner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the Macaulay2 computer algebra system and the Mathematica package BasisDet.

Keywords

Cite

@article{arxiv.1310.4445,
  title  = {Multi-loop Integrand Reduction with Computational Algebraic Geometry},
  author = {Simon Badger and Hjalte Frellesvig and Yang Zhang},
  journal= {arXiv preprint arXiv:1310.4445},
  year   = {2015}
}

Comments

Contribution to the 15th International Workshop on advanced computing and analysis techniques (ACAT 2013), 16-21 May, Beijing, China. 8 pages, 2 figures

R2 v1 2026-06-22T01:48:19.434Z