Multi-loop Integrand Reduction with Computational Algebraic Geometry

15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research

物理学;计算机科学

Badger, Simon^1 ; Frellesvig, Hjalte^2,3 ; Zhang, Yang^3

Theory Division, Physics Department, CERN, CH-1211 Geneva 23, Switzerland^1

Instituto Nazionale di Fisica Nucleare, Sezione di Roma, P.le Aldo Moro 2, 00185 Rome, Italy^2

Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark^3

关键词: Automated construction;    Computational algebraic geometry;    Computer algebra systems;    Gauge theory;    Mathematica packages;    Primary decomposition;    Recent progress;    Reduction method;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/523/1/012061/pdf
DOI  :  10.1088/1742-6596/523/1/012061

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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 Grobner 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.