Multi-loop Integrand Reduction with Computational Algebraic Geometry

摘要

We discuss recent progress in multi-loop integrand reduction methods.Motivated by the possibility of an automated construction of multi-loopamplitudes via generalized unitarity cuts we describe a procedure to obtain ageneral parameterisation of any multi-loop integrand in a renormalizable gaugetheory. The method relies on computational algebraic geometry techniques suchas Gr\"obner bases and primary decomposition of ideals. We present some resultsfor two and three loop amplitudes obtained with the help of the Macaulay2computer algebra system and the Mathematica package BasisDet.