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 Gröbner 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.
Highlights
There has been huge progress recently in the programme to fully automate one-loop amplitude computations
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
Summary
There has been huge progress recently in the programme to fully automate one-loop amplitude computations. We describe the integrand reduction procedure valid in D-dimensions for an arbitrary loop amplitude. 2. Multi-loop integrand reduction with computational algebraic geometry The multi-loop amplitudes in this paper will refer to colour ordered primitive amplitudes which have a fixed ordering for the external legs and a well defined set of internal propagators.
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