2012

Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods

Zhang, Yang

Understand

We present an algorithm for the integrand-level reduction of multi-loop amplitudes of renormalizable field theories, based on computational algebraic geometry.

This algorithm uses (1) the Gr\"obner basis method to determine the basis for integrand-level reduction, (2) the primary decomposition of an ideal to classify all inequivalent solutions of unitarity cuts.
The resulting basis and cut solutions can be used to reconstruct the integrand from unitarity cuts, via polynomial fitting techniques.
The basis determination part of the algorithm has been implemented in the Mathematica package, BasisDet.

Built on

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