Abstract
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 Gr̈obner 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. The primary decomposition part can be readily carried out by algebraic geometry softwares, with the output of the package BasisDet. The algorithm works in both D = 4 and D = 4-2∈ dimensions, and we present some two and three-loop examples of applications of this algorithm.
| Original language | English |
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| Journal | Journal of High Energy Physics (Online) |
| Volume | 2012 |
| Issue number | 9 |
| Pages (from-to) | 042 |
| ISSN | 1126-6708 |
| DOIs | |
| Publication status | Published - 1 Sept 2012 |