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arXiv · 1509.08897

Scattering Equations and Global Duality of Residues

Mads Sogaard·Yang Zhang
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Abstract

We examine the polynomial form of the scattering equations by means of computational algebraic geometry. The scattering equations are the backbone of the Cachazo-He-Yuan (CHY) representation of the S-matrix. We explain how the Bezoutian matrix facilitates the calculation of amplitudes in the CHY formalism, without explicitly solving the scattering equations or summing over the individual residues. Since for $n$-particle scattering, the size of the Bezoutian matrix grows only as $(n-3)\times(n-3)$, our algorithm is very efficient for analytic and numeric amplitude computations.

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Mads Sogaard, Yang Zhang. 2015-09-29. Scattering Equations and Global Duality of Residues. https://doi.org/10.1103/physrevd.93.105009

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