Scattering equations and global duality of residues
Mads Søgaard, Yang Zhang · Physical review. D/Physical review. D. · 2016
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 $(n\ensuremath{-}3)\ifmmode\times\else\texttimes\fi{}(n\ensuremath{-}3)$, our algorithm is very efficient for analytic and numeric amplitude computations.