Abstract
A double-cover extension of the scattering equation formalism of Cachazo, He and Yuan (CHY) leads us to conjecture covariant factorization formulas of n-particle scattering amplitudes in Yang-Mills theories. Evidence is given that these factorization relations are related to Berends-Giele recursions through repeated use of partial fraction identities involving linearized propagators.
Highlights
The CHY formalism of scattering equations of Cachazo, He, and Yuan provide an intriguing novel way of computing gauge and gravity S-matrix elements [1,2,3]
As we demonstrate in this paper, the double-cover formalism adds a new ingredient to the standard CHY formalism that is much more difficult to extract in the single-cover formulation
We start with a brief review of the CHY formalism and give the corresponding expressions in the doublecover formulation of Ref. [7]
Summary
The CHY formalism of scattering equations of Cachazo, He, and Yuan provide an intriguing novel way of computing gauge and gravity S-matrix elements [1,2,3]. Fixing three of the variables in the standard manner, only (n − 3) variables za are left This precisely matches the (n − 3) independent scattering equations after imposing overall momentum conservation. Is huge, and finding all these solutions is computationally difficult even for moderate values of n Summing over these independent solutions can be done more directly, through general integration rules developed in Refs. The double-cover formalism naturally expresses the scattering amplitude so that it is factorized into different channels. The propagator that forms the bridge between two factorized pieces arises as the link between two separate CP1 pieces, intuitively explaining why the double cover naturally expresses amplitudes in a factorized manner. We start with a brief review of the CHY formalism and give the corresponding expressions in the doublecover formulation of Ref.
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