Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories

Abstract

In this work we show how a double-cover (DC) extension of the Cachazo, He and Yuan formalism (CHY) can be used to provide a new realization for the factorization of the amplitudes involving gluons and scalar fields. First, we propose a graphic representation for a color-ordered Yang-Mills (YM) and special Yang-Mills-Scalar (YMS) amplitudes within the scattering equation formalism. Using the DC prescription, we are able to obtain an algorithm (integration-rules) which decomposes amplitudes in terms of three-point building-blocks. It is important to remark that the pole structure of this method is totally different to ordinary factorization (which is a consequence of the scattering equations). Finally, as a byproduct, we show that the soft limit in the CHY approach, at leading order, becomes trivial by using the technology described in this paper.

arXiv comment50+7 pages and typos fixed. Some modifications were made to improve the text

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• Scattering Equations and Factorization of Amplitudes II: Effective Field Theories
• Transmuting off-shell CHY integrals in the double-cover framework
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• A Novel On-Shell Recursive Relation