Abstract
We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for n scattering particles into a σ-moduli multivariate polynomial of what we call the standard form. We show that a standard form polynomial must have a specific ladder type monomial structure, which has finite size at any n, with highest multivariate degree given by (n − 3)(n − 4)/2. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop level, we employ the global residue theorem to derive a prescription that evaluates any CHY amplitude by means of collecting simple residues at infinity only. The prescription is then applied explicitly to some tree and one-loop amplitude examples.
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Zlotnikov, M. Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes. J. High Energ. Phys. 2016, 143 (2016). https://doi.org/10.1007/JHEP08(2016)143
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DOI: https://doi.org/10.1007/JHEP08(2016)143