Abstract
In this paper we construct a CHY representation for all tree-level primitive QCD amplitudes. The quarks may be massless or massive. We define a generalised cyclic factor Ĉ(w, z) and a generalised permutation invariant function Ê(z, p, ε). The amplitude is then given as a contour integral encircling the solutions of the scattering equations with the product ĈÊ as integrand. Equivalently, it is given as a sum over the inequivalent solutions of the scattering equations, where the summand consists of a Jacobian times the product Ĉ Ê. This representation separates information: The generalised cyclic factor does not depend on the helicities of the external particles, the generalised permutation invariant function does not depend on the ordering of the external particles.
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de la Cruz, L., Kniss, A. & Weinzierl, S. The CHY representation of tree-level primitive QCD amplitudes. J. High Energ. Phys. 2015, 217 (2015). https://doi.org/10.1007/JHEP11(2015)217
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DOI: https://doi.org/10.1007/JHEP11(2015)217