The CHY representation of tree-level primitive QCD amplitudes

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 $\hat{C}(w,z)$ and a generalised permutation invariant function $\hat{E}(z,p,\varepsilon)$. The amplitude is then given as a contour integral encircling the solutions of the scattering equations with the product $\hat{C} \hat{E}$ 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 $\hat{C} \hat{E}$. 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.