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.
Highlights
Ingredients for the gluon amplitudes are the Parke-Taylor factor C(w, z), defining the cyclic order and a permutation invariant function E(z, p, ε), containing the information on the helicities of the external particles
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
Parke-Taylor factor does not depend on the helicities of the external particles, the permutation invariant function does not depend on the ordering of the external particles
Summary
We define words and shuffle algebras and review the various relations among primitive amplitudes. Dyck words are a convenient tool to label amplitudes with several quark-anti-quark pairs. At the end of this section we present a minimal amplitude basis
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
