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 $\hat{E}(z,p,\epsilon )$. 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.

32 pages, version to be published

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Cited by in corpus (9)

• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Connected formulas for amplitudes in standard model
• Properties of scattering forms and their relation to associahedra
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• Double copies of fermions as only gravitational interacting matter
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• CHY formula and MHV amplitudes
• Compatible Cycles and CHY Integrals