Abstract
We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD.
Highlights
Loops and legs are tied together through the singularity structure and unitarity
After we review the color and kinematic structure of gauge theory amplitudes in section 2, we proceed to the lowerpoint examples that lead to the main result of section 3 — the new color decomposition for a generic QCD amplitude
In this paper we explored and organized the color and kinematic content of general tree amplitudes in QCD with flavored massive quarks and massless gluons
Summary
We review some general properties of the color and kinematic structure of tree-level scattering amplitudes in QCD. Amplitudes involving only gluons or at most one quark-antiquark pair have a similar form and structure, and are well studied in the literature. The role of the quartic ones is to make the amplitudes constructed from the Feynman rules gauge invariant, and they carry no new physical information with respect to the cubic interactions. This nontrivial statement is made apparent by the on-shell recursion [6, 7], which relies only on input from the three-point amplitudes of the theory. The color factors ci in eq (2.2) are constructed from the cubic graphs using only two building blocks: the structure constants fabc for three-gluon vertices and generators Tia ̄ for quark-gluon vertices, as shown in figure 1. We review how to assemble the diagrams into gauge-invariant building blocks, i.e. the primitive amplitudes
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
