Color-Kinematics Duality for QCD Amplitudes

TL;DR

This paper demonstrates that color-kinematics duality applies to tree-level QCD amplitudes with massive quarks, providing a new color decomposition and amplitude relations that extend the duality beyond gluons.

Contribution

It introduces a novel color decomposition for QCD tree amplitudes with arbitrary quark content and proves the presence of color-kinematics duality in these amplitudes.

Findings

Color-kinematics duality holds for QCD with massive quarks.

New amplitude relations reduce the basis to (n-3)!(2k-2)/k! primitives.

Decomposition applicable to supersymmetric and D-dimensional QCD extensions.

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.