Color-Kinematics Duality for QCD Amplitudes

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.

33 pages + refs, 7 figures, 4 tables; v3 minor corrections, journal version

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Cited by in corpus (97)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
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• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Perturbative spacetimes from Yang-Mills theory
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• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• Double copy for massive quantum particles with spin
• Gravitational Radiation from Color-Kinematics Duality
• The self-dual classical double copy, and the Eguchi-Hanson instanton
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• Compton Black-Hole Scattering for $s\le 5/2$
• Gravity Amplitudes as Generalized Double Copies
• A worldsheet for Kerr
• BCJ numerators from reduced Pfaffian
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• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• A new gauge-invariant double copy for heavy-mass effective theory
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• Gluons and gravitons at one loop from ambitwistor strings
• Higher-loop amplitude monodromy relations in string and gauge theory
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Weyl doubling
• The double copy for heavy particles
• On the Double Copy for Spinning Matter
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Monopoles, shockwaves and the classical double copy
• Helicity amplitudes for QCD with massive quarks
• Simple encoding of higher derivative gauge and gravity counterterms
• Gravity On-shell Diagrams
• Unraveling conformal gravity amplitudes
• New heavenly double copies
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• The Double Copy of Massive Scalar-QCD
• Generalizations of the Double-Copy: the KLT Bootstrap
• Classical Spin Gravitational Compton Scattering
• Loop-Level Double-Copy for Massive Quantum Particles
• Classical Limit of Higher-Spin String Amplitudes
• Scattering Amplitudes in Quantum Field Theory
• Chiral approach to massive higher spins
• Multi-Quark Colour Decompositions from Unitarity
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
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• Manifesting enhanced cancellations in supergravity: integrands versus integrals
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• Double copies of fermions as only gravitational interacting matter
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• The $L_{\infty }$ structure of gauge theories with matter
• Extracting Einstein from the Loop-Level Double-Copy
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Recursion relations for scattering amplitudes with massive particles
• Unified web for expansions of amplitudes
• Tree level amplitudes from soft theorems
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• The ChPT: top-down and bottom-up
• A Portable Parton-Level Event Generator for the High-Luminosity LHC
• New relations for graviton-matter amplitudes
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• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• On Positive Geometry and Scattering Forms for Matter Particles
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Open associahedra and scattering forms
• Loop-level double-copy for massive fermions in the fundamental
• BCJ, worldsheet quantum algebra and KZ equations
• Double copy for tree-level form factors. Part I. Foundations
• Transmutation operators and expansions for $1$-loop Feynman integrands
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• Next-to-MHV Yang-Mills kinematic algebra
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Streamlining resummed QCD calculations using Monte Carlo integration
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• Tree and $1$-loop fundamental BCJ relations from soft theorems
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Note on scalar-graviton and scalar-photon-graviton amplitudes
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• Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions
• The seeds of EFT double copy
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity