Off-shell Currents and Color-Kinematics Duality

Abstract

We elaborate on the color-kinematics duality for off-shell diagrams in gauge theories coupled to matter, by investigating the scattering process $gg\to ss,q\bar{q},gg$, and show that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduce to a color-kinematics violating term due to the contributions of sub-graphs only. Such anomaly vanishes when the four particles connected by the Jacobi relation are on their mass shell with vanishing squared momenta, being either external or cut particles, where the validity of the color-kinematics duality is recovered. We discuss the role of the off-shell decomposition in the direct construction of higher-multiplicity numerators satisfying color-kinematics identity in four as well as in $d$ dimensions, for the latter employing the Four Dimensional Formalism variant of the Four Dimensional Helicity scheme. We provide explicit examples for the QCD process $gg\to q\bar{q}g$.

Accepted version for publication in PLB. Manuscript extended: 19 pages, 15 figures; C/K duality for tree-level amplitudes in dimensional regularization added; references added; title modified

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Cited by in corpus (16)

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• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Loop-tree duality from vertices and edges
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Classical off-shell currents
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• BCJ relations from a new symmetry of gauge-theory amplitudes
• A scattering amplitudes approach to hard thermal loops
• BCJ Relations for One-Loop QCD Integral Coefficients
• Generalised unitarity for dimensionally regulated amplitudes within FDF
• Color-factor symmetry and BCJ relations for QCD amplitudes
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• A stroll through the loop-tree duality