Dual-color decompositions at one-loop level in Yang-Mills theory

Abstract

In this work, we extend the construction of dual color decomposition in Yang-Mills theory to one-loop level, i.e., we show how to write one-loop integrands in Yang-Mills theory to the dual DDM-form and the dual trace-form. In dual forms, integrands are decomposed in terms of color-ordered one-loop integrands for color scalar theory with proper dual color coefficients.In dual DDM decomposition, The dual color coefficients can be obtained directly from BCJ-form by applying Jacobi-like identities for kinematic factors. In dual trace decomposition, the dual trace factors can be obtained by imposing one-loop KK relations, reflection relation and their relation with the kinematic factors in dual DDM-form.

26 pages,5 figures

References in corpus (11)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• The Kinematic Algebra From the Self-Dual Sector
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• The Kinematic Algebras from the Scattering Equations
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Fundamental BCJ Relation in N=4 SYM From The Connected Formulation
• New Relations for Gauge-Theory Amplitudes with Matter
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• Note on symmetric BCJ numerator

Cited by in corpus (19)

• Black holes and the double copy
• The classical double copy for Taub-NUT spacetime
• The double copy: Bremsstrahlung and accelerating black holes
• The Kerr-Schild double copy in curved spacetime
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Exact solutions for the biadjoint scalar field
• S-duality and the Double Copy
• Topology and Wilson lines: global aspects of the double copy
• Weyl doubling
• Monopoles, shockwaves and the classical double copy
• Biadjoint wires
• Twistor Space Origins of the Newman-Penrose Map
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• One-loop off-shell amplitudes from classical equations of motion
• One-Loop Yang-Mills Integrands from Scattering Equations
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• The Weyl double copy from twistor space
• Note on off-shell relations in nonlinear sigma model