Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter

Abstract

Four-point one-loop nonsupersymmetric pure Yang-Mills amplitudes with the duality between color and kinematics manifest have been constructed in previous work. Here, we extend the discussion to fermions and scalars circulating in the loop with all external gluons. This gives another nontrivial loop-level example showing that the duality between color and kinematics holds in nonsupersymmetric gauge theory. The construction is valid in any spacetime dimension and written in terms of formal polarization vectors. We also convert these expressions into a four-dimensional form with explicit external helicity states. Using this, we compare our results to one-loop duality-satisfying amplitudes that are already present in literature.

23 page, 6 figures, REVTex, ancillary Mathematica file containing four-point one-loop BCJ numerators; v2: ancillary file updated to better match labelling conventions in body of paper, minor corrections

References in corpus (14)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Direct Extraction Of One Loop Rational Terms
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction

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• On-Shell Perspectives on the Massless Limit of Massive Supergravity