BCJ relations from a new symmetry of gauge-theory amplitudes

Abstract

We introduce a new set of symmetries obeyed by tree-level gauge-theory amplitudes involving at least one gluon. The symmetry acts as a momentum-dependent shift on the color factors of the amplitude. Using the radiation vertex expansion, we prove the invariance under this color-factor shift of the $n$-gluon amplitude, as well as amplitudes involving massless or massive particles in an arbitrary representation of the gauge group with spin zero, one-half, or one. The Bern-Carrasco-Johansson relations are a direct consequence of this symmetry. We also introduce the cubic vertex expansion of an amplitude, and use it to derive a generalized-gauge-invariant constraint on the kinematic numerators of the amplitude. We show that the amplitudes of the bi-adjoint scalar theory are invariant under the color-factor symmetry, and use this to derive the null eigenvectors of the propagator matrix. We generalize the color-factor shift to loop level, and prove the invariance under this shift of one-loop $n$-gluon amplitudes in any theory that admits a color-kinematic-dual representation of numerators. We show that the one-loop color-factor symmetry implies known relations among the integrands of one-loop color-ordered amplitudes.

52 pages, 7 figures; v2: various clarifications, added figures and references, published version

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Cited by in corpus (6)

• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Covariant Color-Kinematics Duality
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• One-loop monodromy relations on single cuts
• The $pp\to W(\to l\nu )+\gamma$ process at next-to-next-to-leading order
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods