BCJ relations from a new symmetry of gauge-theory amplitudes

Understand

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.