Color-factor symmetry and BCJ relations for QCD amplitudes

TL;DR

This paper uncovers a new color-factor symmetry in gauge-theory amplitudes that enforces BCJ relations among primitive amplitudes, enhancing understanding of gauge invariance and amplitude relations in QCD.

Contribution

It introduces a novel symmetry acting on color factors that leads to gauge-invariant constraints and directly implies BCJ relations for QCD amplitudes.

Findings

Identifies a momentum-dependent color-factor symmetry in tree-level amplitudes.

Derives gauge-invariant constraints on kinematic numerators.

Provides a direct derivation of BCJ relations for primitive amplitudes.

Abstract

Tree-level $n$-point gauge-theory amplitudes with $n-2k$ gluons and $k$ pairs of (massless or massive) particles in the fundamental (or other) representation of the gauge group are invariant under a set of symmetries that act as momentum-dependent shifts on the color factors in the cubic decomposition of the amplitude. These symmetries lead to gauge-invariant constraints on the kinematic numerators. They also directly imply the BCJ relations among the Melia-basis primitive amplitudes previously obtained by Johansson and Ochirov.