New Relations for Gauge-Theory Amplitudes with Matter

TL;DR

The paper extends BCJ-like, helicity-independent relations from pure gluon amplitudes to gauge-theory amplitudes with matter, using supersymmetric Ward identities to relate matter and gluon MHV amplitudes via a simple $h$-dependent factor and a sign convention for fermions. It formulates a generalized matter BCJ relation expressed as a POP (partially ordered permutations) sum with kinematic factors, and verifies it for all $n$-point MHV amplitudes and for six- and seven-point NMHV configurations using BCFW recursion. The work also derives explicit four- and five-point matter relations and demonstrates agreement with quark, gluino, and adjoint-scalar cases, providing a framework potentially applicable to loop calculations via unitarity cuts. Overall, the results suggest that the color-kinematics (BCJ) structure extends beyond gluons to include common matter representations, offering a path to reduced amplitude bases in mixed-matter gauge theories.

Abstract

We extend a recently discovered set of relations for gauge-theory amplitudes to non-gluonic matter. For all MHV amplitudes we find that these can be made to hold for scalar/fermion/quark cases by inclusion of a factor derived via Ward identities. For six- and seven-point amplitudes with non-gluonic matter we explicitly confirm these relations for NMHV helicity configurations.