Expanding single-trace YMS amplitudes with gauge-invariant coefficients

Abstract In this note, we use the new bottom-up method based on soft theorems to recursively construct the expansion of single-trace Yang–Mills-scalar amplitudes. The resulting expansion manifests the gauge invariance for any polarization carried by external gluons, as well as the permutation symmetry among external gluons. Our result is equivalent to that found by Clifford Cheung and James Mangan via the so-called covariant color–kinematics duality approach.