Expanding single trace YMS amplitudes with gauge invariant coefficients

TL;DR

This paper introduces a recursive method based on soft theorems to expand single-trace Yang-Mills-scalar amplitudes, ensuring gauge invariance and permutation symmetry.

Contribution

It presents a new bottom-up recursive approach that explicitly maintains gauge invariance and permutation symmetry in amplitude expansions.

Findings

The expansion is equivalent to the covariant color-kinematic duality approach.

The method guarantees gauge invariance for any polarization of external gluons.

Permutation symmetry among external gluons is manifest in the expansion.

Abstract

In this note, we use the new bottom up method based on soft theorems to construct the expansion of single-trace Yang-Mills-scalar amplitudes recursively. The resulted 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-kinematic duality approach.