Scaffolding Residues in Yang-Mills-Scalar \`a la CHY

TL;DR

This paper develops a method to derive pure gluon and graviton amplitudes from scalar amplitudes in Yang-Mills-Scalar theories using CHY formalism, revealing structural insights and new computational techniques.

Contribution

It introduces a novel 'scaffolding' residue approach to extract pure gauge and gravity amplitudes from scalar amplitudes within the CHY framework, connecting different theories.

Findings

Derived pure n-gluon amplitudes from 2n-scalar amplitudes.

Produced n-graviton amplitudes from scalar amplitudes in Einstein-Maxwell-Scalar theory.

Analyzed partial 'scaffolding' residues and their relation to multi-collinear limits.

Abstract

Motivated by recent work by Arkani-Hamed et al. arXiv:2401.00041, we compute the ''scaffolding'' residue of $2n$-scalar Yang-Mills-Scalar amplitudes to obtain pure $n$-gluon amplitudes \`a la Cachazo-He-Yuan (CHY). In particular, we show how the Pfaffian of $\Psi$, which is a matrix rich in structure, emerges from that of the simple $A$ matrix. The same CHY computation straightforwardly produces $n$-graviton amplitudes from $2n$-scalar amplitudes in the Einstein-Maxwell-Scalar theory. We also consider partial ''scaffolding'' residues, i.e., general multi-collinear limits and their interplay with color-dressed amplitudes.