New relations for scattering amplitudes in Yang-Mills theory at loop level

TL;DR

This paper introduces new relations for one-loop scattering amplitudes in Yang-Mills theory, derived from scaling behaviors, with potential implications for higher-loop relations and collider physics.

Contribution

It develops novel tools based on permutation and cyclic sum scaling to derive relations for one-loop amplitudes in Yang-Mills theory, extending to all loop orders.

Findings

Relations for one-loop amplitudes derived

Evidence for all-loop order relations

Explicit examples with matter coupling

Abstract

The calculation of scattering amplitudes in Yang-Mills theory at loop level is important for the analysis of background processes at particle colliders as well as our understanding of perturbation theory at the quantum level. We present tools to derive relations for especially one loop amplitudes, as well as several explicit examples for gauge theory coupled to a wide variety of matter. These tools originate in certain scaling behavior of permutation and cyclic sums of Yang-Mills tree amplitudes and loop integrands. In the latter case evidence exists for relations at all loop orders.