Integrands of Less-Supersymmetric Yang-Mills at One Loop

TL;DR

This paper develops a prescriptive basis for one-loop integrands in less-supersymmetric Yang-Mills theory, enabling clearer amplitude representations with well-defined singularities and finite ratio functions.

Contribution

It introduces a novel bubble power-counting basis for one-loop integrands in less-supersymmetric Yang-Mills theory, with explicit constructions for MHV and NMHV amplitudes.

Findings

All integrands have unambiguous leading singularities except for certain massless bubbles.

The basis is mostly pure and divided into UV- and IR-finite sectors.

Resulting ratio functions are UV- and IR-finite with fixed transcendental weight.

Abstract

We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric Yang-Mills theory. With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory. For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NMHV. The basis we construct is mostly pure and is divided into to separately UV- and IR-finite sectors of fixed transcendental weight, resulting in UV- and IR-finite ratio functions of n-particle helicity amplitudes.