Generalized unitarity and six-dimensional helicity

Abstract

We combine the unitarity method with the six-dimensional helicity formalism of Cheung and O'Connell to construct loop-level scattering amplitudes. As a first example, we construct dimensionally regularized QCD one-loop four-point amplitudes. As a nontrivial multiloop example, we confirm that the recently constructed four-loop four-point amplitude of $\mathcal{N}=4$ super-Yang-Mills theory, including nonplanar contributions, is valid for dimensions $D\ensuremath{\le}6$. We comment on the connection of our approach to the recently discussed Higgs infrared regulator and on dual conformal properties in six dimensions.