One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity

Abstract

We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain the pieces that are constructible from four-dimensional unitarity cuts and the rational pieces that are missed by them, while retaining a helicity formalism. We illustrate the procedure using four- and five-point one-loop amplitudes in QCD, including examples with external fermions. We also demonstrate the technique's effectiveness in next-to-leading order QCD corrections to Higgs processes by computing the next-to-leading order correction to the Higgs plus three positive-helicity gluons amplitude in the large top-quark mass limit.

Figures (11)

• Figure 1: A general quadruple cut. Loop momenta flow clockwise.
• Figure 2: A general triple cut.
• Figure 3: Double and triple cuts contributing to bubble coefficients.
• Figure 4: Cuts for the four-point amplitude. We show triple and double cuts in the $s_{23}$ channel; in general we must also evaluate cuts in the $s_{12}$ channel.
• Figure 5: The four-point quadruple cut. Two pairs of three-point amplitudes are grouped together (indicated by blue ovals) to form two easier-to-use four-point tree amplitudes. The cut propagators of the four-point tree amplitudes are canceled by multiplying by inverse propagators prior to imposing the cut conditions.