D-dimensional unitarity cut method

TL;DR

This work tackles the challenge of computing one-loop amplitudes with massless propagators in $d=4-2\epsilon$ by extending unitarity cuts to arbitrary dimensions. The method splits the loop momentum into a four-dimensional part and a $(-2\epsilon)$-dimensional component, performing a four-dimensional spinor-integrated phase-space and treating the remaining mass parameter via dimensional shifts. Coefficients of master integrals—bubbles, triangles, boxes, and pentagons—are obtained without fully integrating in $d$ dimensions, and a set of derived dimensional-shift identities maps higher-dimensional masters back to $4-2\epsilon$ master integrals. The approach is compatible with others such as OPP and Anastasiou reductions, extensible to massive propagators, and promises efficient, automatable one-loop computations for collider phenomenology.

Abstract

We develop a unitarity method to compute one-loop amplitudes with massless propagators in d=4-2*epsilon dimensions. We compute double cuts of the loop amplitudes via a decomposition into a four-dimensional and a -2*epsilon-dimensional integration. The four-dimensional integration is performed using spinor integration or other efficient techniques. The remaining integral in -2*epsilon dimensions is cast in terms of bubble, triangle, box, and pentagon master integrals using dimensional shift identities. The method yields results valid for arbitrary values of epsilon.