D-dimensional unitarity cut method

Charalampos Anastasiou,Ruth Britto,Pierpaolo Mastrolia,Bo Feng,Zoltan Kunszt

doi:10.1016/j.physletb.2006.12.022

Abstract

Abstract We develop a unitarity method to compute one-loop amplitudes with massless propagators in d = 4 − 2 ϵ dimensions. We compute double cuts of the loop amplitudes via a decomposition into a four-dimensional and a − 2 ϵ -dimensional integration. The four-dimensional integration is performed using spinor integration or other efficient techniques. The remaining integral in − 2 ϵ 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 ϵ.

Highlights

In modern collider experiments complex events with multijets, vector bosons and jets, top quarks and jets, etc. are frequently produced
In this Letter, we have presented a new unitarity method for the reduction of one-loop amplitudes to master integrals in arbitrary dimensions
We have generalized the method of spinor integration via the holomorphic anomaly to massive phase-space integrals

Summary

Introduction

In modern collider experiments complex events with multijets, vector bosons and jets, top quarks and jets, etc. are frequently produced. New methods to compute the rational parts separately were introduced recently They compute these terms by either developing [13,14,15,16,17] recursion relations for amplitudes [18,19], or by using specialized diagrammatic reductions [20,21,22,23]. The calculation of general unitarity cuts remains formidable While it is simpler than a direct Feynman graph evaluation, eventually, one resorts to traditional reduction methods to complete their computation. In this Letter, we develop an efficient d-dimensional unitary cut method, reducing one-loop amplitudes to master inte-.

Reduction to master integrals

Alternatives to spinor integration

Summary