Dimensional schemes for cross sections at NNLO

TL;DR

This paper extends the analysis of dimensional regularization schemes to real corrections in NNLO calculations, demonstrating scheme independence and simplifying double-real corrections for two-jet production.

Contribution

It introduces a method to compute real corrections at NNLO in different schemes, confirming scheme independence and simplifying calculations for two-jet production.

Findings

Double-real corrections obtained by integrating four-dimensional matrix elements in dimensional reduction.

Cross section remains regularization-scheme independent at NNLO.

Method simplifies the computation of real corrections in different schemes.

Abstract

So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of physical cross sections at next-to-next-to-leading order. As a case study we consider two-jet production in electron-positron annihilation and describe how to compute the various parts separately in different schemes. In particular, we verify that using dimensional reduction the double-real corrections are obtained simply by integrating the four-dimensional matrix element over the phase space. In addition, we confirm that the cross section is regularization-scheme independent.