Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?

TL;DR

This paper investigates whether the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes are necessary in NNLO calculations, proposing a method to bypass their explicit computation using the finite remainder of two-loop amplitudes.

Contribution

It demonstrates that the O(epsilon)- and O(epsilon^2)-terms can be avoided if the finite remainder of the two-loop amplitude is known, simplifying NNLO calculations.

Findings

The calculation of O(epsilon)- and O(epsilon^2)-terms can be circumvented.

A method using the finite remainder function reduces computational complexity.

Explicit O(epsilon)- and O(epsilon^2)-terms are not always necessary in NNLO computations.

Abstract

This article discusses the occurences of one-loop amplitudes within a next-to-next-to-leading order calculation. In an NNLO calculation the one-loop amplitude enters squared and one would therefore naively expect that the O(epsilon)- and O(epsilon^2)-terms of the one-loop amplitudes are required. I show that the calculation of these terms can be avoided if a method is known, which computes the O(epsilon^0)-terms of the finite remainder function of the two-loop amplitude.