Direct Extraction Of One Loop Rational Terms

TL;DR

This paper introduces a novel method for directly extracting rational parts of one-loop scattering amplitudes using generalized unitarity in D=4-2ε dimensions, improving accuracy over standard techniques.

Contribution

The method enables direct calculation of rational terms from massive tree amplitudes without relying on pentagon contributions, using a massive integral basis and large mass limit analysis.

Findings

Successfully computed rational parts of gluon amplitudes with up to six legs.

Validated the method with amplitudes involving massless fermions.

Demonstrated the approach's effectiveness in various amplitude configurations.

Abstract

We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in $4-2\e$ dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted from the large mass limit which can be performed analytically or numerically. We check the method by computing the rational parts of all gluon helicity amplitudes with up to six external legs. We also present a simple application to amplitudes with external massless fermions.