Holomorphic Anomaly Of Unitarity Cuts And One-Loop Gauge Theory Amplitudes

TL;DR

This paper introduces a method leveraging the holomorphic anomaly to efficiently compute specific unitarity cuts of one-loop N=4 gluon amplitudes, including MHV and next-to-MHV cases, with explicit results for certain cuts.

Contribution

It presents a novel application of the holomorphic anomaly to streamline the calculation of unitarity cuts in one-loop gauge theory amplitudes, extending computational techniques in quantum field theory.

Findings

Computed the (1,2,3)-cut of n-gluon one-loop amplitude explicitly.

Expressed results in terms of scalar box functions.

Discussed potential generalizations to all unitarity cuts.

Abstract

We show how the holomorphic anomaly found in hep-th/0409245 can be used to efficiently compute certain classes of unitarity cuts of one-loop N=4 amplitudes of gluons. These classes include all cuts of n-gluon one-loop MHV amplitudes and of n-gluon next-to-MHV amplitudes with helicities (1+,2+,3+,4-,..., n-). As an application of this method, we present the explicit computation of the (1,2,3)-cut of the n-gluon one-loop N=4 leading-color amplitude A_{n;1}(1+,2+,3+,4-,..., n-). The answer is given in terms of scalar box functions and provides information about the corresponding amplitudes. A possible way to generalize this method to all kinds of unitarity cuts is also discussed.