One-loop Higgs plus four gluon amplitudes: Full analytic results

TL;DR

This paper provides a complete analytic calculation of one-loop Higgs plus four gluon amplitudes in the large top quark mass limit, using unitarity and recursive techniques, relevant for Higgs production in high-energy physics.

Contribution

It presents the first full analytic results for the phi-NMHV amplitude with one positive and three negative helicity gluons at one loop, combining unitarity and recursive methods.

Findings

Analytic expressions for Higgs plus four gluon amplitudes obtained.

Results applicable to Higgs plus jet production in gluon fusion.

Completes the set of helicity configurations for these amplitudes.

Abstract

We consider one-loop amplitudes of a Higgs boson coupled to gluons in the limit of a large top quark mass. We treat the Higgs as the real part of a complex field phi that couples to the self-dual field strengths and compute the one-loop corrections to the phi-NMHV amplitude, which contains one gluon of positive helicity whilst the remaining three have negative helicity. We use four-dimensional unitarity to construct the cut-containing contributions and a hybrid of Feynman diagram and recursive based techniques to determine the rational piece. Knowledge of the phi-NMHV contribution completes the analytic calculation of the Higgs plus four gluon amplitude. For completeness we also include expressions for the remaining helicity configurations which have been calculated elsewhere. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark is large compared to all other scales in the problem.