Gluon Fusion Production at NLO: Merging the Transverse Momentum and the High-Energy Expansions

TL;DR

This paper develops a method to accurately compute virtual corrections for gluon fusion processes by merging small transverse momentum and high-energy expansions, enabling fast, precise, and flexible evaluations across phase space.

Contribution

It introduces a novel approach that combines two expansion techniques with Padé approximants to extend validity and improve accuracy in virtual correction calculations.

Findings

Reproduces numerical results with less than 1% error.

Provides a fast, flexible evaluation method for virtual corrections.

Supports different top quark mass renormalization schemes.

Abstract

The virtual corrections to $gg\to HH$ and $gg\to ZH$ are analytically evaluated combining an expansion in the small transverse momentum of the final particles with an expansion valid at high energies. The two expansion methods describe complementary regions of the phase space and we merge their results, extending the range of validity of both expansions using Pad\'e approximants. We show that this approach can reproduce the available numerical results retaining the exact top quark mass dependence with an accuracy well below the 1% level. Our results allow a fast and flexible evaluation of the virtual corrections of the considered processes. Furthermore, they are available in different renormalisation schemes of the top quark mass.