Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

TL;DR

This work addresses the precise calculation of two-loop QCD corrections to Higgs production via gluon fusion, $gg \rightarrow H$, in the presence of massive quarks and scalar quarks. It combines Laporta-based reduction with automated tools and derives all necessary master integrals using the differential-equation method, followed by analytic continuation to the physical regions. The authors provide full analytic results for both fermionic and scalar-quark loops, including a new scalar-quark amplitude and an independent cross-check of the established fermionic result, with expressions in terms of harmonic polylogarithms up to weight four. The master-integral basis and automated framework developed here enable robust NLO predictions and can be applied to more complex $2\rightarrow 1$ and $2\rightarrow 2$ processes in the SM and its extensions, including SUSY scenarios.

Abstract

We compute all two-loop master integrals which are required for the evaluation of next-to-leading order QCD corrections in Higgs boson production via gluon fusion. Many two-loop amplitudes for 2 -> 1 processes in the Standard Model and beyond can be expressed in terms of these integrals using automated reduction techniques. These integrals also form a subset of the master integrals for more complicated 2 -> 2 amplitudes with massive propagators in the loops. As a first application, we evaluate the two-loop amplitude for Higgs boson production in gluon fusion via a massive quark. Our result is the first independent check of the calculation of Spira, Djouadi, Graudenz and Zerwas. We also present for the first time the two-loop amplitude for gg -> h via a massive squark.