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

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.