Supersymmetric next-to-next-to-leading order corrections to Higgs boson production in gluon fusion

We compute the total cross section for the production of a light CP even Higgs boson within the framework of supersymmetric QCD up to next-to-next-to-leading order. Technical subtleties in connection to the evaluation of three-loop Feynman integrals with many mass scales are discussed in detail and explicit results for the counterterms of the evanescent couplings are provided. The new results are applied to several phenomenological scenarios which are in accordance with the recent discovery at the LHC. In a large part of the still allowed parameter space the $K$ factor of the supersymmetric theory is close to the one of the Standard Model. However, for the case where one of the top squarks is light, a deviation of more than 5% in the next-to-next-to-leading order prediction of the cross section can be observed where at the same time the predicted Higgs boson mass has a value of about 125 GeV.