The virtual two-loop corrections for Higgs production in gluon fusion are calculated analytically in QCD for arbitrary Higgs and quark masses. Both scalar and pseudo-scalar Higgs bosons are considered. The results are obtained by expanding the known one-dimensional integral representation in terms of m H /m q , and matching it with a suitably chosen ansatz of Harmonic Polylogarithms. This ansatz is motivated by the known analytic result for the Higgs decay rate into two photons. The method also allows us to check this result and to extend it to the pseudo-scalar decay rate.

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Within the framework of QCD we compute renormalization constants for the strong coupling and the quark masses to four-loop order. We apply the DR scheme and put special emphasis on the additional couplings which have to be taken into account. This concerns the ε-scalar-quark Yukawa coupling as well as the vertex containing four ε-scalars. For a supersymmetric Yang Mills theory, we find, in contrast to a previous claim, that the evanescent Yukawa coupling equals the strong coupling constant through three loops as required by supersymmetry.

The light CP even Higgs boson mass, Mh, is calculated to three-loop accuracy within the Minimal Supersymmetric Standard Model (MSSM). The result is expressed in terms of DRbar parameters and implemented in the computer program H3m. The calculation is based on the proper approximations and their combination in various regions of the parameter space. The three-loop effects to Mh are typically of the order of a few hundred MeV and opposite in sign to the two-loop corrections. The remaining theory uncertainty due to higher order perturbative corrections is estimated to be less than 1 GeV.Comment: 39 pages, 13 figures. v2: minor changes, typos fixe

Dimensional Reduction is applied to QCD in order to compute various renormalization constants in the DR scheme at higher orders in perturbation theory. In particular, the β function and the anomalous dimension of the quark masses are derived to three-loop order. Special emphasis is put on the proper treatment of the so-called ε-scalars and the additional couplings which have to be considered.