Gluon fusion is the main production mechanism for Higgs particles at the LHC. We present the QCD corrections to the fusion cross sections for the Higgs boson in the Standard Model, and for the neutral Higgs bosons in the minimal supersymmetric extension of the Standard Model. The QCD corrections are in general large and they increase the cross sections significantly. In two steps preceding the calculation of the production processes, we determine the QCD radiative corrections to Higgs decays into two photons and gluons.

Gluon fusion is the ·main production mechanism for Higgs bosons with masses up to several hundred GeV in pp collisions at LHC and SSC. We present the QCD corrections to the fusion cross section for arbitrary Higgs and top mass valueso gg --+ H(g), gq --+ Hq and qq --+ Hg. The QCD corrections are positive and they increase the cross section cr(pp--+ H) by about a factor 1.5 to 1. 7. The analysis applies to the production of Higgs particles in the Standard Model and also to the production of the C'P-even Higgs particles in extensions of the Higgs sector as required for example by supersymmetric theories.Most of the building blocks of the Stan~d Model have been tested to a very high precision in recent years. However, the Higgs mechanism [1]; one of the cornerstones of this theory, has not yet been proven experimentally to be the basic mechanism for the generation of the fundamental particle masses. To accomodate the well-established electromagnetic and weak phenomena, this mechanism requires the existence of at least one weak isodoublet scalar field of which one degree of freedom manisfests itself as. a real physical particle for small enough masses. The discovery of the Higgs particle is the ezperimentum cntcis for the canonical formulation of the electroweak interactions. For Higgs boson masses up to ~700 GeV the dominant production mechanism in high-energy proton-proton collisions is gluon-gluon fusion (5]. The Higgs bosons couple to gluons through a heavy-quark triaugle loop. In this note we present the QCD corrections to the cross section u(pp--+H+X) of the fusion process, gg --+ H(g) and gq --+ Hq, qq --+ Hg( 1) for arbitrary Higgs boson and (loop] quark masses, Fig.1. This analysis extends previous work of Refs.[6] and (7] in which the Higgs boson mass was assumed to be much smaller than the looPquark mass. The analysis of the next-to-leading order QCD corrections to the Higgs production cross section is required for two reasons: (i) The lowest order prediction ofthe cross section u(pp --+ H) depends strongly on the renormalization and factorization scales. The next-to-leading order stabilizes the prediction and leaves us only with a mild residual dependence on these parameters.(ii) Since the QCD corrections turn out to be positive and large, the calculation is a posteriori also of high experimental significance. The transverse momentum spectra of the Higgs bosons have been considered at various levels of theoretical refinement in Refs.(S].Heavy quarks Q provide the dominant contribution to the coupling of Higgs bosons to gluons. Neglecting finite-width effects, the cross section for the production of Higgs particles in pp collisions is given to lowest order (Fig.1a) by (5,6,7] with

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