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Many search strategies for the Standard Model Higgs boson apply specificselection criteria on hadronic jets observed in association with the Higgsboson decay products, either in the form of a jet veto, or by defining eventsamples according to jet multiplicity. To improve the theoretical descriptionof Higgs-boson-plus-jet production (and the closely related Higgs bosontransverse momentum distribution), we derive the two-loop QCD corrections tothe helicity amplitudes for the processes $H \to ggg$ and $H\to q \bar q g$ inan effective theory with infinite top quark mass. The helicity amplitudes areextracted from the coefficients appearing in the general tensorial structurefor each process. The coefficients are derived from the Feynman graphamplitudes by means of projectors within the conventional dimensionalregularization scheme. The infrared pole structure of our result agrees withthe expectation from infrared factorization and the finite parts of theamplitudes are expressed in terms of one- and two-dimensional harmonicpolylogarithms.

Two-Loop QCD Corrections to the Helicity Amplitudes for $H \to$ 3 partons