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

Many search strategies for the Standard Model Higgs boson apply specific selection criteria on hadronic jets observed in association with the Higgs boson decay products, either in the form of a jet veto, or by defining event samples according to jet multiplicity. To improve the theoretical description of Higgs-boson-plus-jet production (and the closely related Higgs boson transverse momentum distribution), we derive the two-loop QCD corrections to the helicity amplitudes for the processes $H \to ggg$ and $H\to q \bar q g$ in an effective theory with infinite top quark mass. The helicity amplitudes are extracted from the coefficients appearing in the general tensorial structure for each process. The coefficients are derived from the Feynman graph amplitudes by means of projectors within the conventional dimensional regularization scheme. The infrared pole structure of our result agrees with the expectation from infrared factorization and the finite parts of the amplitudes are expressed in terms of one- and two-dimensional harmonic polylogarithms.