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As a first step in the aim of arriving at a differential description ofneutral Higgs boson decays into heavy quarks, $h \to Q {\bar Q}X$, to secondorder in the QCD coupling $\alpha_S$, we have computed the $hQ{\bar Q}$amplitude at the two-loop level in QCD for a general neutral Higgs boson whichhas both scalar and pseudoscalar couplings to quarks. This amplitude is givenin terms of a scalar and a pseudoscalar vertex form factor, for which wepresent closed analytic expressions in terms of one-dimensional harmonicpolylogarithms of maximum weight 4. The results hold for arbitraryfour-momentum squared, $q^2$, of the Higgs boson and of the heavy quark mass,$m$. Moreover we derive the approximate expressions of these form factors nearthreshold and in the asymptotic regime $m^2/q^2 \ll 1$.Comment: 56 pages, 2 figure

Decays of scalar and pseudoscalar Higgs bosons into fermions: Two-loop QCD corrections to the Higgs-quark-antiquark amplitude