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

As a first step in the aim of arriving at a differential description of neutral Higgs boson decays into heavy quarks, h→QQ̄X, to second order in the QCD coupling αS, we have computed the hQQ̄ amplitude at the two-loop level in QCD for a general neutral Higgs boson which has both scalar and pseudoscalar couplings to quarks. This amplitude is given in terms of a scalar and a pseudoscalar vertex form factor, for which we present closed analytic expressions in terms of one-dimensional harmonic polylogarithms of maximum weight 4. The results hold for arbitrary four-momentum squared, q2, of the Higgs boson and of the heavy-quark mass, m. Moreover, we derive the approximate expressions of these form factors near threshold and in the asymptotic regime m2/q2 1. © 2005 The American Physical Society.