Measuring the Higgs Yukawa Couplings at a Next Linear Collider

We investigate the inclusive production of a Higgs boson with a pair of heavy quarks (t-tbar b-bbar), in e^+e^- collisions at high energies, sqrt(s)=500 GeV and sqrt(s)=1 TeV. We consider both the Standard Model and the supersymmetric case. In both cases O(alpha_s) QCD corrections are included. The associated production of a Higgs boson with a t-tbar pair is extremely sensitive to the top-Higgs Yukawa coupling and may allow the precision measurement of this coupling. In some regions of the supersymmetric parameter space the associated production of a Higgs boson with a b-bbar pair receives large resonant contributions and can have a significant rate.