QCD Corrections to Associated Higgs Boson Production

We compute QCD corrections to the processes $e^{+}{e}^{-}\to t\bar{t}{h}^0$ and $pp\to t\bar{t}{h}^0$ by treating the Higgs boson as a parton which radiates off a heavy quark. This approximatiion is valid in the limits $M_h<<M_t$ and $M_h, M_t<<\sqrt{s}$\mathrm{.}Thecorrectionsincreasetheratefor$pp\to t \bar t h^0$ at the LHC by a factor of 1.2 to 1.5 over the lowest order rate for an intermediate mass Higgs boson, $M_h<180GeV$. The QCD corrections are small for $e^{+}{e}^{-}\to t\bar{t}{h}^0$ at $\sqrt{s}=1TeV$.