QCD corrections to heavy quark production in hadron-hadron collisions

We investigate the QCD corrections to the cross section and single-particle inclusive differential distributions for $p + p̄ → Q(Q̄)$ + X where Q and Q̄ are heavy quarks. We calculate the order α$_S$ corrections to the parton reaction $q + q̄ → Q + Q̄$ which involves the computation of the virtual gluon contributions and the soft and hard contributions from the reaction $q + q̄ → Q + Q̄ + g$. The contributions from the channels $g + q(q̄) → Q + Q̄ + q(q̄)$ are also calculated. Including the order αS corrections to $g + g → Q + Q̄$ from our previous paper, we give exact results for the order $α^3_S$ cross sections and single-particle inclusive differential distributions for the production of t and b quarks in $pp̄$ collisions at energies presently available at the CERN $Spp̄S$ and the Fermilab tevatron. Results for future pp colliders are also presented. Finally we compare the results of the simple approximations to the order αS corrections with the exact results