  We present a complete set of one-loop matrix elements relevant for the
hadroproduction of heavy quarks in next-to-leading order employing dimensional
regularization to isolate ultraviolet and soft divergences. All results of the
perturbative calculation are given in detail. These one-loop matrix elements
can also be used as input in the determination of the corresponding
next-to-leading order cross sections for heavy flavor photoproduction and in
photon-photon reactions, as well as for any of the relevant crossed processes.
Our results are tested against the results of other related studies in which
unpolarized and longitudinally polarized processes were considered.
