One-loop corrections to four-point functions with two external massive fermions and two external massless partons

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.