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One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up to O(epsilon^2)

We present complete analytical ${\mathcal O}(ε^2)$ results on the one-loop amplitudes relevant for the NNLO quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.