Heavy-quark production in gluon fusion at two loops in QCD

We present the two-loop virtual QCD corrections to the production of heavy quarks in gluon fusion. The results are exact in the limit when all kinematical invariants are large compared to the mass of the heavy quark up to terms suppressed by powers of the heavy-quark mass. Our derivation uses a simple relation between massless and massive QCD scattering amplitudes as well as a direct calculation of the massive amplitude at two loops. The results presented here together with those obtained previously for quark–quark scattering form important parts of the next-to-next-to-leading order QCD corrections to heavy-quark production in hadron–hadron collisions.