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We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$one-loop squared corrections to the production of heavy quark pairs inquark-antiquark annihilations. These are part of the next-to-next-to-leadingorder ${\cal O}(\alpha_s^4)$ radiative QCD corrections to this process. Ourresults, with the full mass dependence retained, are presented in a closed andvery compact form, in the dimensional regularization scheme. We have found veryintriguing factorization properties for the finite part of the amplitudes.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ results for heavy  quark pair production in quark--antiquark collisions: The one-loop squared  contributions