HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables

HYPERDIRE is a project devoted to the creation of a set of Mathematica-based programs for the differential reduction of hypergeometric functions. The current version allows for manipulations involving the full set of Horn-type hypergeometric functions of two variables, including 30 functions.

Heavy quark pair production in gluon fusion at next-to-next-to-leading ${cal O}(alpha_s^4)$ order: One-loop squared contributions

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 in the gluon-gluon fusion process. Together with the previously derived results on the $q bar{q}$ production channel the results of this paper complete the calculation of the one-loop squared contributions of the next-to-next-to-leading order ${cal O}(alpha_s^4)$ radiative QCD corrections to the hadroproduction of heavy flavors. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization.