Status of Eikonal Two-Loop Calculations with Massive Quarks

The calculation of threshold corrections to hard scattering cross sections beyond leading logarithms requires the calculation of loop diagrams in the eikonal approximation [1]. One-loop calculations have been performed for all 2 → 2 partonic processes in heavy quark [2] and jet [3] production. The soft anomalous dimension matrix ΓS at one-loop allows the resummation of soft-gluon corrections at next-to-leading logarithm (NLL) accuracy [2]. The exponentiation follows from the renormalization group evolution of ΓS and involves the calculation of the ultraviolet (UV) poles in dimensional regularization of one-loop diagrams with eikonal lines. To extend resummation to next-to-next-to-leading logarithms (NNLL) two-loop calculations are required. For massless quark-antiquark scattering the two-loop ΓS was completed in [4]. For heavy quark production, however, the result is not known. In this contribution we present several results for two-loop diagrams involved in the calculation of the two-loop ΓS for massive quarks. In the eikonal approximation the usual Feynman rules are simplified by letting the