Two-Loop Divergences of QCD Scattering Amplitudes with Massive Partons

We provide a complete description of the two-loop infrared singularities of scattering amplitudes with an arbitrary number of massive and massless partons in non-Abelian gauge theories. To this end, we calculate the two universal functions that completely specify the structure of three-parton correlations in the soft anomalous-dimension matrix at two-loop order in closed analytic form. Both functions are found to be suppressed like $O(m^4/s^2)$ in the limit of small parton masses, in accordance with mass factorization theorems. On the other hand, they are unsuppressed near the threshold for pair production of two heavy particles. As an application, we calculate the two-loop anomalous-dimension matrix for $q\overline{q}\to t\overline{t}$ near threshold and show that it is not diagonal in the $s$-channel singlet-octet basis.