  We study two-loop anomalous dimension matrices in QCD and related gauge
theories for products of Wilson lines coupled at a point. We verify by an
analysis in Euclidean space that the contributions to these matrices from
diagrams that link three massive Wilson lines do not vanish in general. We
show, however, that for two-to-two processes the two-loop anomalous dimension
matrix is diagonal in the same color-exchange basis as the one-loop matrix for
arbitrary masses at absolute threshold and for scattering at ninety degrees in
the center of mass. This result is important for applications of threshold
resummation in heavy quark production.
