The resummation of soft gluon exchange for QCD hard scattering requires a
matrix of anomalous dimensions, which has been computed through two loops. The
two-loop matrix is proportional to the one-loop matrix. Recently there have
been proposals that this proportionality extends to higher loops. One can test
such proposals by computing the dependence of this matrix on the matter content
in a generic gauge theory. It is shown that for the matter-dependent part the
proportionality extends to three loops for arbitrary massless processes.Comment: 5 pages, 2 figures; v2 minor clarifications, references adde