  The relation between the pole quark mass and the $\overline{MS}$-renormalized
mass is governed by an infrared renormalon singularity, which leads to an
ambiguity of order $\Lambda_{QCD}$ in the definition of the pole mass. We use
the renormalization group and heavy quark effective theory to determine the
exact nature of this singularity up to an overall normalization. In the abelian
gauge theory, the normalization is computed partially to next-to-leading order
in the flavour expansion.
