  The inter-quark potential is dominated by anti-screening effects which
underly asymptotic freedom. We calculate the order g^6 anti-screening
contribution from light fermions and demonstrate that these effects introduce a
non-local divergence. These divergences are shown to make it impossible to
define a coupling renormalisation scheme that renormalises this minimal,
anti-screening potential. Hence the beta function cannot be divided into
screening and anti-screening parts beyond lowest order. However, we then
demonstrate that renormalisation can be carried out in terms of the
anti-screening potential.
