  We consider correlation functions containing the axial current of one light
and one heavy quark in the static approximation as well as in full QCD, using
the lattice regularization. Up to one-loop order of perturbation theory, we
study the difference between the full and the effective theory in the continuum
limit. In the full theory we find a term non-analytic in 1/m, revealing the
asymptotic character of the 1/m-expansion. In general, deviations from the
m-to-infinity limit turn out to be small and are well described by the first
non-trivial terms when m is a factor 2-3 above the external scale. We also
investigate the mass dependence of discretization errors, and find that the
behaviour of the correlation functions at finite lattice spacing differs
significantly from that in the continuum limit when the quark mass is large.
