The non-diagonal correlators of vector and scalar currents are
considered at three-loop order in QCD. The full mass dependence is
computed in the case where one of the quarks is massless and the other one
carries mass $M$.
We exploit the decoupling relations between the full
theory and the heavy quark effective theory
(HQET) in order to obtain the
logarithmic parts of the leading threshold terms.
With the help of conformal mapping and
Pad\'e approximation numerical estimates for the
non-logarithmic terms are extracted which in turn lead to a prediction
of the correlator in HQET at order $\alpha_s^2$.
As applications of the vector and scalar correlator we
consider the single-top-quark production via the process $q\bar{q}\to
t\bar{b}$ and the decay rate of a charged Higgs boson into hadrons,
respectively.
In both cases the computed NLO corrections are shown to be numerically
much less important than the leading ones.
On the contrary, the NLO order QCD corrections to the HQET
sum rule for the leptonic decay rate of a heavy-light meson
proves to be comparable to the leading one.