  Puzzled or surprised by the almost incredible accuracy occasionally claimed
in the literature to be achievable for numerical outcomes of QCD sum-rule
analyses, we scrutinized the usual procedure employed for the extraction of the
parameters of individual bound states from dispersive sum rules by taking
advantage of the exact solvability of a quantum-mechanical harmonic-oscillator
model: It turns out that the determination of the ground-state parameters (that
is, decay constant and form factor) by requiring independence from the Borel
mass in its stability window does not necessarily yield their exact numerical
values. For instance, the comparison of the sum-rule predictions for
bound-state parameters with their numerical values known precisely in our
harmonic-oscillator model reveals that standard sum-rule procedures
underestimate the ground-state decay constant by some 4% and its form factor by
almost 15%; such systematic uncertainties cannot be inferred from our
correlators' accuracy better than 1% in the window of Borel stability: they are
uncontrollable.
