  Our recently completed analysis of the decay constants of both pseudoscalar
and vector beauty mesons reveals that in the bottom-quark sector two specific
features of the sum-rule predictions show up: (i) For the input value of the
bottom-quark mass in the $\overline{\rm MS}$ scheme
$\overline{m}_b(\overline{m}_b)\approx4.18\;\mbox{GeV},$ the sum-rule result
$f_B\approx210$-$220\;\mbox{MeV}$ for the $B$ meson decay constant is
substantially larger than the recent lattice-QCD finding
$f_B\approx190\;\mbox{MeV}.$ Requiring QCD sum rules to reproduce the
lattice-QCD value of $f_B$ yields a significantly larger $b$-quark mass:
$\overline{m}_b(\overline{m}_b)=4.247\;\mbox{GeV}.$ (ii) Whereas QCD sum-rule
predictions for the charmed-meson decay constants $f_D,$ $f_{D_s},$ $f_{D^*}$
and $f_{D_s^*}$ are practically independent of the choice of renormalization
scale, in the beauty sector the results for the decay constants - and
especially for the ratio $f_{B^*}/f_B$ - prove to be very sensitive to the
specific scale setting.
