Decay Constants of Beauty Mesons from QCD Sum Rules

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 $\overline{\mathrm{M}\mathrm{S}}$ scheme ${\bar{m}}_b({\bar{m}}_b)\approx 4.18GeV,$ the sum-rule result $f_B\approx 210$-$220MeV$ for the $B$ meson decay constant is substantially larger than the recent lattice-QCD finding $f_B\approx 190MeV\mathrm{.}$ Requiring QCD sum rules to reproduce the lattice-QCD value of $f_B$ yields a significantly larger $b$-quark mass: ${\bar{m}}_b({\bar{m}}_b)=4.247GeV\mathrm{.}$ (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants $f_D,$ $f_{D_s},$ $f_{D^{\ast }}$ and $f_{D_s^{\ast }}$ are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants - and especially for the ratio $f_{B^{\ast }}\mathrm{/}{f}_B$ - prove to be very sensitive to the specific scale setting.