Decay Constants of Beauty Mesons from QCD Sum Rules

Abstract

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 $\overline{\mathrm{MS}}$ scheme $\overline{m}_b(\overline{m}_b)\approx4.18\;\mbox{GeV},$ the sum-rule result $f_B\approx 210$-$220\;\mbox{MeV}$ 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 $f_D,$ $f_{D_s},$ $f_{D^{\ast }}$ 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 $f_{B^{\ast }}/f_B$ - prove to be very sensitive to the specific scale setting.

6 pages, 2 figures, talk presented at "QCD@Work 2014 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (16 - 19 June 2014, Giovinazzo, Bari, Italy)