Heavy-light meson decay constant from QCD sum rules in the three-loop approximation

Abstract

In this paper we compute the decay constant of the pseudoscalar heavy-light mesons in the heavy quark effective theory framework of QCD sum rules. In our analysis we include the recently evaluated three-loop result of order ${\ensuremath{\alpha}}_{s}^{2}$ for the heavy-light current correlator. The value of the bottom quark mass, which essentially limits the accuracy of the sum rules for B meson, is extracted from the nonrelativistic sum rules for $\ensuremath{\Upsilon}$ resonances in the next-to-next-to-leading approximation. We find stability of our result with respect to all types of corrections and the specific form of the sum rule which reduces the uncertainty. Our results ${f}_{B}=206\ifmmode\pm\else\textpm\fi{}20 \mathrm{MeV}$ and ${f}_{D}=195\ifmmode\pm\else\textpm\fi{}20 \mathrm{MeV}$ for the B and D meson decay constants are in impressive agreement with recent lattice calculations.