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

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 ${\alpha }_s^2$ 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 ${\rm Y}$ 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 $f_B=206\mathrm{}\pm 20\hspace{0.5em}\mathrm{MeV}$ and $f_D=195\mathrm{}\pm 20\hspace{0.5em}\mathrm{MeV}$ for the B and D meson decay constants are in impressive agreement with recent lattice calculations.