Heavy-Light Meson Decay Constant from QCD Sum Rules in Three-Loop Approximation

In this paper we compute the decay constant of the pseudo-scalar 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 $\Upsilon$ resonances in the next-to-next-to-leading approximation. We find an impressive stability of our result with respect to all types of corrections and the specific form of the sum rule which essentially reduces the uncertainty. Our results $f_B=206\pm 20$ MeV and $f_D=195\pm 20$ MeV for the B and D meson decay constants are in impressive agreement with recent lattice calculations.