Abstract
The 1/ m corrections to the B-meson decay constant ƒ B (and the D-meson decay constant ƒ D) of the heavy quark effective theory are calculated in the Green function approach. The corrections are found to be sensitive to the difference of the meson mass m B and the heavy quark mass m b. For m b=4.8 1 GeV we obtain a 100% correction to the heavy quark limit m b= m B. The scaling law of the ratio ƒ B/ƒ D is, however, quite well satisfied because of cancellations. For reasonable values of quark masses we obtain ƒ B = (130±20) MeV and ƒ D = (170±10) MeV .
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