The decay constants of the pseudoscalar mesons B and $B_s$ are evaluated from QCD sum rules for the pseudoscalar two-point function. Recently calculated perturbative three-loop QCD corrections are incorporated into the sum rule. An analysis in terms of the bottom quark pole mass turns out to be unreliable due to large higher order radiative corrections. On the contrary, in the $\overline{\mathrm{MS}}$ scheme the higher order corrections are under good theoretical control and a reliable determination of $f_B$ and $f_{B_s}$ becomes feasible. Including variations of all input parameters within reasonable ranges, our final results for the pseudoscalar meson decay constants are $f_B=210\mathrm{}\pm 19\mathrm{MeV}$ and $f_{B_s}=244\mathrm{}\pm 21\mathrm{MeV}.$ Employing additional information on the product $\sqrt{B_B}{f}_B$ from global fits to the unitarity triangle, we are in a position to also extract the B-meson B parameter $B_B=1.26\mathrm{}\pm \mathrm{0.45.}$ Our results are quite compatible with analogous determinations of the above quantities in lattice QCD.

• Received 24 August 2001

DOI:https://doi.org/10.1103/PhysRevD.65.056005