Precision for B-meson matrix elements

We demonstrate how HQET and the Step Scaling Method for B-physics, pioneered by the Tor Vergata group, can be combined to reach a further improved precision. The observables considered are the mass of the b-quark and the B-s-meson decay constant. The demonstration is carried out in quenched lattice QCD. We start from a small volume, where one can use a standard O(a)-improved relativistic action for the b-quark, and compute two step scaling functions which relate the observables to the large volume ones. In all steps we extrapolate to the continuum limit, separately in HQET and in QCD for masses below m(b). The physical point mb is then reached by an interpolation of the continuum results in 1/m. The essential, expected and verified, feature is that the step scaling fuctions have a weak mass-dependence resulting in an easy interpolation to the physical point. With r(0) = 0.5 fm and the experimental B-s and K masses as input, we find F-Bs = 191(6) MeV and the renormalization group invariant mass M-b = 6.88( 10) GeV, translating into (m) over bar (b)((m) over bar (b)) = 4.42( 6) GeV in the (M) over bar(S) over bar scheme. This approach seems very promising for full QCD.