Lattice HQET with exponentially improved statistical precision

We modify the Eichten-Hill action of static quarks on the lattice in order to achieve a reduction of statistical errors but retaining the O(a)-improvement properties of that action. Statistical fluctuations are reduced by a factor which grows exponentially with Euclidean time, x0. For the first time, B-meson correlation functions are computed with good statistical precision in the static approximation for x0 >1 fm. At lattice spacings a∼0.1 fm, a∼0.08 fm and a∼0.07 fm the Bs-meson decay constant is determined in static and quenched approximations. A correction due to the finite mass of the b-quark is estimated by combining these static results with a recent determination of FDs (orig.)