Lattice HQET with exponentially improved statistical precision

We introduce an alternative discretization for static quarks on the lattice retaining the 0 (a)-improvement properties of the Eichten-Hill action. In this formulation, statistical fluctuations are reduced by a factor which grows exponentially with Euclidean time, x(0). For the first time, B-meson correlation functions are computed with good statistical precision in the static approximation for x(0) > 1 fm. At lattice spacings a approximate to 0.1, 0.08, 0.07 fm, the B-S-meson decay constant is determined in the combined static and quenched approximation. A correction due to the finite mass of the b-quark is estimated by interpolating between the static result and a recent determination of F-Ds. (C) 2003 Published by Elsevier B.V.