B meson leptonic decay constant with quenched lattice NRQCD -: art. no. 074501

We present a lattice NRQCD study of the B meson decay constant in the quenched approximation with emphasis given to the scaling behavior. The NRQCD action and the heavy-light axial vector current we use include all terms of order 1/M and the perturbative O(alpha(s)a) and O(alpha(s)/M) corrections. Using simulations at three values of couplings beta = 5.7, 5.9, and 6.1 on lattices of sizes 12(3) x 32, 16(3) x 48, and 24(3) x 64, we find a significant a dependence disappears in f(B) if the O(alpha(s)a) correction is included in the axial vector current. We observe that beta = 5.9- 6.1 is the window where systematic errors are expected to be minimum within one-loop improved theory. Our final results are f(B) = 170(5)(15) MeV, f(Bs) = 191(4)(17)(-0 +4) MeV, and f(Bs) / f(B) = 1.12(2)(1)(-0 +3), where the first error is statistical, the second is systematic, and the third is due to the uncertainty of the strange quark mass, while quenching errors are not included.