Bmeson leptonic decay constant with quenched lattice NRQCD

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 $O\left({\alpha }_{s}a\right)$ 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 ${12}^3\times 32,$ ${16}^3\times 48,$ and ${24}^3\times 64,$ we find a significant a dependence disappears in $f_B$ if the $O\left({\alpha }_{s}a\right)$ correction is included in the axial vector current. We observe that $\beta =5.9\mathrm{}-6.1$ is the window where systematic errors are expected to be minimum within one-loop improved theory. Our final results are $f_B=170\mathrm{}\left(5\right)\mathrm{}\left(15\right)\mathrm{}$ MeV, $f_{B_s}{=191\mathrm{}\left(4\right)\mathrm{}\left(17\right)(}_{-0}^{+4\mathrm{}})$ MeV, and $f_{B_s}{/f}_B{=1.12\mathrm{}\left(2\right)\mathrm{}\left(1\right)(}_{-0}^{+3\mathrm{}}),$ 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.