B meson 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 current we use include all terms of order 1/M and the perturbative $O({\alpha }_{s}a)$ and $O({\alpha }_s\mathrm{/}M)$ corrections. Using simulations at three value of couplings $\beta$=5.7, 5.9 and 6.1 on lattices of size ${12}^3\times 32,{16}^3\times 48$ and ${24}^3\times 64$, we find no significant $a$ dependence in $f_B$ if the $O({\alpha }_{s}a)$ correction is included in the axial current. We obtain $f_B=167(7)(15)$ MeV, $f_{B_s}= 191(4)(17)(^{+4}{-0})$MeVand$f{B_s}/f_B =1.15(3)(1)(^{+3}_{-0})$, with the first error being statistical, the second systematic, and the third due to uncertainty of strange quark mass, while quenching errors being not included.