B meson leptonic decay constant with quenched lattice NRQCD

Abstract

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 $O(\hat{I}{\pm }_{s}a)$ and $O(\hat{I}{\pm }_s/M)$ corrections. Using simulations at three value of couplings ${\hat{I}}^2$=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 $O(\hat{I}{\pm }_{s}a)$ correction is included in the axial current. We obtain $f_B=167(7)(15)$ MeV, $f_{B_s}=191(4)(17){(}_{-0}^{+4})$ MeV and $f_{B_s}/f_B=1.15(3)(1){(}_{-0}^{+3})$, 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.

31 pages, 24 eps figures