Scaling behavior of $f_B$ with NRQCD

We investigate the scaling behavior of the $B$ meson decay constant $f_B$ and $f_{B_s}$ at $\beta$$=$$5.7,5.9,6.1$, employing the NRQCD heavy quark action and the clover light quark action. Mixing effect from dimension-4 operator in the heavy-light axial-vector current is studied, and we find that the $a$ dependence of $f_B$ is significantly reduced. Our preliminary result for the decay constants in the quenched approximation is $f_B$$=$$162{(}_{-18}^{+35})$ MeV, $f_{B_s}$$=$$190{(}_{-19}^{+40})$ MeV, and $f_{B_s}\mathrm{/}{f}_B$$=$$1.18{(}_{-6}^{+6})$.