Scaling and further tests of heavy meson decay constant determinations from nonrelativistic QCD

We present results for the $B_s$ meson decay constant $f_{B_s}$ from simulations at three lattice spacings in the range $a^{-1}=1.1\mathrm{}$ to 2.6 GeV using NRQCD heavy quarks and clover light quarks in the quenched approximation. We study the scaling of this quantity and check the consistency between mesons decaying from rest and from a state with a nonzero spatial momentum. The cancellation of power law contributions that arise in the NRQCD formulation of heavy-light currents is discussed. On the coarsest lattice the $D_s$ meson decay constant $f_{D_s}$ is calculated. Our best values for the decay constants are given by $f_{B_s}=187\mathrm{}\left(4\right)\mathrm{}\left(4\right)\mathrm{}\left(11\right)\mathrm{}\left(2\right)\mathrm{}\left(7\right)\mathrm{}\left(6\right)\mathrm{}\hspace{0.5em}\mathrm{MeV}$ and $f_{D_s}{=223\mathrm{}\left(6\right)\mathrm{}\left(31\right)\mathrm{}\left(38\right)\mathrm{}\left(23\right)\mathrm{}\left(9\right)(}_{-1}^{+3\mathrm{}})\hspace{0.5em}\mathrm{MeV}.$