Lattice calculation of heavy-light decay constants with two flavors of dynamical quarks

We present results for $f_B,$ $f_{B_s},$ $f_D,$ $f_{D_s}$ and their ratios in the presence of two flavors of light sea quarks ${(N}_f=2).\mathrm{}$ We use Wilson light valence quarks and Wilson and static heavy valence quarks; the sea quarks are simulated with staggered fermions. Additional quenched simulations with nonperturbatively improved clover fermions allow us to improve our control of the continuum extrapolation. For our central values the masses of the sea quarks are not extrapolated to the physical u, d masses; that is, the central values are “partially quenched.” A calculation using “fat-link clover” valence fermions is also discussed but is not included in our final results. We find, for example, $f_B{=190\mathrm{}\left(7\right)(}_{-17}^{+24\mathrm{}}{\left)\right(}_{-2}^{+11\mathrm{}}{\left)\right(}_{-0}^{+8\mathrm{}})\mathrm{MeV},$ $f_{B_s}{/f}_B{=1.16\mathrm{}\left(1\right)\mathrm{}\left(2\right)\mathrm{}\left(2\right)(}_{-0}^{+4\mathrm{}}),$ $f_{D_s}{=241\mathrm{}\left(5\right)(}_{-26}^{+27\mathrm{}}{\left)\right(}_{-4}^{+9\mathrm{}}{\left)\right(}_{-0}^{+5\mathrm{}})\mathrm{MeV},$ and $f_B{/f}_{D_s}{=0.79\mathrm{}\left(2\right)(}_{-4}^{+5\mathrm{}}{\left)\right(3\left)\right(}_{-0}^{+5\mathrm{}}),$ where in each case the first error is statistical and the remaining three are systematic: the error within the partially quenched $N_f=2\mathrm{}$ approximation, the error due to the missing strange sea quark and to partial quenching, and an estimate of the effects of chiral logarithms at small quark mass. The last error, though quite significant in decay constant ratios, appears to be smaller than has been recently suggested by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other lattice computations to date, the lattice $u,d$ quark masses are not very light and chiral log effects may not be fully under control.