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 ($N_f=2$). 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." We find, for example, $f_B = 190 (7) (^{+24}_{-17}) (^{+11}_{-2})$ MeV, $f_{B_s}/f_B = 1.16 (1) (2) (2)$, $f_{D_s} = 241 (5) (^{+27}_{-26}) (^{+9}_{-4})$ MeV, and $f_{B}/f_{D_s} = 0.79 (2) (^{+5}_{-4}) (3)$, where the errors are statistical, systematic (within the partially quenched $N_f=2$ approximation), and systematic (due to the missing strange sea quark and to partial quenching), respectively. A calculation using "fat-link clover" valence fermions is also discussed but is not included in our final results.