Lattice Determination of Heavy-Light Decay Constants

We report on the MILC collaboration’s calculation of $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$, and their ratios. Our central values come from the quenched approximation, but the quenching error is estimated from $N_F=2$ dynamical staggered lattices. We use Wilson light valence quarks and Wilson and static heavy quarks. We find, for example, $f_B=157 \pm 11 {}^{+25}{-9} {}^{+23}{-0} \MeV$,$f_{B_s}/f_B = 1.11 \pm 0.02 {}^{+0.04}{-0.03} \pm 0.03$,$f{D_s} = 210 \pm 9 {}^{+25}{-9} {}^{+17}{-1} \MeV$and$f_{B}/f_{D_s} = 0.75 \pm 0.03 {}^{+0.04}{-0.02} {}^{+0.08}{-0.00}$, where the errors are statistical, systematic (within the quenched approximation), and systematic (of quenching), respectively.