B Mixing on the Lattice: F[sub B], F[sub B[sub S]] and Related Quantities

The MILC collaboration computation of heavy-light decay constants isdescribed. Results for f_B, f_B_s, f_D, f_D_s and their ratios arepresented. These results are still preliminary, but the analysis is close tobeing completed. Sources of systematic error, both within the quenchedapproximation and from quenching itself, are estimated, although the latterestimate is rather crude. A sample of our results is: f_B=153 ± 10^+36_-13^+13_-0 MeV, f_B_s/f_B = 1.10 ± 0.02^+0.05_-0.03^+0.03_-0.02, and f_B/f_D_s = 0.76 ± 0.03^+0.07_-0.04^+0.02_-0.01, where the errors are statistical,systematic (within the quenched approximation), and systematic (of quenching),respectively. The largest source of error comes from the extrapolation to thecontinuum. The second largest source is the chiral extrapolation. At present,the central values are based on linear chiral extrapolations; a shift toquadratic extrapolations would for example raise f_B by ≈ 20 MeV andthereby make the error within the quenched approximation more symmetric.