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 $N_F=2\mathrm{}$ dynamical staggered lattices. We use Wilson light valence quarks and Wilson and static heavy quarks. We find, for example, $f_B=157\mathrm{}\pm {11}_{-9-0\mathrm{}}^{+25+23\mathrm{}}\mathrm{MeV}$, $f_{B_s}/f_B=1.11\mathrm{}\pm 0.02_{-0.03\mathrm{}}^{+0.04\mathrm{}}\pm 0.03$, $f_{D_s}=210\mathrm{}\pm 9_{-9-1\mathrm{}}^{+25+17\mathrm{}}\mathrm{MeV}$, and $f_B/f_{D_s}=0.75\mathrm{}\pm 0.03_{-0.02-0.00\mathrm{}}^{+0.04+0.08\mathrm{}}$, where the errors are statistical, systematic (within the quenched approximation), and systematic (of quenching), respectively.

• Received 19 June 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.4812