B and D Meson Decay Constants in Lattice QCD

We have calculated the decay constants of B and $D$ mesons with lattice QCD. We use an $O(a)$ improved action that takes light quark actions as a starting point, tuned so that it can be directly applied at the physical masses of the $b$ and $c$ quarks. Our results are $f_B = 164 \err{+14}{-11} \pm 8$ MeV, $f_{B_s} = 185 \err{+13}{-8} \pm 9$ MeV, $f_D = 194 \err{+14}{-10} \pm 10$ MeV, and $f_{D_s} = 213 \err{+14}{-11} \pm 11$ MeV in the quenched approximation. The first error in each case is statistical, and the second is from perturbation theory. We show that discretization errors are under control in our approach, and smaller than our statistical errors. The effects of the quenched approximation may raise our quenched result by up to 10%.