Heavy-light mesons with quenched lattice NRQCD: Results on decay constants

We present a quenched lattice calculation of heavy-light meson decay constants, using nonrelativistic (NRQCD) heavy quarks in the mass region of the $b$ quark and heavier, and clover-improved light quarks. The NRQCD Hamiltonian and the heavy-light current include the corrections at first order in the expansion in the inverse heavy quark mass. We study the dependence of the decay constants on the heavy meson mass $M,$ for light quarks with the tree level ${(c}_{\mathrm{SW}}=1),$ as well as the tadpole-improved clover coefficient. We compare decay constants from NRQCD with results from clover ${(c}_{\mathrm{SW}}=1)$ heavy quarks. Having calculated the current renormalization constant $Z_A$ in one-loop perturbation theory, we demonstrate how the heavy mass dependence of the pseudoscalar decay constant changes after renormalization. We quote a result for $f_B$ from NRQCD including the full one-loop matching factors at $O(\alpha /M).\mathrm{}$