Mesonic decay constants in lattice NRQCD

Abstract

Lattice NRQCD with leading finite lattice spacing errors removed is used to calculate decay constants of mesons made up of heavy quarks. Quenched simulations are done with a tadpole improved gauge action containing plaquette and six-link rectangular terms. The tadpole factor is estimated using the Landau link. For each of the three values of the coupling constant considered, quarkonia are calculated for five masses spanning the range from charmonium through bottomonium, and one set of quark masses is tuned to the ${B}_{c}.$ ``Perturbative'' and nonperturbative meson masses are compared. One-loop perturbative matching of lattice NRQCD with continuum QCD for the heavy-heavy vector and axial vector currents is performed. The data are consistent with ${\mathrm{af}}_{V}\ensuremath{\propto}\sqrt{{M}_{V}a}$ and ${f}_{{B}_{c}}=420(13)\mathrm{MeV}.$ The error quoted for ${f}_{{B}_{c}}$ is purely statistical. Systematic errors, including the potentially large effect due to quenching, have not yet been evaluated.