Lattice NRQCD with leading finite lattice spacing errors removed is used to
calculate decay constants of mesons made up of heavy quarks. Quenched simu
lations are done with a tadpole improved gauge action containing plaquette
and six-link rectangular terms. The tadpole factor is estimated using the L
andau link. For each of the three values of the coupling constant considere
d, quarkonia are calculated for five masses spanning the range from charmon
ium through bottomonium, and one set of quark masses is tuned to the B-c. "
Perturbative'' and nonperturbative meson masses are compared. One-loop pert
urbative matching of lattice NRQCD with continuum QCD for the heavy-heavy v
ector and axial vector currents is performed. The data are consistent with
af(v)proportional to root M(v)a and f(Bc) = 420(13) MeV. The error quoted f
or f(Bc) is purely statistical. Systematic errors, including the potentiall
y large effect due to quenching, have not yet been evaluated. [S0556-2821(9
9)04711-6].