A LATTICE COMPUTATION OF THE DECAY CONSTANT OF THE BETA-MESON

We compute the decay constant of the B-meson, f(B), on a 10(2) x 20 x 40 lattice at beta = 6.0, with Wilson fermions, using 30 gauge field configurations, generated in the quenched approximation. For the propagator of the b-quark we keep only the leading term in the 1/m(b) expansion. To improve our results we use, as the interpolating fields for the B-meson, lattice operators which are "smeared" over several lattice sites. We observe a clear signal for the lightest B-meson state, and obtain the value f(B) = 310 +/- 25 +/- 50 MeV, where the first error is statistical and the second represents our uncertainity in the value of the lattice spacing. This result, combined with earlier lattice measurements of f(D) (f(D) congruent-to 180 MeV), denomstrates that the asymptotic scaling law for the decay constants of heavy pseudoscalar mesons P, (i.e. f(P) square-root-M-(P) approximately constant), has large corrections for charmed mesons. We estimate that the non-scaling corrections will reduce the above value of f(B) by about 25%.