The Leptonic Decay Constants of Q̄q Mesons and the Lattice Resolution

We present a high statistics study of the leptonic decay constant fP of heavy pseudoscalar mesons using propagating heavy Wilson quarks within the quenched approximation, on lattices covering sizes from about 0.7 fm to 2 fm. Varying β between 5.74 and 6.26 we observe a sizeable a dependence of fP when one uses the quark field normalization that was suggested by Kronfeld and Mackenzie, compared with the weaker dependence observed for the standard relativistic norm. The two schemes come into agreement when one extrapolates to a → 0. The extrapolations needed to reach the continuum quantity fB introduce large errors and lead to the value fB = 0.18(5) GeV in the quenched approximation. This suggests that much more effort will be needed to obtain an accurate lattice prediction for fB. work supported in part by DFG grant Schi 257/3-1. Present address: Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus.