The Leptonic Decay Constants of $\bar{Q}q$ Mesons and the Lattice Resolution

Abstract

We present a high statistics study of the leptonic decay constant $f_P$ 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 $\beta$ between 5.74 and 6.26 we observe a sizeable $a$ dependence of $f_P$ 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 $a\to 0$. The extrapolations needed to reach the continuum quantity $f_B$ introduce large errors and lead to the value $f_B=0.18(5)$~GeV in the quenched approximation. This suggests that much more effort will be needed to obtain an accurate lattice prediction for $f_B$.

arXiv comment11 pages Latex + 5 tables + 8 postscript figures, unix shell archive, DESY preprint DESY 93-179

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• The Charm Quark on the Lattice
• Heavy Quark Physics
• Quenched Lattice Results for $f_B$ and $f_D$
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• Status of Heavy Quark Physics on the Lattice
• B Mixing
• Beautiful Baryons from Lattice QCD
• Heavy-Light Mesons with Quenched Lattice NRQCD: Results on Decay Constants
• Heavy Light Weak Matrix Elements
• Heavy-light baryonic mass splittings from the lattice
• Phenomenological Determination of the Beauty Meson Decay Parameter $f_B$ and the CP-Violating Angle $\delta$