Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1994-10-21
Nucl.Phys. B437 (1995) 641-666
Physics
High Energy Physics
High Energy Physics - Lattice
33 pages, latex text file and postscript figures all uuencoded into a single file, ROME preprint 94/1041
Scientific paper
10.1016/0550-3213(94)00591-2
We present an analysis of the continuum extrapolation of $f_B$ in the static approximation from lattice data. The method described here aims to uncover the systematic effects which enter in this extrapolation and has not been described before. Our conclusions are that we see statistical evidence for scaling of $f_B^{stat}$ for inverse lattice spacings $\gtap 2$ GeV but not for $\ltap 2$ GeV. We observe a lack of {\em asymptotic} scaling for a variety of quantities, including $f_B^{stat}$, at all energy scales considered. This can be associated with finite lattice spacing systematics. Once these effects are taken into account, we obtain a value of 230(35) MeV for $f_B^{stat}$ in the continuum where the error represents uncertainties due to both the statistics and the continuum extrapolation. In this method there is no error due to uncertainties in the renormalization constant connecting the lattice and continuum effective theories.
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