F eb 1 99 8 A calculation of the B B parameter in the static limit

We calculate the BB parameter, relevant for B 0 –B0 mixing, from a lattice gauge theory simulation at β = 6.0. The bottom quarks are simulated in the static theory, the light quarks with Wilson fermions. Improved smearing functions produced by a variational technique, most, are used to reduce statistical errors and minimize excited-state contamination of the groundstate signal. We obtain BB(4.33GeV) = 0.98 +4 −4 (statistical) +3 −18 (systematic) which corresponds to B̂B = 1.40 +6 −6 (statistical) +4 −26 (systematic) for the oneloop renormalization-scheme-independent parameter. The systematic errors include the uncertainty due to alternative (less favored) treatments of the perturbatively-calculated mixing coefficients; this uncertainty is at least as large as residual differences between Wilson-static and clover-static results. Our result agrees with extrapolations of results from relativistic (Wilson) heavy quark simulations. 12.38.Gc,14.40.Nd,12.39.Hg,12.38.Bx Typeset using REVTEX ∗Now at Department of Physics, University of Utah, Salt Lake City, UT 84112