A calculation of the $B_B$ parameter in the static limit

Abstract

We calculate the $B_B$ parameter, relevant for ${\overline{B}}^0$ -- $B^0$ mixing, from a lattice gauge theory simulation at ${\hat{I}}^2=6.0$. 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 ground-state signal. We obtain $B_B(4.33GeV)=0.98_{-4}^{+4}$ (statistical) ${}_{-18}^{+3}$ (systematic) which corresponds to ${\hat{B}}_B=1.40_{-6}^{+6}$ (statistical) ${}_{-26}^{+4}$ (systematic) for the one-loop 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.

39 pages (REVTeX) including 10 figures (PostScript); Final version accepted for publication: Added new section for clarity; Included comparison to recent results by other groups; slight numerical changes; Essential conclusions remain the same