Calculation of theBBparameter 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 $\ensuremath{\beta}=6.0$. 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 ${B}_{B}(4.33\mathrm{GeV}{)=0.98}_{\ensuremath{-}4}^{+4}(\mathrm{stat}{)}_{\ensuremath{-}18}^{+3}(\mathrm{syst})$ which corresponds to $B{\^{}}_{B}$ = ${1.40}_{\ensuremath{-}6}^{+6}(\mathrm{stat}{)}_{\ensuremath{-}26}^{+4}(\mathrm{syst})$ 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.