Calculation of the B_B parameter in the static limit

We calculate the B_B parameter, relevant for B̅ 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 ground-state signal. We obtain B_B(4.33 GeV)=0.98_-4⁺⁴ (stat)_-18⁺³ (syst) which corresponds to B⁁_B = 1.40_-6⁺⁶ (stat)_-26⁺⁴ (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.