We present results of a lattice analysis of the B parameter, BB, the
decay constant fB, and several mass splittings using the static
approximation. Results were obtained for 60 quenched gauge configurations
computed at β=6.2 on a lattice size of 243×48. Light quark
propagators were calculated using the O(a)-improved Sheikholeslami-Wohlert
action. We find \Bbstat(m_b) = 0.69\er{3}{4} {\rm(stat)}\er{2}{1}
{\rm(syst)}, corresponding to \Bbstat = 1.02\er{5}{6}\er{3}{2}, and \fbstat
= 266\err{18}{20}\err{28}{27} \mev, f_{B_s}^2 B_{B_s}/f_B^2 B_B =
1.34\er{9}{8}\er{5}{3}, where a variational fitting technique was used to
extract \fbstat. For the mass splittings we obtain M_{B_s}-M_{B_d} =
87\err{15}{12}\err{6}{12} \mev, M_{\Lambda_b}-M_{B_d} =
420\errr{100}{90}\err{30}{30} \mev and M_{B^*}^2-M_B^2 =
0.281\err{15}{16}\err{40}{37} \gev^2. We compare different smearing techniques
intended to improve the signal/noise ratio. From a detailed assessment of
systematic effects we conclude that the main systematic uncertainties are
associated with the renormalisation constants relating a lattice matrix element
to its continuum counterpart. The dependence of our findings on lattice
artefacts is to be investigated in the future.Comment: 40 pages, uuencoded compressed tar file, containing one LaTeX file
and 14 postscript files (to be included with epsf). Minor change in the value
of the B parameter. Contains corrected value for the B*-B mass splitting.
Version accepted for publication in Phys. Rev.
