Heavy Quark Spectroscopy and Matrix Elements: A Lattice Study using the Static Approximation

We present results of a lattice analysis of the $B$ parameter, $B_B$, the decay constant $f_B$, and several mass splittings using the static approximation. Results were obtained for 60 quenched gauge configurations computed at $\beta=6.2$ on a lattice size of $24^3\times48$. 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.