Heavy quark spectroscopy and matrix elements: A lattice study using the static approximation.

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 SheikholeslamiWohlert action. We find Bstatic B (mb) = 0.69 +3 −4 (stat) +2 −1 (syst), corresponding to Bstatic B = 1.02 +5 −6 +3 −2 , and f static B = 266 +18 −20 +28 −27 MeV, f2 Bs BBs/f 2 B BB = 1.34 +9 −8 +5 −3 , where a variational fitting technique was used to extract f static B . For the mass splittings we obtain MBs −MBd = 87 +15 −12 + 6 −12 MeV, MΛb −MBd = 420 +100 − 90 +30 −30 MeV and M2 B∗−M B = 0.281 +15 −16 +40 −37 GeV. 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. Present address: Edinburgh Parallel Computing Centre, Edinburgh EH9 3JZ, Scotland Present address: DESY-IFH, Platanenalle 6, D-15738 Zeuthen, Germany Present address: Physics Department, University of Wales, Swansea SA2 8PP, UK